TSTP Solution File: ANA027-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA027-1 : 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 : n014.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 : Mon May 20 18:41:18 EDT 2024
% Result : Unsatisfiable 9.91s 1.80s
% Output : Refutation 10.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5115
% Syntax : Number of formulae : 8998 (3123 unt; 0 def)
% Number of atoms : 20104 (3009 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 19192 (8086 ~;8379 |; 0 &)
% (2727 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2806 (2804 usr;2728 prp; 0-3 aty)
% Number of functors : 237 ( 237 usr; 46 con; 0-18 aty)
% Number of variables : 12053 (12053 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f33341,plain,
$false,
inference(avatar_sat_refutation,[],[f3229,f3233,f3238,f3243,f3248,f3253,f3258,f3263,f3268,f3273,f3278,f3283,f3288,f3293,f3298,f3303,f3308,f3313,f3318,f3323,f3328,f3333,f3338,f3343,f3348,f3353,f3358,f3363,f3368,f3373,f3378,f3383,f3388,f3393,f3398,f3403,f3408,f3413,f3418,f3423,f3428,f3433,f3438,f3443,f3448,f3453,f3458,f3463,f3468,f3473,f3478,f3483,f3488,f3493,f3498,f3503,f3508,f3513,f3518,f3523,f3528,f3533,f3538,f3543,f3548,f3553,f3558,f3563,f3568,f3573,f3578,f3583,f3588,f3593,f3598,f3603,f3608,f3613,f3618,f3623,f3628,f3633,f3638,f3643,f3648,f3653,f3658,f3663,f3668,f3673,f3678,f3683,f3688,f3693,f3698,f3703,f3708,f3713,f3718,f3723,f3728,f3733,f3738,f3743,f3748,f3753,f3758,f3763,f3768,f3773,f3778,f3783,f3788,f3793,f3798,f3803,f3807,f3811,f3816,f3821,f3826,f3831,f3836,f3840,f3845,f3850,f3854,f3858,f3862,f3866,f3871,f3876,f3881,f3885,f3889,f3893,f3898,f3902,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3943,f3947,f3951,f3955,f3959,f3963,f3967,f3971,f3975,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4215,f4219,f4223,f4227,f4231,f4235,f4239,f4243,f4247,f4251,f4255,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4327,f4331,f4335,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4391,f4395,f4399,f4403,f4407,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4619,f4623,f4627,f4631,f4635,f4639,f4643,f4647,f4651,f4655,f4659,f4663,f4667,f4671,f4675,f4679,f4683,f4687,f4691,f4695,f4699,f4703,f4707,f4711,f4715,f4719,f4723,f4727,f4731,f4735,f4739,f4743,f4747,f4751,f4755,f4759,f4763,f4767,f4771,f4775,f4779,f4783,f4787,f4791,f4795,f4799,f4803,f4807,f4811,f4815,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5143,f5147,f5151,f5155,f5159,f5163,f5167,f5171,f5175,f5179,f5183,f5187,f5191,f5195,f5199,f5203,f5207,f5211,f5215,f5219,f5223,f5227,f5231,f5235,f5239,f5243,f5247,f5251,f5255,f5259,f5263,f5267,f5271,f5275,f5279,f5283,f5287,f5291,f5295,f5299,f5303,f5307,f5311,f5315,f5319,f5323,f5327,f5331,f5335,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5419,f5423,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f5459,f5463,f5467,f5471,f5475,f5479,f5483,f5487,f5491,f5495,f5499,f5503,f5507,f5511,f5515,f5519,f5523,f5527,f5531,f5535,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5603,f5607,f5611,f5615,f5619,f5623,f5627,f5631,f5635,f5639,f5643,f5647,f5651,f5655,f5659,f5663,f5667,f5671,f5675,f5679,f5683,f5687,f5691,f5695,f5699,f5703,f5707,f5711,f5715,f5719,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f5803,f5807,f5811,f5815,f5819,f5823,f5827,f5831,f5835,f5839,f5843,f5847,f5851,f5855,f5859,f5863,f5867,f5871,f5875,f5879,f5883,f5887,f5891,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5951,f5955,f5959,f5963,f5967,f5971,f5975,f5979,f5983,f5987,f5991,f5995,f5999,f6003,f6007,f6011,f6015,f6019,f6023,f6027,f6031,f6035,f6039,f6043,f6047,f6051,f6055,f6059,f6063,f6067,f6071,f6075,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6119,f6123,f6127,f6131,f6135,f6139,f6143,f6147,f6151,f6155,f6159,f6163,f6167,f6171,f6175,f6179,f6183,f6187,f6191,f6195,f6199,f6203,f6207,f6211,f6215,f6219,f6223,f6227,f6231,f6235,f6239,f6243,f6247,f6251,f6255,f6259,f6263,f6267,f6271,f6275,f6279,f6283,f6287,f6291,f6295,f6299,f6303,f6307,f6311,f6315,f6319,f6323,f6327,f6331,f6335,f6339,f6343,f6347,f6351,f6355,f6359,f6363,f6367,f6371,f6375,f6379,f6383,f6387,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6451,f6455,f6459,f6463,f6467,f6471,f6475,f6479,f6483,f6487,f6491,f6495,f6499,f6503,f6507,f6511,f6515,f6519,f6523,f6527,f6531,f6535,f6539,f6543,f6547,f6551,f6555,f6559,f6563,f6567,f6571,f6575,f6579,f6583,f6587,f6591,f6595,f6599,f6603,f6607,f6611,f6615,f6619,f6623,f6627,f6631,f6635,f6639,f6643,f6647,f6651,f6655,f6659,f6663,f6667,f6671,f6675,f6679,f6683,f6687,f6691,f6695,f6699,f6703,f6707,f6711,f6715,f6719,f6723,f6727,f6731,f6735,f6739,f6743,f6747,f6751,f6755,f6759,f6763,f6767,f6771,f6775,f6779,f6783,f6787,f6791,f6795,f6799,f6803,f6807,f6811,f6815,f6819,f6823,f6827,f6831,f6835,f6839,f6843,f6847,f6851,f6855,f6859,f6863,f6867,f6871,f6875,f6879,f6883,f6887,f6891,f6895,f6899,f6903,f6907,f6911,f6915,f6919,f6923,f6927,f6931,f6935,f6939,f6943,f6947,f6951,f6955,f6959,f6963,f6967,f6971,f6975,f6979,f6983,f6987,f6991,f6995,f6999,f7003,f7007,f7011,f7015,f7019,f7023,f7027,f7031,f7035,f7039,f7043,f7047,f7051,f7055,f7059,f7063,f7067,f7071,f7075,f7080,f7085,f7089,f7094,f7101,f7122,f7781,f7806,f7831,f7856,f7881,f7904,f7919,f7934,f7949,f7969,f8043,f8068,f8093,f8118,f8143,f8168,f8193,f8218,f8243,f8268,f8314,f8334,f8356,f8371,f8386,f8401,f8425,f8450,f8475,f8500,f8549,f8553,f8557,f8561,f8565,f8569,f8573,f8577,f8582,f8586,f8590,f8594,f8598,f8602,f8606,f8610,f8614,f8619,f8624,f8629,f8634,f8638,f8642,f8646,f8651,f8655,f8659,f8663,f8667,f8671,f8676,f8680,f8684,f8688,f8693,f8698,f8703,f8708,f8713,f8718,f8723,f8728,f8733,f8738,f8743,f8748,f8753,f8758,f8763,f8768,f8773,f8777,f8782,f8786,f8790,f8794,f8798,f8803,f8808,f8813,f8817,f8821,f8825,f8830,f8834,f8838,f8842,f8847,f8852,f8856,f8861,f8866,f8870,f8874,f8879,f8883,f8887,f8891,f8895,f8899,f8903,f8907,f8911,f8915,f8919,f8924,f8928,f8932,f8937,f8941,f8946,f8963,f8982,f8987,f8992,f8998,f9003,f9009,f9013,f9017,f9021,f9026,f9030,f9034,f9038,f9042,f9046,f9050,f9054,f9058,f9062,f9066,f9071,f9075,f9079,f9083,f9087,f9091,f9095,f9099,f9103,f9107,f9111,f9116,f9120,f9124,f9128,f9132,f9136,f9140,f9144,f9148,f9152,f9156,f9161,f9165,f9169,f9173,f9177,f9181,f9185,f9190,f9194,f9198,f9202,f9209,f9213,f9217,f9221,f9225,f9229,f9233,f9237,f9241,f9245,f9250,f9254,f9258,f9262,f9266,f9270,f9274,f9278,f9282,f9286,f9290,f9295,f9299,f9303,f9307,f9311,f9315,f9319,f9323,f9327,f9331,f9335,f9340,f9344,f9348,f9352,f9357,f9361,f9365,f9369,f9373,f9377,f9381,f9386,f9390,f9394,f9398,f9402,f9406,f9410,f9414,f9418,f9422,f9426,f9431,f9435,f9439,f9443,f9447,f9452,f9456,f9461,f9465,f9470,f9474,f9479,f9529,f9651,f9808,f9812,f9816,f9820,f9824,f9828,f9832,f9841,f9845,f9849,f9853,f9857,f9861,f9865,f9869,f9873,f9877,f9882,f9886,f9890,f9894,f9898,f9902,f9906,f9910,f9914,f9918,f9922,f9926,f9930,f9934,f9938,f9942,f9946,f9950,f9954,f9958,f9966,f9970,f9974,f9978,f9982,f9986,f9990,f9994,f9998,f10002,f10006,f10010,f10014,f10018,f10022,f10026,f10030,f10034,f10038,f10042,f10050,f10054,f10059,f10064,f10068,f10072,f10076,f10224,f10229,f10233,f10237,f10241,f10245,f10249,f10253,f10257,f10275,f10279,f10283,f10287,f10291,f10295,f10299,f10303,f10307,f10311,f10320,f10324,f10328,f10332,f10336,f10340,f10344,f10348,f10352,f10356,f10364,f10368,f10372,f10376,f10380,f10384,f10388,f10392,f10396,f10400,f10406,f10410,f10414,f10418,f10422,f10426,f10430,f10434,f10438,f10442,f10448,f10452,f10456,f10460,f10464,f10468,f10472,f10476,f10480,f10484,f10497,f10502,f10506,f10510,f10514,f10518,f10522,f10526,f10530,f10534,f10546,f10550,f10554,f10558,f10562,f10566,f10570,f10574,f10578,f10582,f10607,f10611,f10615,f10815,f10819,f10823,f10827,f10831,f10835,f10876,f10880,f10884,f10888,f10892,f10896,f10900,f10904,f10908,f10912,f10947,f10951,f10955,f10959,f10963,f10967,f10971,f10975,f10979,f10983,f11010,f11014,f11018,f11022,f11026,f11030,f11034,f11038,f11042,f11046,f11050,f11054,f11058,f11062,f11066,f11070,f11074,f11078,f11082,f11086,f11110,f11114,f11118,f11122,f11126,f11130,f11134,f11138,f11142,f11146,f11169,f11173,f11177,f11181,f11185,f11189,f11193,f11197,f11201,f11205,f11228,f11232,f11236,f11240,f11244,f11248,f11252,f11256,f11260,f11264,f11288,f11618,f11622,f11642,f11646,f11650,f11654,f11658,f11662,f11666,f11670,f11674,f11678,f11683,f11687,f11691,f11695,f11699,f11703,f11707,f11711,f11715,f11719,f11723,f11728,f11732,f11736,f11740,f11744,f11748,f11752,f11757,f11761,f11765,f11769,f11773,f11777,f11781,f11785,f11789,f11793,f11797,f11801,f11805,f11809,f11815,f11819,f11823,f11827,f11831,f11835,f11839,f11843,f11847,f11851,f11856,f11860,f11864,f11868,f11872,f11876,f11880,f11884,f11888,f11892,f11896,f11901,f11905,f11909,f11913,f11917,f11921,f11925,f11930,f11934,f11939,f11944,f11951,f11955,f11959,f11963,f11967,f11986,f12017,f12062,f12082,f12098,f12238,f12243,f12247,f12251,f12255,f12259,f12263,f12268,f12272,f12276,f12280,f12285,f12289,f12293,f12297,f12301,f12305,f12309,f12313,f12317,f12321,f12330,f12334,f12338,f12342,f12346,f12350,f12354,f12358,f12362,f12366,f12374,f12378,f12382,f12386,f12390,f12394,f12398,f12402,f12406,f12410,f12414,f12418,f12422,f12426,f12430,f12434,f12438,f12442,f12446,f12450,f12454,f12458,f12462,f12466,f12470,f12474,f12478,f12482,f12486,f12490,f12494,f12498,f12502,f12506,f12510,f12514,f12519,f12528,f12532,f12536,f12540,f12544,f12548,f12585,f12591,f12643,f12684,f12744,f12848,f12908,f12955,f12967,f12971,f12975,f12979,f12983,f12987,f12991,f12995,f12999,f13003,f13007,f13011,f13015,f13019,f13023,f13027,f13031,f13035,f13039,f13043,f13047,f13051,f13055,f13059,f13063,f13067,f13072,f13077,f13081,f13085,f13089,f13093,f13097,f13101,f13105,f13109,f13113,f13117,f13121,f13125,f13129,f13133,f13137,f13141,f13145,f13149,f13153,f13157,f13161,f13165,f13169,f13173,f13177,f13181,f13185,f13189,f13193,f13197,f13201,f13205,f13209,f13214,f13218,f13222,f13226,f13230,f13234,f13238,f13242,f13246,f13250,f13254,f13258,f13262,f13266,f13270,f13274,f13278,f13282,f13286,f13290,f13294,f13299,f13303,f13307,f13311,f13315,f13319,f13323,f13327,f13331,f13335,f13339,f13346,f13350,f13354,f13358,f13362,f13366,f13370,f13374,f13378,f13382,f13386,f13390,f13394,f13398,f13402,f13406,f13410,f13414,f13418,f13422,f13426,f13430,f13434,f13438,f13442,f13446,f13450,f13454,f13458,f13462,f13466,f13470,f13474,f14085,f14295,f14299,f14303,f14307,f14311,f14315,f14319,f14323,f14327,f14331,f14335,f14346,f14350,f14354,f14358,f14362,f14366,f14370,f14374,f14378,f14382,f14386,f14390,f14394,f14398,f14402,f14406,f14410,f14414,f14418,f14422,f14426,f14443,f14447,f14451,f14455,f14459,f14463,f14467,f14471,f14475,f14479,f14484,f14488,f14492,f14496,f14500,f14504,f14508,f14512,f14516,f14520,f14524,f14529,f14533,f14537,f14541,f14545,f14549,f14553,f14557,f14561,f14565,f14570,f14574,f14578,f14582,f14586,f14590,f14594,f14598,f14602,f14606,f14610,f14615,f14619,f14623,f14627,f14631,f14635,f14639,f14643,f14647,f14651,f14655,f14659,f14663,f14667,f14671,f14675,f14679,f14684,f14691,f14695,f14700,f14704,f14709,f14717,f14721,f14726,f14758,f14762,f14766,f14770,f14774,f14778,f14782,f14786,f14843,f14920,f15047,f15260,f15369,f15856,f15860,f15864,f15868,f15872,f15876,f15880,f15884,f15888,f15896,f15900,f15904,f15908,f15912,f15916,f15920,f15924,f15928,f15932,f15937,f15941,f15945,f15949,f15953,f15957,f15961,f15965,f15969,f15973,f15977,f15983,f15987,f15991,f15995,f15999,f16003,f16007,f16011,f16015,f16019,f16024,f16028,f16032,f16036,f16040,f16044,f16048,f16052,f16056,f16060,f16064,f16070,f16074,f16078,f16082,f16086,f16090,f16094,f16098,f16102,f16106,f16115,f16119,f16123,f16127,f16131,f16135,f16139,f16143,f16147,f16151,f16155,f16159,f16163,f16167,f16172,f16179,f16183,f16187,f16191,f16318,f16580,f16846,f17167,f17186,f17190,f17194,f17198,f17202,f17206,f17212,f17216,f17220,f17224,f17228,f17232,f17236,f17240,f17244,f17248,f17252,f17256,f17260,f17264,f17268,f17272,f17276,f17280,f17284,f17288,f17292,f17298,f17302,f17306,f17310,f17314,f17318,f17322,f17326,f17330,f17334,f17338,f17342,f17346,f17350,f17354,f17358,f17362,f17366,f17370,f17374,f17378,f17382,f17386,f17390,f17394,f17398,f17402,f17406,f17410,f17414,f17418,f17422,f17427,f17431,f17436,f17460,f17465,f17483,f17488,f17508,f17513,f17517,f17521,f17525,f17529,f17533,f17537,f17541,f17545,f17549,f17554,f17961,f18122,f18248,f18432,f18498,f18502,f18506,f18510,f18514,f18518,f18522,f18526,f18530,f18534,f18538,f18542,f18546,f18550,f18573,f18577,f18581,f18585,f18589,f18593,f18597,f18601,f18606,f18610,f18625,f18629,f18633,f18637,f18641,f18645,f18649,f18653,f18657,f18661,f18674,f18678,f18682,f18686,f18690,f18694,f18698,f18702,f18706,f18710,f18733,f18737,f18741,f18745,f18749,f18753,f18757,f18761,f18765,f18769,f18773,f18777,f18781,f18785,f18789,f18793,f18797,f18801,f18805,f18809,f18813,f18818,f18822,f18826,f18831,f18850,f18855,f18906,f18911,f18915,f19007,f19012,f19108,f19113,f19143,f19148,f19168,f19173,f19181,f19186,f19196,f19202,f19208,f19212,f19216,f19220,f19226,f19232,f19236,f19240,f19244,f19248,f19254,f19289,f19310,f19326,f19469,f19799,f20231,f20424,f20745,f20816,f20820,f20824,f20828,f20832,f20839,f20843,f20847,f20851,f20855,f20859,f20863,f20867,f20871,f20875,f20879,f20883,f20887,f20891,f20895,f20899,f20903,f20907,f20911,f20915,f20919,f20925,f20929,f20933,f20937,f20941,f20945,f20949,f20953,f20957,f20961,f20967,f20971,f20975,f20979,f20983,f20987,f20991,f20995,f20999,f21003,f21008,f21012,f21016,f21020,f21024,f21028,f21032,f21036,f21040,f21046,f21106,f21112,f21202,f21207,f21230,f21234,f21238,f21258,f21263,f21268,f21273,f21278,f21283,f21287,f21291,f21295,f21299,f21304,f21321,f21325,f21329,f21334,f21339,f21362,f21366,f21371,f21375,f21380,f21388,f21392,f21397,f21401,f21409,f21413,f21417,f21421,f21425,f21574,f21871,f22098,f22386,f22390,f22394,f22398,f22402,f22406,f22410,f22414,f22418,f22422,f22426,f22430,f22434,f22438,f22444,f22450,f22454,f22458,f22475,f22479,f22483,f22487,f22491,f22495,f22499,f22503,f22507,f22511,f22515,f22519,f22523,f22527,f22531,f22535,f22539,f22543,f22547,f22551,f22555,f22566,f22570,f22576,f22791,f22962,f22966,f23296,f23622,f23626,f23630,f23635,f23639,f23643,f23648,f23652,f23656,f23660,f23664,f23668,f23672,f23676,f23680,f23684,f23688,f23704,f23708,f23768,f23800,f23959,f24215,f24219,f24223,f24227,f24231,f24235,f24239,f24243,f24247,f24251,f24255,f24259,f24263,f24267,f24271,f24275,f24279,f24283,f24287,f24324,f24329,f24335,f24356,f24361,f24373,f24377,f24381,f24386,f24390,f24410,f24415,f24435,f24439,f24443,f24448,f24675,f24761,f24765,f24869,f24873,f24877,f24881,f24885,f24889,f24893,f24897,f24901,f24905,f24909,f24913,f24917,f24921,f24925,f24929,f24941,f24945,f24949,f24953,f24957,f24961,f24965,f24969,f24973,f24977,f24981,f24985,f24989,f24993,f24997,f25001,f25005,f25009,f25013,f25017,f25021,f25048,f25052,f25056,f25060,f25064,f25068,f25072,f25076,f25080,f25084,f25088,f25092,f25096,f25100,f25104,f25108,f25112,f25116,f25120,f25124,f25128,f25163,f25167,f25171,f25175,f25179,f25186,f25204,f25211,f25233,f25237,f25241,f25245,f25249,f25255,f25327,f25331,f25335,f25339,f25346,f25350,f25354,f25358,f25363,f25394,f25400,f25441,f25677,f25685,f26075,f26298,f26302,f26309,f26313,f26317,f26321,f26325,f26329,f26333,f26337,f26341,f26345,f26349,f26353,f26357,f26361,f26365,f26369,f26373,f26377,f26381,f26385,f26389,f26393,f26397,f26401,f26405,f26409,f26413,f26417,f26421,f26531,f26678,f26950,f27107,f27111,f27115,f27119,f27126,f27130,f27134,f27138,f27142,f27146,f27150,f27154,f27158,f27162,f27167,f27171,f27175,f27179,f27183,f27187,f27191,f27196,f27221,f27226,f27287,f27291,f27295,f27300,f28151,f28155,f28159,f28210,f28214,f28218,f28223,f28228,f28232,f28236,f28240,f28244,f28248,f28299,f28303,f28309,f28315,f28403,f28407,f28411,f28415,f28420,f28424,f28434,f28438,f28515,f28519,f28841,f28846,f28883,f28887,f28891,f28895,f28899,f28906,f28910,f29060,f29065,f29069,f29073,f29077,f29081,f29085,f29089,f29093,f29097,f29101,f29105,f29110,f29114,f29118,f29122,f29249,f29434,f29440,f29444,f29448,f29452,f29457,f29606,f29610,f29614,f29618,f29622,f29626,f29630,f29634,f29638,f29642,f29646,f29651,f29655,f29659,f29663,f29667,f29671,f29675,f29679,f29683,f29687,f29691,f29695,f29699,f29703,f29707,f29711,f29717,f29725,f29731,f29751,f29757,f29773,f29779,f29828,f29834,f29847,f29852,f29856,f30435,f30487,f30491,f30499,f30503,f30507,f30511,f30515,f30519,f30524,f30612,f30616,f30620,f30624,f30628,f30632,f30636,f30918,f30922,f30994,f30998,f31002,f31006,f31010,f31014,f31018,f31022,f31028,f31048,f31191,f31195,f31199,f31203,f31242,f31344,f31349,f31354,f31359,f31364,f31368,f31372,f31376,f31380,f31384,f31388,f31392,f31470,f31474,f31478,f31482,f31486,f31490,f31494,f31556,f31642,f31647,f31651,f31678,f31686,f31690,f31694,f31698,f31703,f31708,f31713,f31796,f31800,f31804,f31808,f31820,f31824,f31828,f31832,f31837,f31859,f31894,f31901,f31933,f31938,f31954,f31993,f31998,f32010,f32014,f32018,f32022,f32062,f32066,f32070,f32074,f32209,f32215,f32253,f32257,f32273,f32277,f32298,f32321,f32325,f32367,f32394,f32408,f32418,f32431,f32438,f32451,f32455,f32459,f32464,f32480,f32487,f32507,f32512,f32516,f32600,f32613,f32621,f32625,f32651,f32655,f32659,f32663,f32667,f32671,f32675,f32679,f32688,f32693,f32698,f32703,f32708,f32713,f32722,f32727,f32732,f32737,f32742,f32747,f32751,f32755,f32760,f32765,f32773,f32829,f33109,f33135,f33139,f33143,f33147,f33151,f33155,f33159,f33164,f33168,f33172,f33176,f33180,f33184,f33188,f33192,f33196,f33200,f33204,f33211,f33215,f33219,f33223,f33227,f33231,f33235,f33239,f33243,f33247,f33252,f33256,f33260,f33265,f33269,f33273,f33277,f33286,f33290,f33294,f33302,f33307,f33311,f33315,f33319,f33323,f33327,f33331,f33335,f33339,f33340]) ).
fof(f33340,plain,
( ~ spl0_965
| ~ spl0_2649
| ~ spl0_1473
| ~ spl0_2668 ),
inference(avatar_split_clause,[],[f32776,f32729,f11915,f32618,f8447]) ).
fof(f8447,plain,
( spl0_965
<=> class_Orderings_Olinorder(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f32618,plain,
( spl0_2649
<=> c_lessequals(v_g(v_x),v_f(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2649])]) ).
fof(f11915,plain,
( spl0_1473
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X12,X10,X0)
| ~ c_less(X10,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f32729,plain,
( spl0_2668
<=> c_less(v_f(v_x),v_g(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2668])]) ).
fof(f32776,plain,
( ~ c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ~ class_Orderings_Olinorder(t_b)
| ~ spl0_1473
| ~ spl0_2668 ),
inference(resolution,[],[f32731,f11916]) ).
fof(f11916,plain,
( ! [X10,X0,X12] :
( ~ c_less(X10,X12,X0)
| ~ c_lessequals(X12,X10,X0)
| ~ class_Orderings_Olinorder(X0) )
| ~ spl0_1473 ),
inference(avatar_component_clause,[],[f11915]) ).
fof(f32731,plain,
( c_less(v_f(v_x),v_g(v_x),t_b)
| ~ spl0_2668 ),
inference(avatar_component_clause,[],[f32729]) ).
fof(f33339,plain,
( spl0_2727
| ~ spl0_20
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f10742,f10404,f3320,f33337]) ).
fof(f33337,plain,
( spl0_2727
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2727])]) ).
fof(f3320,plain,
( spl0_20
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f10404,plain,
( spl0_1284
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(X10,c_1,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f10742,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_20
| ~ spl0_1284 ),
inference(resolution,[],[f10405,f3322]) ).
fof(f3322,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f3320]) ).
fof(f10405,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(X10,c_1,X0) = X10 )
| ~ spl0_1284 ),
inference(avatar_component_clause,[],[f10404]) ).
fof(f33335,plain,
( spl0_2726
| ~ spl0_83
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f10741,f10404,f3635,f33333]) ).
fof(f33333,plain,
( spl0_2726
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2726])]) ).
fof(f3635,plain,
( spl0_83
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f10741,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_83
| ~ spl0_1284 ),
inference(resolution,[],[f10405,f3637]) ).
fof(f3637,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f3635]) ).
fof(f33331,plain,
( spl0_2725
| ~ spl0_20
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f10737,f10398,f3320,f33329]) ).
fof(f33329,plain,
( spl0_2725
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2725])]) ).
fof(f10398,plain,
( spl0_1283
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f10737,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_20
| ~ spl0_1283 ),
inference(resolution,[],[f10399,f3322]) ).
fof(f10399,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X10,X0) = X10 )
| ~ spl0_1283 ),
inference(avatar_component_clause,[],[f10398]) ).
fof(f33327,plain,
( spl0_2724
| ~ spl0_83
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f10736,f10398,f3635,f33325]) ).
fof(f33325,plain,
( spl0_2724
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2724])]) ).
fof(f10736,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_83
| ~ spl0_1283 ),
inference(resolution,[],[f10399,f3637]) ).
fof(f33323,plain,
( spl0_2723
| ~ spl0_13
| ~ spl0_1282 ),
inference(avatar_split_clause,[],[f10719,f10394,f3285,f33321]) ).
fof(f33321,plain,
( spl0_2723
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2723])]) ).
fof(f3285,plain,
( spl0_13
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f10394,plain,
( spl0_1282
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_minus(X3,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f10719,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_13
| ~ spl0_1282 ),
inference(resolution,[],[f10395,f3287]) ).
fof(f3287,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f3285]) ).
fof(f10395,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_minus(X3,X3,X0) )
| ~ spl0_1282 ),
inference(avatar_component_clause,[],[f10394]) ).
fof(f33319,plain,
( spl0_2722
| ~ spl0_13
| ~ spl0_1281 ),
inference(avatar_split_clause,[],[f10716,f10390,f3285,f33317]) ).
fof(f33317,plain,
( spl0_2722
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2722])]) ).
fof(f10390,plain,
( spl0_1281
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X10,c_0,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f10716,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_13
| ~ spl0_1281 ),
inference(resolution,[],[f10391,f3287]) ).
fof(f10391,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X10,c_0,X0) = X10 )
| ~ spl0_1281 ),
inference(avatar_component_clause,[],[f10390]) ).
fof(f33315,plain,
( spl0_2721
| ~ spl0_8
| ~ spl0_1280 ),
inference(avatar_split_clause,[],[f10714,f10386,f3260,f33313]) ).
fof(f33313,plain,
( spl0_2721
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2721])]) ).
fof(f3260,plain,
( spl0_8
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f10386,plain,
( spl0_1280
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f10714,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_8
| ~ spl0_1280 ),
inference(resolution,[],[f10387,f3262]) ).
fof(f3262,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f3260]) ).
fof(f10387,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X10,X0) = X10 )
| ~ spl0_1280 ),
inference(avatar_component_clause,[],[f10386]) ).
fof(f33311,plain,
( spl0_2720
| ~ spl0_8
| ~ spl0_1279 ),
inference(avatar_split_clause,[],[f10709,f10382,f3260,f33309]) ).
fof(f33309,plain,
( spl0_2720
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2720])]) ).
fof(f10382,plain,
( spl0_1279
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(X10,c_0,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f10709,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_8
| ~ spl0_1279 ),
inference(resolution,[],[f10383,f3262]) ).
fof(f10383,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(X10,c_0,X0) = X10 )
| ~ spl0_1279 ),
inference(avatar_component_clause,[],[f10382]) ).
fof(f33307,plain,
( spl0_2719
| ~ spl0_1026
| ~ spl0_1241
| ~ spl0_1275 ),
inference(avatar_split_clause,[],[f10700,f10366,f10061,f8805,f33304]) ).
fof(f33304,plain,
( spl0_2719
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2719])]) ).
fof(f8805,plain,
( spl0_1026
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f10061,plain,
( spl0_1241
<=> 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_1241])]) ).
fof(f10366,plain,
( spl0_1275
<=> ! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f10700,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_1026
| ~ spl0_1241
| ~ spl0_1275 ),
inference(forward_demodulation,[],[f10698,f8807]) ).
fof(f8807,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_1026 ),
inference(avatar_component_clause,[],[f8805]) ).
fof(f10698,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_1241
| ~ spl0_1275 ),
inference(superposition,[],[f10367,f10063]) ).
fof(f10063,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_1241 ),
inference(avatar_component_clause,[],[f10061]) ).
fof(f10367,plain,
( ! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB0))
| ~ spl0_1275 ),
inference(avatar_component_clause,[],[f10366]) ).
fof(f33302,plain,
( spl0_2718
| ~ spl0_101
| ~ spl0_1258 ),
inference(avatar_split_clause,[],[f10645,f10289,f3725,f33300]) ).
fof(f33300,plain,
( spl0_2718
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2718])]) ).
fof(f3725,plain,
( spl0_101
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f10289,plain,
( spl0_1258
<=> ! [X0,X10] :
( ~ class_LOrder_Omeet__semilorder(X0)
| c_LOrder_Omeet(X10,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f10645,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_101
| ~ spl0_1258 ),
inference(resolution,[],[f10290,f3727]) ).
fof(f3727,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_101 ),
inference(avatar_component_clause,[],[f3725]) ).
fof(f10290,plain,
( ! [X10,X0] :
( ~ class_LOrder_Omeet__semilorder(X0)
| c_LOrder_Omeet(X10,X10,X0) = X10 )
| ~ spl0_1258 ),
inference(avatar_component_clause,[],[f10289]) ).
fof(f33294,plain,
( spl0_2717
| ~ spl0_30
| ~ spl0_1258 ),
inference(avatar_split_clause,[],[f10644,f10289,f3370,f33292]) ).
fof(f33292,plain,
( spl0_2717
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2717])]) ).
fof(f3370,plain,
( spl0_30
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f10644,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_30
| ~ spl0_1258 ),
inference(resolution,[],[f10290,f3372]) ).
fof(f3372,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f3370]) ).
fof(f33290,plain,
( spl0_2716
| ~ spl0_108
| ~ spl0_1257 ),
inference(avatar_split_clause,[],[f10642,f10285,f3760,f33288]) ).
fof(f33288,plain,
( spl0_2716
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2716])]) ).
fof(f3760,plain,
( spl0_108
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f10285,plain,
( spl0_1257
<=> ! [X0,X10] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| c_LOrder_Ojoin(X10,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f10642,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_108
| ~ spl0_1257 ),
inference(resolution,[],[f10286,f3762]) ).
fof(f3762,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_108 ),
inference(avatar_component_clause,[],[f3760]) ).
fof(f10286,plain,
( ! [X10,X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| c_LOrder_Ojoin(X10,X10,X0) = X10 )
| ~ spl0_1257 ),
inference(avatar_component_clause,[],[f10285]) ).
fof(f33286,plain,
( spl0_2715
| ~ spl0_31
| ~ spl0_1257 ),
inference(avatar_split_clause,[],[f10641,f10285,f3375,f33284]) ).
fof(f33284,plain,
( spl0_2715
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2715])]) ).
fof(f3375,plain,
( spl0_31
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f10641,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_1257 ),
inference(resolution,[],[f10286,f3377]) ).
fof(f3377,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3375]) ).
fof(f33277,plain,
( ~ spl0_93
| spl0_2714
| ~ spl0_990
| ~ spl0_1255 ),
inference(avatar_split_clause,[],[f10640,f10277,f8640,f33275,f3685]) ).
fof(f3685,plain,
( spl0_93
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f33275,plain,
( spl0_2714
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2714])]) ).
fof(f8640,plain,
( spl0_990
<=> ! [X10] : c_NatArith_Oof__nat(X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f10277,plain,
( spl0_1255
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_NatArith_Oof__nat(X11,X0),c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f10640,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_990
| ~ spl0_1255 ),
inference(superposition,[],[f10278,f8641]) ).
fof(f8641,plain,
( ! [X10] : c_NatArith_Oof__nat(X10,tc_nat) = X10
| ~ spl0_990 ),
inference(avatar_component_clause,[],[f8640]) ).
fof(f10278,plain,
( ! [X0,X11] :
( c_in(c_NatArith_Oof__nat(X11,X0),c_IntDef_ONats,X0)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0) )
| ~ spl0_1255 ),
inference(avatar_component_clause,[],[f10277]) ).
fof(f33273,plain,
( spl0_2713
| ~ spl0_1194
| ~ spl0_1234 ),
inference(avatar_split_clause,[],[f10188,f10028,f9863,f33271]) ).
fof(f33271,plain,
( spl0_2713
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2713])]) ).
fof(f9863,plain,
( spl0_1194
<=> ! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f10028,plain,
( spl0_1234
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f10188,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_1194
| ~ spl0_1234 ),
inference(resolution,[],[f10029,f9864]) ).
fof(f9864,plain,
( ! [X24] :
( ~ c_Divides_Oop_Advd(c_0,X24,tc_IntDef_Oint)
| c_0 = X24 )
| ~ spl0_1194 ),
inference(avatar_component_clause,[],[f9863]) ).
fof(f10029,plain,
( ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1234 ),
inference(avatar_component_clause,[],[f10028]) ).
fof(f33269,plain,
( spl0_2712
| ~ spl0_1194
| ~ spl0_1233 ),
inference(avatar_split_clause,[],[f10157,f10024,f9863,f33267]) ).
fof(f33267,plain,
( spl0_2712
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2712])]) ).
fof(f10024,plain,
( spl0_1233
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f10157,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_1194
| ~ spl0_1233 ),
inference(resolution,[],[f10025,f9864]) ).
fof(f10025,plain,
( ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1233 ),
inference(avatar_component_clause,[],[f10024]) ).
fof(f33265,plain,
( spl0_2711
| ~ spl0_131
| ~ spl0_1191 ),
inference(avatar_split_clause,[],[f10088,f9851,f3868,f33262]) ).
fof(f33262,plain,
( spl0_2711
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2711])]) ).
fof(f3868,plain,
( spl0_131
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f9851,plain,
( spl0_1191
<=> ! [X11] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f10088,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_131
| ~ spl0_1191 ),
inference(superposition,[],[f9852,f3870]) ).
fof(f3870,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f3868]) ).
fof(f9852,plain,
( ! [X11] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint))
| ~ spl0_1191 ),
inference(avatar_component_clause,[],[f9851]) ).
fof(f33260,plain,
( spl0_2710
| ~ spl0_204
| ~ spl0_1098 ),
inference(avatar_split_clause,[],[f9730,f9142,f4165,f33258]) ).
fof(f33258,plain,
( spl0_2710
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Ozero(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2710])]) ).
fof(f4165,plain,
( spl0_204
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f9142,plain,
( spl0_1098
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f9730,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Ozero(tc_fun(X1,X0)) )
| ~ spl0_204
| ~ spl0_1098 ),
inference(resolution,[],[f9143,f4166]) ).
fof(f4166,plain,
( ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) )
| ~ spl0_204 ),
inference(avatar_component_clause,[],[f4165]) ).
fof(f9143,plain,
( ! [X8,X7] :
( class_OrderedGroup_Ocomm__monoid__add(tc_fun(X7,X8))
| ~ class_OrderedGroup_Ocomm__monoid__add(X8) )
| ~ spl0_1098 ),
inference(avatar_component_clause,[],[f9142]) ).
fof(f33256,plain,
( spl0_2709
| ~ spl0_194
| ~ spl0_1097 ),
inference(avatar_split_clause,[],[f9726,f9138,f4125,f33254]) ).
fof(f33254,plain,
( spl0_2709
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_OrderedGroup_Osemigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2709])]) ).
fof(f4125,plain,
( spl0_194
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f9138,plain,
( spl0_1097
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f9726,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_OrderedGroup_Osemigroup__add(tc_fun(X1,X0)) )
| ~ spl0_194
| ~ spl0_1097 ),
inference(resolution,[],[f9139,f4126]) ).
fof(f4126,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) )
| ~ spl0_194 ),
inference(avatar_component_clause,[],[f4125]) ).
fof(f9139,plain,
( ! [X8,X7] :
( class_OrderedGroup_Oab__semigroup__add(tc_fun(X7,X8))
| ~ class_OrderedGroup_Ocomm__monoid__add(X8) )
| ~ spl0_1097 ),
inference(avatar_component_clause,[],[f9138]) ).
fof(f33252,plain,
( spl0_2708
| ~ spl0_1059
| ~ spl0_1474
| ~ spl0_2668 ),
inference(avatar_split_clause,[],[f32775,f32729,f11919,f8960,f33249]) ).
fof(f33249,plain,
( spl0_2708
<=> c_lessequals(v_f(v_x),v_g(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2708])]) ).
fof(f8960,plain,
( spl0_1059
<=> class_Orderings_Oorder(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f11919,plain,
( spl0_1474
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X12,X10,X0)
| c_lessequals(X12,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f32775,plain,
( ~ class_Orderings_Oorder(t_b)
| c_lessequals(v_f(v_x),v_g(v_x),t_b)
| ~ spl0_1474
| ~ spl0_2668 ),
inference(resolution,[],[f32731,f11920]) ).
fof(f11920,plain,
( ! [X10,X0,X12] :
( ~ c_less(X12,X10,X0)
| ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X10,X0) )
| ~ spl0_1474 ),
inference(avatar_component_clause,[],[f11919]) ).
fof(f33247,plain,
( spl0_2707
| ~ spl0_195
| ~ spl0_1097 ),
inference(avatar_split_clause,[],[f9725,f9138,f4129,f33245]) ).
fof(f33245,plain,
( spl0_2707
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2707])]) ).
fof(f4129,plain,
( spl0_195
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f9725,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) )
| ~ spl0_195
| ~ spl0_1097 ),
inference(resolution,[],[f9139,f4130]) ).
fof(f4130,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) )
| ~ spl0_195 ),
inference(avatar_component_clause,[],[f4129]) ).
fof(f33243,plain,
( spl0_2706
| ~ spl0_341
| ~ spl0_1096 ),
inference(avatar_split_clause,[],[f9724,f9134,f4713,f33241]) ).
fof(f33241,plain,
( spl0_2706
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2706])]) ).
fof(f4713,plain,
( spl0_341
<=> ! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f9134,plain,
( spl0_1096
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f9724,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) )
| ~ spl0_341
| ~ spl0_1096 ),
inference(resolution,[],[f9135,f4714]) ).
fof(f4714,plain,
( ! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) )
| ~ spl0_341 ),
inference(avatar_component_clause,[],[f4713]) ).
fof(f9135,plain,
( ! [X8,X7] :
( class_OrderedGroup_Osemigroup__add(tc_fun(X7,X8))
| ~ class_OrderedGroup_Osemigroup__add(X8) )
| ~ spl0_1096 ),
inference(avatar_component_clause,[],[f9134]) ).
fof(f33239,plain,
( spl0_2705
| ~ spl0_467
| ~ spl0_1086 ),
inference(avatar_split_clause,[],[f9620,f9093,f5217,f33237]) ).
fof(f33237,plain,
( spl0_2705
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocomm__monoid__mult(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2705])]) ).
fof(f5217,plain,
( spl0_467
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f9093,plain,
( spl0_1086
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f9620,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocomm__monoid__mult(tc_fun(X1,X0)) )
| ~ spl0_467
| ~ spl0_1086 ),
inference(resolution,[],[f9094,f5218]) ).
fof(f5218,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) )
| ~ spl0_467 ),
inference(avatar_component_clause,[],[f5217]) ).
fof(f9094,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Ocomm__semiring__1(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1086 ),
inference(avatar_component_clause,[],[f9093]) ).
fof(f33235,plain,
( spl0_2704
| ~ spl0_901
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f9605,f9089,f6953,f33233]) ).
fof(f33233,plain,
( spl0_2704
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Omonoid__mult(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2704])]) ).
fof(f6953,plain,
( spl0_901
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f9089,plain,
( spl0_1085
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f9605,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Omonoid__mult(tc_fun(X1,X0)) )
| ~ spl0_901
| ~ spl0_1085 ),
inference(resolution,[],[f9090,f6954]) ).
fof(f6954,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) )
| ~ spl0_901 ),
inference(avatar_component_clause,[],[f6953]) ).
fof(f9090,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Osemiring__1(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f9089]) ).
fof(f33231,plain,
( spl0_2703
| ~ spl0_374
| ~ spl0_1084 ),
inference(avatar_split_clause,[],[f9600,f9085,f4845,f33229]) ).
fof(f33229,plain,
( spl0_2703
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Oone(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2703])]) ).
fof(f4845,plain,
( spl0_374
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f9085,plain,
( spl0_1084
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f9600,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Oone(tc_fun(X1,X0)) )
| ~ spl0_374
| ~ spl0_1084 ),
inference(resolution,[],[f9086,f4846]) ).
fof(f4846,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) )
| ~ spl0_374 ),
inference(avatar_component_clause,[],[f4845]) ).
fof(f9086,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1084 ),
inference(avatar_component_clause,[],[f9085]) ).
fof(f33227,plain,
( spl0_2702
| ~ spl0_851
| ~ spl0_1081 ),
inference(avatar_split_clause,[],[f9563,f9073,f6753,f33225]) ).
fof(f33225,plain,
( spl0_2702
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Ominus(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2702])]) ).
fof(f6753,plain,
( spl0_851
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f9073,plain,
( spl0_1081
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f9563,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Ominus(tc_fun(X1,X0)) )
| ~ spl0_851
| ~ spl0_1081 ),
inference(resolution,[],[f9074,f6754]) ).
fof(f6754,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) )
| ~ spl0_851 ),
inference(avatar_component_clause,[],[f6753]) ).
fof(f9074,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Oring(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1081 ),
inference(avatar_component_clause,[],[f9073]) ).
fof(f33223,plain,
( spl0_2701
| ~ spl0_850
| ~ spl0_1081 ),
inference(avatar_split_clause,[],[f9562,f9073,f6749,f33221]) ).
fof(f33221,plain,
( spl0_2701
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Oab__group__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2701])]) ).
fof(f6749,plain,
( spl0_850
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f9562,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Oab__group__add(tc_fun(X1,X0)) )
| ~ spl0_850
| ~ spl0_1081 ),
inference(resolution,[],[f9074,f6750]) ).
fof(f6750,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) )
| ~ spl0_850 ),
inference(avatar_component_clause,[],[f6749]) ).
fof(f33219,plain,
( spl0_2700
| ~ spl0_897
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f9551,f9064,f6937,f33217]) ).
fof(f33217,plain,
( spl0_2700
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2700])]) ).
fof(f6937,plain,
( spl0_897
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f9064,plain,
( spl0_1079
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f9551,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X1,X0)) )
| ~ spl0_897
| ~ spl0_1079 ),
inference(resolution,[],[f9065,f6938]) ).
fof(f6938,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) )
| ~ spl0_897 ),
inference(avatar_component_clause,[],[f6937]) ).
fof(f9065,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Osemiring__0__cancel(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1079 ),
inference(avatar_component_clause,[],[f9064]) ).
fof(f33215,plain,
( spl0_2699
| ~ spl0_889
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f9543,f9064,f6905,f33213]) ).
fof(f33213,plain,
( spl0_2699
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2699])]) ).
fof(f6905,plain,
( spl0_889
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f9543,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X1,X0)) )
| ~ spl0_889
| ~ spl0_1079 ),
inference(resolution,[],[f9065,f6906]) ).
fof(f6906,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) )
| ~ spl0_889 ),
inference(avatar_component_clause,[],[f6905]) ).
fof(f33211,plain,
( spl0_2698
| ~ spl0_886
| ~ spl0_1076 ),
inference(avatar_split_clause,[],[f9524,f9052,f6893,f33209]) ).
fof(f33209,plain,
( spl0_2698
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Ozero(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2698])]) ).
fof(f6893,plain,
( spl0_886
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f9052,plain,
( spl0_1076
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f9524,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Ozero(tc_fun(X1,X0)) )
| ~ spl0_886
| ~ spl0_1076 ),
inference(resolution,[],[f9053,f6894]) ).
fof(f6894,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) )
| ~ spl0_886 ),
inference(avatar_component_clause,[],[f6893]) ).
fof(f9053,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Osemiring__0(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1076 ),
inference(avatar_component_clause,[],[f9052]) ).
fof(f33204,plain,
( spl0_2697
| ~ spl0_885
| ~ spl0_1076 ),
inference(avatar_split_clause,[],[f9523,f9052,f6889,f33202]) ).
fof(f33202,plain,
( spl0_2697
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2697])]) ).
fof(f6889,plain,
( spl0_885
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f9523,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X1,X0)) )
| ~ spl0_885
| ~ spl0_1076 ),
inference(resolution,[],[f9053,f6890]) ).
fof(f6890,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) )
| ~ spl0_885 ),
inference(avatar_component_clause,[],[f6889]) ).
fof(f33200,plain,
( spl0_2696
| ~ spl0_431
| ~ spl0_1075 ),
inference(avatar_split_clause,[],[f9513,f9048,f5073,f33198]) ).
fof(f33198,plain,
( spl0_2696
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Oab__semigroup__mult(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2696])]) ).
fof(f5073,plain,
( spl0_431
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f9048,plain,
( spl0_1075
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f9513,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Oab__semigroup__mult(tc_fun(X1,X0)) )
| ~ spl0_431
| ~ spl0_1075 ),
inference(resolution,[],[f9049,f5074]) ).
fof(f5074,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) )
| ~ spl0_431 ),
inference(avatar_component_clause,[],[f5073]) ).
fof(f9049,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Ocomm__semiring(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1075 ),
inference(avatar_component_clause,[],[f9048]) ).
fof(f33196,plain,
( spl0_2695
| ~ spl0_874
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f9509,f9044,f6845,f33194]) ).
fof(f33194,plain,
( spl0_2695
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2695])]) ).
fof(f6845,plain,
( spl0_874
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f9044,plain,
( spl0_1074
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f9509,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X1,X0)) )
| ~ spl0_874
| ~ spl0_1074 ),
inference(resolution,[],[f9045,f6846]) ).
fof(f6846,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) )
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f6845]) ).
fof(f9045,plain,
( ! [X8,X7] :
( class_Ring__and__Field_Osemiring(tc_fun(X7,X8))
| ~ class_Ring__and__Field_Ocomm__ring__1(X8) )
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f9044]) ).
fof(f33192,plain,
( spl0_2694
| ~ spl0_875
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f9508,f9044,f6849,f33190]) ).
fof(f33190,plain,
( spl0_2694
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Osemigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2694])]) ).
fof(f6849,plain,
( spl0_875
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f9508,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Osemigroup__add(tc_fun(X1,X0)) )
| ~ spl0_875
| ~ spl0_1074 ),
inference(resolution,[],[f9045,f6850]) ).
fof(f6850,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) )
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f6849]) ).
fof(f33188,plain,
( spl0_2693
| ~ spl0_876
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f9507,f9044,f6853,f33186]) ).
fof(f33186,plain,
( spl0_2693
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2693])]) ).
fof(f6853,plain,
( spl0_876
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f9507,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) )
| ~ spl0_876
| ~ spl0_1074 ),
inference(resolution,[],[f9045,f6854]) ).
fof(f6854,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) )
| ~ spl0_876 ),
inference(avatar_component_clause,[],[f6853]) ).
fof(f33184,plain,
( spl0_2692
| ~ spl0_877
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f9506,f9044,f6857,f33182]) ).
fof(f33182,plain,
( spl0_2692
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2692])]) ).
fof(f6857,plain,
( spl0_877
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f9506,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X1,X0)) )
| ~ spl0_877
| ~ spl0_1074 ),
inference(resolution,[],[f9045,f6858]) ).
fof(f6858,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) )
| ~ spl0_877 ),
inference(avatar_component_clause,[],[f6857]) ).
fof(f33180,plain,
( spl0_2691
| ~ spl0_878
| ~ spl0_1074 ),
inference(avatar_split_clause,[],[f9505,f9044,f6861,f33178]) ).
fof(f33178,plain,
( spl0_2691
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Otimes(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2691])]) ).
fof(f6861,plain,
( spl0_878
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f9505,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| class_HOL_Otimes(tc_fun(X1,X0)) )
| ~ spl0_878
| ~ spl0_1074 ),
inference(resolution,[],[f9045,f6862]) ).
fof(f6862,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) )
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f6861]) ).
fof(f33176,plain,
( spl0_2690
| ~ spl0_288
| ~ spl0_1072 ),
inference(avatar_split_clause,[],[f9499,f9036,f4501,f33174]) ).
fof(f33174,plain,
( spl0_2690
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Oone(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2690])]) ).
fof(f4501,plain,
( spl0_288
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f9036,plain,
( spl0_1072
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f9499,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Oone(tc_fun(X1,X0)) )
| ~ spl0_288
| ~ spl0_1072 ),
inference(resolution,[],[f9037,f4502]) ).
fof(f4502,plain,
( ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) )
| ~ spl0_288 ),
inference(avatar_component_clause,[],[f4501]) ).
fof(f9037,plain,
( ! [X8,X7] :
( class_OrderedGroup_Omonoid__mult(tc_fun(X7,X8))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X8) )
| ~ spl0_1072 ),
inference(avatar_component_clause,[],[f9036]) ).
fof(f33172,plain,
( spl0_2689
| ~ spl0_196
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f9496,f9032,f4133,f33170]) ).
fof(f33170,plain,
( spl0_2689
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2689])]) ).
fof(f4133,plain,
( spl0_196
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f9032,plain,
( spl0_1071
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f9496,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X1,X0)) )
| ~ spl0_196
| ~ spl0_1071 ),
inference(resolution,[],[f9033,f4134]) ).
fof(f4134,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) )
| ~ spl0_196 ),
inference(avatar_component_clause,[],[f4133]) ).
fof(f9033,plain,
( ! [X8,X7] :
( class_OrderedGroup_Oab__semigroup__mult(tc_fun(X7,X8))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X8) )
| ~ spl0_1071 ),
inference(avatar_component_clause,[],[f9032]) ).
fof(f33168,plain,
( spl0_2688
| ~ spl0_197
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f9495,f9032,f4137,f33166]) ).
fof(f33166,plain,
( spl0_2688
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Otimes(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2688])]) ).
fof(f4137,plain,
( spl0_197
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f9495,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Otimes(tc_fun(X1,X0)) )
| ~ spl0_197
| ~ spl0_1071 ),
inference(resolution,[],[f9033,f4138]) ).
fof(f4138,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) )
| ~ spl0_197 ),
inference(avatar_component_clause,[],[f4137]) ).
fof(f33164,plain,
( spl0_2687
| ~ spl0_1102
| ~ spl0_1536
| ~ spl0_2638 ),
inference(avatar_split_clause,[],[f32497,f32448,f12432,f9158,f33161]) ).
fof(f33161,plain,
( spl0_2687
<=> c_0 = c_OrderedGroup_Onprt(v_f(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2687])]) ).
fof(f9158,plain,
( spl0_1102
<=> class_OrderedGroup_Olordered__ab__group(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f12432,plain,
( spl0_1536
<=> ! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_0 = c_OrderedGroup_Onprt(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f32448,plain,
( spl0_2638
<=> c_lessequals(c_0,v_f(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2638])]) ).
fof(f32497,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Onprt(v_f(v_x),t_b)
| ~ spl0_1536
| ~ spl0_2638 ),
inference(resolution,[],[f32450,f12433]) ).
fof(f12433,plain,
( ! [X0,X12] :
( ~ c_lessequals(c_0,X12,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(X12,X0) )
| ~ spl0_1536 ),
inference(avatar_component_clause,[],[f12432]) ).
fof(f32450,plain,
( c_lessequals(c_0,v_f(v_x),t_b)
| ~ spl0_2638 ),
inference(avatar_component_clause,[],[f32448]) ).
fof(f33159,plain,
( spl0_2686
| ~ spl0_342
| ~ spl0_1070 ),
inference(avatar_split_clause,[],[f9494,f9028,f4717,f33157]) ).
fof(f33157,plain,
( spl0_2686
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| class_HOL_Otimes(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2686])]) ).
fof(f4717,plain,
( spl0_342
<=> ! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f9028,plain,
( spl0_1070
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f9494,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| class_HOL_Otimes(tc_fun(X1,X0)) )
| ~ spl0_342
| ~ spl0_1070 ),
inference(resolution,[],[f9029,f4718]) ).
fof(f4718,plain,
( ! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) )
| ~ spl0_342 ),
inference(avatar_component_clause,[],[f4717]) ).
fof(f9029,plain,
( ! [X8,X7] :
( class_OrderedGroup_Osemigroup__mult(tc_fun(X7,X8))
| ~ class_OrderedGroup_Osemigroup__mult(X8) )
| ~ spl0_1070 ),
inference(avatar_component_clause,[],[f9028]) ).
fof(f33155,plain,
( spl0_2685
| ~ spl0_188
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f9488,f9019,f4101,f33153]) ).
fof(f33153,plain,
( spl0_2685
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_HOL_Ozero(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2685])]) ).
fof(f4101,plain,
( spl0_188
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f9019,plain,
( spl0_1068
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Oab__group__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f9488,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_HOL_Ozero(tc_fun(X1,X0)) )
| ~ spl0_188
| ~ spl0_1068 ),
inference(resolution,[],[f9020,f4102]) ).
fof(f4102,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) )
| ~ spl0_188 ),
inference(avatar_component_clause,[],[f4101]) ).
fof(f9020,plain,
( ! [X8,X7] :
( class_OrderedGroup_Oab__group__add(tc_fun(X7,X8))
| ~ class_OrderedGroup_Oab__group__add(X8) )
| ~ spl0_1068 ),
inference(avatar_component_clause,[],[f9019]) ).
fof(f33151,plain,
( spl0_2684
| ~ spl0_187
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f9487,f9019,f4097,f33149]) ).
fof(f33149,plain,
( spl0_2684
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2684])]) ).
fof(f4097,plain,
( spl0_187
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f9487,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X1,X0)) )
| ~ spl0_187
| ~ spl0_1068 ),
inference(resolution,[],[f9020,f4098]) ).
fof(f4098,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) )
| ~ spl0_187 ),
inference(avatar_component_clause,[],[f4097]) ).
fof(f33147,plain,
( spl0_2683
| ~ spl0_186
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f9486,f9019,f4093,f33145]) ).
fof(f33145,plain,
( spl0_2683
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_HOL_Ominus(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2683])]) ).
fof(f4093,plain,
( spl0_186
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f9486,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_HOL_Ominus(tc_fun(X1,X0)) )
| ~ spl0_186
| ~ spl0_1068 ),
inference(resolution,[],[f9020,f4094]) ).
fof(f4094,plain,
( ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) )
| ~ spl0_186 ),
inference(avatar_component_clause,[],[f4093]) ).
fof(f33143,plain,
( spl0_2682
| ~ spl0_198
| ~ spl0_1067 ),
inference(avatar_split_clause,[],[f9485,f9015,f4141,f33141]) ).
fof(f33141,plain,
( spl0_2682
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2682])]) ).
fof(f4141,plain,
( spl0_198
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f9015,plain,
( spl0_1067
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f9485,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X1,X0)) )
| ~ spl0_198
| ~ spl0_1067 ),
inference(resolution,[],[f9016,f4142]) ).
fof(f4142,plain,
( ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) )
| ~ spl0_198 ),
inference(avatar_component_clause,[],[f4141]) ).
fof(f9016,plain,
( ! [X8,X7] :
( class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X7,X8))
| ~ class_OrderedGroup_Oab__group__add(X8) )
| ~ spl0_1067 ),
inference(avatar_component_clause,[],[f9015]) ).
fof(f33139,plain,
( spl0_2681
| ~ spl0_202
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f9481,f9011,f4157,f33137]) ).
fof(f33137,plain,
( spl0_2681
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_OrderedGroup_Osemigroup__add(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2681])]) ).
fof(f4157,plain,
( spl0_202
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f9011,plain,
( spl0_1066
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f9481,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_OrderedGroup_Osemigroup__add(tc_fun(X1,X0)) )
| ~ spl0_202
| ~ spl0_1066 ),
inference(resolution,[],[f9012,f4158]) ).
fof(f4158,plain,
( ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) )
| ~ spl0_202 ),
inference(avatar_component_clause,[],[f4157]) ).
fof(f9012,plain,
( ! [X8,X7] :
( class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X7,X8))
| ~ class_OrderedGroup_Oab__group__add(X8) )
| ~ spl0_1066 ),
inference(avatar_component_clause,[],[f9011]) ).
fof(f33135,plain,
( spl0_2680
| ~ spl0_203
| ~ spl0_1066 ),
inference(avatar_split_clause,[],[f9480,f9011,f4161,f33133]) ).
fof(f33133,plain,
( spl0_2680
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2680])]) ).
fof(f4161,plain,
( spl0_203
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f9480,plain,
( ! [X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| class_HOL_Oplus(tc_fun(X1,X0)) )
| ~ spl0_203
| ~ spl0_1066 ),
inference(resolution,[],[f9012,f4162]) ).
fof(f4162,plain,
( ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) )
| ~ spl0_203 ),
inference(avatar_component_clause,[],[f4161]) ).
fof(f33109,plain,
( spl0_2679
| ~ spl0_965
| ~ spl0_3
| ~ spl0_2397 ),
inference(avatar_split_clause,[],[f26938,f26395,f3235,f8447,f33107]) ).
fof(f33107,plain,
( spl0_2679
<=> ! [X0] : c_minus(c_SetInterval_OatLeastLessThan(v_g(v_x),X0,t_b),c_SetInterval_OatLeastLessThan(v_g(v_x),v_k(v_x),t_b),tc_set(t_b)) = c_SetInterval_OatLeastLessThan(v_k(v_x),X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2679])]) ).
fof(f3235,plain,
( spl0_3
<=> c_lessequals(v_g(v_x),v_k(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f26395,plain,
( spl0_2397
<=> ! [X24,X11,X0,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X23,X11,X0)
| c_minus(c_SetInterval_OatLeastLessThan(X23,X24,X0),c_SetInterval_OatLeastLessThan(X23,X11,X0),tc_set(X0)) = c_SetInterval_OatLeastLessThan(X11,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2397])]) ).
fof(f26938,plain,
( ! [X0] :
( ~ class_Orderings_Olinorder(t_b)
| c_minus(c_SetInterval_OatLeastLessThan(v_g(v_x),X0,t_b),c_SetInterval_OatLeastLessThan(v_g(v_x),v_k(v_x),t_b),tc_set(t_b)) = c_SetInterval_OatLeastLessThan(v_k(v_x),X0,t_b) )
| ~ spl0_3
| ~ spl0_2397 ),
inference(resolution,[],[f26396,f3237]) ).
fof(f3237,plain,
( c_lessequals(v_g(v_x),v_k(v_x),t_b)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f3235]) ).
fof(f26396,plain,
( ! [X0,X11,X24,X23] :
( ~ c_lessequals(X23,X11,X0)
| ~ class_Orderings_Olinorder(X0)
| c_minus(c_SetInterval_OatLeastLessThan(X23,X24,X0),c_SetInterval_OatLeastLessThan(X23,X11,X0),tc_set(X0)) = c_SetInterval_OatLeastLessThan(X11,X24,X0) )
| ~ spl0_2397 ),
inference(avatar_component_clause,[],[f26395]) ).
fof(f32829,plain,
( spl0_2678
| ~ spl0_1225
| ~ spl0_2650 ),
inference(avatar_split_clause,[],[f32626,f32623,f9992,f32827]) ).
fof(f32827,plain,
( spl0_2678
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(v_k(X0),v_k(X0),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2678])]) ).
fof(f9992,plain,
( spl0_1225
<=> ! [X0,X26] : c_emptyset = c_minus(X26,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f32623,plain,
( spl0_2650
<=> ! [X0,X1] : c_minus(c_SetInterval_OatLeastLessThan(c_0,X0,t_b),c_SetInterval_OatLeastLessThan(c_0,v_k(X1),t_b),tc_set(t_b)) = c_SetInterval_OatLeastLessThan(v_k(X1),X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2650])]) ).
fof(f32626,plain,
( ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(v_k(X0),v_k(X0),t_b)
| ~ spl0_1225
| ~ spl0_2650 ),
inference(superposition,[],[f32624,f9993]) ).
fof(f9993,plain,
( ! [X0,X26] : c_emptyset = c_minus(X26,X26,tc_set(X0))
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f9992]) ).
fof(f32624,plain,
( ! [X0,X1] : c_minus(c_SetInterval_OatLeastLessThan(c_0,X0,t_b),c_SetInterval_OatLeastLessThan(c_0,v_k(X1),t_b),tc_set(t_b)) = c_SetInterval_OatLeastLessThan(v_k(X1),X0,t_b)
| ~ spl0_2650 ),
inference(avatar_component_clause,[],[f32623]) ).
fof(f32773,plain,
( ~ spl0_2676
| spl0_2677
| ~ spl0_1138
| ~ spl0_1535 ),
inference(avatar_split_clause,[],[f12792,f12428,f9309,f32771,f32767]) ).
fof(f32767,plain,
( spl0_2676
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2676])]) ).
fof(f32771,plain,
( spl0_2677
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2677])]) ).
fof(f9309,plain,
( spl0_1138
<=> ! [X11] : c_0 = c_minus(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f12428,plain,
( spl0_1535
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_0 != c_minus(X3,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f12792,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_1138
| ~ spl0_1535 ),
inference(trivial_inequality_removal,[],[f12785]) ).
fof(f12785,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_1138
| ~ spl0_1535 ),
inference(superposition,[],[f12429,f9310]) ).
fof(f9310,plain,
( ! [X11] : c_0 = c_minus(c_0,X11,tc_nat)
| ~ spl0_1138 ),
inference(avatar_component_clause,[],[f9309]) ).
fof(f12429,plain,
( ! [X3,X0,X1] :
( c_0 != c_minus(X3,X1,X0)
| X1 = X3
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_1535 ),
inference(avatar_component_clause,[],[f12428]) ).
fof(f32765,plain,
( spl0_2675
| spl0_992
| ~ spl0_1419 ),
inference(avatar_split_clause,[],[f12018,f11693,f8648,f32762]) ).
fof(f32762,plain,
( spl0_2675
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2675])]) ).
fof(f8648,plain,
( spl0_992
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f11693,plain,
( spl0_1419
<=> ! [X0,X26] :
( c_0 = c_Finite__Set_Ocard(X26,X0)
| c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f12018,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_992
| ~ spl0_1419 ),
inference(resolution,[],[f11694,f8650]) ).
fof(f8650,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_992 ),
inference(avatar_component_clause,[],[f8648]) ).
fof(f11694,plain,
( ! [X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_0 = c_Finite__Set_Ocard(X26,X0) )
| ~ spl0_1419 ),
inference(avatar_component_clause,[],[f11693]) ).
fof(f32760,plain,
( spl0_2674
| ~ spl0_8
| ~ spl0_132
| ~ spl0_1279
| ~ spl0_1478 ),
inference(avatar_split_clause,[],[f11947,f11937,f10382,f3873,f3260,f32757]) ).
fof(f32757,plain,
( spl0_2674
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2674])]) ).
fof(f3873,plain,
( spl0_132
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f11937,plain,
( spl0_1478
<=> ! [X11] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f11947,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_8
| ~ spl0_132
| ~ spl0_1279
| ~ spl0_1478 ),
inference(forward_demodulation,[],[f11946,f10709]) ).
fof(f11946,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_132
| ~ spl0_1478 ),
inference(superposition,[],[f11938,f3875]) ).
fof(f3875,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_132 ),
inference(avatar_component_clause,[],[f3873]) ).
fof(f11938,plain,
( ! [X11] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1478 ),
inference(avatar_component_clause,[],[f11937]) ).
fof(f32755,plain,
( spl0_2673
| ~ spl0_1170
| ~ spl0_1383 ),
inference(avatar_split_clause,[],[f11538,f11167,f9441,f32753]) ).
fof(f32753,plain,
( spl0_2673
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2673])]) ).
fof(f9441,plain,
( spl0_1170
<=> ! [X0,X3,X26] : c_emptyset != c_insert(X3,X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f11167,plain,
( spl0_1383
<=> ! [X0] : c_Pow(c_emptyset,X0) = c_insert(c_emptyset,c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f11538,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_1170
| ~ spl0_1383 ),
inference(superposition,[],[f9442,f11168]) ).
fof(f11168,plain,
( ! [X0] : c_Pow(c_emptyset,X0) = c_insert(c_emptyset,c_emptyset,tc_set(X0))
| ~ spl0_1383 ),
inference(avatar_component_clause,[],[f11167]) ).
fof(f9442,plain,
( ! [X3,X0,X26] : c_emptyset != c_insert(X3,X26,X0)
| ~ spl0_1170 ),
inference(avatar_component_clause,[],[f9441]) ).
fof(f32751,plain,
( spl0_2672
| ~ spl0_1170
| ~ spl0_1359 ),
inference(avatar_split_clause,[],[f11438,f11032,f9441,f32749]) ).
fof(f32749,plain,
( spl0_2672
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2672])]) ).
fof(f11032,plain,
( spl0_1359
<=> ! [X14] : c_List_Olistset(c_List_Olist_ONil,X14) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X14)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f11438,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_1170
| ~ spl0_1359 ),
inference(superposition,[],[f9442,f11033]) ).
fof(f11033,plain,
( ! [X14] : c_List_Olistset(c_List_Olist_ONil,X14) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X14))
| ~ spl0_1359 ),
inference(avatar_component_clause,[],[f11032]) ).
fof(f32747,plain,
( ~ spl0_2671
| ~ spl0_1170
| ~ spl0_1305 ),
inference(avatar_split_clause,[],[f10787,f10499,f9441,f32744]) ).
fof(f32744,plain,
( spl0_2671
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2671])]) ).
fof(f10499,plain,
( spl0_1305
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f10787,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_1170
| ~ spl0_1305 ),
inference(superposition,[],[f9442,f10501]) ).
fof(f10501,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_1305 ),
inference(avatar_component_clause,[],[f10499]) ).
fof(f32742,plain,
( spl0_2670
| ~ spl0_47
| ~ spl0_1219 ),
inference(avatar_split_clause,[],[f10130,f9968,f3455,f32739]) ).
fof(f32739,plain,
( spl0_2670
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2670])]) ).
fof(f3455,plain,
( spl0_47
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f9968,plain,
( spl0_1219
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f10130,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_47
| ~ spl0_1219 ),
inference(resolution,[],[f9969,f3457]) ).
fof(f3457,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_47 ),
inference(avatar_component_clause,[],[f3455]) ).
fof(f9969,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_0,X0) )
| ~ spl0_1219 ),
inference(avatar_component_clause,[],[f9968]) ).
fof(f32737,plain,
( spl0_2669
| ~ spl0_47
| ~ spl0_1218 ),
inference(avatar_split_clause,[],[f10129,f9964,f3455,f32734]) ).
fof(f32734,plain,
( spl0_2669
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2669])]) ).
fof(f9964,plain,
( spl0_1218
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f10129,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_47
| ~ spl0_1218 ),
inference(resolution,[],[f9965,f3457]) ).
fof(f9965,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_0,X0) )
| ~ spl0_1218 ),
inference(avatar_component_clause,[],[f9964]) ).
fof(f32732,plain,
( ~ spl0_1123
| spl0_2668
| ~ spl0_1734
| ~ spl0_2634 ),
inference(avatar_split_clause,[],[f32409,f32405,f14453,f32729,f9247]) ).
fof(f9247,plain,
( spl0_1123
<=> class_OrderedGroup_Opordered__ab__group__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f14453,plain,
( spl0_1734
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f32405,plain,
( spl0_2634
<=> c_less(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2634])]) ).
fof(f32409,plain,
( c_less(v_f(v_x),v_g(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_1734
| ~ spl0_2634 ),
inference(resolution,[],[f32407,f14454]) ).
fof(f14454,plain,
( ! [X3,X0,X1] :
( ~ c_less(c_minus(X3,X1,X0),c_0,X0)
| c_less(X3,X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_1734 ),
inference(avatar_component_clause,[],[f14453]) ).
fof(f32407,plain,
( c_less(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b)
| ~ spl0_2634 ),
inference(avatar_component_clause,[],[f32405]) ).
fof(f32727,plain,
( spl0_2667
| ~ spl0_61
| ~ spl0_1215 ),
inference(avatar_split_clause,[],[f10125,f9948,f3525,f32724]) ).
fof(f32724,plain,
( spl0_2667
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2667])]) ).
fof(f3525,plain,
( spl0_61
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f9948,plain,
( spl0_1215
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f10125,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_61
| ~ spl0_1215 ),
inference(resolution,[],[f9949,f3527]) ).
fof(f3527,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_61 ),
inference(avatar_component_clause,[],[f3525]) ).
fof(f9949,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X0) )
| ~ spl0_1215 ),
inference(avatar_component_clause,[],[f9948]) ).
fof(f32722,plain,
( ~ spl0_2665
| spl0_2666
| ~ spl0_1025
| ~ spl0_1209 ),
inference(avatar_split_clause,[],[f10124,f9924,f8800,f32719,f32715]) ).
fof(f32715,plain,
( spl0_2665
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2665])]) ).
fof(f32719,plain,
( spl0_2666
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2666])]) ).
fof(f8800,plain,
( spl0_1025
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f9924,plain,
( spl0_1209
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f10124,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_1025
| ~ spl0_1209 ),
inference(superposition,[],[f9925,f8802]) ).
fof(f8802,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_1025 ),
inference(avatar_component_clause,[],[f8800]) ).
fof(f9925,plain,
( ! [X0] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_1209 ),
inference(avatar_component_clause,[],[f9924]) ).
fof(f32713,plain,
( spl0_2664
| ~ spl0_26
| ~ spl0_1202 ),
inference(avatar_split_clause,[],[f10103,f9896,f3350,f32710]) ).
fof(f32710,plain,
( spl0_2664
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2664])]) ).
fof(f3350,plain,
( spl0_26
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f9896,plain,
( spl0_1202
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_1 = c_NatArith_Oof__nat(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f10103,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_26
| ~ spl0_1202 ),
inference(resolution,[],[f9897,f3352]) ).
fof(f3352,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3350]) ).
fof(f9897,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_1 = c_NatArith_Oof__nat(c_1,X0) )
| ~ spl0_1202 ),
inference(avatar_component_clause,[],[f9896]) ).
fof(f32708,plain,
( spl0_2663
| ~ spl0_56
| ~ spl0_1201 ),
inference(avatar_split_clause,[],[f10101,f9892,f3500,f32705]) ).
fof(f32705,plain,
( spl0_2663
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2663])]) ).
fof(f3500,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f9892,plain,
( spl0_1201
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = c_NatArith_Oof__nat(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f10101,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_1201 ),
inference(resolution,[],[f9893,f3502]) ).
fof(f3502,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f3500]) ).
fof(f9893,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = c_NatArith_Oof__nat(c_0,X0) )
| ~ spl0_1201 ),
inference(avatar_component_clause,[],[f9892]) ).
fof(f32703,plain,
( spl0_2662
| ~ spl0_28
| ~ spl0_1193 ),
inference(avatar_split_clause,[],[f10093,f9859,f3360,f32700]) ).
fof(f32700,plain,
( spl0_2662
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2662])]) ).
fof(f3360,plain,
( spl0_28
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f9859,plain,
( spl0_1193
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_1 = c_IntDef_Oof__int(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f10093,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_28
| ~ spl0_1193 ),
inference(resolution,[],[f9860,f3362]) ).
fof(f3362,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3360]) ).
fof(f9860,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_1 = c_IntDef_Oof__int(c_1,X0) )
| ~ spl0_1193 ),
inference(avatar_component_clause,[],[f9859]) ).
fof(f32698,plain,
( spl0_2661
| ~ spl0_58
| ~ spl0_1192 ),
inference(avatar_split_clause,[],[f10092,f9855,f3510,f32695]) ).
fof(f32695,plain,
( spl0_2661
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2661])]) ).
fof(f3510,plain,
( spl0_58
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f9855,plain,
( spl0_1192
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_IntDef_Oof__int(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f10092,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_58
| ~ spl0_1192 ),
inference(resolution,[],[f9856,f3512]) ).
fof(f3512,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_58 ),
inference(avatar_component_clause,[],[f3510]) ).
fof(f9856,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_IntDef_Oof__int(c_0,X0) )
| ~ spl0_1192 ),
inference(avatar_component_clause,[],[f9855]) ).
fof(f32693,plain,
( spl0_2660
| ~ spl0_132
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f10085,f9843,f3873,f32690]) ).
fof(f32690,plain,
( spl0_2660
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2660])]) ).
fof(f9843,plain,
( spl0_1189
<=> ! [X24] : c_IntDef_Oint(X24) = c_HOL_Oabs(c_IntDef_Oint(X24),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f10085,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_132
| ~ spl0_1189 ),
inference(superposition,[],[f9844,f3875]) ).
fof(f9844,plain,
( ! [X24] : c_IntDef_Oint(X24) = c_HOL_Oabs(c_IntDef_Oint(X24),tc_IntDef_Oint)
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9843]) ).
fof(f32688,plain,
( spl0_2659
| ~ spl0_131
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f10084,f9843,f3868,f32685]) ).
fof(f32685,plain,
( spl0_2659
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2659])]) ).
fof(f10084,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_131
| ~ spl0_1189 ),
inference(superposition,[],[f9844,f3870]) ).
fof(f32679,plain,
( spl0_2658
| ~ spl0_341
| ~ spl0_980 ),
inference(avatar_split_clause,[],[f8969,f8596,f4713,f32677]) ).
fof(f32677,plain,
( spl0_2658
<=> ! [X0] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| class_HOL_Oplus(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2658])]) ).
fof(f8596,plain,
( spl0_980
<=> ! [X8] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f8969,plain,
( ! [X0] :
( ~ class_OrderedGroup_Osemigroup__add(X0)
| class_HOL_Oplus(tc_set(X0)) )
| ~ spl0_341
| ~ spl0_980 ),
inference(resolution,[],[f8597,f4714]) ).
fof(f8597,plain,
( ! [X8] :
( class_OrderedGroup_Osemigroup__add(tc_set(X8))
| ~ class_OrderedGroup_Osemigroup__add(X8) )
| ~ spl0_980 ),
inference(avatar_component_clause,[],[f8596]) ).
fof(f32675,plain,
( spl0_2657
| ~ spl0_288
| ~ spl0_973 ),
inference(avatar_split_clause,[],[f8958,f8567,f4501,f32673]) ).
fof(f32673,plain,
( spl0_2657
<=> ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Oone(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2657])]) ).
fof(f8567,plain,
( spl0_973
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f8958,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Oone(tc_set(X0)) )
| ~ spl0_288
| ~ spl0_973 ),
inference(resolution,[],[f8568,f4502]) ).
fof(f8568,plain,
( ! [X8] :
( class_OrderedGroup_Omonoid__mult(tc_set(X8))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X8) )
| ~ spl0_973 ),
inference(avatar_component_clause,[],[f8567]) ).
fof(f32671,plain,
( spl0_2656
| ~ spl0_196
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8955,f8563,f4133,f32669]) ).
fof(f32669,plain,
( spl0_2656
<=> ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_OrderedGroup_Osemigroup__mult(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2656])]) ).
fof(f8563,plain,
( spl0_972
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f8955,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_OrderedGroup_Osemigroup__mult(tc_set(X0)) )
| ~ spl0_196
| ~ spl0_972 ),
inference(resolution,[],[f8564,f4134]) ).
fof(f8564,plain,
( ! [X8] :
( class_OrderedGroup_Oab__semigroup__mult(tc_set(X8))
| ~ class_OrderedGroup_Ocomm__monoid__mult(X8) )
| ~ spl0_972 ),
inference(avatar_component_clause,[],[f8563]) ).
fof(f32667,plain,
( spl0_2655
| ~ spl0_197
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8954,f8563,f4137,f32665]) ).
fof(f32665,plain,
( spl0_2655
<=> ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Otimes(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2655])]) ).
fof(f8954,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| class_HOL_Otimes(tc_set(X0)) )
| ~ spl0_197
| ~ spl0_972 ),
inference(resolution,[],[f8564,f4138]) ).
fof(f32663,plain,
( spl0_2654
| ~ spl0_204
| ~ spl0_971 ),
inference(avatar_split_clause,[],[f8953,f8559,f4165,f32661]) ).
fof(f32661,plain,
( spl0_2654
<=> ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Ozero(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2654])]) ).
fof(f8559,plain,
( spl0_971
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f8953,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Ozero(tc_set(X0)) )
| ~ spl0_204
| ~ spl0_971 ),
inference(resolution,[],[f8560,f4166]) ).
fof(f8560,plain,
( ! [X8] :
( class_OrderedGroup_Ocomm__monoid__add(tc_set(X8))
| ~ class_OrderedGroup_Ocomm__monoid__add(X8) )
| ~ spl0_971 ),
inference(avatar_component_clause,[],[f8559]) ).
fof(f32659,plain,
( spl0_2653
| ~ spl0_194
| ~ spl0_970 ),
inference(avatar_split_clause,[],[f8949,f8555,f4125,f32657]) ).
fof(f32657,plain,
( spl0_2653
<=> ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_OrderedGroup_Osemigroup__add(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2653])]) ).
fof(f8555,plain,
( spl0_970
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f8949,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_OrderedGroup_Osemigroup__add(tc_set(X0)) )
| ~ spl0_194
| ~ spl0_970 ),
inference(resolution,[],[f8556,f4126]) ).
fof(f8556,plain,
( ! [X8] :
( class_OrderedGroup_Oab__semigroup__add(tc_set(X8))
| ~ class_OrderedGroup_Ocomm__monoid__add(X8) )
| ~ spl0_970 ),
inference(avatar_component_clause,[],[f8555]) ).
fof(f32655,plain,
( spl0_2652
| ~ spl0_195
| ~ spl0_970 ),
inference(avatar_split_clause,[],[f8948,f8555,f4129,f32653]) ).
fof(f32653,plain,
( spl0_2652
<=> ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Oplus(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2652])]) ).
fof(f8948,plain,
( ! [X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| class_HOL_Oplus(tc_set(X0)) )
| ~ spl0_195
| ~ spl0_970 ),
inference(resolution,[],[f8556,f4130]) ).
fof(f32651,plain,
( spl0_2651
| ~ spl0_342
| ~ spl0_969 ),
inference(avatar_split_clause,[],[f8947,f8551,f4717,f32649]) ).
fof(f32649,plain,
( spl0_2651
<=> ! [X0] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| class_HOL_Otimes(tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2651])]) ).
fof(f8551,plain,
( spl0_969
<=> ! [X8] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f8947,plain,
( ! [X0] :
( ~ class_OrderedGroup_Osemigroup__mult(X0)
| class_HOL_Otimes(tc_set(X0)) )
| ~ spl0_342
| ~ spl0_969 ),
inference(resolution,[],[f8552,f4718]) ).
fof(f8552,plain,
( ! [X8] :
( class_OrderedGroup_Osemigroup__mult(tc_set(X8))
| ~ class_OrderedGroup_Osemigroup__mult(X8) )
| ~ spl0_969 ),
inference(avatar_component_clause,[],[f8551]) ).
fof(f32625,plain,
( spl0_2650
| ~ spl0_965
| ~ spl0_2
| ~ spl0_2397 ),
inference(avatar_split_clause,[],[f26937,f26395,f3231,f8447,f32623]) ).
fof(f3231,plain,
( spl0_2
<=> ! [X29] : c_lessequals(c_0,v_k(X29),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f26937,plain,
( ! [X0,X1] :
( ~ class_Orderings_Olinorder(t_b)
| c_minus(c_SetInterval_OatLeastLessThan(c_0,X0,t_b),c_SetInterval_OatLeastLessThan(c_0,v_k(X1),t_b),tc_set(t_b)) = c_SetInterval_OatLeastLessThan(v_k(X1),X0,t_b) )
| ~ spl0_2
| ~ spl0_2397 ),
inference(resolution,[],[f26396,f3232]) ).
fof(f3232,plain,
( ! [X29] : c_lessequals(c_0,v_k(X29),t_b)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f3231]) ).
fof(f32621,plain,
( spl0_2649
| ~ spl0_2083
| ~ spl0_2637 ),
inference(avatar_split_clause,[],[f32442,f32436,f20742,f32618]) ).
fof(f20742,plain,
( spl0_2083
<=> c_lessequals(v_k(v_x),v_f(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f32436,plain,
( spl0_2637
<=> ! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2637])]) ).
fof(f32442,plain,
( c_lessequals(v_g(v_x),v_f(v_x),t_b)
| ~ spl0_2083
| ~ spl0_2637 ),
inference(resolution,[],[f32437,f20744]) ).
fof(f20744,plain,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| ~ spl0_2083 ),
inference(avatar_component_clause,[],[f20742]) ).
fof(f32437,plain,
( ! [X0] :
( ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) )
| ~ spl0_2637 ),
inference(avatar_component_clause,[],[f32436]) ).
fof(f32613,plain,
( spl0_2648
| ~ spl0_1102
| ~ spl0_113
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f12865,f12444,f3785,f9158,f32610]) ).
fof(f32610,plain,
( spl0_2648
<=> c_minus(v_f(v_x),v_k(v_x),t_b) = c_OrderedGroup_Opprt(c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2648])]) ).
fof(f3785,plain,
( spl0_113
<=> c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f12444,plain,
( spl0_1539
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_OrderedGroup_Opprt(X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f12865,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_minus(v_f(v_x),v_k(v_x),t_b) = c_OrderedGroup_Opprt(c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ spl0_113
| ~ spl0_1539 ),
inference(resolution,[],[f12445,f3787]) ).
fof(f3787,plain,
( c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f3785]) ).
fof(f12445,plain,
( ! [X10,X0] :
( ~ c_lessequals(c_0,X10,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_OrderedGroup_Opprt(X10,X0) = X10 )
| ~ spl0_1539 ),
inference(avatar_component_clause,[],[f12444]) ).
fof(f32600,plain,
( spl0_2647
| ~ spl0_1069
| ~ spl0_113
| ~ spl0_1534 ),
inference(avatar_split_clause,[],[f12783,f12424,f3785,f9023,f32597]) ).
fof(f32597,plain,
( spl0_2647
<=> c_minus(v_f(v_x),v_k(v_x),t_b) = c_HOL_Oabs(c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2647])]) ).
fof(f9023,plain,
( spl0_1069
<=> class_OrderedGroup_Olordered__ab__group__abs(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f12424,plain,
( spl0_1534
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_HOL_Oabs(X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f12783,plain,
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| c_minus(v_f(v_x),v_k(v_x),t_b) = c_HOL_Oabs(c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ spl0_113
| ~ spl0_1534 ),
inference(resolution,[],[f12425,f3787]) ).
fof(f12425,plain,
( ! [X10,X0] :
( ~ c_lessequals(c_0,X10,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X10,X0) = X10 )
| ~ spl0_1534 ),
inference(avatar_component_clause,[],[f12424]) ).
fof(f32516,plain,
( spl0_2646
| ~ spl0_1177
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f10078,f9814,f9472,f32514]) ).
fof(f32514,plain,
( spl0_2646
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2646])]) ).
fof(f9472,plain,
( spl0_1177
<=> ! [X10] : c_div(X10,c_1,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f9814,plain,
( spl0_1183
<=> ! [X11,X24] : c_lessequals(c_div(X24,X11,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f10078,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_1177
| ~ spl0_1183 ),
inference(superposition,[],[f9815,f9473]) ).
fof(f9473,plain,
( ! [X10] : c_div(X10,c_1,tc_nat) = X10
| ~ spl0_1177 ),
inference(avatar_component_clause,[],[f9472]) ).
fof(f9815,plain,
( ! [X11,X24] : c_lessequals(c_div(X24,X11,tc_nat),X24,tc_nat)
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f9814]) ).
fof(f32512,plain,
( spl0_2645
| ~ spl0_131
| ~ spl0_995 ),
inference(avatar_split_clause,[],[f8976,f8661,f3868,f32509]) ).
fof(f32509,plain,
( spl0_2645
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2645])]) ).
fof(f8661,plain,
( spl0_995
<=> ! [X11] : c_lessequals(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f8976,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_131
| ~ spl0_995 ),
inference(superposition,[],[f8662,f3870]) ).
fof(f8662,plain,
( ! [X11] : c_lessequals(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint)
| ~ spl0_995 ),
inference(avatar_component_clause,[],[f8661]) ).
fof(f32507,plain,
( ~ spl0_2644
| ~ spl0_131
| ~ spl0_993 ),
inference(avatar_split_clause,[],[f8972,f8653,f3868,f32504]) ).
fof(f32504,plain,
( spl0_2644
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2644])]) ).
fof(f8653,plain,
( spl0_993
<=> ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f8972,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_131
| ~ spl0_993 ),
inference(superposition,[],[f8654,f3870]) ).
fof(f8654,plain,
( ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint)
| ~ spl0_993 ),
inference(avatar_component_clause,[],[f8653]) ).
fof(f32487,plain,
( spl0_2643
| ~ spl0_1059
| ~ spl0_113
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f17094,f16145,f3785,f8960,f32485]) ).
fof(f32485,plain,
( spl0_2643
<=> ! [X0] :
( ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),X0,t_b)
| c_lessequals(c_0,X0,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2643])]) ).
fof(f16145,plain,
( spl0_1882
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X12,X10,X0)
| ~ c_lessequals(X10,X35,X0)
| c_lessequals(X12,X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f17094,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_minus(v_f(v_x),v_k(v_x),t_b),X0,t_b)
| c_lessequals(c_0,X0,t_b) )
| ~ spl0_113
| ~ spl0_1882 ),
inference(resolution,[],[f16146,f3787]) ).
fof(f16146,plain,
( ! [X10,X0,X35,X12] :
( ~ c_lessequals(X12,X10,X0)
| ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X35,X0)
| c_lessequals(X12,X35,X0) )
| ~ spl0_1882 ),
inference(avatar_component_clause,[],[f16145]) ).
fof(f32480,plain,
( spl0_2642
| ~ spl0_1059
| ~ spl0_113
| ~ spl0_1661 ),
inference(avatar_split_clause,[],[f13985,f13325,f3785,f8960,f32477]) ).
fof(f32477,plain,
( spl0_2642
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2642])]) ).
fof(f13325,plain,
( spl0_1661
<=> ! [X9,X0,X72] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X72,X9,X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X72,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f13985,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ spl0_113
| ~ spl0_1661 ),
inference(resolution,[],[f13326,f3787]) ).
fof(f13326,plain,
( ! [X72,X0,X9] :
( ~ c_lessequals(X72,X9,X0)
| ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X72,X0) )
| ~ spl0_1661 ),
inference(avatar_component_clause,[],[f13325]) ).
fof(f32464,plain,
( spl0_2641
| ~ spl0_1059
| ~ spl0_113
| ~ spl0_1651 ),
inference(avatar_split_clause,[],[f13938,f13284,f3785,f8960,f32461]) ).
fof(f32461,plain,
( spl0_2641
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2641])]) ).
fof(f13284,plain,
( spl0_1651
<=> ! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X24,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f13938,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_minus(v_f(v_x),v_k(v_x),t_b),c_0,t_b)
| ~ spl0_113
| ~ spl0_1651 ),
inference(resolution,[],[f13285,f3787]) ).
fof(f13285,plain,
( ! [X0,X11,X24] :
( ~ c_lessequals(X11,X24,X0)
| ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X24,X11,X0) )
| ~ spl0_1651 ),
inference(avatar_component_clause,[],[f13284]) ).
fof(f32459,plain,
( spl0_2640
| ~ spl0_146
| ~ spl0_1780 ),
inference(avatar_split_clause,[],[f15674,f14641,f3933,f32457]) ).
fof(f32457,plain,
( spl0_2640
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2640])]) ).
fof(f3933,plain,
( spl0_146
<=> ! [X0,X12] : c_in(X12,c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f14641,plain,
( spl0_1780
<=> ! [X3,X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_in(c_Pair(X3,X3,X0,X0),X19,tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f15674,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_146
| ~ spl0_1780 ),
inference(resolution,[],[f14642,f3934]) ).
fof(f3934,plain,
( ! [X0,X12] : c_in(X12,c_UNIV,X0)
| ~ spl0_146 ),
inference(avatar_component_clause,[],[f3933]) ).
fof(f14642,plain,
( ! [X3,X0,X19] :
( ~ c_in(c_Pair(X3,X3,X0,X0),X19,tc_prod(X0,X0))
| ~ c_Wellfounded__Recursion_Owf(X19,X0) )
| ~ spl0_1780 ),
inference(avatar_component_clause,[],[f14641]) ).
fof(f32455,plain,
( spl0_2639
| ~ spl0_1463
| ~ spl0_1780 ),
inference(avatar_split_clause,[],[f15669,f14641,f11874,f32453]) ).
fof(f32453,plain,
( spl0_2639
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2639])]) ).
fof(f11874,plain,
( spl0_1463
<=> ! [X0,X12] : c_in(c_Pair(X12,X12,X0,X0),c_Relation_OId,tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f15669,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1463
| ~ spl0_1780 ),
inference(resolution,[],[f14642,f11875]) ).
fof(f11875,plain,
( ! [X0,X12] : c_in(c_Pair(X12,X12,X0,X0),c_Relation_OId,tc_prod(X0,X0))
| ~ spl0_1463 ),
inference(avatar_component_clause,[],[f11874]) ).
fof(f32451,plain,
( spl0_2638
| ~ spl0_2083
| ~ spl0_2635 ),
inference(avatar_split_clause,[],[f32422,f32416,f20742,f32448]) ).
fof(f32416,plain,
( spl0_2635
<=> ! [X0,X1] :
( ~ c_lessequals(v_k(X0),X1,t_b)
| c_lessequals(c_0,X1,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2635])]) ).
fof(f32422,plain,
( c_lessequals(c_0,v_f(v_x),t_b)
| ~ spl0_2083
| ~ spl0_2635 ),
inference(resolution,[],[f32417,f20744]) ).
fof(f32417,plain,
( ! [X0,X1] :
( ~ c_lessequals(v_k(X0),X1,t_b)
| c_lessequals(c_0,X1,t_b) )
| ~ spl0_2635 ),
inference(avatar_component_clause,[],[f32416]) ).
fof(f32438,plain,
( spl0_2637
| ~ spl0_1059
| ~ spl0_3
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f17096,f16145,f3235,f8960,f32436]) ).
fof(f17096,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(v_x),X0,t_b)
| c_lessequals(v_g(v_x),X0,t_b) )
| ~ spl0_3
| ~ spl0_1882 ),
inference(resolution,[],[f16146,f3237]) ).
fof(f32431,plain,
( spl0_2636
| ~ spl0_1102
| ~ spl0_113
| ~ spl0_1536 ),
inference(avatar_split_clause,[],[f12809,f12432,f3785,f9158,f32428]) ).
fof(f32428,plain,
( spl0_2636
<=> c_0 = c_OrderedGroup_Onprt(c_minus(v_f(v_x),v_k(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2636])]) ).
fof(f12809,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Onprt(c_minus(v_f(v_x),v_k(v_x),t_b),t_b)
| ~ spl0_113
| ~ spl0_1536 ),
inference(resolution,[],[f12433,f3787]) ).
fof(f32418,plain,
( spl0_2635
| ~ spl0_1059
| ~ spl0_2
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f17095,f16145,f3231,f8960,f32416]) ).
fof(f17095,plain,
( ! [X0,X1] :
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(v_k(X0),X1,t_b)
| c_lessequals(c_0,X1,t_b) )
| ~ spl0_2
| ~ spl0_1882 ),
inference(resolution,[],[f16146,f3232]) ).
fof(f32408,plain,
( spl0_2634
| ~ spl0_965
| spl0_114
| ~ spl0_1472 ),
inference(avatar_split_clause,[],[f12190,f11911,f3790,f8447,f32405]) ).
fof(f3790,plain,
( spl0_114
<=> c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f11911,plain,
( spl0_1472
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X12,X10,X0)
| c_less(X10,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f12190,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_less(c_minus(v_f(v_x),v_g(v_x),t_b),c_0,t_b)
| spl0_114
| ~ spl0_1472 ),
inference(resolution,[],[f11912,f3792]) ).
fof(f3792,plain,
( ~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b)
| spl0_114 ),
inference(avatar_component_clause,[],[f3790]) ).
fof(f11912,plain,
( ! [X10,X0,X12] :
( c_lessequals(X12,X10,X0)
| ~ class_Orderings_Olinorder(X0)
| c_less(X10,X12,X0) )
| ~ spl0_1472 ),
inference(avatar_component_clause,[],[f11911]) ).
fof(f32394,plain,
spl0_2633,
inference(avatar_split_clause,[],[f1627,f32392]) ).
fof(f32392,plain,
( spl0_2633
<=> ! [X17,X18,X19,X20,X0,X16,X21,X22] :
( ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| ~ c_in(c_Pair(X17,X21,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X17,X18,X0,X16),c_Datatype__Universe_OScons(X21,X22,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2633])]) ).
fof(f1627,axiom,
! [X21,X0,X18,X19,X16,X17,X22,X20] :
( ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| ~ c_in(c_Pair(X17,X21,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X17,X18,X0,X16),c_Datatype__Universe_OScons(X21,X22,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodI_0) ).
fof(f32367,plain,
spl0_2632,
inference(avatar_split_clause,[],[f1631,f32365]) ).
fof(f32365,plain,
( spl0_2632
<=> ! [X33,X20,X0,X16,X19] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdsumE__3(X20,X33,X0,X16),c_Main_OdsumE__4(X20,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdsumE__1(X19,X33,X0,X16),c_Main_OdsumE__2(X19,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2632])]) ).
fof(f1631,axiom,
! [X0,X19,X16,X33,X20] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdsumE__3(X20,X33,X0,X16),c_Main_OdsumE__4(X20,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdsumE__1(X19,X33,X0,X16),c_Main_OdsumE__2(X19,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_3) ).
fof(f32325,plain,
spl0_2631,
inference(avatar_split_clause,[],[f1630,f32323]) ).
fof(f32323,plain,
( spl0_2631
<=> ! [X33,X20,X0,X16,X19] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X20,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X20,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33
| c_in(c_Pair(c_Main_OdsumE__1(X19,X33,X0,X16),c_Main_OdsumE__2(X19,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2631])]) ).
fof(f1630,axiom,
! [X0,X19,X16,X33,X20] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X20,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X20,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33
| c_in(c_Pair(c_Main_OdsumE__1(X19,X33,X0,X16),c_Main_OdsumE__2(X19,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_2) ).
fof(f32321,plain,
spl0_2630,
inference(avatar_split_clause,[],[f1629,f32319]) ).
fof(f32319,plain,
( spl0_2630
<=> ! [X33,X20,X0,X16,X19] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X19,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X19,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33
| c_in(c_Pair(c_Main_OdsumE__3(X20,X33,X0,X16),c_Main_OdsumE__4(X20,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2630])]) ).
fof(f1629,axiom,
! [X0,X19,X16,X33,X20] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X19,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X19,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33
| c_in(c_Pair(c_Main_OdsumE__3(X20,X33,X0,X16),c_Main_OdsumE__4(X20,X33,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_1) ).
fof(f32298,plain,
spl0_2629,
inference(avatar_split_clause,[],[f1628,f32296]) ).
fof(f32296,plain,
( spl0_2629
<=> ! [X33,X20,X0,X16,X19] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X20,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X20,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X19,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X19,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2629])]) ).
fof(f1628,axiom,
! [X0,X19,X16,X33,X20] :
( ~ c_in(X33,c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X20,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X20,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X19,X33,X0,X16),X0,X16),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X19,X33,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X33 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdsumE_0) ).
fof(f32277,plain,
spl0_2628,
inference(avatar_split_clause,[],[f1624,f32275]) ).
fof(f32275,plain,
( spl0_2628
<=> ! [X20,X0,X16,X25,X19] :
( ~ c_in(X25,c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X25,X19,X20,X0,X16),c_Main_OdprodE__2(X25,X19,X20,X0,X16),X0,X16),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X25,X19,X20,X0,X16),c_Main_OdprodE__4(X25,X19,X20,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2628])]) ).
fof(f1624,axiom,
! [X0,X19,X16,X25,X20] :
( ~ c_in(X25,c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X25,X19,X20,X0,X16),c_Main_OdprodE__2(X25,X19,X20,X0,X16),X0,X16),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X25,X19,X20,X0,X16),c_Main_OdprodE__4(X25,X19,X20,X0,X16),X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_0) ).
fof(f32273,plain,
( spl0_2627
| ~ spl0_1102
| ~ spl0_1536
| ~ spl0_2178 ),
inference(avatar_split_clause,[],[f21990,f21869,f12432,f9158,f32271]) ).
fof(f32271,plain,
( spl0_2627
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(X0,c_0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2627])]) ).
fof(f21869,plain,
( spl0_2178
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f21990,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Onprt(c_Orderings_Omax(X0,c_0,t_b),t_b) )
| ~ spl0_1536
| ~ spl0_2178 ),
inference(resolution,[],[f21870,f12433]) ).
fof(f21870,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,t_b),t_b)
| ~ spl0_2178 ),
inference(avatar_component_clause,[],[f21869]) ).
fof(f32257,plain,
spl0_2626,
inference(avatar_split_clause,[],[f1633,f32255]) ).
fof(f32255,plain,
( spl0_2626
<=> ! [X18,X19,X20,X0,X16,X22] :
( ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X18,X0,X16),c_Datatype__Universe_OIn1(X22,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2626])]) ).
fof(f1633,axiom,
! [X0,X18,X19,X16,X22,X20] :
( ~ c_in(c_Pair(X18,X22,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X18,X0,X16),c_Datatype__Universe_OIn1(X22,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f32253,plain,
spl0_2625,
inference(avatar_split_clause,[],[f1632,f32251]) ).
fof(f32251,plain,
( spl0_2625
<=> ! [X17,X19,X0,X16,X21,X20] :
( ~ c_in(c_Pair(X17,X21,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X17,X0,X16),c_Datatype__Universe_OIn0(X21,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2625])]) ).
fof(f1632,axiom,
! [X21,X0,X19,X16,X17,X20] :
( ~ c_in(c_Pair(X17,X21,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X17,X0,X16),c_Datatype__Universe_OIn0(X21,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f32215,plain,
( spl0_2624
| ~ spl0_61
| ~ spl0_2012
| ~ spl0_2013
| ~ spl0_2623 ),
inference(avatar_split_clause,[],[f32211,f32207,f18672,f18659,f3525,f32213]) ).
fof(f32213,plain,
( spl0_2624
<=> ! [X34,X33] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2624])]) ).
fof(f18659,plain,
( spl0_2012
<=> ! [X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0) = c_plus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f18672,plain,
( spl0_2013
<=> ! [X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f32207,plain,
( spl0_2623
<=> ! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2623])]) ).
fof(f32211,plain,
( ! [X34,X33] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2012
| ~ spl0_2013
| ~ spl0_2623 ),
inference(forward_demodulation,[],[f32210,f19857]) ).
fof(f19857,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_61
| ~ spl0_2012 ),
inference(resolution,[],[f18660,f3527]) ).
fof(f18660,plain,
( ! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0) = c_plus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) )
| ~ spl0_2012 ),
inference(avatar_component_clause,[],[f18659]) ).
fof(f32210,plain,
( ! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2623 ),
inference(forward_demodulation,[],[f32208,f19858]) ).
fof(f19858,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_61
| ~ spl0_2013 ),
inference(resolution,[],[f18673,f3527]) ).
fof(f18673,plain,
( ! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0) )
| ~ spl0_2013 ),
inference(avatar_component_clause,[],[f18672]) ).
fof(f32208,plain,
( ! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2623 ),
inference(avatar_component_clause,[],[f32207]) ).
fof(f32209,plain,
spl0_2623,
inference(avatar_split_clause,[],[f3202,f32207]) ).
fof(f3202,plain,
! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3201,f1050]) ).
fof(f1050,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(f3201,plain,
! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3200,f1048]) ).
fof(f1048,axiom,
! [X33] : c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X33),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3200,plain,
! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f346,f1050]) ).
fof(f346,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,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(f32074,plain,
spl0_2622,
inference(avatar_split_clause,[],[f1626,f32072]) ).
fof(f32072,plain,
( spl0_2622
<=> ! [X20,X0,X16,X25,X19] :
( ~ c_in(X25,c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdprodE__1(X25,X19,X20,X0,X16),c_Main_OdprodE__3(X25,X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2622])]) ).
fof(f1626,axiom,
! [X0,X19,X16,X25,X20] :
( ~ c_in(X25,c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdprodE__1(X25,X19,X20,X0,X16),c_Main_OdprodE__3(X25,X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X19,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_2) ).
fof(f32070,plain,
spl0_2621,
inference(avatar_split_clause,[],[f1625,f32068]) ).
fof(f32068,plain,
( spl0_2621
<=> ! [X20,X0,X16,X25,X19] :
( ~ c_in(X25,c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdprodE__2(X25,X19,X20,X0,X16),c_Main_OdprodE__4(X25,X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2621])]) ).
fof(f1625,axiom,
! [X0,X19,X16,X25,X20] :
( ~ c_in(X25,c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))))
| c_in(c_Pair(c_Main_OdprodE__2(X25,X19,X20,X0,X16),c_Main_OdprodE__4(X25,X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X20,tc_prod(tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OdprodE_1) ).
fof(f32066,plain,
spl0_2620,
inference(avatar_split_clause,[],[f514,f32064]) ).
fof(f32064,plain,
( spl0_2620
<=> ! [X10,X19,X0,X12,X3,X1] :
( c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X12,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2620])]) ).
fof(f514,axiom,
! [X3,X10,X0,X1,X19,X12] :
( c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X12,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_1) ).
fof(f32062,plain,
spl0_2619,
inference(avatar_split_clause,[],[f395,f32060]) ).
fof(f32060,plain,
( spl0_2619
<=> ! [X10,X40,X0,X12,X19,X39] :
( c_in(c_Pair(X12,X10,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X39,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2619])]) ).
fof(f395,axiom,
! [X40,X10,X0,X39,X19,X12] :
( c_in(c_Pair(X12,X10,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X39,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_1) ).
fof(f32022,plain,
spl0_2618,
inference(avatar_split_clause,[],[f397,f32020]) ).
fof(f32020,plain,
( spl0_2618
<=> ! [X40,X0,X12,X10,X19,X39] :
( c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(X40,tc_List_Olist(X0))
| c_in(c_Pair(X39,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2618])]) ).
fof(f397,axiom,
! [X40,X39,X0,X10,X19,X12] :
( c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(X40,tc_List_Olist(X0))
| c_in(c_Pair(X39,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_3) ).
fof(f32018,plain,
spl0_2617,
inference(avatar_split_clause,[],[f263,f32016]) ).
fof(f32016,plain,
( spl0_2617
<=> ! [X12,X10] :
( ~ c_in(c_Pair(X12,X10,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(X12,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(X10,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_2617])]) ).
fof(f263,axiom,
! [X10,X12] :
( ~ c_in(c_Pair(X12,X10,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(X12,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(X10,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(f32014,plain,
( spl0_2616
| ~ spl0_1102
| ~ spl0_1538
| ~ spl0_2177 ),
inference(avatar_split_clause,[],[f21694,f21572,f12440,f9158,f32012]) ).
fof(f32012,plain,
( spl0_2616
<=> ! [X0] : c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(c_0,X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2616])]) ).
fof(f12440,plain,
( spl0_1538
<=> ! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_OrderedGroup_Opprt(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f21572,plain,
( spl0_2177
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_b),X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f21694,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(c_0,X0,t_b),t_b) )
| ~ spl0_1538
| ~ spl0_2177 ),
inference(resolution,[],[f21573,f12441]) ).
fof(f12441,plain,
( ! [X0,X12] :
( ~ c_lessequals(X12,c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(X12,X0) )
| ~ spl0_1538 ),
inference(avatar_component_clause,[],[f12440]) ).
fof(f21573,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_b),X0,t_b)
| ~ spl0_2177 ),
inference(avatar_component_clause,[],[f21572]) ).
fof(f32010,plain,
spl0_2615,
inference(avatar_split_clause,[],[f262,f32008]) ).
fof(f32008,plain,
( spl0_2615
<=> ! [X12,X10] :
( c_in(c_Pair(X12,X10,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(X12,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(X10,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_2615])]) ).
fof(f262,axiom,
! [X10,X12] :
( c_in(c_Pair(X12,X10,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(X12,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(X10,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(f31998,plain,
( spl0_2614
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2613 ),
inference(avatar_split_clause,[],[f31994,f31991,f18672,f3525,f31996]) ).
fof(f31996,plain,
( spl0_2614
<=> ! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2614])]) ).
fof(f31991,plain,
( spl0_2613
<=> ! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2613])]) ).
fof(f31994,plain,
( ! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2613 ),
inference(forward_demodulation,[],[f31992,f19858]) ).
fof(f31992,plain,
( ! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2613 ),
inference(avatar_component_clause,[],[f31991]) ).
fof(f31993,plain,
spl0_2613,
inference(avatar_split_clause,[],[f3196,f31991]) ).
fof(f3196,plain,
! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3195,f1050]) ).
fof(f3195,plain,
! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3194,f1048]) ).
fof(f3194,plain,
! [X34,X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f355,f1050]) ).
fof(f355,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,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(X34,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(f31954,plain,
spl0_2612,
inference(avatar_split_clause,[],[f685,f31952]) ).
fof(f31952,plain,
( spl0_2612
<=> ! [X44,X40,X0,X16,X43,X39] :
( c_Nat_Osize(X40,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X16))
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X43,tc_List_Olist(X16))
| c_List_Ozip(c_append(X39,X40,X0),c_append(X43,X44,X16),X0,X16) = c_append(c_List_Ozip(X39,X43,X0,X16),c_List_Ozip(X40,X44,X0,X16),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2612])]) ).
fof(f685,axiom,
! [X40,X39,X0,X44,X16,X43] :
( c_Nat_Osize(X40,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X16))
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X43,tc_List_Olist(X16))
| c_List_Ozip(c_append(X39,X40,X0),c_append(X43,X44,X16),X0,X16) = c_append(c_List_Ozip(X39,X43,X0,X16),c_List_Ozip(X40,X44,X0,X16),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__append_0) ).
fof(f31938,plain,
( spl0_2611
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2610 ),
inference(avatar_split_clause,[],[f31934,f31931,f18672,f3525,f31936]) ).
fof(f31936,plain,
( spl0_2611
<=> ! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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)),X33),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2611])]) ).
fof(f31931,plain,
( spl0_2610
<=> ! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2610])]) ).
fof(f31934,plain,
( ! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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)),X33),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2610 ),
inference(forward_demodulation,[],[f31932,f19858]) ).
fof(f31932,plain,
( ! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2610 ),
inference(avatar_component_clause,[],[f31931]) ).
fof(f31933,plain,
spl0_2610,
inference(avatar_split_clause,[],[f3199,f31931]) ).
fof(f3199,plain,
! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3198,f1050]) ).
fof(f3198,plain,
! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3197,f1048]) ).
fof(f3197,plain,
! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f344,f1050]) ).
fof(f344,axiom,
! [X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,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(f31901,plain,
( spl0_2609
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_2012
| ~ spl0_2608 ),
inference(avatar_split_clause,[],[f31897,f31892,f18659,f11072,f3525,f31899]) ).
fof(f31899,plain,
( spl0_2609
<=> ! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2609])]) ).
fof(f11072,plain,
( spl0_1369
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_uminus(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f31892,plain,
( spl0_2608
<=> ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2608])]) ).
fof(f31897,plain,
( ! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_2012
| ~ spl0_2608 ),
inference(forward_demodulation,[],[f31896,f11495]) ).
fof(f11495,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_61
| ~ spl0_1369 ),
inference(resolution,[],[f11073,f3527]) ).
fof(f11073,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_uminus(c_1,X0) )
| ~ spl0_1369 ),
inference(avatar_component_clause,[],[f11072]) ).
fof(f31896,plain,
( ! [X34,X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2012
| ~ spl0_2608 ),
inference(forward_demodulation,[],[f31895,f19857]) ).
fof(f31895,plain,
( ! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X33,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2012
| ~ spl0_2608 ),
inference(forward_demodulation,[],[f31893,f19857]) ).
fof(f31893,plain,
( ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2608 ),
inference(avatar_component_clause,[],[f31892]) ).
fof(f31894,plain,
spl0_2608,
inference(avatar_split_clause,[],[f345,f31892]) ).
fof(f345,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,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(f31859,plain,
spl0_2607,
inference(avatar_split_clause,[],[f398,f31857]) ).
fof(f31857,plain,
( spl0_2607
<=> ! [X40,X0,X12,X10,X19,X39] :
( c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| ~ c_in(c_Pair(X12,X10,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2607])]) ).
fof(f398,axiom,
! [X40,X39,X0,X10,X19,X12] :
( c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| ~ c_in(c_Pair(X12,X10,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_4) ).
fof(f31837,plain,
( spl0_2606
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2605 ),
inference(avatar_split_clause,[],[f31833,f31830,f18672,f3525,f31835]) ).
fof(f31835,plain,
( spl0_2606
<=> ! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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)),X33),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2606])]) ).
fof(f31830,plain,
( spl0_2605
<=> ! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2605])]) ).
fof(f31833,plain,
( ! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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)),X33),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_2013
| ~ spl0_2605 ),
inference(forward_demodulation,[],[f31831,f19858]) ).
fof(f31831,plain,
( ! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2605 ),
inference(avatar_component_clause,[],[f31830]) ).
fof(f31832,plain,
spl0_2605,
inference(avatar_split_clause,[],[f3193,f31830]) ).
fof(f3193,plain,
! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3192,f1050]) ).
fof(f3192,plain,
! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3191,f1048]) ).
fof(f3191,plain,
! [X33] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f353,f1050]) ).
fof(f353,axiom,
! [X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X33,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(X33,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(f31828,plain,
spl0_2604,
inference(avatar_split_clause,[],[f1675,f31826]) ).
fof(f31826,plain,
( spl0_2604
<=> ! [X40,X0,X10,X19,X39] :
( ~ c_in(c_Pair(X39,c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X19,X39,X10,X40,X0),X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2604])]) ).
fof(f1675,axiom,
! [X40,X39,X10,X0,X19] :
( ~ c_in(c_Pair(X39,c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X19,X39,X10,X40,X0),X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_1) ).
fof(f31824,plain,
( spl0_2603
| ~ spl0_1102
| ~ spl0_1538
| ~ spl0_2170 ),
inference(avatar_split_clause,[],[f21457,f21395,f12440,f9158,f31822]) ).
fof(f31822,plain,
( spl0_2603
<=> ! [X0] : c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(X0,c_0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2603])]) ).
fof(f21395,plain,
( spl0_2170
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_b),X1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f21457,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Opprt(c_Orderings_Omin(X0,c_0,t_b),t_b) )
| ~ spl0_1538
| ~ spl0_2170 ),
inference(resolution,[],[f21396,f12441]) ).
fof(f21396,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,t_b),X1,t_b)
| ~ spl0_2170 ),
inference(avatar_component_clause,[],[f21395]) ).
fof(f31820,plain,
spl0_2602,
inference(avatar_split_clause,[],[f1672,f31818]) ).
fof(f31818,plain,
( spl0_2602
<=> ! [X40,X0,X10,X19,X39] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X10,X40,X0),X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(X40,c_Main_Olistrel__Cons1__2(X19,X39,X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2602])]) ).
fof(f1672,axiom,
! [X40,X10,X0,X39,X19] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X10,X40,X0),X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(X40,c_Main_Olistrel__Cons1__2(X19,X39,X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_1) ).
fof(f31808,plain,
( spl0_2601
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2597 ),
inference(avatar_split_clause,[],[f31714,f31711,f14559,f11866,f31806]) ).
fof(f31806,plain,
( spl0_2601
<=> ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2601])]) ).
fof(f11866,plain,
( spl0_1461
<=> ! [X0,X16,X3,X10] : c_snd(c_Pair(X3,X10,X16,X0),X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f14559,plain,
( spl0_1760
<=> ! [X16,X0,X35] : c_Pair(c_Main_Osurj__pair__1(X35,X0,X16),c_Main_Osurj__pair__2(X35,X0,X16),X0,X16) = X35 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f31711,plain,
( spl0_2597
<=> ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2597])]) ).
fof(f31714,plain,
( ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2597 ),
inference(forward_demodulation,[],[f31712,f15511]) ).
fof(f15511,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1461
| ~ spl0_1760 ),
inference(superposition,[],[f11867,f14560]) ).
fof(f14560,plain,
( ! [X0,X16,X35] : c_Pair(c_Main_Osurj__pair__1(X35,X0,X16),c_Main_Osurj__pair__2(X35,X0,X16),X0,X16) = X35
| ~ spl0_1760 ),
inference(avatar_component_clause,[],[f14559]) ).
fof(f11867,plain,
( ! [X3,X10,X0,X16] : c_snd(c_Pair(X3,X10,X16,X0),X16,X0) = X10
| ~ spl0_1461 ),
inference(avatar_component_clause,[],[f11866]) ).
fof(f31712,plain,
( ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2597 ),
inference(avatar_component_clause,[],[f31711]) ).
fof(f31804,plain,
( spl0_2600
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2596 ),
inference(avatar_split_clause,[],[f31709,f31706,f14559,f11862,f31802]) ).
fof(f31802,plain,
( spl0_2600
<=> ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2600])]) ).
fof(f11862,plain,
( spl0_1460
<=> ! [X10,X0,X16,X1] : c_fst(c_Pair(X10,X1,X0,X16),X0,X16) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f31706,plain,
( spl0_2596
<=> ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2596])]) ).
fof(f31709,plain,
( ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2596 ),
inference(forward_demodulation,[],[f31707,f15512]) ).
fof(f15512,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1460
| ~ spl0_1760 ),
inference(superposition,[],[f11863,f14560]) ).
fof(f11863,plain,
( ! [X10,X0,X1,X16] : c_fst(c_Pair(X10,X1,X0,X16),X0,X16) = X10
| ~ spl0_1460 ),
inference(avatar_component_clause,[],[f11862]) ).
fof(f31707,plain,
( ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2596 ),
inference(avatar_component_clause,[],[f31706]) ).
fof(f31800,plain,
( spl0_2599
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2595 ),
inference(avatar_split_clause,[],[f31704,f31701,f14559,f11866,f31798]) ).
fof(f31798,plain,
( spl0_2599
<=> ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2599])]) ).
fof(f31701,plain,
( spl0_2595
<=> ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2595])]) ).
fof(f31704,plain,
( ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2595 ),
inference(forward_demodulation,[],[f31702,f15511]) ).
fof(f31702,plain,
( ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2595 ),
inference(avatar_component_clause,[],[f31701]) ).
fof(f31796,plain,
( spl0_2598
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2594 ),
inference(avatar_split_clause,[],[f31699,f31696,f14559,f11862,f31794]) ).
fof(f31794,plain,
( spl0_2598
<=> ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2598])]) ).
fof(f31696,plain,
( spl0_2594
<=> ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2594])]) ).
fof(f31699,plain,
( ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2594 ),
inference(forward_demodulation,[],[f31697,f15512]) ).
fof(f31697,plain,
( ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2594 ),
inference(avatar_component_clause,[],[f31696]) ).
fof(f31713,plain,
spl0_2597,
inference(avatar_split_clause,[],[f3190,f31711]) ).
fof(f3190,plain,
! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f340,f350]) ).
fof(f350,axiom,
! [X37,X19] : c_IntDiv_OnegateSnd(c_Pair(X37,X19,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X37,c_uminus(X19,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f340,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X33,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(f31708,plain,
spl0_2596,
inference(avatar_split_clause,[],[f3189,f31706]) ).
fof(f3189,plain,
! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f330,f350]) ).
fof(f330,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X33,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(f31703,plain,
spl0_2595,
inference(avatar_split_clause,[],[f3188,f31701]) ).
fof(f3188,plain,
! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f337,f350]) ).
fof(f337,axiom,
! [X34,X33] :
( ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X33,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(f31698,plain,
spl0_2594,
inference(avatar_split_clause,[],[f3187,f31696]) ).
fof(f3187,plain,
! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f327,f350]) ).
fof(f327,axiom,
! [X34,X33] :
( ~ c_lessequals(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X33,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(f31694,plain,
spl0_2593,
inference(avatar_split_clause,[],[f516,f31692]) ).
fof(f31692,plain,
( spl0_2593
<=> ! [X53,X0,X12,X10,X19] :
( ~ c_in(c_Pair(X53,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(c_List_Olist_OCons(X12,X53,X0),c_List_Olist_OCons(X12,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).
fof(f516,axiom,
! [X10,X0,X19,X53,X12] :
( ~ c_in(c_Pair(X53,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(c_List_Olist_OCons(X12,X53,X0),c_List_Olist_OCons(X12,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
fof(f31690,plain,
spl0_2592,
inference(avatar_split_clause,[],[f399,f31688]) ).
fof(f31688,plain,
( spl0_2592
<=> ! [X40,X0,X12,X19,X39] :
( ~ c_in(c_Pair(X39,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X12,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2592])]) ).
fof(f399,axiom,
! [X40,X39,X0,X19,X12] :
( ~ c_in(c_Pair(X39,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0)))
| c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X12,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
fof(f31686,plain,
spl0_2591,
inference(avatar_split_clause,[],[f82,f31684]) ).
fof(f31684,plain,
( spl0_2591
<=> ! [X20,X0,X16,X19] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X19,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).
fof(f82,axiom,
! [X0,X19,X16,X20] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X19,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f31678,plain,
spl0_2590,
inference(avatar_split_clause,[],[f81,f31676]) ).
fof(f31676,plain,
( spl0_2590
<=> ! [X20,X0,X16,X19] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X19,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2590])]) ).
fof(f81,axiom,
! [X0,X19,X16,X20] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X19,X20,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X19,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),c_Relation_ODomain(X20,tc_set(tc_Datatype__Universe_Onode(X0,X16)),tc_set(tc_Datatype__Universe_Onode(X0,X16))),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f31651,plain,
( spl0_2589
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_2587 ),
inference(avatar_split_clause,[],[f31643,f31640,f11072,f3525,f31649]) ).
fof(f31649,plain,
( spl0_2589
<=> ! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2589])]) ).
fof(f31640,plain,
( spl0_2587
<=> ! [X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2587])]) ).
fof(f31643,plain,
( ! [X33] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_2587 ),
inference(forward_demodulation,[],[f31641,f11495]) ).
fof(f31641,plain,
( ! [X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2587 ),
inference(avatar_component_clause,[],[f31640]) ).
fof(f31647,plain,
spl0_2588,
inference(avatar_split_clause,[],[f599,f31645]) ).
fof(f31645,plain,
( spl0_2588
<=> ! [X23,X40,X0,X16,X39] :
( ~ c_less(X23,c_Nat_Osize(X40,tc_List_Olist(X16)),tc_nat)
| ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Ozip(X39,X40,X0,X16),X23,tc_prod(X0,X16)) = c_Pair(c_List_Onth(X39,X23,X0),c_List_Onth(X40,X23,X16),X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2588])]) ).
fof(f599,axiom,
! [X40,X39,X0,X16,X23] :
( ~ c_less(X23,c_Nat_Osize(X40,tc_List_Olist(X16)),tc_nat)
| ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Ozip(X39,X40,X0,X16),X23,tc_prod(X0,X16)) = c_Pair(c_List_Onth(X39,X23,X0),c_List_Onth(X40,X23,X16),X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
fof(f31642,plain,
spl0_2587,
inference(avatar_split_clause,[],[f343,f31640]) ).
fof(f343,axiom,
! [X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(X33,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(f31556,plain,
( spl0_2586
| spl0_114
| ~ spl0_2575 ),
inference(avatar_split_clause,[],[f31443,f31378,f3790,f31553]) ).
fof(f31553,plain,
( spl0_2586
<=> c_less(c_minus(v_f(v_x),v_g(v_x),t_b),c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2586])]) ).
fof(f31378,plain,
( spl0_2575
<=> ! [X0] :
( c_lessequals(c_0,X0,t_b)
| c_less(X0,c_1,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2575])]) ).
fof(f31443,plain,
( c_less(c_minus(v_f(v_x),v_g(v_x),t_b),c_1,t_b)
| spl0_114
| ~ spl0_2575 ),
inference(resolution,[],[f31379,f3792]) ).
fof(f31379,plain,
( ! [X0] :
( c_lessequals(c_0,X0,t_b)
| c_less(X0,c_1,t_b) )
| ~ spl0_2575 ),
inference(avatar_component_clause,[],[f31378]) ).
fof(f31494,plain,
spl0_2585,
inference(avatar_split_clause,[],[f1706,f31492]) ).
fof(f31492,plain,
( spl0_2585
<=> ! [X3,X82,X0,X20,X16,X25,X19,X1] :
( ~ c_in(c_Pair(X1,X25,X16,X82),X19,tc_prod(X16,X82))
| ~ c_in(c_Pair(X3,X1,X0,X16),X20,tc_prod(X0,X16))
| c_in(c_Pair(X3,X25,X0,X82),c_Relation_Orel__comp(X19,X20,X16,X82,X0),tc_prod(X0,X82)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2585])]) ).
fof(f1706,axiom,
! [X82,X3,X0,X1,X19,X16,X25,X20] :
( ~ c_in(c_Pair(X1,X25,X16,X82),X19,tc_prod(X16,X82))
| ~ c_in(c_Pair(X3,X1,X0,X16),X20,tc_prod(X0,X16))
| c_in(c_Pair(X3,X25,X0,X82),c_Relation_Orel__comp(X19,X20,X16,X82,X0),tc_prod(X0,X82)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f31490,plain,
spl0_2584,
inference(avatar_split_clause,[],[f1674,f31488]) ).
fof(f31488,plain,
( spl0_2584
<=> ! [X40,X0,X10,X19,X39] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X19,X39,X10,X40,X0),c_Main_Olistrel__Cons2__2(X19,X39,X10,X40,X0),X0) = X39
| ~ c_in(c_Pair(X39,c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2584])]) ).
fof(f1674,axiom,
! [X40,X39,X10,X0,X19] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X19,X39,X10,X40,X0),c_Main_Olistrel__Cons2__2(X19,X39,X10,X40,X0),X0) = X39
| ~ c_in(c_Pair(X39,c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
fof(f31486,plain,
spl0_2583,
inference(avatar_split_clause,[],[f1671,f31484]) ).
fof(f31484,plain,
( spl0_2583
<=> ! [X40,X0,X10,X19,X39] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X19,X39,X10,X40,X0),c_Main_Olistrel__Cons1__2(X19,X39,X10,X40,X0),X0) = X39
| ~ c_in(c_Pair(c_List_Olist_OCons(X10,X40,X0),X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).
fof(f1671,axiom,
! [X40,X39,X10,X0,X19] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X19,X39,X10,X40,X0),c_Main_Olistrel__Cons1__2(X19,X39,X10,X40,X0),X0) = X39
| ~ c_in(c_Pair(c_List_Olist_OCons(X10,X40,X0),X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
fof(f31482,plain,
spl0_2582,
inference(avatar_split_clause,[],[f513,f31480]) ).
fof(f31480,plain,
( spl0_2582
<=> ! [X10,X0,X12,X3,X19,X1] :
( X1 = X3
| c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).
fof(f513,axiom,
! [X3,X10,X0,X1,X19,X12] :
( X1 = X3
| c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
fof(f31478,plain,
spl0_2581,
inference(avatar_split_clause,[],[f394,f31476]) ).
fof(f31476,plain,
( spl0_2581
<=> ! [X10,X40,X0,X12,X19,X39] :
( X10 = X12
| c_in(c_Pair(X12,X10,X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2581])]) ).
fof(f394,axiom,
! [X40,X10,X0,X39,X19,X12] :
( X10 = X12
| c_in(c_Pair(X12,X10,X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
fof(f31474,plain,
spl0_2580,
inference(avatar_split_clause,[],[f277,f31472]) ).
fof(f31472,plain,
( spl0_2580
<=> ! [X34,X10,X12,X36] :
( c_plus(X12,X34,tc_nat) != c_plus(X36,X10,tc_nat)
| c_in(c_Pair(c_Pair(X12,X10,tc_nat,tc_nat),c_Pair(X36,X34,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_2580])]) ).
fof(f277,axiom,
! [X10,X36,X34,X12] :
( c_plus(X12,X34,tc_nat) != c_plus(X36,X10,tc_nat)
| c_in(c_Pair(c_Pair(X12,X10,tc_nat,tc_nat),c_Pair(X36,X34,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(f31470,plain,
spl0_2579,
inference(avatar_split_clause,[],[f276,f31468]) ).
fof(f31468,plain,
( spl0_2579
<=> ! [X34,X10,X12,X36] :
( c_plus(X12,X34,tc_nat) = c_plus(X36,X10,tc_nat)
| ~ c_in(c_Pair(c_Pair(X12,X10,tc_nat,tc_nat),c_Pair(X36,X34,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_2579])]) ).
fof(f276,axiom,
! [X10,X36,X34,X12] :
( c_plus(X12,X34,tc_nat) = c_plus(X36,X10,tc_nat)
| ~ c_in(c_Pair(c_Pair(X12,X10,tc_nat,tc_nat),c_Pair(X36,X34,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(f31392,plain,
( spl0_2578
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2570 ),
inference(avatar_split_clause,[],[f31360,f31357,f14559,f11866,f31390]) ).
fof(f31390,plain,
( spl0_2578
<=> ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2578])]) ).
fof(f31357,plain,
( spl0_2570
<=> ! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2570])]) ).
fof(f31360,plain,
( ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2570 ),
inference(forward_demodulation,[],[f31358,f15511]) ).
fof(f31358,plain,
( ! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2570 ),
inference(avatar_component_clause,[],[f31357]) ).
fof(f31388,plain,
( spl0_2577
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2569 ),
inference(avatar_split_clause,[],[f31355,f31352,f14559,f11866,f31386]) ).
fof(f31386,plain,
( spl0_2577
<=> ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2577])]) ).
fof(f31352,plain,
( spl0_2569
<=> ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2569])]) ).
fof(f31355,plain,
( ! [X34,X33] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2569 ),
inference(forward_demodulation,[],[f31353,f15511]) ).
fof(f31353,plain,
( ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2569 ),
inference(avatar_component_clause,[],[f31352]) ).
fof(f31384,plain,
( spl0_2576
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2568 ),
inference(avatar_split_clause,[],[f31350,f31347,f14559,f11862,f31382]) ).
fof(f31382,plain,
( spl0_2576
<=> ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2576])]) ).
fof(f31347,plain,
( spl0_2568
<=> ! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2568])]) ).
fof(f31350,plain,
( ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2568 ),
inference(forward_demodulation,[],[f31348,f15512]) ).
fof(f31348,plain,
( ! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2568 ),
inference(avatar_component_clause,[],[f31347]) ).
fof(f31380,plain,
( ~ spl0_965
| spl0_2575
| ~ spl0_1472
| ~ spl0_2531 ),
inference(avatar_split_clause,[],[f30131,f29850,f11911,f31378,f8447]) ).
fof(f29850,plain,
( spl0_2531
<=> ! [X0] :
( ~ c_lessequals(c_1,X0,t_b)
| c_lessequals(c_0,X0,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f30131,plain,
( ! [X0] :
( c_lessequals(c_0,X0,t_b)
| ~ class_Orderings_Olinorder(t_b)
| c_less(X0,c_1,t_b) )
| ~ spl0_1472
| ~ spl0_2531 ),
inference(resolution,[],[f29851,f11912]) ).
fof(f29851,plain,
( ! [X0] :
( ~ c_lessequals(c_1,X0,t_b)
| c_lessequals(c_0,X0,t_b) )
| ~ spl0_2531 ),
inference(avatar_component_clause,[],[f29850]) ).
fof(f31376,plain,
( spl0_2574
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2567 ),
inference(avatar_split_clause,[],[f31345,f31342,f14559,f11862,f31374]) ).
fof(f31374,plain,
( spl0_2574
<=> ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2574])]) ).
fof(f31342,plain,
( spl0_2567
<=> ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2567])]) ).
fof(f31345,plain,
( ! [X34,X33] :
( c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2567 ),
inference(forward_demodulation,[],[f31343,f15512]) ).
fof(f31343,plain,
( ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2567 ),
inference(avatar_component_clause,[],[f31342]) ).
fof(f31372,plain,
spl0_2573,
inference(avatar_split_clause,[],[f1676,f31370]) ).
fof(f31370,plain,
( spl0_2573
<=> ! [X40,X0,X10,X19,X39] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X19,X39,X10,X40,X0),X10,X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(X39,c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2573])]) ).
fof(f1676,axiom,
! [X40,X39,X10,X0,X19] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X19,X39,X10,X40,X0),X10,X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(X39,c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
fof(f31368,plain,
spl0_2572,
inference(avatar_split_clause,[],[f1673,f31366]) ).
fof(f31366,plain,
( spl0_2572
<=> ! [X40,X0,X10,X19,X39] :
( c_in(c_Pair(X10,c_Main_Olistrel__Cons1__1(X19,X39,X10,X40,X0),X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X10,X40,X0),X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2572])]) ).
fof(f1673,axiom,
! [X40,X10,X39,X0,X19] :
( c_in(c_Pair(X10,c_Main_Olistrel__Cons1__1(X19,X39,X10,X40,X0),X0,X0),X19,tc_prod(X0,X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X10,X40,X0),X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
fof(f31364,plain,
spl0_2571,
inference(avatar_split_clause,[],[f396,f31362]) ).
fof(f31362,plain,
( spl0_2571
<=> ! [X10,X40,X0,X12,X19,X39] :
( X10 = X12
| c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(X40,tc_List_Olist(X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2571])]) ).
fof(f396,axiom,
! [X40,X10,X39,X0,X19,X12] :
( X10 = X12
| c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(X40,tc_List_Olist(X0))
| ~ c_in(c_Pair(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
fof(f31359,plain,
spl0_2570,
inference(avatar_split_clause,[],[f342,f31357]) ).
fof(f342,axiom,
! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(f31354,plain,
spl0_2569,
inference(avatar_split_clause,[],[f338,f31352]) ).
fof(f338,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(f31349,plain,
spl0_2568,
inference(avatar_split_clause,[],[f332,f31347]) ).
fof(f332,axiom,
! [X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(f31344,plain,
spl0_2567,
inference(avatar_split_clause,[],[f328,f31342]) ).
fof(f328,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,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(f31242,plain,
( spl0_2566
| ~ spl0_1934
| ~ spl0_2457 ),
inference(avatar_split_clause,[],[f28522,f28422,f17336,f31240]) ).
fof(f31240,plain,
( spl0_2566
<=> ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_b)
| c_1 = c_NatArith_Oof__nat(X0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2566])]) ).
fof(f17336,plain,
( spl0_1934
<=> ! [X0] : c_NatArith_Oof__nat(X0,t_b) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f28422,plain,
( spl0_2457
<=> ! [X0] :
( c_1 != c_IntDef_Oof__int(X0,t_b)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2457])]) ).
fof(f28522,plain,
( ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_b)
| c_1 = c_NatArith_Oof__nat(X0,tc_IntDef_Oint) )
| ~ spl0_1934
| ~ spl0_2457 ),
inference(superposition,[],[f28423,f17337]) ).
fof(f17337,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,t_b) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),t_b)
| ~ spl0_1934 ),
inference(avatar_component_clause,[],[f17336]) ).
fof(f28423,plain,
( ! [X0] :
( c_1 != c_IntDef_Oof__int(X0,t_b)
| c_1 = X0 )
| ~ spl0_2457 ),
inference(avatar_component_clause,[],[f28422]) ).
fof(f31203,plain,
spl0_2565,
inference(avatar_split_clause,[],[f1704,f31201]) ).
fof(f31201,plain,
( spl0_2565
<=> ! [X81,X82,X20,X0,X16,X19] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_Orel__compE__1(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__2(X19,X20,X81,X82,X16,X0),X0,X82),X20,tc_prod(X0,X82)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2565])]) ).
fof(f1704,axiom,
! [X82,X0,X81,X19,X16,X20] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_Orel__compE__1(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__2(X19,X20,X81,X82,X16,X0),X0,X82),X20,tc_prod(X0,X82)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f31199,plain,
spl0_2564,
inference(avatar_split_clause,[],[f1703,f31197]) ).
fof(f31197,plain,
( spl0_2564
<=> ! [X81,X82,X20,X0,X16,X19] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_Orel__compE__2(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__3(X19,X20,X81,X82,X16,X0),X82,X16),X19,tc_prod(X82,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2564])]) ).
fof(f1703,axiom,
! [X82,X0,X81,X19,X16,X20] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_Orel__compE__2(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__3(X19,X20,X81,X82,X16,X0),X82,X16),X19,tc_prod(X82,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f31195,plain,
spl0_2563,
inference(avatar_split_clause,[],[f1641,f31193]) ).
fof(f31193,plain,
( spl0_2563
<=> ! [X36,X0,X16,X26,X30] :
( ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__2(X30,X36,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__1(X26,X36,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2563])]) ).
fof(f1641,axiom,
! [X0,X36,X26,X16,X30] :
( ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__2(X30,X36,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__1(X26,X36,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f31191,plain,
spl0_2562,
inference(avatar_split_clause,[],[f364,f31189]) ).
fof(f31189,plain,
( spl0_2562
<=> ! [X34,X1,X33] :
( c_Numeral_Obit_OB0 = X1
| c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,X1),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2562])]) ).
fof(f364,axiom,
! [X1,X34,X33] :
( c_Numeral_Obit_OB0 = X1
| c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,X1),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f31048,plain,
spl0_2561,
inference(avatar_split_clause,[],[f3096,f31046]) ).
fof(f31046,plain,
( spl0_2561
<=> ! [X34,X24] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2561])]) ).
fof(f3096,plain,
! [X34,X24] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3095,f1050]) ).
fof(f3095,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3094,f2861]) ).
fof(f2861,plain,
! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat),
inference(definition_unfolding,[],[f995,f1438,f1438]) ).
fof(f1438,axiom,
! [X36] : c_Suc(X36) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f995,axiom,
! [X11,X24] : c_Suc(c_plus(X24,X11,tc_nat)) = c_plus(c_Suc(X24),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f3094,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2911,f3061]) ).
fof(f3061,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3060,f1050]) ).
fof(f3060,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,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,[],[f3059,f1048]) ).
fof(f3059,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,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,[],[f2880,f1050]) ).
fof(f2880,plain,
! [X11] : c_plus(X11,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(X11,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f776,f1438,f1438]) ).
fof(f776,axiom,
! [X11] : c_Suc(c_Suc(X11)) = c_plus(X11,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(f2911,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,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(X24,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(definition_unfolding,[],[f774,f1438,f1438,f1438]) ).
fof(f774,axiom,
! [X34,X24] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X24))),c_Numeral_Onumber__of(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f31028,plain,
( spl0_2560
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2559 ),
inference(avatar_split_clause,[],[f31024,f31020,f22574,f13448,f13139,f8657,f3868,f31026]) ).
fof(f31026,plain,
( spl0_2560
<=> ! [X34,X24] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X24,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2560])]) ).
fof(f8657,plain,
( spl0_994
<=> ! [X10] : c_IntDef_Onat(c_IntDef_Oint(X10)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f13139,plain,
( spl0_1615
<=> ! [X11,X24] : c_IntDef_Oint(c_plus(X24,X11,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f13448,plain,
( spl0_1691
<=> ! [X24] : c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f22574,plain,
( spl0_2221
<=> ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).
fof(f31020,plain,
( spl0_2559
<=> ! [X34,X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2559])]) ).
fof(f31024,plain,
( ! [X34,X24] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X24,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2559 ),
inference(forward_demodulation,[],[f31023,f22575]) ).
fof(f22575,plain,
( ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat)
| ~ spl0_2221 ),
inference(avatar_component_clause,[],[f22574]) ).
fof(f31023,plain,
( ! [X34,X24] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X24,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(X34,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2559 ),
inference(forward_demodulation,[],[f31021,f14217]) ).
fof(f14217,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691 ),
inference(forward_demodulation,[],[f14216,f8658]) ).
fof(f8658,plain,
( ! [X10] : c_IntDef_Onat(c_IntDef_Oint(X10)) = X10
| ~ spl0_994 ),
inference(avatar_component_clause,[],[f8657]) ).
fof(f14216,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_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691 ),
inference(forward_demodulation,[],[f14178,f13695]) ).
fof(f13695,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_131
| ~ spl0_1615 ),
inference(superposition,[],[f13140,f3870]) ).
fof(f13140,plain,
( ! [X11,X24] : c_IntDef_Oint(c_plus(X24,X11,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint)
| ~ spl0_1615 ),
inference(avatar_component_clause,[],[f13139]) ).
fof(f14178,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_994
| ~ spl0_1691 ),
inference(superposition,[],[f8658,f13449]) ).
fof(f13449,plain,
( ! [X24] : c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat))
| ~ spl0_1691 ),
inference(avatar_component_clause,[],[f13448]) ).
fof(f31021,plain,
( ! [X34,X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ spl0_2559 ),
inference(avatar_component_clause,[],[f31020]) ).
fof(f31022,plain,
spl0_2559,
inference(avatar_split_clause,[],[f3093,f31020]) ).
fof(f3093,plain,
! [X34,X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3092,f1050]) ).
fof(f3092,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3091,f2861]) ).
fof(f3091,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X34,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2910,f3061]) ).
fof(f2910,plain,
! [X34,X24] : 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),X24,tc_nat),c_Numeral_Onumber__of(X34,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(X24,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
inference(definition_unfolding,[],[f773,f1438,f1438,f1438]) ).
fof(f773,axiom,
! [X34,X24] : c_div(c_Suc(c_Suc(c_Suc(X24))),c_Numeral_Onumber__of(X34,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),X24,tc_nat),c_Numeral_Onumber__of(X34,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f31018,plain,
spl0_2558,
inference(avatar_split_clause,[],[f2988,f31016]) ).
fof(f31016,plain,
( spl0_2558
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2558])]) ).
fof(f2988,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1618,f1610]) ).
fof(f1610,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f1618,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f31014,plain,
spl0_2557,
inference(avatar_split_clause,[],[f2987,f31012]) ).
fof(f31012,plain,
( spl0_2557
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2557])]) ).
fof(f2987,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1615,f1610]) ).
fof(f1615,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f31010,plain,
spl0_2556,
inference(avatar_split_clause,[],[f1640,f31008]) ).
fof(f31008,plain,
( spl0_2556
<=> ! [X26,X0,X36,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__1(X26,X36,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2556])]) ).
fof(f1640,axiom,
! [X0,X36,X26,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__1(X26,X36,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f31006,plain,
spl0_2555,
inference(avatar_split_clause,[],[f1639,f31004]) ).
fof(f31004,plain,
( spl0_2555
<=> ! [X30,X0,X36,X16,X26] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__2(X30,X36,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).
fof(f1639,axiom,
! [X0,X36,X26,X16,X30] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OusumE__2(X30,X36,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f31002,plain,
( spl0_2554
| ~ spl0_1471
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f18714,f18246,f11907,f31000]) ).
fof(f31000,plain,
( spl0_2554
<=> ! [X0,X1] :
( ~ c_in(X1,c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b)
| X0 = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2554])]) ).
fof(f11907,plain,
( spl0_1471
<=> ! [X0,X1,X3] :
( X1 = X3
| ~ c_in(X1,c_insert(X3,c_emptyset,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f18246,plain,
( spl0_1977
<=> ! [X0] : c_insert(X0,c_emptyset,t_b) = c_SetInterval_OatLeastAtMost(X0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f18714,plain,
( ! [X0,X1] :
( ~ c_in(X1,c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b)
| X0 = X1 )
| ~ spl0_1471
| ~ spl0_1977 ),
inference(superposition,[],[f11908,f18247]) ).
fof(f18247,plain,
( ! [X0] : c_insert(X0,c_emptyset,t_b) = c_SetInterval_OatLeastAtMost(X0,X0,t_b)
| ~ spl0_1977 ),
inference(avatar_component_clause,[],[f18246]) ).
fof(f11908,plain,
( ! [X3,X0,X1] :
( ~ c_in(X1,c_insert(X3,c_emptyset,X0),X0)
| X1 = X3 )
| ~ spl0_1471 ),
inference(avatar_component_clause,[],[f11907]) ).
fof(f30998,plain,
spl0_2553,
inference(avatar_split_clause,[],[f515,f30996]) ).
fof(f30996,plain,
( spl0_2553
<=> ! [X10,X19,X0,X12,X3,X1] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2553])]) ).
fof(f515,axiom,
! [X3,X10,X0,X1,X19,X12] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(c_List_Olist_OCons(X3,X12,X0),c_List_Olist_OCons(X1,X10,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
fof(f30994,plain,
spl0_2552,
inference(avatar_split_clause,[],[f354,f30992]) ).
fof(f30992,plain,
( spl0_2552
<=> ! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).
fof(f354,axiom,
! [X34,X33] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f30922,plain,
spl0_2551,
inference(avatar_split_clause,[],[f2959,f30920]) ).
fof(f30920,plain,
( spl0_2551
<=> ! [X34,X0,X12,X39] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).
fof(f2959,plain,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),tc_nat),X0),X0) ),
inference(definition_unfolding,[],[f662,f660,f660]) ).
fof(f660,axiom,
! [X72,X0,X11] : c_List_Osublist(X72,c_SetInterval_OlessThan(X11,tc_nat),X0) = c_List_Otake(X11,X72,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f662,axiom,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X34,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olist_OCons(X12,c_List_Otake(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f30918,plain,
spl0_2550,
inference(avatar_split_clause,[],[f1638,f30916]) ).
fof(f30916,plain,
( spl0_2550
<=> ! [X26,X0,X36,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).
fof(f1638,axiom,
! [X0,X36,X26,X16,X30] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X30,X36,X0,X16),X0,X16) = X36
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X26,X36,X0,X16),X0,X16) = X36
| ~ c_in(X36,c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f30636,plain,
spl0_2549,
inference(avatar_split_clause,[],[f2907,f30634]) ).
fof(f30634,plain,
( spl0_2549
<=> ! [X11,X40,X0,X39] : c_List_Osublist(c_append(X39,X40,X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_append(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Osublist(X40,c_SetInterval_OlessThan(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),tc_nat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).
fof(f2907,plain,
! [X40,X39,X0,X11] : c_List_Osublist(c_append(X39,X40,X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_append(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Osublist(X40,c_SetInterval_OlessThan(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),tc_nat),X0),X0),
inference(definition_unfolding,[],[f665,f660,f660,f660]) ).
fof(f665,axiom,
! [X40,X39,X0,X11] : c_List_Otake(X11,c_append(X39,X40,X0),X0) = c_append(c_List_Otake(X11,X39,X0),c_List_Otake(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f30632,plain,
spl0_2548,
inference(avatar_split_clause,[],[f1736,f30630]) ).
fof(f30630,plain,
( spl0_2548
<=> ! [X36,X0,X16,X26,X30] :
( ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2548])]) ).
fof(f1736,axiom,
! [X0,X36,X26,X16,X30] :
( ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f30628,plain,
spl0_2547,
inference(avatar_split_clause,[],[f1705,f30626]) ).
fof(f30626,plain,
( spl0_2547
<=> ! [X81,X82,X20,X0,X16,X19] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_Orel__compE__1(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__3(X19,X20,X81,X82,X16,X0),X0,X16) = X81 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2547])]) ).
fof(f1705,axiom,
! [X82,X0,X81,X19,X16,X20] :
( ~ c_in(X81,c_Relation_Orel__comp(X19,X20,X82,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_Orel__compE__1(X19,X20,X81,X82,X16,X0),c_Main_Orel__compE__3(X19,X20,X81,X82,X16,X0),X0,X16) = X81 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f30624,plain,
spl0_2546,
inference(avatar_split_clause,[],[f892,f30622]) ).
fof(f30622,plain,
( spl0_2546
<=> ! [X34,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2546])]) ).
fof(f892,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f30620,plain,
spl0_2545,
inference(avatar_split_clause,[],[f886,f30618]) ).
fof(f30618,plain,
( spl0_2545
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2545])]) ).
fof(f886,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f30616,plain,
spl0_2544,
inference(avatar_split_clause,[],[f880,f30614]) ).
fof(f30614,plain,
( spl0_2544
<=> ! [X34,X16,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).
fof(f880,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f30612,plain,
spl0_2543,
inference(avatar_split_clause,[],[f874,f30610]) ).
fof(f30610,plain,
( spl0_2543
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2543])]) ).
fof(f874,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f30524,plain,
( spl0_2542
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2541 ),
inference(avatar_split_clause,[],[f30520,f30517,f22574,f9346,f9305,f30522]) ).
fof(f30522,plain,
( spl0_2542
<=> ! [X0,X11,X3] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).
fof(f9305,plain,
( spl0_1137
<=> ! [X10] : c_plus(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f9346,plain,
( spl0_1147
<=> ! [X10] : c_plus(c_0,X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f30517,plain,
( spl0_2541
<=> ! [X0,X11,X3] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).
fof(f30520,plain,
( ! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_plus(c_1,c_1,tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2541 ),
inference(forward_demodulation,[],[f30518,f22662]) ).
fof(f22662,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_1137
| ~ spl0_1147
| ~ spl0_2221 ),
inference(forward_demodulation,[],[f22579,f9306]) ).
fof(f9306,plain,
( ! [X10] : c_plus(X10,c_0,tc_nat) = X10
| ~ spl0_1137 ),
inference(avatar_component_clause,[],[f9305]) ).
fof(f22579,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_1147
| ~ spl0_2221 ),
inference(superposition,[],[f22575,f9347]) ).
fof(f9347,plain,
( ! [X10] : c_plus(c_0,X10,tc_nat) = X10
| ~ spl0_1147 ),
inference(avatar_component_clause,[],[f9346]) ).
fof(f30518,plain,
( ! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) )
| ~ spl0_2541 ),
inference(avatar_component_clause,[],[f30517]) ).
fof(f30519,plain,
spl0_2541,
inference(avatar_split_clause,[],[f3184,f30517]) ).
fof(f3184,plain,
! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(forward_demodulation,[],[f3183,f1050]) ).
fof(f3183,plain,
! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(forward_demodulation,[],[f3182,f1048]) ).
fof(f3182,plain,
! [X3,X0,X11] :
( c_Nat_Opower(c_uminus(X3,X0),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X11,tc_nat),X0) = c_Nat_Opower(X3,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X11,tc_nat),X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0) ),
inference(forward_demodulation,[],[f769,f1050]) ).
fof(f769,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Nat_Opower(c_uminus(X3,X0),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),X11,tc_nat),X0) = c_Nat_Opower(X3,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),X11,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f30515,plain,
spl0_2540,
inference(avatar_split_clause,[],[f2975,f30513]) ).
fof(f30513,plain,
( spl0_2540
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).
fof(f2975,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1617,f1610]) ).
fof(f1617,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f30511,plain,
spl0_2539,
inference(avatar_split_clause,[],[f2974,f30509]) ).
fof(f30509,plain,
( spl0_2539
<=> ! [X10,X0,X12,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).
fof(f2974,plain,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1614,f1610]) ).
fof(f1614,axiom,
! [X10,X0,X19,X12] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0)
| ~ c_in(c_Pair(X12,X10,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f30507,plain,
spl0_2538,
inference(avatar_split_clause,[],[f2881,f30505]) ).
fof(f30505,plain,
( spl0_2538
<=> ! [X77,X0] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).
fof(f2881,plain,
! [X0,X77] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0,X0),
inference(definition_unfolding,[],[f1605,f1610,f1610,f1610]) ).
fof(f1605,axiom,
! [X0,X77] : c_Transitive__Closure_Ortrancl(X77,X0) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X77,X0),c_Transitive__Closure_Ortrancl(X77,X0),X0,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f30503,plain,
( spl0_2537
| ~ spl0_2179
| ~ spl0_2531 ),
inference(avatar_split_clause,[],[f30129,f29850,f22096,f30501]) ).
fof(f30501,plain,
( spl0_2537
<=> ! [X0] : c_lessequals(c_0,c_Orderings_Omax(c_1,X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2537])]) ).
fof(f22096,plain,
( spl0_2179
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f30129,plain,
( ! [X0] : c_lessequals(c_0,c_Orderings_Omax(c_1,X0,t_b),t_b)
| ~ spl0_2179
| ~ spl0_2531 ),
inference(resolution,[],[f29851,f22097]) ).
fof(f22097,plain,
( ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,t_b),t_b)
| ~ spl0_2179 ),
inference(avatar_component_clause,[],[f22096]) ).
fof(f30499,plain,
spl0_2536,
inference(avatar_split_clause,[],[f1637,f30497]) ).
fof(f30497,plain,
( spl0_2536
<=> ! [X18,X0,X16,X17,X26,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OScons(X17,X18,X0,X16),c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2536])]) ).
fof(f1637,axiom,
! [X0,X18,X26,X16,X17,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OScons(X17,X18,X0,X16),c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f30491,plain,
( spl0_2535
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2532 ),
inference(avatar_split_clause,[],[f29857,f29854,f14559,f11866,f30489]) ).
fof(f30489,plain,
( spl0_2535
<=> ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2535])]) ).
fof(f29854,plain,
( spl0_2532
<=> ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).
fof(f29857,plain,
( ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2532 ),
inference(forward_demodulation,[],[f29855,f15511]) ).
fof(f29855,plain,
( ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2532 ),
inference(avatar_component_clause,[],[f29854]) ).
fof(f30487,plain,
( spl0_2534
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2530 ),
inference(avatar_split_clause,[],[f29848,f29845,f14559,f11862,f30485]) ).
fof(f30485,plain,
( spl0_2534
<=> ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2534])]) ).
fof(f29845,plain,
( spl0_2530
<=> ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).
fof(f29848,plain,
( ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2530 ),
inference(forward_demodulation,[],[f29846,f15512]) ).
fof(f29846,plain,
( ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2530 ),
inference(avatar_component_clause,[],[f29845]) ).
fof(f30435,plain,
( spl0_2533
| ~ spl0_2178
| ~ spl0_2531 ),
inference(avatar_split_clause,[],[f30128,f29850,f21869,f30433]) ).
fof(f30433,plain,
( spl0_2533
<=> ! [X0] : c_lessequals(c_0,c_Orderings_Omax(X0,c_1,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2533])]) ).
fof(f30128,plain,
( ! [X0] : c_lessequals(c_0,c_Orderings_Omax(X0,c_1,t_b),t_b)
| ~ spl0_2178
| ~ spl0_2531 ),
inference(resolution,[],[f29851,f21870]) ).
fof(f29856,plain,
spl0_2532,
inference(avatar_split_clause,[],[f3141,f29854]) ).
fof(f3141,plain,
! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f339,f350]) ).
fof(f339,axiom,
! [X33] :
( ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,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(X33,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(f29852,plain,
( spl0_2531
| ~ spl0_1059
| ~ spl0_1654
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f17093,f16145,f13296,f8960,f29850]) ).
fof(f13296,plain,
( spl0_1654
<=> c_lessequals(c_0,c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f17093,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(t_b)
| ~ c_lessequals(c_1,X0,t_b)
| c_lessequals(c_0,X0,t_b) )
| ~ spl0_1654
| ~ spl0_1882 ),
inference(resolution,[],[f16146,f13298]) ).
fof(f13298,plain,
( c_lessequals(c_0,c_1,t_b)
| ~ spl0_1654 ),
inference(avatar_component_clause,[],[f13296]) ).
fof(f29847,plain,
spl0_2530,
inference(avatar_split_clause,[],[f3140,f29845]) ).
fof(f3140,plain,
! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f329,f350]) ).
fof(f329,axiom,
! [X33] :
( ~ c_less(c_Numeral_Onumber__of(X33,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,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(X33,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(f29834,plain,
( spl0_2529
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2528 ),
inference(avatar_split_clause,[],[f29830,f29826,f22574,f13448,f13139,f9346,f9305,f8657,f3868,f29832]) ).
fof(f29832,plain,
( spl0_2529
<=> ! [X24] : c_div(c_plus(X24,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(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).
fof(f29826,plain,
( spl0_2528
<=> ! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,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(X24,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_2528])]) ).
fof(f29830,plain,
( ! [X24] : c_div(c_plus(X24,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(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2528 ),
inference(forward_demodulation,[],[f29829,f14217]) ).
fof(f29829,plain,
( ! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X24,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2528 ),
inference(forward_demodulation,[],[f29827,f22662]) ).
fof(f29827,plain,
( ! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,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(X24,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_2528 ),
inference(avatar_component_clause,[],[f29826]) ).
fof(f29828,plain,
spl0_2528,
inference(avatar_split_clause,[],[f3090,f29826]) ).
fof(f3090,plain,
! [X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X24,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(X24,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,[],[f3089,f3061]) ).
fof(f3089,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f3088,f1050]) ).
fof(f3088,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f3087,f1048]) ).
fof(f3087,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f2909,f1050]) ).
fof(f2909,plain,
! [X24] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,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(X24,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,[],[f778,f1438,f1438,f1438]) ).
fof(f778,axiom,
! [X24] : c_div(c_Suc(c_Suc(X24)),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(X24,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(f29779,plain,
( spl0_2527
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2526 ),
inference(avatar_split_clause,[],[f29775,f29771,f22574,f13448,f13139,f8657,f3868,f29777]) ).
fof(f29777,plain,
( spl0_2527
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2527])]) ).
fof(f29771,plain,
( spl0_2526
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f29775,plain,
( ! [X11,X24] : c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2526 ),
inference(forward_demodulation,[],[f29774,f22575]) ).
fof(f29774,plain,
( ! [X11,X24] : c_Divides_Oop_Amod(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_1,c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2526 ),
inference(forward_demodulation,[],[f29772,f14217]) ).
fof(f29772,plain,
( ! [X11,X24] : c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat)
| ~ spl0_2526 ),
inference(avatar_component_clause,[],[f29771]) ).
fof(f29773,plain,
spl0_2526,
inference(avatar_split_clause,[],[f3082,f29771]) ).
fof(f3082,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3081,f1050]) ).
fof(f3081,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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,[],[f3080,f2861]) ).
fof(f3080,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,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,[],[f2904,f3061]) ).
fof(f2904,plain,
! [X11,X24] : c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat) = c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f871,f1438,f1438,f1438]) ).
fof(f871,axiom,
! [X11,X24] : c_Divides_Oop_Amod(X24,c_Suc(c_Suc(c_Suc(X11))),tc_nat) = c_Divides_Oop_Amod(X24,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),X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f29757,plain,
( spl0_2525
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2524 ),
inference(avatar_split_clause,[],[f29753,f29749,f22574,f13448,f13139,f8657,f3868,f29755]) ).
fof(f29755,plain,
( spl0_2525
<=> ! [X11,X24] : c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f29749,plain,
( spl0_2524
<=> ! [X11,X24] : c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).
fof(f29753,plain,
( ! [X11,X24] : c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_1,c_plus(c_1,c_plus(c_1,X11,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2524 ),
inference(forward_demodulation,[],[f29752,f22575]) ).
fof(f29752,plain,
( ! [X11,X24] : c_div(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_1,c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2524 ),
inference(forward_demodulation,[],[f29750,f14217]) ).
fof(f29750,plain,
( ! [X11,X24] : c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat)
| ~ spl0_2524 ),
inference(avatar_component_clause,[],[f29749]) ).
fof(f29751,plain,
spl0_2524,
inference(avatar_split_clause,[],[f3079,f29749]) ).
fof(f3079,plain,
! [X11,X24] : c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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(X24,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X11,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3078,f1050]) ).
fof(f3078,plain,
! [X11,X24] : c_div(X24,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),X11,tc_nat),tc_nat) = c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X11,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,[],[f3077,f2861]) ).
fof(f3077,plain,
! [X11,X24] : c_div(X24,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),X11,tc_nat),tc_nat) = c_div(X24,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,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,[],[f2903,f3061]) ).
fof(f2903,plain,
! [X11,X24] : c_div(X24,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),X11,tc_nat),tc_nat) = c_div(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f779,f1438,f1438,f1438]) ).
fof(f779,axiom,
! [X11,X24] : c_div(X24,c_Suc(c_Suc(c_Suc(X11))),tc_nat) = c_div(X24,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),X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f29731,plain,
( spl0_2523
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2522 ),
inference(avatar_split_clause,[],[f29727,f29723,f22574,f13448,f13139,f8657,f3868,f29729]) ).
fof(f29729,plain,
( spl0_2523
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).
fof(f29723,plain,
( spl0_2522
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f29727,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2522 ),
inference(forward_demodulation,[],[f29726,f14217]) ).
fof(f29726,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16)
| ~ spl0_2221
| ~ spl0_2522 ),
inference(forward_demodulation,[],[f29724,f22575]) ).
fof(f29724,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16)
| ~ spl0_2522 ),
inference(avatar_component_clause,[],[f29723]) ).
fof(f29725,plain,
spl0_2522,
inference(avatar_split_clause,[],[f3076,f29723]) ).
fof(f3076,plain,
! [X0,X9,X16,X17] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2902,f3061]) ).
fof(f2902,plain,
! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f99,f1438,f1438,f1438]) ).
fof(f99,axiom,
! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X9)),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X9),X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f29717,plain,
( spl0_2521
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2520 ),
inference(avatar_split_clause,[],[f29713,f29709,f22574,f13448,f13139,f8657,f3868,f29715]) ).
fof(f29715,plain,
( spl0_2521
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).
fof(f29709,plain,
( spl0_2520
<=> ! [X17,X0,X9,X16] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2520])]) ).
fof(f29713,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),X17,X0,X16),X0,X16)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2221
| ~ spl0_2520 ),
inference(forward_demodulation,[],[f29712,f14217]) ).
fof(f29712,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X9,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16)
| ~ spl0_2221
| ~ spl0_2520 ),
inference(forward_demodulation,[],[f29710,f22575]) ).
fof(f29710,plain,
( ! [X0,X9,X16,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16)
| ~ spl0_2520 ),
inference(avatar_component_clause,[],[f29709]) ).
fof(f29711,plain,
spl0_2520,
inference(avatar_split_clause,[],[f3075,f29709]) ).
fof(f3075,plain,
! [X0,X9,X16,X17] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(X9,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2901,f3061]) ).
fof(f2901,plain,
! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f98,f1438,f1438,f1438]) ).
fof(f98,axiom,
! [X0,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X9)),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X9),X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f29707,plain,
spl0_2519,
inference(avatar_split_clause,[],[f1738,f29705]) ).
fof(f29705,plain,
( spl0_2519
<=> ! [X30,X0,X36,X16,X26] :
( c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).
fof(f1738,axiom,
! [X0,X36,X26,X16,X30] :
( c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X30,X36,X16,X0),X16,X0) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f29703,plain,
spl0_2518,
inference(avatar_split_clause,[],[f1737,f29701]) ).
fof(f29701,plain,
( spl0_2518
<=> ! [X26,X0,X36,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f1737,axiom,
! [X0,X36,X26,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X26,X36,X0,X16),X0,X16) = X36 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f29699,plain,
spl0_2517,
inference(avatar_split_clause,[],[f1634,f29697]) ).
fof(f29697,plain,
( spl0_2517
<=> ! [X0,X16,X25,X26,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X26,X30,X25,X0,X16),c_Main_OuprodE__2(X26,X30,X25,X0,X16),X0,X16) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f1634,axiom,
! [X0,X26,X16,X25,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X26,X30,X25,X0,X16),c_Main_OuprodE__2(X26,X30,X25,X0,X16),X0,X16) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f29695,plain,
spl0_2516,
inference(avatar_split_clause,[],[f897,f29693]) ).
fof(f29693,plain,
( spl0_2516
<=> ! [X34,X16,X25,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_plus(X1,X25,X16),X16) = c_plus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f897,axiom,
! [X1,X16,X34,X25] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_plus(X1,X25,X16),X16) = c_plus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f29691,plain,
( ~ spl0_1123
| spl0_2515
| spl0_1698
| ~ spl0_1570
| ~ spl0_1735 ),
inference(avatar_split_clause,[],[f15255,f14457,f12906,f14082,f29689,f9247]) ).
fof(f29689,plain,
( spl0_2515
<=> ! [X0] : ~ c_less(X0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).
fof(f14082,plain,
( spl0_1698
<=> c_less(c_0,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f12906,plain,
( spl0_1570
<=> ! [X0] : c_0 = c_minus(X0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f14457,plain,
( spl0_1735
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f15255,plain,
( ! [X0] :
( c_less(c_0,c_0,t_b)
| ~ c_less(X0,X0,t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b) )
| ~ spl0_1570
| ~ spl0_1735 ),
inference(superposition,[],[f14458,f12907]) ).
fof(f12907,plain,
( ! [X0] : c_0 = c_minus(X0,X0,t_b)
| ~ spl0_1570 ),
inference(avatar_component_clause,[],[f12906]) ).
fof(f14458,plain,
( ! [X3,X0,X1] :
( c_less(c_minus(X3,X1,X0),c_0,X0)
| ~ c_less(X3,X1,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0) )
| ~ spl0_1735 ),
inference(avatar_component_clause,[],[f14457]) ).
fof(f29687,plain,
spl0_2514,
inference(avatar_split_clause,[],[f896,f29685]) ).
fof(f29685,plain,
( spl0_2514
<=> ! [X34,X16,X25,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_minus(X1,X25,X16),X16) = c_minus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).
fof(f896,axiom,
! [X1,X16,X34,X25] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_Numeral_Onumber__of(X34,X16),c_minus(X1,X25,X16),X16) = c_minus(c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),c_times(c_Numeral_Onumber__of(X34,X16),X25,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f29683,plain,
spl0_2513,
inference(avatar_split_clause,[],[f894,f29681]) ).
fof(f29681,plain,
( spl0_2513
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).
fof(f894,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f29679,plain,
spl0_2512,
inference(avatar_split_clause,[],[f893,f29677]) ).
fof(f29677,plain,
( spl0_2512
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f893,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f29675,plain,
spl0_2511,
inference(avatar_split_clause,[],[f891,f29673]) ).
fof(f29673,plain,
( spl0_2511
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f891,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f29671,plain,
spl0_2510,
inference(avatar_split_clause,[],[f890,f29669]) ).
fof(f29669,plain,
( spl0_2510
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).
fof(f890,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f29667,plain,
spl0_2509,
inference(avatar_split_clause,[],[f888,f29665]) ).
fof(f29665,plain,
( spl0_2509
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f888,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f29663,plain,
spl0_2508,
inference(avatar_split_clause,[],[f887,f29661]) ).
fof(f29661,plain,
( spl0_2508
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f887,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X1,X3,X16)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f29659,plain,
spl0_2507,
inference(avatar_split_clause,[],[f885,f29657]) ).
fof(f29657,plain,
( spl0_2507
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f885,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X1,X3,X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f29655,plain,
spl0_2506,
inference(avatar_split_clause,[],[f884,f29653]) ).
fof(f29653,plain,
( spl0_2506
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f884,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_less(X3,X1,X16)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f29651,plain,
spl0_2505,
inference(avatar_split_clause,[],[f882,f29649]) ).
fof(f29649,plain,
( spl0_2505
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f882,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f29646,plain,
spl0_2504,
inference(avatar_split_clause,[],[f881,f29644]) ).
fof(f29644,plain,
( spl0_2504
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2504])]) ).
fof(f881,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f29642,plain,
spl0_2503,
inference(avatar_split_clause,[],[f879,f29640]) ).
fof(f29640,plain,
( spl0_2503
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2503])]) ).
fof(f879,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f29638,plain,
spl0_2502,
inference(avatar_split_clause,[],[f878,f29636]) ).
fof(f29636,plain,
( spl0_2502
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2502])]) ).
fof(f878,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f29634,plain,
spl0_2501,
inference(avatar_split_clause,[],[f876,f29632]) ).
fof(f29632,plain,
( spl0_2501
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2501])]) ).
fof(f876,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f29630,plain,
spl0_2500,
inference(avatar_split_clause,[],[f875,f29628]) ).
fof(f29628,plain,
( spl0_2500
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f875,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X1,X3,X16)
| c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f29626,plain,
spl0_2499,
inference(avatar_split_clause,[],[f873,f29624]) ).
fof(f29624,plain,
( spl0_2499
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f873,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X1,X3,X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_0,X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f29622,plain,
spl0_2498,
inference(avatar_split_clause,[],[f872,f29620]) ).
fof(f29620,plain,
( spl0_2498
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f872,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| c_lessequals(X3,X1,X16)
| ~ c_less(c_0,c_Numeral_Onumber__of(X34,X16),X16)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f29618,plain,
spl0_2497,
inference(avatar_split_clause,[],[f842,f29616]) ).
fof(f29616,plain,
( spl0_2497
<=> ! [X3,X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_plus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_plus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).
fof(f842,axiom,
! [X3,X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Osemiring(X16)
| c_times(c_plus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_plus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f29614,plain,
spl0_2496,
inference(avatar_split_clause,[],[f841,f29612]) ).
fof(f29612,plain,
( spl0_2496
<=> ! [X3,X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_minus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_minus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).
fof(f841,axiom,
! [X3,X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_Ring__and__Field_Oring(X16)
| c_times(c_minus(X3,X1,X16),c_Numeral_Onumber__of(X34,X16),X16) = c_minus(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f29610,plain,
spl0_2495,
inference(avatar_split_clause,[],[f756,f29608]) ).
fof(f29608,plain,
( spl0_2495
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).
fof(f756,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f29606,plain,
( ~ spl0_1009
| spl0_2494
| ~ spl0_1453
| ~ spl0_1720 ),
inference(avatar_split_clause,[],[f14428,f14384,f11833,f29604,f8725]) ).
fof(f8725,plain,
( spl0_1009
<=> class_OrderedGroup_Oab__group__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f29604,plain,
( spl0_2494
<=> ! [X0] :
( c_0 != X0
| c_0 = c_uminus(X0,t_b) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f11833,plain,
( spl0_1453
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = X3
| c_0 != c_uminus(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f14384,plain,
( spl0_1720
<=> ! [X0] : c_uminus(c_uminus(X0,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f14428,plain,
( ! [X0] :
( c_0 != X0
| c_0 = c_uminus(X0,t_b)
| ~ class_OrderedGroup_Oab__group__add(t_b) )
| ~ spl0_1453
| ~ spl0_1720 ),
inference(superposition,[],[f11834,f14385]) ).
fof(f14385,plain,
( ! [X0] : c_uminus(c_uminus(X0,t_b),t_b) = X0
| ~ spl0_1720 ),
inference(avatar_component_clause,[],[f14384]) ).
fof(f11834,plain,
( ! [X3,X0] :
( c_0 != c_uminus(X3,X0)
| c_0 = X3
| ~ class_OrderedGroup_Oab__group__add(X0) )
| ~ spl0_1453 ),
inference(avatar_component_clause,[],[f11833]) ).
fof(f29457,plain,
( spl0_2493
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2492 ),
inference(avatar_split_clause,[],[f29453,f29450,f13448,f13139,f8657,f3868,f29455]) ).
fof(f29455,plain,
( spl0_2493
<=> ! [X18,X9,X0,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2493])]) ).
fof(f29450,plain,
( spl0_2492
<=> ! [X18,X9,X0,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).
fof(f29453,plain,
( ! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2492 ),
inference(forward_demodulation,[],[f29451,f14217]) ).
fof(f29451,plain,
( ! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16)
| ~ spl0_2492 ),
inference(avatar_component_clause,[],[f29450]) ).
fof(f29452,plain,
spl0_2492,
inference(avatar_split_clause,[],[f2908,f29450]) ).
fof(f2908,plain,
! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16),
inference(definition_unfolding,[],[f102,f1438]) ).
fof(f102,axiom,
! [X0,X18,X9,X16,X17] : c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OScons(X17,X18,X0,X16),X0,X16) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X9,X17,X0,X16),c_Datatype__Universe_Ontrunc(X9,X18,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f29448,plain,
spl0_2491,
inference(avatar_split_clause,[],[f1698,f29446]) ).
fof(f29446,plain,
( spl0_2491
<=> ! [X0,X16,X80,X19] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_OconverseE__1(X19,X80,X16,X0),c_Main_OconverseE__2(X19,X80,X16,X0),X16,X0),X19,tc_prod(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).
fof(f1698,axiom,
! [X0,X80,X19,X16] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_in(c_Pair(c_Main_OconverseE__1(X19,X80,X16,X0),c_Main_OconverseE__2(X19,X80,X16,X0),X16,X0),X19,tc_prod(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f29444,plain,
spl0_2490,
inference(avatar_split_clause,[],[f1225,f29442]) ).
fof(f29442,plain,
( spl0_2490
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X12,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f1225,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X12,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f29440,plain,
spl0_2489,
inference(avatar_split_clause,[],[f1215,f29438]) ).
fof(f29438,plain,
( spl0_2489
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f1215,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f29434,plain,
spl0_2488,
inference(avatar_split_clause,[],[f363,f29432]) ).
fof(f29432,plain,
( spl0_2488
<=> ! [X34,X1,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,X1),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).
fof(f363,axiom,
! [X1,X34,X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,X1),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,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(f29249,plain,
( ~ spl0_1134
| spl0_2487
| ~ spl0_1489
| ~ spl0_1614 ),
inference(avatar_split_clause,[],[f13688,f13135,f12095,f29247,f9292]) ).
fof(f9292,plain,
( spl0_1134
<=> class_Ring__and__Field_Oordered__semidom(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f29247,plain,
( spl0_2487
<=> ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_b)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).
fof(f12095,plain,
( spl0_1489
<=> c_1 = c_NatArith_Oof__nat(c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f13135,plain,
( spl0_1614
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| c_NatArith_Oof__nat(X11,X0) != c_NatArith_Oof__nat(X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f13688,plain,
( ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_b)
| c_1 = X0
| ~ class_Ring__and__Field_Oordered__semidom(t_b) )
| ~ spl0_1489
| ~ spl0_1614 ),
inference(superposition,[],[f13136,f12097]) ).
fof(f12097,plain,
( c_1 = c_NatArith_Oof__nat(c_1,t_b)
| ~ spl0_1489 ),
inference(avatar_component_clause,[],[f12095]) ).
fof(f13136,plain,
( ! [X0,X11,X24] :
( c_NatArith_Oof__nat(X11,X0) != c_NatArith_Oof__nat(X24,X0)
| X11 = X24
| ~ class_Ring__and__Field_Oordered__semidom(X0) )
| ~ spl0_1614 ),
inference(avatar_component_clause,[],[f13135]) ).
fof(f29122,plain,
spl0_2486,
inference(avatar_split_clause,[],[f3029,f29120]) ).
fof(f29120,plain,
( spl0_2486
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f3029,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f734,f1023]) ).
fof(f1023,axiom,
! [X33] : c_Numeral_Obin__minus(X33) = c_Numeral_Obin__mult(c_Numeral_OMin,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f734,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f29118,plain,
spl0_2485,
inference(avatar_split_clause,[],[f3028,f29116]) ).
fof(f29116,plain,
( spl0_2485
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).
fof(f3028,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f733,f1023]) ).
fof(f733,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f29114,plain,
spl0_2484,
inference(avatar_split_clause,[],[f3027,f29112]) ).
fof(f29112,plain,
( spl0_2484
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).
fof(f3027,plain,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f738,f1023]) ).
fof(f738,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f29110,plain,
spl0_2483,
inference(avatar_split_clause,[],[f3026,f29108]) ).
fof(f29108,plain,
( spl0_2483
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f3026,plain,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f736,f1023]) ).
fof(f736,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f29105,plain,
spl0_2482,
inference(avatar_split_clause,[],[f3024,f29103]) ).
fof(f29103,plain,
( spl0_2482
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2482])]) ).
fof(f3024,plain,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f740,f1023]) ).
fof(f740,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f29101,plain,
spl0_2481,
inference(avatar_split_clause,[],[f1739,f29099]) ).
fof(f29099,plain,
( spl0_2481
<=> ! [X26,X0,X36,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).
fof(f1739,axiom,
! [X0,X36,X26,X16,X30] :
( c_in(c_Main_OPlusE__2(X30,X36,X16,X0),X30,X16)
| c_in(c_Main_OPlusE__1(X26,X36,X0,X16),X26,X0)
| ~ c_in(X36,c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f29097,plain,
spl0_2480,
inference(avatar_split_clause,[],[f895,f29095]) ).
fof(f29095,plain,
( spl0_2480
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).
fof(f895,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f29093,plain,
spl0_2479,
inference(avatar_split_clause,[],[f889,f29091]) ).
fof(f29091,plain,
( spl0_2479
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).
fof(f889,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_less(X3,X1,X16)
| ~ c_less(X1,X3,X16)
| c_less(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f29089,plain,
spl0_2478,
inference(avatar_split_clause,[],[f883,f29087]) ).
fof(f29087,plain,
( spl0_2478
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f883,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(X3,c_Numeral_Onumber__of(X34,X16),X16),c_times(X1,c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f29085,plain,
spl0_2477,
inference(avatar_split_clause,[],[f877,f29083]) ).
fof(f29083,plain,
( spl0_2477
<=> ! [X3,X34,X16,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).
fof(f877,axiom,
! [X3,X1,X16,X34] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X16)
| ~ class_Numeral_Onumber(X16)
| ~ c_lessequals(X3,X1,X16)
| ~ c_lessequals(X1,X3,X16)
| c_lessequals(c_times(c_Numeral_Onumber__of(X34,X16),X3,X16),c_times(c_Numeral_Onumber__of(X34,X16),X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f29081,plain,
spl0_2476,
inference(avatar_split_clause,[],[f688,f29079]) ).
fof(f29079,plain,
( spl0_2476
<=> ! [X16,X40,X0,X12,X39] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2476])]) ).
fof(f688,axiom,
! [X40,X39,X0,X16,X12] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f29077,plain,
spl0_2475,
inference(avatar_split_clause,[],[f687,f29075]) ).
fof(f29075,plain,
( spl0_2475
<=> ! [X16,X40,X0,X12,X39] :
( ~ c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).
fof(f687,axiom,
! [X40,X39,X0,X16,X12] :
( ~ c_in(X12,c_List_Oset(X39,X0),X0)
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X16))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X39,X40,X0,X16),X12,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f29073,plain,
spl0_2474,
inference(avatar_split_clause,[],[f683,f29071]) ).
fof(f29071,plain,
( spl0_2474
<=> ! [X10,X40,X0,X12,X16,X39] : c_List_Ozip(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X16),X0,X16) = c_List_Olist_OCons(c_Pair(X12,X10,X0,X16),c_List_Ozip(X39,X40,X0,X16),tc_prod(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).
fof(f683,axiom,
! [X40,X39,X0,X10,X16,X12] : c_List_Ozip(c_List_Olist_OCons(X12,X39,X0),c_List_Olist_OCons(X10,X40,X16),X0,X16) = c_List_Olist_OCons(c_Pair(X12,X10,X0,X16),c_List_Ozip(X39,X40,X0,X16),tc_prod(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f29069,plain,
spl0_2473,
inference(avatar_split_clause,[],[f510,f29067]) ).
fof(f29067,plain,
( spl0_2473
<=> ! [X0,X19,X10] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X10,X0),c_Main_Olexord__Nil__left__2(X10,X0),X0) = X10
| ~ c_in(c_Pair(c_List_Olist_ONil,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).
fof(f510,axiom,
! [X10,X0,X19] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X10,X0),c_Main_Olexord__Nil__left__2(X10,X0),X0) = X10
| ~ c_in(c_Pair(c_List_Olist_ONil,X10,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
fof(f29065,plain,
( ~ spl0_1
| ~ spl0_2472
| spl0_1956
| ~ spl0_1458
| ~ spl0_1589 ),
inference(avatar_split_clause,[],[f13566,f13033,f11853,f17424,f29062,f3226]) ).
fof(f3226,plain,
( spl0_1
<=> class_Ring__and__Field_Oordered__idom(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f29062,plain,
( spl0_2472
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f17424,plain,
( spl0_1956
<=> c_lessequals(c_1,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f11853,plain,
( spl0_1458
<=> c_1 = c_IntDef_Oof__int(c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f13033,plain,
( spl0_1589
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f13566,plain,
( c_lessequals(c_1,c_0,t_b)
| ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1458
| ~ spl0_1589 ),
inference(superposition,[],[f13034,f11855]) ).
fof(f11855,plain,
( c_1 = c_IntDef_Oof__int(c_1,t_b)
| ~ spl0_1458 ),
inference(avatar_component_clause,[],[f11853]) ).
fof(f13034,plain,
( ! [X0,X33] :
( c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0)
| ~ c_lessequals(X33,c_0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1589 ),
inference(avatar_component_clause,[],[f13033]) ).
fof(f29060,plain,
spl0_2471,
inference(avatar_split_clause,[],[f352,f29058]) ).
fof(f29058,plain,
( spl0_2471
<=> ! [X33] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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_2471])]) ).
fof(f352,axiom,
! [X33] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(f28910,plain,
spl0_2470,
inference(avatar_split_clause,[],[f3023,f28908]) ).
fof(f28908,plain,
( spl0_2470
<=> ! [X40,X0,X39] :
( ~ c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(X40,X0)
| c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2470])]) ).
fof(f3023,plain,
! [X40,X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(X40,X0)
| c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ),
inference(definition_unfolding,[],[f452,f1267]) ).
fof(f1267,axiom,
! [X0,X26,X30] : c_inter(X26,X30,X0) = c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f452,axiom,
! [X40,X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(X40,X0)
| c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset != c_inter(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
fof(f28906,plain,
spl0_2469,
inference(avatar_split_clause,[],[f2995,f28904]) ).
fof(f28904,plain,
( spl0_2469
<=> ! [X0,X3,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2469])]) ).
fof(f2995,plain,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1576,f1267,f1267]) ).
fof(f1576,axiom,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_inter(X26,X30,X0)
| c_emptyset = c_inter(c_insert(X3,X26,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_2) ).
fof(f28899,plain,
spl0_2468,
inference(avatar_split_clause,[],[f2993,f28897]) ).
fof(f28897,plain,
( spl0_2468
<=> ! [X0,X3,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2468])]) ).
fof(f2993,plain,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ),
inference(definition_unfolding,[],[f1557,f1267,f1267]) ).
fof(f1557,axiom,
! [X3,X0,X26,X30] :
( c_in(X3,X30,X0)
| c_emptyset != c_inter(X30,X26,X0)
| c_emptyset = c_inter(X30,c_insert(X3,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_2) ).
fof(f28895,plain,
spl0_2467,
inference(avatar_split_clause,[],[f686,f28893]) ).
fof(f28893,plain,
( spl0_2467
<=> ! [X10,X0,X50,X12,X16,X23] : c_List_Ozip(c_List_Oreplicate(X23,X12,X0),c_List_Oreplicate(X50,X10,X16),X0,X16) = c_List_Oreplicate(c_Orderings_Omin(X23,X50,tc_nat),c_Pair(X12,X10,X0,X16),tc_prod(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).
fof(f686,axiom,
! [X50,X10,X0,X16,X12,X23] : c_List_Ozip(c_List_Oreplicate(X23,X12,X0),c_List_Oreplicate(X50,X10,X16),X0,X16) = c_List_Oreplicate(c_Orderings_Omin(X23,X50,tc_nat),c_Pair(X12,X10,X0,X16),tc_prod(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f28891,plain,
spl0_2466,
inference(avatar_split_clause,[],[f592,f28889]) ).
fof(f28889,plain,
( spl0_2466
<=> ! [X11,X0,X23,X39] :
( ~ c_lessequals(c_plus(X11,X23,tc_nat),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Odrop(X11,X39,X0),X23,X0) = c_List_Onth(X39,c_plus(X11,X23,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2466])]) ).
fof(f592,axiom,
! [X39,X0,X11,X23] :
( ~ c_lessequals(c_plus(X11,X23,tc_nat),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Odrop(X11,X39,X0),X23,X0) = c_List_Onth(X39,c_plus(X11,X23,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f28887,plain,
spl0_2465,
inference(avatar_split_clause,[],[f9,f28885]) ).
fof(f28885,plain,
( spl0_2465
<=> ! [X5,X4,X0,X6,X2] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_times(X2,X5,tc_set(X0)),c_times(X4,X6,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2465])]) ).
fof(f9,axiom,
! [X2,X0,X6,X4,X5] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_times(X2,X5,tc_set(X0)),c_times(X4,X6,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono2_0) ).
fof(f28883,plain,
spl0_2464,
inference(avatar_split_clause,[],[f3,f28881]) ).
fof(f28881,plain,
( spl0_2464
<=> ! [X5,X4,X0,X6,X2] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_plus(X2,X5,tc_set(X0)),c_plus(X4,X6,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2464])]) ).
fof(f3,axiom,
! [X2,X0,X6,X4,X5] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| ~ c_lessequals(X5,X6,tc_set(X0))
| c_lessequals(c_plus(X2,X5,tc_set(X0)),c_plus(X4,X6,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono2_0) ).
fof(f28846,plain,
( spl0_2463
| ~ spl0_61
| ~ spl0_1796
| ~ spl0_2459 ),
inference(avatar_split_clause,[],[f28439,f28436,f14715,f3525,f28844]) ).
fof(f28844,plain,
( spl0_2463
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2463])]) ).
fof(f14715,plain,
( spl0_1796
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f28436,plain,
( spl0_2459
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).
fof(f28439,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_61
| ~ spl0_1796
| ~ spl0_2459 ),
inference(forward_demodulation,[],[f28437,f15782]) ).
fof(f15782,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_61
| ~ spl0_1796 ),
inference(resolution,[],[f14716,f3527]) ).
fof(f14716,plain,
( ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0) )
| ~ spl0_1796 ),
inference(avatar_component_clause,[],[f14715]) ).
fof(f28437,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_2459 ),
inference(avatar_component_clause,[],[f28436]) ).
fof(f28841,plain,
( spl0_2462
| ~ spl0_1808
| ~ spl0_2457 ),
inference(avatar_split_clause,[],[f28523,f28422,f14918,f28839]) ).
fof(f28839,plain,
( spl0_2462
<=> ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_b)
| c_1 = c_IntDef_Oint(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2462])]) ).
fof(f14918,plain,
( spl0_1808
<=> ! [X0] : c_IntDef_Oof__int(c_IntDef_Oint(X0),t_b) = c_NatArith_Oof__nat(X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f28523,plain,
( ! [X0] :
( c_1 != c_NatArith_Oof__nat(X0,t_b)
| c_1 = c_IntDef_Oint(X0) )
| ~ spl0_1808
| ~ spl0_2457 ),
inference(superposition,[],[f28423,f14919]) ).
fof(f14919,plain,
( ! [X0] : c_IntDef_Oof__int(c_IntDef_Oint(X0),t_b) = c_NatArith_Oof__nat(X0,t_b)
| ~ spl0_1808 ),
inference(avatar_component_clause,[],[f14918]) ).
fof(f28519,plain,
( spl0_2461
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2441 ),
inference(avatar_split_clause,[],[f28224,f28221,f14559,f11866,f28517]) ).
fof(f28517,plain,
( spl0_2461
<=> ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(f28221,plain,
( spl0_2441
<=> ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2441])]) ).
fof(f28224,plain,
( ! [X33] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1461
| ~ spl0_1760
| ~ spl0_2441 ),
inference(forward_demodulation,[],[f28222,f15511]) ).
fof(f28222,plain,
( ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2441 ),
inference(avatar_component_clause,[],[f28221]) ).
fof(f28515,plain,
( spl0_2460
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2440 ),
inference(avatar_split_clause,[],[f28219,f28216,f14559,f11862,f28513]) ).
fof(f28513,plain,
( spl0_2460
<=> ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).
fof(f28216,plain,
( spl0_2440
<=> ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2440])]) ).
fof(f28219,plain,
( ! [X33] :
( c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1460
| ~ spl0_1760
| ~ spl0_2440 ),
inference(forward_demodulation,[],[f28217,f15512]) ).
fof(f28217,plain,
( ! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2440 ),
inference(avatar_component_clause,[],[f28216]) ).
fof(f28438,plain,
spl0_2459,
inference(avatar_split_clause,[],[f3002,f28436]) ).
fof(f3002,plain,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f753,f1023,f1023]) ).
fof(f753,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
fof(f28434,plain,
spl0_2458,
inference(avatar_split_clause,[],[f2917,f28432]) ).
fof(f28432,plain,
( spl0_2458
<=> ! [X34,X0,X33,X25] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_minus(X25,c_Numeral_Onumber__of(X33,X0),X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).
fof(f2917,plain,
! [X0,X34,X25,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_minus(X25,c_Numeral_Onumber__of(X33,X0),X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0),X25,X0) ),
inference(definition_unfolding,[],[f1001,f1023]) ).
fof(f1001,axiom,
! [X0,X34,X25,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_minus(X25,c_Numeral_Onumber__of(X33,X0),X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X33)),X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f28424,plain,
( ~ spl0_1
| spl0_2457
| ~ spl0_1458
| ~ spl0_1587 ),
inference(avatar_split_clause,[],[f13551,f13025,f11853,f28422,f3226]) ).
fof(f13025,plain,
( spl0_1587
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X33 = X35
| c_IntDef_Oof__int(X35,X0) != c_IntDef_Oof__int(X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f13551,plain,
( ! [X0] :
( c_1 != c_IntDef_Oof__int(X0,t_b)
| c_1 = X0
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
| ~ spl0_1458
| ~ spl0_1587 ),
inference(superposition,[],[f13026,f11855]) ).
fof(f13026,plain,
( ! [X0,X35,X33] :
( c_IntDef_Oof__int(X35,X0) != c_IntDef_Oof__int(X33,X0)
| X33 = X35
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1587 ),
inference(avatar_component_clause,[],[f13025]) ).
fof(f28420,plain,
( spl0_2456
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2455 ),
inference(avatar_split_clause,[],[f28416,f28413,f13448,f13139,f8657,f3868,f28418]) ).
fof(f28418,plain,
( spl0_2456
<=> ! [X77,X11,X14] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_plus(c_1,X11,tc_nat),tc_set(tc_prod(X14,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2456])]) ).
fof(f28413,plain,
( spl0_2455
<=> ! [X77,X11,X14] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_set(tc_prod(X14,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2455])]) ).
fof(f28416,plain,
( ! [X11,X14,X77] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_plus(c_1,X11,tc_nat),tc_set(tc_prod(X14,X14)))
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2455 ),
inference(forward_demodulation,[],[f28414,f14217]) ).
fof(f28414,plain,
( ! [X11,X14,X77] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_set(tc_prod(X14,X14)))
| ~ spl0_2455 ),
inference(avatar_component_clause,[],[f28413]) ).
fof(f28415,plain,
spl0_2455,
inference(avatar_split_clause,[],[f2905,f28413]) ).
fof(f2905,plain,
! [X11,X14,X77] : c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14) = c_Nat_Opower(X77,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_set(tc_prod(X14,X14))),
inference(definition_unfolding,[],[f1285,f1438]) ).
fof(f1285,axiom,
! [X11,X14,X77] : c_Nat_Opower(X77,c_Suc(X11),tc_set(tc_prod(X14,X14))) = c_Relation_Orel__comp(X77,c_Nat_Opower(X77,X11,tc_set(tc_prod(X14,X14))),X14,X14,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f28411,plain,
spl0_2454,
inference(avatar_split_clause,[],[f2900,f28409]) ).
fof(f28409,plain,
( spl0_2454
<=> ! [X0,X3,X26,X30] : c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),c_insert(X3,X30,X0),X0,X0) = c_insert(X3,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2454])]) ).
fof(f2900,plain,
! [X3,X0,X26,X30] : c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),c_insert(X3,X30,X0),X0,X0) = c_insert(X3,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0),
inference(definition_unfolding,[],[f1580,f1267,f1267]) ).
fof(f1580,axiom,
! [X3,X0,X26,X30] : c_inter(c_insert(X3,X26,X0),c_insert(X3,X30,X0),X0) = c_insert(X3,c_inter(X26,X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f28407,plain,
spl0_2453,
inference(avatar_split_clause,[],[f2894,f28405]) ).
fof(f28405,plain,
( spl0_2453
<=> ! [X0,X30,X26] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X26,X0),tc_List_Olist(X0)),c_List_Olists(X30,X0),tc_List_Olist(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2453])]) ).
fof(f2894,plain,
! [X0,X26,X30] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X26,X0),tc_List_Olist(X0)),c_List_Olists(X30,X0),tc_List_Olist(X0),tc_List_Olist(X0)),
inference(definition_unfolding,[],[f531,f1267,f1267]) ).
fof(f531,axiom,
! [X0,X26,X30] : c_List_Olists(c_inter(X26,X30,X0),X0) = c_inter(c_List_Olists(X26,X0),c_List_Olists(X30,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f28403,plain,
spl0_2452,
inference(avatar_split_clause,[],[f2893,f28401]) ).
fof(f28401,plain,
( spl0_2452
<=> ! [X0,X30,X26] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X26,X0),tc_set(X0)),c_Pow(X30,X0),tc_set(X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2452])]) ).
fof(f2893,plain,
! [X0,X26,X30] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X26,X0),tc_set(X0)),c_Pow(X30,X0),tc_set(X0),tc_set(X0)),
inference(definition_unfolding,[],[f1518,f1267,f1267]) ).
fof(f1518,axiom,
! [X0,X26,X30] : c_Pow(c_inter(X26,X30,X0),X0) = c_inter(c_Pow(X26,X0),c_Pow(X30,X0),tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f28315,plain,
( spl0_2451
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2450 ),
inference(avatar_split_clause,[],[f28311,f28307,f13448,f13139,f8657,f3868,f28313]) ).
fof(f28313,plain,
( spl0_2451
<=> ! [X9,X11] : c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_plus(c_1,X9,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),c_plus(c_1,X9,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2451])]) ).
fof(f28307,plain,
( spl0_2450
<=> ! [X9,X11] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2450])]) ).
fof(f28311,plain,
( ! [X11,X9] : c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_plus(c_1,X9,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),c_plus(c_1,X9,tc_nat))
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2450 ),
inference(forward_demodulation,[],[f28310,f14217]) ).
fof(f28310,plain,
( ! [X11,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_plus(c_1,X9,tc_nat)),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2450 ),
inference(forward_demodulation,[],[f28308,f14217]) ).
fof(f28308,plain,
( ! [X11,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2450 ),
inference(avatar_component_clause,[],[f28307]) ).
fof(f28309,plain,
spl0_2450,
inference(avatar_split_clause,[],[f2887,f28307]) ).
fof(f2887,plain,
! [X11,X9] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f56,f1438,f1438,f1438]) ).
fof(f56,axiom,
! [X11,X9] : c_Binomial_Obinomial(c_Suc(X11),c_Suc(X9)) = c_plus(c_Binomial_Obinomial(X11,X9),c_Binomial_Obinomial(X11,c_Suc(X9)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f28303,plain,
spl0_2449,
inference(avatar_split_clause,[],[f2851,f28301]) ).
fof(f28301,plain,
( spl0_2449
<=> ! [X0,X19] : c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2449])]) ).
fof(f2851,plain,
! [X0,X19] : c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1604,f1610,f1610,f1610]) ).
fof(f1604,axiom,
! [X0,X19] : c_Transitive__Closure_Ortrancl(X19,X0) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X19,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f28299,plain,
spl0_2448,
inference(avatar_split_clause,[],[f1699,f28297]) ).
fof(f28297,plain,
( spl0_2448
<=> ! [X0,X16,X80,X19] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_OconverseE__2(X19,X80,X16,X0),c_Main_OconverseE__1(X19,X80,X16,X0),X0,X16) = X80 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).
fof(f1699,axiom,
! [X0,X80,X19,X16] :
( ~ c_in(X80,c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16))
| c_Pair(c_Main_OconverseE__2(X19,X80,X16,X0),c_Main_OconverseE__1(X19,X80,X16,X0),X0,X16) = X80 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f28248,plain,
spl0_2447,
inference(avatar_split_clause,[],[f1210,f28246]) ).
fof(f28246,plain,
( spl0_2447
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X12,X0),c_Numeral_Onumber__of(X33,tc_nat),X0) = c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2447])]) ).
fof(f1210,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X12,X0),c_Numeral_Onumber__of(X33,tc_nat),X0) = c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f28244,plain,
spl0_2446,
inference(avatar_split_clause,[],[f720,f28242]) ).
fof(f28242,plain,
( spl0_2446
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X75),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2446])]) ).
fof(f720,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X75),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f28240,plain,
spl0_2445,
inference(avatar_split_clause,[],[f589,f28238]) ).
fof(f28238,plain,
( spl0_2445
<=> ! [X34,X0,X12,X39] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Numeral_Onumber__of(X34,tc_nat),X0) = c_List_Onth(X39,c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).
fof(f589,axiom,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Numeral_Onumber__of(X34,tc_nat),X0) = c_List_Onth(X39,c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f28236,plain,
spl0_2444,
inference(avatar_split_clause,[],[f467,f28234]) ).
fof(f28234,plain,
( spl0_2444
<=> ! [X11,X40,X0,X39] : c_List_Odrop(X11,c_append(X39,X40,X0),X0) = c_append(c_List_Odrop(X11,X39,X0),c_List_Odrop(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2444])]) ).
fof(f467,axiom,
! [X40,X39,X0,X11] : c_List_Odrop(X11,c_append(X39,X40,X0),X0) = c_append(c_List_Odrop(X11,X39,X0),c_List_Odrop(c_minus(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f28232,plain,
spl0_2443,
inference(avatar_split_clause,[],[f465,f28230]) ).
fof(f28230,plain,
( spl0_2443
<=> ! [X34,X0,X12,X39] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X34,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).
fof(f465,axiom,
! [X39,X0,X34,X12] :
( c_0 = c_Numeral_Onumber__of(X34,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X34,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X34,tc_nat),c_1,tc_nat),X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f28228,plain,
spl0_2442,
inference(avatar_split_clause,[],[f420,f28226]) ).
fof(f28226,plain,
( spl0_2442
<=> ! [X40,X0,X39,X26] :
( ~ c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2442])]) ).
fof(f420,axiom,
! [X40,X39,X0,X26] :
( ~ c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
fof(f28223,plain,
spl0_2441,
inference(avatar_split_clause,[],[f341,f28221]) ).
fof(f341,axiom,
! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(f28218,plain,
spl0_2440,
inference(avatar_split_clause,[],[f331,f28216]) ).
fof(f331,axiom,
! [X33] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X33,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(f28214,plain,
spl0_2439,
inference(avatar_split_clause,[],[f275,f28212]) ).
fof(f28212,plain,
( spl0_2439
<=> ! [X12,X10] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X12,X10,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_2439])]) ).
fof(f275,axiom,
! [X10,X12] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X12,X10,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(f28210,plain,
spl0_2438,
inference(avatar_split_clause,[],[f163,f28208]) ).
fof(f28208,plain,
( spl0_2438
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(X12,c_Finite__Set_OMin(X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2438])]) ).
fof(f163,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(X12,c_Finite__Set_OMin(X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f28159,plain,
spl0_2437,
inference(avatar_split_clause,[],[f160,f28157]) ).
fof(f28157,plain,
( spl0_2437
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2437])]) ).
fof(f160,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X12,X29,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f28155,plain,
spl0_2436,
inference(avatar_split_clause,[],[f156,f28153]) ).
fof(f28153,plain,
( spl0_2436
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(c_Finite__Set_OMax(X26,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).
fof(f156,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_less(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_less(c_Finite__Set_OMax(X26,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f28151,plain,
spl0_2435,
inference(avatar_split_clause,[],[f153,f28149]) ).
fof(f28149,plain,
( spl0_2435
<=> ! [X0,X12,X29,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2435])]) ).
fof(f153,axiom,
! [X0,X29,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X29,X26,X0)
| c_lessequals(X29,X12,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f27300,plain,
( spl0_2434
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2433 ),
inference(avatar_split_clause,[],[f27296,f27293,f22574,f9346,f9305,f27298]) ).
fof(f27298,plain,
( spl0_2434
<=> ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_plus(c_1,c_1,tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2434])]) ).
fof(f27293,plain,
( spl0_2433
<=> ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2433])]) ).
fof(f27296,plain,
( ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_plus(c_1,c_1,tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) )
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2433 ),
inference(forward_demodulation,[],[f27294,f22662]) ).
fof(f27294,plain,
( ! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) )
| ~ spl0_2433 ),
inference(avatar_component_clause,[],[f27293]) ).
fof(f27295,plain,
spl0_2433,
inference(avatar_split_clause,[],[f3181,f27293]) ).
fof(f3181,plain,
! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ),
inference(forward_demodulation,[],[f3180,f1050]) ).
fof(f3180,plain,
! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ),
inference(forward_demodulation,[],[f3179,f1048]) ).
fof(f3179,plain,
! [X16,X33] :
( c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) = c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X16)
| ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16) ),
inference(forward_demodulation,[],[f768,f1050]) ).
fof(f768,axiom,
! [X16,X33] :
( ~ class_Power_Orecpower(X16)
| ~ class_Numeral_Onumber(X16)
| c_Nat_Opower(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X16) = c_times(c_Numeral_Onumber__of(X33,X16),c_Numeral_Onumber__of(X33,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f27291,plain,
spl0_2432,
inference(avatar_split_clause,[],[f3119,f27289]) ).
fof(f27289,plain,
( spl0_2432
<=> ! [X9,X50,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X24,tc_nat),X50,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X24,c_minus(X50,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2432])]) ).
fof(f3119,plain,
! [X50,X9,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X24,tc_nat),X50,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X24,c_minus(X50,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f3118,f2866]) ).
fof(f2866,plain,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),X72,tc_nat),
inference(definition_unfolding,[],[f1434,f1438]) ).
fof(f1434,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Suc(X36),X72,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f3118,plain,
! [X50,X9,X24] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),X24,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X9,X24,tc_nat),X50,tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f2937,f2866]) ).
fof(f2937,plain,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),X24,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat),c_plus(X9,X24,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f692,f1438,f1438]) ).
fof(f692,axiom,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(c_Suc(c_minus(X50,X9,tc_nat)),X24,tc_nat) = c_minus(c_Suc(X50),c_plus(X9,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f27287,plain,
spl0_2431,
inference(avatar_split_clause,[],[f3117,f27285]) ).
fof(f27285,plain,
( spl0_2431
<=> ! [X9,X50,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X50,c_plus(X24,X9,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X50,X9,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).
fof(f3117,plain,
! [X50,X9,X24] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X50,c_plus(X24,X9,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X50,X9,tc_nat),X24,tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f3116,f2865]) ).
fof(f2865,plain,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Finite__Set_Ocard(c_SetInterval_OatMost(X72,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1441,f1438]) ).
fof(f1441,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Suc(X72),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f3116,plain,
! [X50,X9,X24] :
( c_minus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X50,c_plus(X24,X9,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X9,X50,tc_nat) ),
inference(forward_demodulation,[],[f2936,f2865]) ).
fof(f2936,plain,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X50,X9,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X24,X9,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f691,f1438,f1438]) ).
fof(f691,axiom,
! [X50,X9,X24] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X24,c_Suc(c_minus(X50,X9,tc_nat)),tc_nat) = c_minus(c_plus(X24,X9,tc_nat),c_Suc(X50),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f27226,plain,
( spl0_2430
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2429 ),
inference(avatar_split_clause,[],[f27222,f27219,f13448,f13139,f8657,f3868,f27224]) ).
fof(f27224,plain,
( spl0_2430
<=> ! [X0,X12,X26] :
( c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_plus(c_1,c_Finite__Set_Ocard(X26,X0),tc_nat)
| c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2430])]) ).
fof(f27219,plain,
( spl0_2429
<=> ! [X0,X12,X26] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X26,X0),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2429])]) ).
fof(f27222,plain,
( ! [X0,X26,X12] :
( c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_plus(c_1,c_Finite__Set_Ocard(X26,X0),tc_nat)
| c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2429 ),
inference(forward_demodulation,[],[f27220,f14217]) ).
fof(f27220,plain,
( ! [X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X26,X0),tc_nat),tc_nat) )
| ~ spl0_2429 ),
inference(avatar_component_clause,[],[f27219]) ).
fof(f27221,plain,
spl0_2429,
inference(avatar_split_clause,[],[f2992,f27219]) ).
fof(f2992,plain,
! [X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X26,X0),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f174,f1438]) ).
fof(f174,axiom,
! [X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_Finite__Set_Ocard(c_insert(X12,X26,X0),X0) = c_Suc(c_Finite__Set_Ocard(X26,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f27196,plain,
( spl0_2428
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2427 ),
inference(avatar_split_clause,[],[f27192,f27189,f13448,f13139,f8657,f3868,f27194]) ).
fof(f27194,plain,
( spl0_2428
<=> ! [X11,X0,X12,X39] : c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0) = c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_plus(c_1,X11,tc_nat),tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2428])]) ).
fof(f27189,plain,
( spl0_2427
<=> ! [X11,X0,X12,X39] : c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2427])]) ).
fof(f27192,plain,
( ! [X39,X0,X11,X12] : c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0) = c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_plus(c_1,X11,tc_nat),tc_nat),X0)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2427 ),
inference(forward_demodulation,[],[f27190,f14217]) ).
fof(f27190,plain,
( ! [X39,X0,X11,X12] : c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0)
| ~ spl0_2427 ),
inference(avatar_component_clause,[],[f27189]) ).
fof(f27191,plain,
spl0_2427,
inference(avatar_split_clause,[],[f2896,f27189]) ).
fof(f2896,plain,
! [X39,X0,X11,X12] : c_List_Osublist(c_List_Olist_OCons(X12,X39,X0),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),X0) = c_List_Olist_OCons(X12,c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X0),
inference(definition_unfolding,[],[f663,f660,f1438,f660]) ).
fof(f663,axiom,
! [X39,X0,X11,X12] : c_List_Otake(c_Suc(X11),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olist_OCons(X12,c_List_Otake(X11,X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f27187,plain,
spl0_2426,
inference(avatar_split_clause,[],[f1694,f27185]) ).
fof(f27185,plain,
( spl0_2426
<=> ! [X1,X0,X16,X19,X26] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Pair(c_Main_OImageE__1(X26,X1,X19,X16,X0),X1,X16,X0),X19,tc_prod(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2426])]) ).
fof(f1694,axiom,
! [X0,X1,X19,X26,X16] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Pair(c_Main_OImageE__1(X26,X1,X19,X16,X0),X1,X16,X0),X19,tc_prod(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f27183,plain,
spl0_2425,
inference(avatar_split_clause,[],[f1636,f27181]) ).
fof(f27181,plain,
( spl0_2425
<=> ! [X0,X16,X25,X26,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__1(X26,X30,X25,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2425])]) ).
fof(f1636,axiom,
! [X0,X26,X16,X25,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__1(X26,X30,X25,X0,X16),X26,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f27179,plain,
spl0_2424,
inference(avatar_split_clause,[],[f1635,f27177]) ).
fof(f27177,plain,
( spl0_2424
<=> ! [X0,X16,X25,X26,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__2(X26,X30,X25,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).
fof(f1635,axiom,
! [X0,X26,X16,X25,X30] :
( ~ c_in(X25,c_Datatype__Universe_Ouprod(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Main_OuprodE__2(X26,X30,X25,X0,X16),X30,tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f27175,plain,
spl0_2423,
inference(avatar_split_clause,[],[f1279,f27173]) ).
fof(f27173,plain,
( spl0_2423
<=> ! [X19,X0,X3,X16,X1] :
( ~ c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2423])]) ).
fof(f1279,axiom,
! [X3,X0,X1,X19,X16] :
( ~ c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f27171,plain,
spl0_2422,
inference(avatar_split_clause,[],[f1278,f27169]) ).
fof(f27169,plain,
( spl0_2422
<=> ! [X19,X0,X3,X16,X1] :
( c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2422])]) ).
fof(f1278,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(c_Pair(X1,X3,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(c_Pair(X3,X1,X0,X16),c_Relation_Oconverse(X19,X16,X0),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f27167,plain,
( spl0_2421
| ~ spl0_1059
| ~ spl0_1651
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f20835,f20742,f13284,f8960,f27164]) ).
fof(f27164,plain,
( spl0_2421
<=> c_emptyset = c_SetInterval_OatLeastLessThan(v_f(v_x),v_k(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2421])]) ).
fof(f20835,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OatLeastLessThan(v_f(v_x),v_k(v_x),t_b)
| ~ spl0_1651
| ~ spl0_2083 ),
inference(resolution,[],[f20744,f13285]) ).
fof(f27162,plain,
spl0_2420,
inference(avatar_split_clause,[],[f1226,f27160]) ).
fof(f27160,plain,
( spl0_2420
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2420])]) ).
fof(f1226,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f27158,plain,
spl0_2419,
inference(avatar_split_clause,[],[f1216,f27156]) ).
fof(f27156,plain,
( spl0_2419
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).
fof(f1216,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f27154,plain,
spl0_2418,
inference(avatar_split_clause,[],[f771,f27152]) ).
fof(f27152,plain,
( spl0_2418
<=> ! [X34,X33] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).
fof(f771,axiom,
! [X34,X33] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f27150,plain,
spl0_2417,
inference(avatar_split_clause,[],[f722,f27148]) ).
fof(f27148,plain,
( spl0_2417
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2417])]) ).
fof(f722,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f27146,plain,
spl0_2416,
inference(avatar_split_clause,[],[f167,f27144]) ).
fof(f27144,plain,
( spl0_2416
<=> ! [X16,X12,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMin(c_insert(X12,X26,X16),X16) = c_Orderings_Omin(X12,c_Finite__Set_OMin(X26,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).
fof(f167,axiom,
! [X26,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMin(c_insert(X12,X26,X16),X16) = c_Orderings_Omin(X12,c_Finite__Set_OMin(X26,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f27142,plain,
spl0_2415,
inference(avatar_split_clause,[],[f165,f27140]) ).
fof(f27140,plain,
( spl0_2415
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_less(X12,c_Main_OMin__gr__iff__1(X26,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2415])]) ).
fof(f165,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_less(X12,c_Main_OMin__gr__iff__1(X26,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f27138,plain,
spl0_2414,
inference(avatar_split_clause,[],[f164,f27136]) ).
fof(f27136,plain,
( spl0_2414
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__gr__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).
fof(f164,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__gr__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f27134,plain,
spl0_2413,
inference(avatar_split_clause,[],[f162,f27132]) ).
fof(f27132,plain,
( spl0_2413
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_lessequals(X12,c_Main_OMin__ge__iff__1(X26,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2413])]) ).
fof(f162,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| ~ c_lessequals(X12,c_Main_OMin__ge__iff__1(X26,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f27130,plain,
spl0_2412,
inference(avatar_split_clause,[],[f161,f27128]) ).
fof(f27128,plain,
( spl0_2412
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__ge__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2412])]) ).
fof(f161,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMin(X26,X0),X0)
| c_in(c_Main_OMin__ge__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f27126,plain,
spl0_2411,
inference(avatar_split_clause,[],[f158,f27124]) ).
fof(f27124,plain,
( spl0_2411
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_less(c_Main_OMax__less__iff__1(X26,X12,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2411])]) ).
fof(f158,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_less(c_Main_OMax__less__iff__1(X26,X12,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f27119,plain,
spl0_2410,
inference(avatar_split_clause,[],[f157,f27117]) ).
fof(f27117,plain,
( spl0_2410
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__less__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2410])]) ).
fof(f157,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_less(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__less__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f27115,plain,
spl0_2409,
inference(avatar_split_clause,[],[f155,f27113]) ).
fof(f27113,plain,
( spl0_2409
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X26,X12,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2409])]) ).
fof(f155,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X26,X12,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f27111,plain,
spl0_2408,
inference(avatar_split_clause,[],[f154,f27109]) ).
fof(f27109,plain,
( spl0_2408
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__le__iff__1(X26,X12,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2408])]) ).
fof(f154,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMax(X26,X0),X12,X0)
| c_in(c_Main_OMax__le__iff__1(X26,X12,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f27107,plain,
spl0_2407,
inference(avatar_split_clause,[],[f152,f27105]) ).
fof(f27105,plain,
( spl0_2407
<=> ! [X16,X12,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMax(c_insert(X12,X26,X16),X16) = c_Orderings_Omax(X12,c_Finite__Set_OMax(X26,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2407])]) ).
fof(f152,axiom,
! [X26,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Finite__Set_OMax(c_insert(X12,X26,X16),X16) = c_Orderings_Omax(X12,c_Finite__Set_OMax(X26,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f26950,plain,
( spl0_2406
| ~ spl0_1059
| ~ spl0_1661
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f20834,f20742,f13325,f8960,f26947]) ).
fof(f26947,plain,
( spl0_2406
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(v_f(v_x),v_k(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2406])]) ).
fof(f20834,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(v_f(v_x),v_k(v_x),t_b)
| ~ spl0_1661
| ~ spl0_2083 ),
inference(resolution,[],[f20744,f13326]) ).
fof(f26678,plain,
( spl0_2405
| ~ spl0_965
| ~ spl0_1649 ),
inference(avatar_split_clause,[],[f13875,f13276,f8447,f26676]) ).
fof(f26676,plain,
( spl0_2405
<=> ! [X0] : c_SetInterval_OatLeast(X0,t_b) = c_uminus(c_SetInterval_OlessThan(X0,t_b),tc_set(t_b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2405])]) ).
fof(f13276,plain,
( spl0_1649
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatLeast(X9,X0) = c_uminus(c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f13875,plain,
( ! [X0] : c_SetInterval_OatLeast(X0,t_b) = c_uminus(c_SetInterval_OlessThan(X0,t_b),tc_set(t_b))
| ~ spl0_965
| ~ spl0_1649 ),
inference(resolution,[],[f13277,f8449]) ).
fof(f8449,plain,
( class_Orderings_Olinorder(t_b)
| ~ spl0_965 ),
inference(avatar_component_clause,[],[f8447]) ).
fof(f13277,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatLeast(X9,X0) = c_uminus(c_SetInterval_OlessThan(X9,X0),tc_set(X0)) )
| ~ spl0_1649 ),
inference(avatar_component_clause,[],[f13276]) ).
fof(f26531,plain,
( spl0_2404
| ~ spl0_965
| ~ spl0_1648 ),
inference(avatar_split_clause,[],[f13872,f13272,f8447,f26529]) ).
fof(f26529,plain,
( spl0_2404
<=> ! [X0] : c_SetInterval_OatMost(X0,t_b) = c_uminus(c_SetInterval_OgreaterThan(X0,t_b),tc_set(t_b)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2404])]) ).
fof(f13272,plain,
( spl0_1648
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatMost(X9,X0) = c_uminus(c_SetInterval_OgreaterThan(X9,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f13872,plain,
( ! [X0] : c_SetInterval_OatMost(X0,t_b) = c_uminus(c_SetInterval_OgreaterThan(X0,t_b),tc_set(t_b))
| ~ spl0_965
| ~ spl0_1648 ),
inference(resolution,[],[f13273,f8449]) ).
fof(f13273,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatMost(X9,X0) = c_uminus(c_SetInterval_OgreaterThan(X9,X0),tc_set(X0)) )
| ~ spl0_1648 ),
inference(avatar_component_clause,[],[f13272]) ).
fof(f26421,plain,
spl0_2403,
inference(avatar_split_clause,[],[f3001,f26419]) ).
fof(f26419,plain,
( spl0_2403
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2403])]) ).
fof(f3001,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f750,f1023]) ).
fof(f750,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f26417,plain,
spl0_2402,
inference(avatar_split_clause,[],[f3000,f26415]) ).
fof(f26415,plain,
( spl0_2402
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2402])]) ).
fof(f3000,plain,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f751,f1023]) ).
fof(f751,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X75)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f26413,plain,
spl0_2401,
inference(avatar_split_clause,[],[f2973,f26411]) ).
fof(f26411,plain,
( spl0_2401
<=> ! [X11,X24,X23] :
( ~ c_lessequals(c_plus(X23,X24,tc_nat),X11,tc_nat)
| c_List_Oupt(X23,c_plus(X23,X24,tc_nat)) = c_List_Osublist(c_List_Oupt(X23,X11),c_SetInterval_OlessThan(X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2401])]) ).
fof(f2973,plain,
! [X11,X24,X23] :
( ~ c_lessequals(c_plus(X23,X24,tc_nat),X11,tc_nat)
| c_List_Oupt(X23,c_plus(X23,X24,tc_nat)) = c_List_Osublist(c_List_Oupt(X23,X11),c_SetInterval_OlessThan(X24,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f671,f660]) ).
fof(f671,axiom,
! [X11,X24,X23] :
( ~ c_lessequals(c_plus(X23,X24,tc_nat),X11,tc_nat)
| c_List_Otake(X24,c_List_Oupt(X23,X11),tc_nat) = c_List_Oupt(X23,c_plus(X23,X24,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f26409,plain,
spl0_2400,
inference(avatar_split_clause,[],[f2863,f26407]) ).
fof(f26407,plain,
( spl0_2400
<=> ! [X77,X0] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2400])]) ).
fof(f2863,plain,
! [X0,X77] : c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0) = c_Transitive__Closure_Otrancl(c_union(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1606,f1610,f1610]) ).
fof(f1606,axiom,
! [X0,X77] : c_Transitive__Closure_Ortrancl(X77,X0) = c_Transitive__Closure_Ortrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f26405,plain,
spl0_2399,
inference(avatar_split_clause,[],[f1742,f26403]) ).
fof(f26403,plain,
( spl0_2399
<=> ! [X19,X0,X3,X1] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X3,X1,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2399])]) ).
fof(f1742,axiom,
! [X3,X0,X1,X19] :
( ~ c_in(c_Pair(X3,X1,X0,X0),X19,tc_prod(X0,X0))
| c_in(c_Pair(X3,X1,X0,X0),c_Transitive__Closure_Otrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f26401,plain,
spl0_2398,
inference(avatar_split_clause,[],[f1695,f26399]) ).
fof(f26399,plain,
( spl0_2398
<=> ! [X1,X19,X0,X16,X3,X26] :
( ~ c_in(X3,X26,X0)
| c_in(X1,c_Relation_OImage(X19,X26,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2398])]) ).
fof(f1695,axiom,
! [X3,X0,X1,X19,X26,X16] :
( ~ c_in(X3,X26,X0)
| c_in(X1,c_Relation_OImage(X19,X26,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f26397,plain,
spl0_2397,
inference(avatar_split_clause,[],[f1456,f26395]) ).
fof(f1456,axiom,
! [X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X23,X11,X0)
| c_minus(c_SetInterval_OatLeastLessThan(X23,X24,X0),c_SetInterval_OatLeastLessThan(X23,X11,X0),tc_set(X0)) = c_SetInterval_OatLeastLessThan(X11,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f26393,plain,
( spl0_2396
| ~ spl0_965
| ~ spl0_1647 ),
inference(avatar_split_clause,[],[f13869,f13268,f8447,f26391]) ).
fof(f26391,plain,
( spl0_2396
<=> ! [X0] : c_uminus(c_SetInterval_OatMost(X0,t_b),tc_set(t_b)) = c_SetInterval_OgreaterThan(X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2396])]) ).
fof(f13268,plain,
( spl0_1647
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatMost(X9,X0),tc_set(X0)) = c_SetInterval_OgreaterThan(X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f13869,plain,
( ! [X0] : c_uminus(c_SetInterval_OatMost(X0,t_b),tc_set(t_b)) = c_SetInterval_OgreaterThan(X0,t_b)
| ~ spl0_965
| ~ spl0_1647 ),
inference(resolution,[],[f13269,f8449]) ).
fof(f13269,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatMost(X9,X0),tc_set(X0)) = c_SetInterval_OgreaterThan(X9,X0) )
| ~ spl0_1647 ),
inference(avatar_component_clause,[],[f13268]) ).
fof(f26389,plain,
spl0_2395,
inference(avatar_split_clause,[],[f1250,f26387]) ).
fof(f26387,plain,
( spl0_2395
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2395])]) ).
fof(f1250,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f26385,plain,
spl0_2394,
inference(avatar_split_clause,[],[f1249,f26383]) ).
fof(f26383,plain,
( spl0_2394
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_less(X12,X10,tc_nat)
| ~ c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f1249,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_less(X12,X10,tc_nat)
| ~ c_less(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f26381,plain,
spl0_2393,
inference(avatar_split_clause,[],[f1245,f26379]) ).
fof(f26379,plain,
( spl0_2393
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2393])]) ).
fof(f1245,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X12,X10,tc_nat)
| ~ c_less(c_1,X1,X0)
| c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f26377,plain,
spl0_2392,
inference(avatar_split_clause,[],[f1244,f26375]) ).
fof(f26375,plain,
( spl0_2392
<=> ! [X10,X0,X12,X1] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_lessequals(X12,X10,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2392])]) ).
fof(f1244,axiom,
! [X10,X0,X1,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,X1,X0)
| c_lessequals(X12,X10,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X1,X12,X0),c_Nat_Opower(X1,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f26373,plain,
spl0_2391,
inference(avatar_split_clause,[],[f1230,f26371]) ).
fof(f26371,plain,
( spl0_2391
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2391])]) ).
fof(f1230,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f26369,plain,
spl0_2390,
inference(avatar_split_clause,[],[f1227,f26367]) ).
fof(f26367,plain,
( spl0_2390
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2390])]) ).
fof(f1227,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_0,X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f26365,plain,
spl0_2389,
inference(avatar_split_clause,[],[f1224,f26363]) ).
fof(f26363,plain,
( spl0_2389
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2389])]) ).
fof(f1224,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f26361,plain,
spl0_2388,
inference(avatar_split_clause,[],[f1222,f26359]) ).
fof(f26359,plain,
( spl0_2388
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2388])]) ).
fof(f1222,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X12,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f26357,plain,
spl0_2387,
inference(avatar_split_clause,[],[f1219,f26355]) ).
fof(f26355,plain,
( spl0_2387
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2387])]) ).
fof(f1219,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f26353,plain,
spl0_2386,
inference(avatar_split_clause,[],[f1213,f26351]) ).
fof(f26351,plain,
( spl0_2386
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2386])]) ).
fof(f1213,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X12,c_0,X0)
| c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f26349,plain,
( spl0_2385
| ~ spl0_965
| ~ spl0_1646 ),
inference(avatar_split_clause,[],[f13866,f13264,f8447,f26347]) ).
fof(f26347,plain,
( spl0_2385
<=> ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,t_b),tc_set(t_b)) = c_SetInterval_OlessThan(X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).
fof(f13264,plain,
( spl0_1646
<=> ! [X9,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatLeast(X9,X0),tc_set(X0)) = c_SetInterval_OlessThan(X9,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f13866,plain,
( ! [X0] : c_uminus(c_SetInterval_OatLeast(X0,t_b),tc_set(t_b)) = c_SetInterval_OlessThan(X0,t_b)
| ~ spl0_965
| ~ spl0_1646 ),
inference(resolution,[],[f13265,f8449]) ).
fof(f13265,plain,
( ! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatLeast(X9,X0),tc_set(X0)) = c_SetInterval_OlessThan(X9,X0) )
| ~ spl0_1646 ),
inference(avatar_component_clause,[],[f13264]) ).
fof(f26345,plain,
spl0_2384,
inference(avatar_split_clause,[],[f1062,f26343]) ).
fof(f26343,plain,
( spl0_2384
<=> ! [X35,X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_times(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2384])]) ).
fof(f1062,axiom,
! [X0,X34,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_times(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f26341,plain,
spl0_2383,
inference(avatar_split_clause,[],[f1002,f26339]) ).
fof(f26339,plain,
( spl0_2383
<=> ! [X35,X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_plus(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2383])]) ).
fof(f1002,axiom,
! [X0,X34,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_plus(c_Numeral_Onumber__of(X33,X0),X35,X0),X0) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f26337,plain,
spl0_2382,
inference(avatar_split_clause,[],[f755,f26335]) ).
fof(f26335,plain,
( spl0_2382
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).
fof(f755,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f26333,plain,
spl0_2381,
inference(avatar_split_clause,[],[f728,f26331]) ).
fof(f26331,plain,
( spl0_2381
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2381])]) ).
fof(f728,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) != c_Numeral_Onumber__of(X75,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_0) ).
fof(f26329,plain,
spl0_2380,
inference(avatar_split_clause,[],[f719,f26327]) ).
fof(f26327,plain,
( spl0_2380
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2380])]) ).
fof(f719,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f26325,plain,
spl0_2379,
inference(avatar_split_clause,[],[f529,f26323]) ).
fof(f26323,plain,
( spl0_2379
<=> ! [X23,X0,X12,X10,X39] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X39,X23,X12,X0),X23,X10,X0) = c_List_Olist__update(X39,X23,X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2379])]) ).
fof(f529,axiom,
! [X39,X0,X10,X12,X23] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X39,X23,X12,X0),X23,X10,X0) = c_List_Olist__update(X39,X23,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f26321,plain,
spl0_2378,
inference(avatar_split_clause,[],[f528,f26319]) ).
fof(f26319,plain,
( spl0_2378
<=> ! [X40,X0,X12,X10,X39] : c_List_Olist__update(c_append(X39,c_List_Olist_OCons(X12,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X10,X0) = c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2378])]) ).
fof(f528,axiom,
! [X40,X39,X0,X10,X12] : c_List_Olist__update(c_append(X39,c_List_Olist_OCons(X12,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X10,X0) = c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f26317,plain,
spl0_2377,
inference(avatar_split_clause,[],[f249,f26315]) ).
fof(f26315,plain,
( spl0_2377
<=> ! [X12,X10] :
( X10 = X12
| c_IntDef_OAbs__Integ(X12) != c_IntDef_OAbs__Integ(X10)
| ~ c_in(X12,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X10,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2377])]) ).
fof(f249,axiom,
! [X10,X12] :
( X10 = X12
| c_IntDef_OAbs__Integ(X12) != c_IntDef_OAbs__Integ(X10)
| ~ c_in(X12,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X10,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(f26313,plain,
spl0_2376,
inference(avatar_split_clause,[],[f188,f26311]) ).
fof(f26311,plain,
( spl0_2376
<=> ! [X16,X10,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omax(X10,c_Finite__Set_OMin(X26,X16),X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).
fof(f188,axiom,
! [X10,X26,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omax(X10,c_Finite__Set_OMin(X26,X16),X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f26309,plain,
spl0_2375,
inference(avatar_split_clause,[],[f187,f26307]) ).
fof(f26307,plain,
( spl0_2375
<=> ! [X16,X10,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omin(X10,c_Finite__Set_OMax(X26,X16),X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).
fof(f187,axiom,
! [X10,X26,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X10,X26,X16)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_Orderings_Omin(X10,c_Finite__Set_OMax(X26,X16),X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f26302,plain,
spl0_2374,
inference(avatar_split_clause,[],[f116,f26300]) ).
fof(f26300,plain,
( spl0_2374
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) = c_div(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2374])]) ).
fof(f116,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) = c_div(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f26298,plain,
spl0_2373,
inference(avatar_split_clause,[],[f114,f26296]) ).
fof(f26296,plain,
( spl0_2373
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat) = c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2373])]) ).
fof(f114,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat) = c_plus(X9,c_div(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f26075,plain,
( spl0_2372
| ~ spl0_1059
| ~ spl0_3
| ~ spl0_1661 ),
inference(avatar_split_clause,[],[f13984,f13325,f3235,f8960,f26072]) ).
fof(f26072,plain,
( spl0_2372
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(v_k(v_x),v_g(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2372])]) ).
fof(f13984,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(v_k(v_x),v_g(v_x),t_b)
| ~ spl0_3
| ~ spl0_1661 ),
inference(resolution,[],[f13326,f3237]) ).
fof(f25685,plain,
( spl0_2371
| ~ spl0_1059
| ~ spl0_3
| ~ spl0_1651 ),
inference(avatar_split_clause,[],[f13937,f13284,f3235,f8960,f25682]) ).
fof(f25682,plain,
( spl0_2371
<=> c_emptyset = c_SetInterval_OatLeastLessThan(v_k(v_x),v_g(v_x),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2371])]) ).
fof(f13937,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OatLeastLessThan(v_k(v_x),v_g(v_x),t_b)
| ~ spl0_3
| ~ spl0_1651 ),
inference(resolution,[],[f13285,f3237]) ).
fof(f25677,plain,
( ~ spl0_47
| spl0_2370
| ~ spl0_13
| ~ spl0_1450
| ~ spl0_1538
| ~ spl0_2256 ),
inference(avatar_split_clause,[],[f24311,f24245,f12440,f11821,f3285,f25674,f3455]) ).
fof(f25674,plain,
( spl0_2370
<=> c_0 = c_OrderedGroup_Opprt(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2370])]) ).
fof(f11821,plain,
( spl0_1450
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(X3,X0) = c_minus(c_0,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f24245,plain,
( spl0_2256
<=> ! [X0] : c_lessequals(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f24311,plain,
( c_0 = c_OrderedGroup_Opprt(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_13
| ~ spl0_1450
| ~ spl0_1538
| ~ spl0_2256 ),
inference(forward_demodulation,[],[f24297,f12139]) ).
fof(f12139,plain,
( ! [X0] : c_uminus(X0,tc_IntDef_Oint) = c_minus(c_0,X0,tc_IntDef_Oint)
| ~ spl0_13
| ~ spl0_1450 ),
inference(resolution,[],[f11822,f3287]) ).
fof(f11822,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(X3,X0) = c_minus(c_0,X3,X0) )
| ~ spl0_1450 ),
inference(avatar_component_clause,[],[f11821]) ).
fof(f24297,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Opprt(c_minus(c_0,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1538
| ~ spl0_2256 ),
inference(resolution,[],[f24246,f12441]) ).
fof(f24246,plain,
( ! [X0] : c_lessequals(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_2256 ),
inference(avatar_component_clause,[],[f24245]) ).
fof(f25441,plain,
( ~ spl0_47
| spl0_2369
| ~ spl0_8
| ~ spl0_1280
| ~ spl0_1536
| ~ spl0_2333 ),
inference(avatar_split_clause,[],[f25152,f25086,f12432,f10386,f3260,f25438,f3455]) ).
fof(f25438,plain,
( spl0_2369
<=> c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).
fof(f25086,plain,
( spl0_2333
<=> ! [X0] : c_lessequals(X0,c_plus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2333])]) ).
fof(f25152,plain,
( c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_8
| ~ spl0_1280
| ~ spl0_1536
| ~ spl0_2333 ),
inference(forward_demodulation,[],[f25137,f10714]) ).
fof(f25137,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_plus(c_0,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1536
| ~ spl0_2333 ),
inference(resolution,[],[f25087,f12433]) ).
fof(f25087,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2333 ),
inference(avatar_component_clause,[],[f25086]) ).
fof(f25400,plain,
( spl0_2368
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2367 ),
inference(avatar_split_clause,[],[f25396,f25392,f22574,f9346,f9305,f25398]) ).
fof(f25398,plain,
( spl0_2368
<=> ! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2368])]) ).
fof(f25392,plain,
( spl0_2367
<=> ! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,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_2367])]) ).
fof(f25396,plain,
( ! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2367 ),
inference(forward_demodulation,[],[f25395,f22662]) ).
fof(f25395,plain,
( ! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_1137
| ~ spl0_1147
| ~ spl0_2221
| ~ spl0_2367 ),
inference(forward_demodulation,[],[f25393,f22662]) ).
fof(f25393,plain,
( ! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_2367 ),
inference(avatar_component_clause,[],[f25392]) ).
fof(f25394,plain,
spl0_2367,
inference(avatar_split_clause,[],[f3167,f25392]) ).
fof(f3167,plain,
! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3166,f1050]) ).
fof(f3166,plain,
! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3165,f1048]) ).
fof(f3165,plain,
! [X24] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X24,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(X24,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3164,f1050]) ).
fof(f3164,plain,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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,[],[f3163,f1050]) ).
fof(f3163,plain,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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,[],[f3162,f1048]) ).
fof(f3162,plain,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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,[],[f869,f1050]) ).
fof(f869,axiom,
! [X24] :
( c_1 = c_Divides_Oop_Amod(X24,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(X24,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(f25363,plain,
( spl0_2366
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2365 ),
inference(avatar_split_clause,[],[f25359,f25356,f13448,f13139,f8657,f3868,f25361]) ).
fof(f25361,plain,
( spl0_2366
<=> ! [X9,X11,X24] : c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2366])]) ).
fof(f25356,plain,
( spl0_2365
<=> ! [X9,X11,X24] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2365])]) ).
fof(f25359,plain,
( ! [X11,X9,X24] : c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_plus(c_1,X9,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2365 ),
inference(forward_demodulation,[],[f25357,f14217]) ).
fof(f25357,plain,
( ! [X11,X9,X24] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat)
| ~ spl0_2365 ),
inference(avatar_component_clause,[],[f25356]) ).
fof(f25358,plain,
spl0_2365,
inference(avatar_split_clause,[],[f3073,f25356]) ).
fof(f3073,plain,
! [X11,X9,X24] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat) = c_minus(X24,c_plus(X11,X9,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3072,f931]) ).
fof(f931,axiom,
! [X50,X9,X23] : c_minus(c_minus(X23,X50,tc_nat),X9,tc_nat) = c_minus(X23,c_plus(X50,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3072,plain,
! [X11,X9,X24] : c_minus(c_minus(X24,X11,tc_nat),X9,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X11,X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2897,f2866]) ).
fof(f2897,plain,
! [X11,X9,X24] : c_minus(c_minus(X24,X11,tc_nat),X9,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f912,f1438,f1438]) ).
fof(f912,axiom,
! [X11,X9,X24] : c_minus(c_minus(c_Suc(X24),X11,tc_nat),c_Suc(X9),tc_nat) = c_minus(c_minus(X24,X11,tc_nat),X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f25354,plain,
spl0_2364,
inference(avatar_split_clause,[],[f3022,f25352]) ).
fof(f25352,plain,
( spl0_2364
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f3022,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
inference(definition_unfolding,[],[f1034,f1023]) ).
fof(f1034,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(X12)),X0),X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f25350,plain,
spl0_2363,
inference(avatar_split_clause,[],[f3021,f25348]) ).
fof(f25348,plain,
( spl0_2363
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).
fof(f3021,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f1042,f1023]) ).
fof(f1042,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f25346,plain,
spl0_2362,
inference(avatar_split_clause,[],[f3020,f25344]) ).
fof(f25344,plain,
( spl0_2362
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2362])]) ).
fof(f3020,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
inference(definition_unfolding,[],[f1043,f1023]) ).
fof(f1043,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f25339,plain,
spl0_2361,
inference(avatar_split_clause,[],[f3019,f25337]) ).
fof(f25337,plain,
( spl0_2361
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).
fof(f3019,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
inference(definition_unfolding,[],[f1033,f1023]) ).
fof(f1033,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(X12)),X0),X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_Numeral_Onumber__of(X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f25335,plain,
spl0_2360,
inference(avatar_split_clause,[],[f2999,f25333]) ).
fof(f25333,plain,
( spl0_2360
<=> ! [X0,X30,X2,X26] :
( ~ c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,X26,tc_set(X0))
| c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2360])]) ).
fof(f2999,plain,
! [X2,X0,X26,X30] :
( ~ c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,X26,tc_set(X0))
| c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
inference(definition_unfolding,[],[f1505,f1267]) ).
fof(f1505,axiom,
! [X2,X0,X26,X30] :
( ~ c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,X26,tc_set(X0))
| c_lessequals(X2,c_inter(X26,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f25331,plain,
spl0_2359,
inference(avatar_split_clause,[],[f2970,f25329]) ).
fof(f25329,plain,
( spl0_2359
<=> ! [X3,X0,X30,X26] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2359])]) ).
fof(f2970,plain,
! [X3,X0,X26,X30] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1575,f1267,f1267]) ).
fof(f1575,axiom,
! [X3,X0,X26,X30] :
( c_emptyset = c_inter(X26,X30,X0)
| c_emptyset != c_inter(c_insert(X3,X26,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_1) ).
fof(f25327,plain,
spl0_2358,
inference(avatar_split_clause,[],[f2968,f25325]) ).
fof(f25325,plain,
( spl0_2358
<=> ! [X0,X3,X26,X30] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2358])]) ).
fof(f2968,plain,
! [X3,X0,X26,X30] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X30,X0),X26,X0,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X30,X0),c_insert(X3,X26,X0),X0,X0) ),
inference(definition_unfolding,[],[f1556,f1267,f1267]) ).
fof(f1556,axiom,
! [X3,X0,X26,X30] :
( c_emptyset = c_inter(X30,X26,X0)
| c_emptyset != c_inter(X30,c_insert(X3,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__1_1) ).
fof(f25255,plain,
( spl0_2357
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2056
| ~ spl0_2356 ),
inference(avatar_split_clause,[],[f25251,f25247,f19111,f13448,f13139,f9305,f9280,f8657,f3868,f25253]) ).
fof(f25253,plain,
( spl0_2357
<=> ! [X50,X23] :
( c_List_Oupt(X23,c_plus(c_1,X50,tc_nat)) = c_append(c_List_Oupt(X23,X50),c_List_Oreplicate(c_1,X50,tc_nat),tc_nat)
| ~ c_lessequals(X23,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2357])]) ).
fof(f9280,plain,
( spl0_1131
<=> ! [X12,X14] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X12,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f19111,plain,
( spl0_2056
<=> ! [X11,X12,X14] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_plus(c_1,X11,tc_nat),X12,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f25247,plain,
( spl0_2356
<=> ! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2356])]) ).
fof(f25251,plain,
( ! [X50,X23] :
( c_List_Oupt(X23,c_plus(c_1,X50,tc_nat)) = c_append(c_List_Oupt(X23,X50),c_List_Oreplicate(c_1,X50,tc_nat),tc_nat)
| ~ c_lessequals(X23,X50,tc_nat) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2056
| ~ spl0_2356 ),
inference(forward_demodulation,[],[f25250,f19137]) ).
fof(f19137,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056 ),
inference(forward_demodulation,[],[f19114,f9306]) ).
fof(f19114,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_1131
| ~ spl0_2056 ),
inference(superposition,[],[f19112,f9281]) ).
fof(f9281,plain,
( ! [X14,X12] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X12,X14)
| ~ spl0_1131 ),
inference(avatar_component_clause,[],[f9280]) ).
fof(f19112,plain,
( ! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_plus(c_1,X11,tc_nat),X12,X14)
| ~ spl0_2056 ),
inference(avatar_component_clause,[],[f19111]) ).
fof(f25250,plain,
( ! [X50,X23] :
( c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_plus(c_1,X50,tc_nat))
| ~ c_lessequals(X23,X50,tc_nat) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2356 ),
inference(forward_demodulation,[],[f25248,f14217]) ).
fof(f25248,plain,
( ! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) )
| ~ spl0_2356 ),
inference(avatar_component_clause,[],[f25247]) ).
fof(f25249,plain,
spl0_2356,
inference(avatar_split_clause,[],[f2935,f25247]) ).
fof(f2935,plain,
! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f676,f1438]) ).
fof(f676,axiom,
! [X50,X23] :
( ~ c_lessequals(X23,X50,tc_nat)
| c_List_Oupt(X23,c_Suc(X50)) = c_append(c_List_Oupt(X23,X50),c_List_Olist_OCons(X50,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f25245,plain,
spl0_2355,
inference(avatar_split_clause,[],[f2899,f25243]) ).
fof(f25243,plain,
( spl0_2355
<=> ! [X0,X30,X26] : c_union(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2355])]) ).
fof(f2899,plain,
! [X0,X26,X30] : c_union(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)),
inference(definition_unfolding,[],[f1469,f1267]) ).
fof(f1469,axiom,
! [X0,X26,X30] : c_uminus(c_inter(X26,X30,X0),tc_set(X0)) = c_union(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f25241,plain,
spl0_2354,
inference(avatar_split_clause,[],[f2898,f25239]) ).
fof(f25239,plain,
( spl0_2354
<=> ! [X0,X30,X26] : c_uminus(c_union(X26,X30,X0),tc_set(X0)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),c_uminus(X30,tc_set(X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2354])]) ).
fof(f2898,plain,
! [X0,X26,X30] : c_uminus(c_union(X26,X30,X0),tc_set(X0)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),c_uminus(X30,tc_set(X0)),X0,X0),
inference(definition_unfolding,[],[f1471,f1267]) ).
fof(f1471,axiom,
! [X0,X26,X30] : c_uminus(c_union(X26,X30,X0),tc_set(X0)) = c_inter(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f25237,plain,
spl0_2353,
inference(avatar_split_clause,[],[f2892,f25235]) ).
fof(f25235,plain,
( spl0_2353
<=> ! [X24,X11,X0,X39] : c_List_Osublist(c_List_Osublist(X39,c_SetInterval_OlessThan(X24,tc_nat),X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_List_Osublist(X39,c_SetInterval_OlessThan(c_Orderings_Omin(X11,X24,tc_nat),tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2353])]) ).
fof(f2892,plain,
! [X39,X0,X11,X24] : c_List_Osublist(c_List_Osublist(X39,c_SetInterval_OlessThan(X24,tc_nat),X0),c_SetInterval_OlessThan(X11,tc_nat),X0) = c_List_Osublist(X39,c_SetInterval_OlessThan(c_Orderings_Omin(X11,X24,tc_nat),tc_nat),X0),
inference(definition_unfolding,[],[f670,f660,f660,f660]) ).
fof(f670,axiom,
! [X39,X0,X11,X24] : c_List_Otake(X11,c_List_Otake(X24,X39,X0),X0) = c_List_Otake(c_Orderings_Omin(X11,X24,tc_nat),X39,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f25233,plain,
( ~ spl0_47
| spl0_2352
| ~ spl0_8
| ~ spl0_1280
| ~ spl0_1539
| ~ spl0_2333 ),
inference(avatar_split_clause,[],[f25151,f25086,f12444,f10386,f3260,f25230,f3455]) ).
fof(f25230,plain,
( spl0_2352
<=> c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2352])]) ).
fof(f25151,plain,
( c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint)
| ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_8
| ~ spl0_1280
| ~ spl0_1539
| ~ spl0_2333 ),
inference(forward_demodulation,[],[f25136,f10714]) ).
fof(f25136,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_plus(c_0,c_1,tc_IntDef_Oint) = c_OrderedGroup_Opprt(c_plus(c_0,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1539
| ~ spl0_2333 ),
inference(resolution,[],[f25087,f12445]) ).
fof(f25211,plain,
( spl0_2351
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2350 ),
inference(avatar_split_clause,[],[f25207,f25202,f13448,f13139,f8657,f3868,f25209]) ).
fof(f25209,plain,
( spl0_2351
<=> ! [X11,X24] : c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).
fof(f25202,plain,
( spl0_2350
<=> ! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X24,X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).
fof(f25207,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2350 ),
inference(forward_demodulation,[],[f25206,f14217]) ).
fof(f25206,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2350 ),
inference(forward_demodulation,[],[f25205,f14217]) ).
fof(f25205,plain,
( ! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X24,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2350 ),
inference(forward_demodulation,[],[f25203,f14217]) ).
fof(f25203,plain,
( ! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X24,X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2350 ),
inference(avatar_component_clause,[],[f25202]) ).
fof(f25204,plain,
spl0_2350,
inference(avatar_split_clause,[],[f2868,f25202]) ).
fof(f2868,plain,
! [X11,X24] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X24,X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f949,f1438,f1438,f1438]) ).
fof(f949,axiom,
! [X11,X24] : c_Orderings_Omin(c_Suc(X24),c_Suc(X11),tc_nat) = c_Suc(c_Orderings_Omin(X24,X11,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f25186,plain,
( spl0_2349
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2348 ),
inference(avatar_split_clause,[],[f25182,f25177,f13448,f13139,f8657,f3868,f25184]) ).
fof(f25184,plain,
( spl0_2349
<=> ! [X11,X24] : c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).
fof(f25177,plain,
( spl0_2348
<=> ! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X24,X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2348])]) ).
fof(f25182,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2348 ),
inference(forward_demodulation,[],[f25181,f14217]) ).
fof(f25181,plain,
( ! [X11,X24] : c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2348 ),
inference(forward_demodulation,[],[f25180,f14217]) ).
fof(f25180,plain,
( ! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X24,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2348 ),
inference(forward_demodulation,[],[f25178,f14217]) ).
fof(f25178,plain,
( ! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X24,X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2348 ),
inference(avatar_component_clause,[],[f25177]) ).
fof(f25179,plain,
spl0_2348,
inference(avatar_split_clause,[],[f2867,f25177]) ).
fof(f2867,plain,
! [X11,X24] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X24,X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f946,f1438,f1438,f1438]) ).
fof(f946,axiom,
! [X11,X24] : c_Orderings_Omax(c_Suc(X24),c_Suc(X11),tc_nat) = c_Suc(c_Orderings_Omax(X24,X11,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f25175,plain,
spl0_2347,
inference(avatar_split_clause,[],[f1700,f25173]) ).
fof(f25173,plain,
( spl0_2347
<=> ! [X25,X0,X26] :
( ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0))
| c_Pair(c_Main_OdiagE__1(X26,X25,X0),c_Main_OdiagE__1(X26,X25,X0),X0,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2347])]) ).
fof(f1700,axiom,
! [X0,X26,X25] :
( ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0))
| c_Pair(c_Main_OdiagE__1(X26,X25,X0),c_Main_OdiagE__1(X26,X25,X0),X0,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f25171,plain,
spl0_2346,
inference(avatar_split_clause,[],[f1696,f25169]) ).
fof(f25169,plain,
( spl0_2346
<=> ! [X19,X0,X16,X1] :
( ~ c_in(X1,c_Relation_ORange(X19,X16,X0),X0)
| c_in(c_Pair(c_Main_ORangeE__1(X1,X19,X0,X16),X1,X16,X0),X19,tc_prod(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2346])]) ).
fof(f1696,axiom,
! [X0,X1,X19,X16] :
( ~ c_in(X1,c_Relation_ORange(X19,X16,X0),X0)
| c_in(c_Pair(c_Main_ORangeE__1(X1,X19,X0,X16),X1,X16,X0),X19,tc_prod(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f25167,plain,
spl0_2345,
inference(avatar_split_clause,[],[f1690,f25165]) ).
fof(f25165,plain,
( spl0_2345
<=> ! [X19,X0,X3,X16] :
( ~ c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| c_in(c_Pair(X3,c_Main_ODomainE__1(X3,X19,X0,X16),X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2345])]) ).
fof(f1690,axiom,
! [X3,X0,X19,X16] :
( ~ c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| c_in(c_Pair(X3,c_Main_ODomainE__1(X3,X19,X0,X16),X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f25163,plain,
spl0_2344,
inference(avatar_split_clause,[],[f1681,f25161]) ).
fof(f25161,plain,
( spl0_2344
<=> ! [X0,X3,X26,X72] :
( ~ c_in(X3,X26,X0)
| ~ c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_List_Olist_OCons(X3,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2344])]) ).
fof(f1681,axiom,
! [X3,X72,X0,X26] :
( ~ c_in(X3,X26,X0)
| ~ c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_List_Olist_OCons(X3,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f25128,plain,
spl0_2343,
inference(avatar_split_clause,[],[f1643,f25126]) ).
fof(f25126,plain,
( spl0_2343
<=> ! [X18,X0,X16,X26,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn1(X18,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2343])]) ).
fof(f1643,axiom,
! [X0,X18,X26,X16,X30] :
( ~ c_in(X18,X30,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn1(X18,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f25124,plain,
spl0_2342,
inference(avatar_split_clause,[],[f1642,f25122]) ).
fof(f25122,plain,
( spl0_2342
<=> ! [X17,X0,X16,X26,X30] :
( ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn0(X17,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2342])]) ).
fof(f1642,axiom,
! [X0,X26,X16,X17,X30] :
( ~ c_in(X17,X26,tc_set(tc_Datatype__Universe_Onode(X0,X16)))
| c_in(c_Datatype__Universe_OIn0(X17,X0,X16),c_Datatype__Universe_Ousum(X26,X30,X0,X16),tc_set(tc_Datatype__Universe_Onode(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f25120,plain,
spl0_2341,
inference(avatar_split_clause,[],[f1460,f25118]) ).
fof(f25118,plain,
( spl0_2341
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X24,X23,X0)
| ~ c_lessequals(X50,X11,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2341])]) ).
fof(f1460,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X24,X23,X0)
| ~ c_lessequals(X50,X11,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f25116,plain,
spl0_2340,
inference(avatar_split_clause,[],[f1458,f25114]) ).
fof(f25114,plain,
( spl0_2340
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X50,X11,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2340])]) ).
fof(f1458,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X50,X11,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f25112,plain,
spl0_2339,
inference(avatar_split_clause,[],[f1457,f25110]) ).
fof(f25110,plain,
( spl0_2339
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X24,X23,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2339])]) ).
fof(f1457,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X50,X23,X0)
| c_lessequals(X24,X23,X0)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f25108,plain,
spl0_2338,
inference(avatar_split_clause,[],[f1270,f25106]) ).
fof(f25106,plain,
( spl0_2338
<=> ! [X3,X19,X0,X16,X1] :
( ~ c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).
fof(f1270,axiom,
! [X3,X0,X1,X19,X16] :
( ~ c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f25104,plain,
spl0_2337,
inference(avatar_split_clause,[],[f1269,f25102]) ).
fof(f25102,plain,
( spl0_2337
<=> ! [X3,X19,X0,X16,X1] :
( c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2337])]) ).
fof(f1269,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(c_Pair(X3,X1,X16,X0),X19,tc_prod(X16,X0))
| ~ c_in(X1,c_Relation_OImage(X19,c_insert(X3,c_emptyset,X16),X16,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f25100,plain,
spl0_2336,
inference(avatar_split_clause,[],[f1229,f25098]) ).
fof(f25098,plain,
( spl0_2336
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2336])]) ).
fof(f1229,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f25096,plain,
spl0_2335,
inference(avatar_split_clause,[],[f1212,f25094]) ).
fof(f25094,plain,
( spl0_2335
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2335])]) ).
fof(f1212,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f25092,plain,
spl0_2334,
inference(avatar_split_clause,[],[f1068,f25090]) ).
fof(f25090,plain,
( spl0_2334
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2334])]) ).
fof(f1068,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X3,X0),c_HOL_Oabs(X1,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f25088,plain,
( spl0_2333
| ~ spl0_46
| ~ spl0_2041
| ~ spl0_2256 ),
inference(avatar_split_clause,[],[f24290,f24245,f18803,f3450,f25086]) ).
fof(f3450,plain,
( spl0_46
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f18803,plain,
( spl0_2041
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_minus(X3,X1,X0),X25,X0)
| c_lessequals(X3,c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f24290,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| c_lessequals(X0,c_plus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2041
| ~ spl0_2256 ),
inference(resolution,[],[f24246,f18804]) ).
fof(f18804,plain,
( ! [X3,X0,X1,X25] :
( ~ c_lessequals(c_minus(X3,X1,X0),X25,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_plus(X25,X1,X0),X0) )
| ~ spl0_2041 ),
inference(avatar_component_clause,[],[f18803]) ).
fof(f25084,plain,
spl0_2332,
inference(avatar_split_clause,[],[f1015,f25082]) ).
fof(f25082,plain,
( spl0_2332
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) = c_uminus(c_Numeral_Onumber__of(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).
fof(f1015,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) = c_uminus(c_Numeral_Onumber__of(X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f25080,plain,
spl0_2331,
inference(avatar_split_clause,[],[f704,f25078]) ).
fof(f25078,plain,
( spl0_2331
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_lessequals(X11,X24,tc_nat)
| c_NatArith_Oof__nat(c_minus(X24,X11,tc_nat),X0) = c_minus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2331])]) ).
fof(f704,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_lessequals(X11,X24,tc_nat)
| c_NatArith_Oof__nat(c_minus(X24,X11,tc_nat),X0) = c_minus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f25076,plain,
spl0_2330,
inference(avatar_split_clause,[],[f566,f25074]) ).
fof(f25074,plain,
( spl0_2330
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2330])]) ).
fof(f566,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f25072,plain,
spl0_2329,
inference(avatar_split_clause,[],[f565,f25070]) ).
fof(f25070,plain,
( spl0_2329
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2329])]) ).
fof(f565,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f25068,plain,
spl0_2328,
inference(avatar_split_clause,[],[f564,f25066]) ).
fof(f25066,plain,
( spl0_2328
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2328])]) ).
fof(f564,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f25064,plain,
spl0_2327,
inference(avatar_split_clause,[],[f563,f25062]) ).
fof(f25062,plain,
( spl0_2327
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2327])]) ).
fof(f563,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f25060,plain,
spl0_2326,
inference(avatar_split_clause,[],[f562,f25058]) ).
fof(f25058,plain,
( spl0_2326
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2326])]) ).
fof(f562,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f25056,plain,
spl0_2325,
inference(avatar_split_clause,[],[f561,f25054]) ).
fof(f25054,plain,
( spl0_2325
<=> ! [X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2325])]) ).
fof(f561,axiom,
! [X65,X28,X58,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f25052,plain,
spl0_2324,
inference(avatar_split_clause,[],[f560,f25050]) ).
fof(f25050,plain,
( spl0_2324
<=> ! [X59,X65,X28,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2324])]) ).
fof(f560,axiom,
! [X65,X28,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f25048,plain,
spl0_2323,
inference(avatar_split_clause,[],[f559,f25046]) ).
fof(f25046,plain,
( spl0_2323
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2323])]) ).
fof(f559,axiom,
! [X65,X28,X10,X58,X59,X71,X70,X0,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f25021,plain,
spl0_2322,
inference(avatar_split_clause,[],[f558,f25019]) ).
fof(f25019,plain,
( spl0_2322
<=> ! [X59,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2322])]) ).
fof(f558,axiom,
! [X65,X58,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f25017,plain,
spl0_2321,
inference(avatar_split_clause,[],[f557,f25015]) ).
fof(f25015,plain,
( spl0_2321
<=> ! [X59,X28,X65,X58,X10,X0,X71,X68,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2321])]) ).
fof(f557,axiom,
! [X65,X28,X58,X59,X71,X10,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f25013,plain,
spl0_2320,
inference(avatar_split_clause,[],[f556,f25011]) ).
fof(f25011,plain,
( spl0_2320
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2320])]) ).
fof(f556,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f25009,plain,
spl0_2319,
inference(avatar_split_clause,[],[f555,f25007]) ).
fof(f25007,plain,
( spl0_2319
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2319])]) ).
fof(f555,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f25005,plain,
spl0_2318,
inference(avatar_split_clause,[],[f554,f25003]) ).
fof(f25003,plain,
( spl0_2318
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2318])]) ).
fof(f554,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f25001,plain,
spl0_2317,
inference(avatar_split_clause,[],[f553,f24999]) ).
fof(f24999,plain,
( spl0_2317
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2317])]) ).
fof(f553,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f24997,plain,
spl0_2316,
inference(avatar_split_clause,[],[f552,f24995]) ).
fof(f24995,plain,
( spl0_2316
<=> ! [X28,X59,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).
fof(f552,axiom,
! [X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f24993,plain,
spl0_2315,
inference(avatar_split_clause,[],[f551,f24991]) ).
fof(f24991,plain,
( spl0_2315
<=> ! [X59,X28,X65,X58,X10,X0,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2315])]) ).
fof(f551,axiom,
! [X65,X28,X58,X59,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__rec(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f24989,plain,
spl0_2314,
inference(avatar_split_clause,[],[f550,f24987]) ).
fof(f24987,plain,
( spl0_2314
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2314])]) ).
fof(f550,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X10,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble8,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f24985,plain,
spl0_2313,
inference(avatar_split_clause,[],[f549,f24983]) ).
fof(f24983,plain,
( spl0_2313
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2313])]) ).
fof(f549,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X10,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble7,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f24981,plain,
( spl0_2312
| ~ spl0_46
| ~ spl0_2037
| ~ spl0_2080 ),
inference(avatar_split_clause,[],[f20426,f19797,f18787,f3450,f24979]) ).
fof(f24979,plain,
( spl0_2312
<=> ! [X0] : c_less(X0,c_plus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2312])]) ).
fof(f18787,plain,
( spl0_2037
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_minus(X3,X1,X0),X25,X0)
| c_less(X3,c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f19797,plain,
( spl0_2080
<=> ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f20426,plain,
( ! [X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| c_less(X0,c_plus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2037
| ~ spl0_2080 ),
inference(resolution,[],[f18788,f19798]) ).
fof(f19798,plain,
( ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_2080 ),
inference(avatar_component_clause,[],[f19797]) ).
fof(f18788,plain,
( ! [X3,X0,X1,X25] :
( ~ c_less(c_minus(X3,X1,X0),X25,X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,c_plus(X25,X1,X0),X0) )
| ~ spl0_2037 ),
inference(avatar_component_clause,[],[f18787]) ).
fof(f24977,plain,
spl0_2311,
inference(avatar_split_clause,[],[f548,f24975]) ).
fof(f24975,plain,
( spl0_2311
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2311])]) ).
fof(f548,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X10,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble6,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f24973,plain,
spl0_2310,
inference(avatar_split_clause,[],[f547,f24971]) ).
fof(f24971,plain,
( spl0_2310
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f547,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X10,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble5,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f24969,plain,
spl0_2309,
inference(avatar_split_clause,[],[f546,f24967]) ).
fof(f24967,plain,
( spl0_2309
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).
fof(f546,axiom,
! [X65,X28,X58,X59,X10,X71,X70,X0,X68,X69,X62,X27,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X10,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble4,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f24965,plain,
spl0_2308,
inference(avatar_split_clause,[],[f545,f24963]) ).
fof(f24963,plain,
( spl0_2308
<=> ! [X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2308])]) ).
fof(f545,axiom,
! [X65,X28,X58,X10,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X10,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble3,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f24961,plain,
spl0_2307,
inference(avatar_split_clause,[],[f544,f24959]) ).
fof(f24959,plain,
( spl0_2307
<=> ! [X59,X65,X28,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2307])]) ).
fof(f544,axiom,
! [X65,X28,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X10,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble2,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f24957,plain,
spl0_2306,
inference(avatar_split_clause,[],[f543,f24955]) ).
fof(f24955,plain,
( spl0_2306
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2306])]) ).
fof(f543,axiom,
! [X65,X28,X10,X58,X59,X71,X70,X0,X68,X69,X62,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X10,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f24953,plain,
spl0_2305,
inference(avatar_split_clause,[],[f542,f24951]) ).
fof(f24951,plain,
( spl0_2305
<=> ! [X59,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2305])]) ).
fof(f542,axiom,
! [X65,X58,X10,X59,X71,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X10,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f24949,plain,
spl0_2304,
inference(avatar_split_clause,[],[f541,f24947]) ).
fof(f24947,plain,
( spl0_2304
<=> ! [X59,X28,X65,X58,X10,X0,X71,X68,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).
fof(f541,axiom,
! [X65,X28,X58,X59,X71,X10,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X69,X10,c_List_Onibble_ONibbleF,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f24945,plain,
spl0_2303,
inference(avatar_split_clause,[],[f540,f24943]) ).
fof(f24943,plain,
( spl0_2303
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).
fof(f540,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X68,X10,X70,c_List_Onibble_ONibbleE,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f24941,plain,
spl0_2302,
inference(avatar_split_clause,[],[f539,f24939]) ).
fof(f24939,plain,
( spl0_2302
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).
fof(f539,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X67,X10,X69,X70,c_List_Onibble_ONibbleD,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f24929,plain,
spl0_2301,
inference(avatar_split_clause,[],[f538,f24927]) ).
fof(f24927,plain,
( spl0_2301
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).
fof(f538,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X66,X10,X68,X69,X70,c_List_Onibble_ONibbleC,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f24925,plain,
spl0_2300,
inference(avatar_split_clause,[],[f537,f24923]) ).
fof(f24923,plain,
( spl0_2300
<=> ! [X59,X28,X65,X58,X10,X0,X71,X70,X69,X62,X27,X68,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).
fof(f537,axiom,
! [X65,X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X65,X10,X67,X68,X69,X70,c_List_Onibble_ONibbleB,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f24921,plain,
spl0_2299,
inference(avatar_split_clause,[],[f536,f24919]) ).
fof(f24919,plain,
( spl0_2299
<=> ! [X28,X59,X58,X10,X0,X71,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f536,axiom,
! [X28,X58,X59,X71,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X71,X10,X66,X67,X68,X69,X70,c_List_Onibble_ONibbleA,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f24917,plain,
spl0_2298,
inference(avatar_split_clause,[],[f535,f24915]) ).
fof(f24915,plain,
( spl0_2298
<=> ! [X59,X28,X65,X58,X10,X0,X70,X69,X62,X27,X68,X60,X63,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2298])]) ).
fof(f535,axiom,
! [X65,X28,X58,X59,X10,X70,X0,X68,X69,X62,X27,X63,X60,X66,X61,X67,X64] : c_List_Onibble_Onibble__case(X28,X27,X58,X59,X60,X61,X62,X63,X64,X10,X65,X66,X67,X68,X69,X70,c_List_Onibble_ONibble9,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f24913,plain,
spl0_2297,
inference(avatar_split_clause,[],[f523,f24911]) ).
fof(f24911,plain,
( spl0_2297
<=> ! [X51,X14,X56,X3] :
( ~ c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist_OCons(X3,c_List_Olist__inter(X51,X56,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2297])]) ).
fof(f523,axiom,
! [X51,X3,X56,X14] :
( ~ c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist_OCons(X3,c_List_Olist__inter(X51,X56,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f24909,plain,
spl0_2296,
inference(avatar_split_clause,[],[f508,f24907]) ).
fof(f24907,plain,
( spl0_2296
<=> ! [X40,X0,X16,X39] : c_Nat_Osize(c_List_Ozip(X39,X40,X0,X16),tc_List_Olist(tc_prod(X0,X16))) = c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X16)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2296])]) ).
fof(f508,axiom,
! [X40,X39,X0,X16] : c_Nat_Osize(c_List_Ozip(X39,X40,X0,X16),tc_List_Olist(tc_prod(X0,X16))) = c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X16)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f24905,plain,
spl0_2295,
inference(avatar_split_clause,[],[f417,f24903]) ).
fof(f24903,plain,
( spl0_2295
<=> ! [X44,X40,X0,X43,X39] :
( X43 = X44
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2295])]) ).
fof(f417,axiom,
! [X40,X39,X0,X44,X43] :
( X43 = X44
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f24901,plain,
spl0_2294,
inference(avatar_split_clause,[],[f416,f24899]) ).
fof(f24899,plain,
( spl0_2294
<=> ! [X44,X43,X40,X0,X39] :
( X39 = X40
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).
fof(f416,axiom,
! [X40,X39,X0,X44,X43] :
( X39 = X40
| c_Nat_Osize(X43,tc_List_Olist(X0)) != c_Nat_Osize(X44,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f24897,plain,
spl0_2293,
inference(avatar_split_clause,[],[f415,f24895]) ).
fof(f24895,plain,
( spl0_2293
<=> ! [X44,X40,X0,X43,X39] :
( X43 = X44
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2293])]) ).
fof(f415,axiom,
! [X40,X39,X0,X44,X43] :
( X43 = X44
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f24893,plain,
spl0_2292,
inference(avatar_split_clause,[],[f414,f24891]) ).
fof(f24891,plain,
( spl0_2292
<=> ! [X44,X43,X40,X0,X39] :
( X39 = X40
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2292])]) ).
fof(f414,axiom,
! [X40,X39,X0,X44,X43] :
( X39 = X40
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(X40,tc_List_Olist(X0))
| c_append(X39,X43,X0) != c_append(X40,X44,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f24889,plain,
( spl0_2291
| ~ spl0_1499
| ~ spl0_2283 ),
inference(avatar_split_clause,[],[f24782,f24673,f12274,f24887]) ).
fof(f24887,plain,
( spl0_2291
<=> ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2291])]) ).
fof(f12274,plain,
( spl0_1499
<=> ! [X35,X33] :
( ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f24673,plain,
( spl0_2283
<=> ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2283])]) ).
fof(f24782,plain,
( ! [X0] : ~ c_lessequals(c_plus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1499
| ~ spl0_2283 ),
inference(resolution,[],[f24674,f12275]) ).
fof(f12275,plain,
( ! [X35,X33] :
( c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1499 ),
inference(avatar_component_clause,[],[f12274]) ).
fof(f24674,plain,
( ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ spl0_2283 ),
inference(avatar_component_clause,[],[f24673]) ).
fof(f24885,plain,
spl0_2290,
inference(avatar_split_clause,[],[f362,f24883]) ).
fof(f24883,plain,
( spl0_2290
<=> ! [X34,X33] : c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2290])]) ).
fof(f362,axiom,
! [X34,X33] : c_div(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_Numeral_Onumber__of(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X33,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(f24881,plain,
spl0_2289,
inference(avatar_split_clause,[],[f177,f24879]) ).
fof(f24879,plain,
( spl0_2289
<=> ! [X0,X3,X26,X30] :
( ~ c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2289])]) ).
fof(f177,axiom,
! [X3,X0,X26,X30] :
( ~ c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f24877,plain,
spl0_2288,
inference(avatar_split_clause,[],[f176,f24875]) ).
fof(f24875,plain,
( spl0_2288
<=> ! [X0,X3,X26,X30] :
( c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).
fof(f176,axiom,
! [X3,X0,X26,X30] :
( c_in(c_minus(X26,X30,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_minus(X26,c_insert(X3,X30,X0),tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f24873,plain,
spl0_2287,
inference(avatar_split_clause,[],[f8,f24871]) ).
fof(f24871,plain,
( spl0_2287
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_times(X3,X1,X0),c_times(X2,X4,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f8,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_times(X3,X1,X0),c_times(X2,X4,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro_0) ).
fof(f24869,plain,
spl0_2286,
inference(avatar_split_clause,[],[f2,f24867]) ).
fof(f24867,plain,
( spl0_2286
<=> ! [X4,X0,X3,X2,X1] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_plus(X3,X1,X0),c_plus(X2,X4,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1,X4] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| ~ c_in(X1,X4,X0)
| c_in(c_plus(X3,X1,X0),c_plus(X2,X4,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__intro_0) ).
fof(f24765,plain,
( spl0_2285
| ~ spl0_61
| ~ spl0_1796
| ~ spl0_2267 ),
inference(avatar_split_clause,[],[f24325,f24322,f14715,f3525,f24763]) ).
fof(f24763,plain,
( spl0_2285
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).
fof(f24322,plain,
( spl0_2267
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f24325,plain,
( ! [X34,X75] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_61
| ~ spl0_1796
| ~ spl0_2267 ),
inference(forward_demodulation,[],[f24323,f15782]) ).
fof(f24323,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_2267 ),
inference(avatar_component_clause,[],[f24322]) ).
fof(f24761,plain,
( spl0_2284
| ~ spl0_61
| ~ spl0_1796
| ~ spl0_2266 ),
inference(avatar_split_clause,[],[f24288,f24285,f14715,f3525,f24759]) ).
fof(f24759,plain,
( spl0_2284
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f24285,plain,
( spl0_2266
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).
fof(f24288,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_61
| ~ spl0_1796
| ~ spl0_2266 ),
inference(forward_demodulation,[],[f24286,f15782]) ).
fof(f24286,plain,
( ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) )
| ~ spl0_2266 ),
inference(avatar_component_clause,[],[f24285]) ).
fof(f24675,plain,
( spl0_2283
| ~ spl0_1501
| ~ spl0_2275 ),
inference(avatar_split_clause,[],[f24461,f24384,f12283,f24673]) ).
fof(f12283,plain,
( spl0_1501
<=> ! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f24384,plain,
( spl0_2275
<=> ! [X0] : ~ c_lessequals(X0,c_minus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).
fof(f24461,plain,
( ! [X0] : ~ c_less(X0,X0,tc_IntDef_Oint)
| ~ spl0_1501
| ~ spl0_2275 ),
inference(resolution,[],[f24385,f12284]) ).
fof(f12284,plain,
( ! [X35,X33] :
( c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1501 ),
inference(avatar_component_clause,[],[f12283]) ).
fof(f24385,plain,
( ! [X0] : ~ c_lessequals(X0,c_minus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_2275 ),
inference(avatar_component_clause,[],[f24384]) ).
fof(f24448,plain,
( spl0_2282
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2281 ),
inference(avatar_split_clause,[],[f24444,f24441,f14768,f10066,f9354,f8934,f8815,f8805,f24446]) ).
fof(f24446,plain,
( spl0_2282
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).
fof(f8815,plain,
( spl0_1028
<=> ! [X10] : c_Numeral_Obin__add(c_Numeral_OPls,X10) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f8934,plain,
( spl0_1056
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f9354,plain,
( spl0_1149
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f10066,plain,
( spl0_1242
<=> ! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f14768,plain,
( spl0_1802
<=> ! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f24441,plain,
( spl0_2281
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).
fof(f24444,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2281 ),
inference(forward_demodulation,[],[f24442,f15806]) ).
fof(f15806,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802 ),
inference(forward_demodulation,[],[f15805,f8807]) ).
fof(f15805,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_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802 ),
inference(forward_demodulation,[],[f15804,f9356]) ).
fof(f9356,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_1149 ),
inference(avatar_component_clause,[],[f9354]) ).
fof(f15804,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_1028
| ~ spl0_1056
| ~ spl0_1242
| ~ spl0_1802 ),
inference(forward_demodulation,[],[f15803,f8816]) ).
fof(f8816,plain,
( ! [X10] : c_Numeral_Obin__add(c_Numeral_OPls,X10) = X10
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8815]) ).
fof(f15803,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_1056
| ~ spl0_1242
| ~ spl0_1802 ),
inference(forward_demodulation,[],[f15797,f10067]) ).
fof(f10067,plain,
( ! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin)
| ~ spl0_1242 ),
inference(avatar_component_clause,[],[f10066]) ).
fof(f15797,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_1056
| ~ spl0_1802 ),
inference(superposition,[],[f14769,f8936]) ).
fof(f8936,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_1056 ),
inference(avatar_component_clause,[],[f8934]) ).
fof(f14769,plain,
( ! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),c_Numeral_Obit_OB1)
| ~ spl0_1802 ),
inference(avatar_component_clause,[],[f14768]) ).
fof(f24442,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_2281 ),
inference(avatar_component_clause,[],[f24441]) ).
fof(f24443,plain,
spl0_2281,
inference(avatar_split_clause,[],[f3220,f24441]) ).
fof(f3220,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f3017,f1050]) ).
fof(f3017,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f213,f1023]) ).
fof(f213,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f24439,plain,
spl0_2280,
inference(avatar_split_clause,[],[f3218,f24437]) ).
fof(f24437,plain,
( spl0_2280
<=> ! [X0,X10] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2280])]) ).
fof(f3218,plain,
! [X10,X0] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3015,f1050]) ).
fof(f3015,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f209,f1023]) ).
fof(f209,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f24435,plain,
spl0_2279,
inference(avatar_split_clause,[],[f3216,f24433]) ).
fof(f24433,plain,
( spl0_2279
<=> ! [X0,X12] :
( 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).
fof(f3216,plain,
! [X0,X12] :
( 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f3013,f1050]) ).
fof(f3013,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| 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,X12)),X0),X0) ),
inference(definition_unfolding,[],[f221,f1023]) ).
fof(f221,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| 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(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f24415,plain,
( spl0_2278
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2277 ),
inference(avatar_split_clause,[],[f24411,f24408,f14768,f10066,f9354,f8934,f8815,f8805,f24413]) ).
fof(f24413,plain,
( spl0_2278
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2278])]) ).
fof(f24408,plain,
( spl0_2277
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).
fof(f24411,plain,
( ! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2277 ),
inference(forward_demodulation,[],[f24409,f15806]) ).
fof(f24409,plain,
( ! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_2277 ),
inference(avatar_component_clause,[],[f24408]) ).
fof(f24410,plain,
spl0_2277,
inference(avatar_split_clause,[],[f3213,f24408]) ).
fof(f3213,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3011,f1050]) ).
fof(f3011,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f217,f1023]) ).
fof(f217,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f24390,plain,
( spl0_2276
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2274 ),
inference(avatar_split_clause,[],[f24382,f24379,f14768,f10066,f9354,f8934,f8815,f8805,f24388]) ).
fof(f24388,plain,
( spl0_2276
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f24379,plain,
( spl0_2274
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f24382,plain,
( ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2274 ),
inference(forward_demodulation,[],[f24380,f15806]) ).
fof(f24380,plain,
( ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) )
| ~ spl0_2274 ),
inference(avatar_component_clause,[],[f24379]) ).
fof(f24386,plain,
( ~ spl0_33
| spl0_2275
| ~ spl0_1473
| ~ spl0_2080 ),
inference(avatar_split_clause,[],[f19893,f19797,f11915,f24384,f3385]) ).
fof(f3385,plain,
( spl0_33
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f19893,plain,
( ! [X0] :
( ~ c_lessequals(X0,c_minus(X0,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1473
| ~ spl0_2080 ),
inference(resolution,[],[f19798,f11916]) ).
fof(f24381,plain,
spl0_2274,
inference(avatar_split_clause,[],[f3210,f24379]) ).
fof(f3210,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f3009,f1050]) ).
fof(f3009,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f212,f1023]) ).
fof(f212,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f24377,plain,
spl0_2273,
inference(avatar_split_clause,[],[f3208,f24375]) ).
fof(f24375,plain,
( spl0_2273
<=> ! [X0,X10] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).
fof(f3208,plain,
! [X10,X0] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3007,f1050]) ).
fof(f3007,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f208,f1023]) ).
fof(f208,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f24373,plain,
spl0_2272,
inference(avatar_split_clause,[],[f3206,f24371]) ).
fof(f24371,plain,
( spl0_2272
<=> ! [X0,X12] :
( ~ 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).
fof(f3206,plain,
! [X0,X12] :
( ~ 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,X12)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0) ),
inference(forward_demodulation,[],[f3005,f1050]) ).
fof(f3005,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ 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,X12)),X0),X0) ),
inference(definition_unfolding,[],[f220,f1023]) ).
fof(f220,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_1,X0)
| ~ 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(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f24361,plain,
( spl0_2271
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2270 ),
inference(avatar_split_clause,[],[f24357,f24354,f14768,f10066,f9354,f8934,f8815,f8805,f24359]) ).
fof(f24359,plain,
( spl0_2271
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).
fof(f24354,plain,
( spl0_2270
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).
fof(f24357,plain,
( ! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2270 ),
inference(forward_demodulation,[],[f24355,f15806]) ).
fof(f24355,plain,
( ! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) )
| ~ spl0_2270 ),
inference(avatar_component_clause,[],[f24354]) ).
fof(f24356,plain,
spl0_2270,
inference(avatar_split_clause,[],[f3203,f24354]) ).
fof(f3203,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3003,f1050]) ).
fof(f3003,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f216,f1023]) ).
fof(f216,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f24335,plain,
( spl0_2269
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2268 ),
inference(avatar_split_clause,[],[f24331,f24327,f13464,f3525,f24333]) ).
fof(f24333,plain,
( spl0_2269
<=> ! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f13464,plain,
( spl0_1695
<=> ! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f24327,plain,
( spl0_2268
<=> ! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,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_2268])]) ).
fof(f24331,plain,
( ! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2268 ),
inference(forward_demodulation,[],[f24330,f14284]) ).
fof(f14284,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_61
| ~ spl0_1695 ),
inference(resolution,[],[f13465,f3527]) ).
fof(f13465,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0) )
| ~ spl0_1695 ),
inference(avatar_component_clause,[],[f13464]) ).
fof(f24330,plain,
( ! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2268 ),
inference(forward_demodulation,[],[f24328,f14284]) ).
fof(f24328,plain,
( ! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2268 ),
inference(avatar_component_clause,[],[f24327]) ).
fof(f24329,plain,
spl0_2268,
inference(avatar_split_clause,[],[f3161,f24327]) ).
fof(f3161,plain,
! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3160,f1050]) ).
fof(f3160,plain,
! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3159,f1048]) ).
fof(f3159,plain,
! [X12] :
( c_0 = c_Divides_Oop_Amod(X12,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(X12,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3158,f1050]) ).
fof(f3158,plain,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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,[],[f3157,f1050]) ).
fof(f3157,plain,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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,[],[f3156,f1048]) ).
fof(f3156,plain,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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,[],[f1202,f1050]) ).
fof(f1202,axiom,
! [X12] :
( c_1 = c_Divides_Oop_Amod(X12,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(X12,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(f24324,plain,
spl0_2267,
inference(avatar_split_clause,[],[f2998,f24322]) ).
fof(f2998,plain,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f749,f1023]) ).
fof(f749,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X75),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f24287,plain,
spl0_2266,
inference(avatar_split_clause,[],[f2997,f24285]) ).
fof(f2997,plain,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f752,f1023]) ).
fof(f752,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X75),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f24283,plain,
spl0_2265,
inference(avatar_split_clause,[],[f1654,f24281]) ).
fof(f24281,plain,
( spl0_2265
<=> ! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| ~ c_in(c_Main_Ofinite__Union__1(X26,X0),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).
fof(f1654,axiom,
! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| ~ c_in(c_Main_Ofinite__Union__1(X26,X0),c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f24279,plain,
spl0_2264,
inference(avatar_split_clause,[],[f1653,f24277]) ).
fof(f24277,plain,
( spl0_2264
<=> ! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| c_in(c_Main_Ofinite__Union__1(X26,X0),X26,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).
fof(f1653,axiom,
! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(tc_set(X0)))
| c_in(c_Main_Ofinite__Union__1(X26,X0),X26,tc_set(X0))
| c_in(c_Union(X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f24275,plain,
spl0_2263,
inference(avatar_split_clause,[],[f1246,f24273]) ).
fof(f24273,plain,
( spl0_2263
<=> ! [X24,X11,X0,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| ~ c_less(c_1,X3,X0)
| c_Nat_Opower(X3,X11,X0) != c_Nat_Opower(X3,X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).
fof(f1246,axiom,
! [X3,X0,X11,X24] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| ~ c_less(c_1,X3,X0)
| c_Nat_Opower(X3,X11,X0) != c_Nat_Opower(X3,X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f24271,plain,
spl0_2262,
inference(avatar_split_clause,[],[f1221,f24269]) ).
fof(f24269,plain,
( spl0_2262
<=> ! [X12,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_uminus(c_Nat_Opower(X12,X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).
fof(f1221,axiom,
! [X0,X11,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_uminus(c_Nat_Opower(X12,X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f24267,plain,
spl0_2261,
inference(avatar_split_clause,[],[f1214,f24265]) ).
fof(f24265,plain,
( spl0_2261
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| c_lessequals(X12,c_0,X0)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).
fof(f1214,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X12
| c_lessequals(X12,c_0,X0)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f24263,plain,
spl0_2260,
inference(avatar_split_clause,[],[f867,f24261]) ).
fof(f24261,plain,
( spl0_2260
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).
fof(f867,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f24259,plain,
spl0_2259,
inference(avatar_split_clause,[],[f866,f24257]) ).
fof(f24257,plain,
( spl0_2259
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).
fof(f866,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_less(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f24255,plain,
spl0_2258,
inference(avatar_split_clause,[],[f863,f24253]) ).
fof(f24253,plain,
( spl0_2258
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).
fof(f863,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f24251,plain,
spl0_2257,
inference(avatar_split_clause,[],[f862,f24249]) ).
fof(f24249,plain,
( spl0_2257
<=> ! [X34,X16,X3] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).
fof(f862,axiom,
! [X3,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_Numeral_Onumber__of(X34,X16),X16)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f24247,plain,
( spl0_2256
| ~ spl0_29
| ~ spl0_1474
| ~ spl0_2080 ),
inference(avatar_split_clause,[],[f19892,f19797,f11919,f3365,f24245]) ).
fof(f3365,plain,
( spl0_29
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f19892,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(tc_IntDef_Oint)
| c_lessequals(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint) )
| ~ spl0_1474
| ~ spl0_2080 ),
inference(resolution,[],[f19798,f11920]) ).
fof(f24243,plain,
spl0_2255,
inference(avatar_split_clause,[],[f856,f24241]) ).
fof(f24241,plain,
( spl0_2255
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2255])]) ).
fof(f856,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f24239,plain,
spl0_2254,
inference(avatar_split_clause,[],[f855,f24237]) ).
fof(f24237,plain,
( spl0_2254
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2254])]) ).
fof(f855,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_less(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f24235,plain,
spl0_2253,
inference(avatar_split_clause,[],[f840,f24233]) ).
fof(f24233,plain,
( spl0_2253
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).
fof(f840,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16)
| c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f24231,plain,
spl0_2252,
inference(avatar_split_clause,[],[f839,f24229]) ).
fof(f24229,plain,
( spl0_2252
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).
fof(f839,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ c_lessequals(c_Numeral_Onumber__of(X34,X16),c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_Numeral_Onumber__of(X34,X16),X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f24227,plain,
spl0_2251,
inference(avatar_split_clause,[],[f770,f24225]) ).
fof(f24225,plain,
( spl0_2251
<=> ! [X34,X33] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).
fof(f770,axiom,
! [X34,X33] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X33,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f24223,plain,
spl0_2250,
inference(avatar_split_clause,[],[f649,f24221]) ).
fof(f24221,plain,
( spl0_2250
<=> ! [X0,X12,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Oset(c_List_Oremove1(X12,X39,X0),X0) = c_minus(c_List_Oset(X39,X0),c_insert(X12,c_emptyset,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f649,axiom,
! [X39,X0,X12] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Oset(c_List_Oremove1(X12,X39,X0),X0) = c_minus(c_List_Oset(X39,X0),c_insert(X12,c_emptyset,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f24219,plain,
spl0_2249,
inference(avatar_split_clause,[],[f168,f24217]) ).
fof(f24217,plain,
( spl0_2249
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMin(X26,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f168,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(c_Finite__Set_OMin(X26,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f24215,plain,
spl0_2248,
inference(avatar_split_clause,[],[f150,f24213]) ).
fof(f24213,plain,
( spl0_2248
<=> ! [X0,X12,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMax(X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f150,axiom,
! [X0,X26,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X12,X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_lessequals(X12,c_Finite__Set_OMax(X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f23959,plain,
( ~ spl0_33
| spl0_2247
| ~ spl0_1751
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f19618,f19467,f14522,f23957,f3385]) ).
fof(f23957,plain,
( spl0_2247
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).
fof(f14522,plain,
( spl0_1751
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f19467,plain,
( spl0_2079
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f19618,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X0,X1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1751
| ~ spl0_2079 ),
inference(resolution,[],[f19468,f14523]) ).
fof(f14523,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16)
| c_lessequals(X12,X35,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1751 ),
inference(avatar_component_clause,[],[f14522]) ).
fof(f19468,plain,
( ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ spl0_2079 ),
inference(avatar_component_clause,[],[f19467]) ).
fof(f23800,plain,
( spl0_2246
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2231 ),
inference(avatar_split_clause,[],[f23644,f23641,f19111,f9305,f9280,f23798]) ).
fof(f23798,plain,
( spl0_2246
<=> ! [X40,X0,X10,X39] :
( c_append(c_List_Orev(X40,X0),c_List_Oreplicate(c_1,X10,X0),X0) = X39
| c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f23641,plain,
( spl0_2231
<=> ! [X40,X0,X10,X39] :
( c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0)
| c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) = X39 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).
fof(f23644,plain,
( ! [X40,X10,X0,X39] :
( c_append(c_List_Orev(X40,X0),c_List_Oreplicate(c_1,X10,X0),X0) = X39
| c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0) )
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2231 ),
inference(forward_demodulation,[],[f23642,f19137]) ).
fof(f23642,plain,
( ! [X40,X10,X0,X39] :
( c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0)
| c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) = X39 )
| ~ spl0_2231 ),
inference(avatar_component_clause,[],[f23641]) ).
fof(f23768,plain,
( spl0_2245
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_2228 ),
inference(avatar_split_clause,[],[f23631,f23628,f11072,f3525,f23766]) ).
fof(f23766,plain,
( spl0_2245
<=> ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).
fof(f23628,plain,
( spl0_2228
<=> ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2228])]) ).
fof(f23631,plain,
( ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_2228 ),
inference(forward_demodulation,[],[f23629,f11495]) ).
fof(f23629,plain,
( ! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_2228 ),
inference(avatar_component_clause,[],[f23628]) ).
fof(f23708,plain,
spl0_2244,
inference(avatar_split_clause,[],[f3136,f23706]) ).
fof(f23706,plain,
( spl0_2244
<=> ! [X75] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).
fof(f3136,plain,
! [X75] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2961,f2814]) ).
fof(f2814,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f910,f1438]) ).
fof(f910,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2961,plain,
! [X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,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(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f766,f1438]) ).
fof(f766,axiom,
! [X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f23704,plain,
spl0_2243,
inference(avatar_split_clause,[],[f2967,f23702]) ).
fof(f23702,plain,
( spl0_2243
<=> ! [X38,X0,X19] :
( ~ c_in(X38,X19,tc_prod(X0,X0))
| c_in(X38,c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f2967,plain,
! [X38,X0,X19] :
( ~ c_in(X38,X19,tc_prod(X0,X0))
| c_in(X38,c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
inference(definition_unfolding,[],[f1740,f1610]) ).
fof(f1740,axiom,
! [X38,X0,X19] :
( ~ c_in(X38,X19,tc_prod(X0,X0))
| c_in(X38,c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f23688,plain,
spl0_2242,
inference(avatar_split_clause,[],[f2965,f23686]) ).
fof(f23686,plain,
( spl0_2242
<=> ! [X39,X0,X40] :
( ~ c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).
fof(f2965,plain,
! [X40,X39,X0] :
( ~ c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X39,X0),X0),c_List_Oset(X40,X0),X0,X0) ),
inference(definition_unfolding,[],[f451,f1267]) ).
fof(f451,axiom,
! [X40,X39,X0] :
( ~ c_List_Odistinct(c_append(X39,X40,X0),X0)
| c_emptyset = c_inter(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f23684,plain,
spl0_2241,
inference(avatar_split_clause,[],[f2916,f23682]) ).
fof(f23682,plain,
( spl0_2241
<=> ! [X0,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_uminus(c_Numeral_Onumber__of(X33,X0),X0),X35,X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f2916,plain,
! [X0,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_uminus(c_Numeral_Onumber__of(X33,X0),X0),X35,X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0),X35,X0) ),
inference(definition_unfolding,[],[f1059,f1023]) ).
fof(f1059,axiom,
! [X0,X35,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_uminus(c_Numeral_Onumber__of(X33,X0),X0),X35,X0) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X33),X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f23680,plain,
spl0_2240,
inference(avatar_split_clause,[],[f2890,f23678]) ).
fof(f23678,plain,
( spl0_2240
<=> ! [X40,X14,X12,X39] : c_append(c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14),X40,X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,X40,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f2890,plain,
! [X40,X39,X14,X12] : c_append(c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14),X40,X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,X40,X14),X14),
inference(definition_unfolding,[],[f481,f479,f479]) ).
fof(f479,axiom,
! [X39,X0,X12] : c_List_Oitrev(X39,X12,X0) = c_append(c_List_Orev(X39,X0),X12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f481,axiom,
! [X40,X39,X14,X12] : c_List_Oitrev(c_List_Olist_OCons(X12,X39,X14),X40,X14) = c_List_Oitrev(X39,c_List_Olist_OCons(X12,X40,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f23676,plain,
spl0_2239,
inference(avatar_split_clause,[],[f1678,f23674]) ).
fof(f23674,plain,
( spl0_2239
<=> ! [X0,X39,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f1678,axiom,
! [X39,X0,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f23672,plain,
spl0_2238,
inference(avatar_split_clause,[],[f1677,f23670]) ).
fof(f23670,plain,
( spl0_2238
<=> ! [X0,X39,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(c_List_Olist_ONil,X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2238])]) ).
fof(f1677,axiom,
! [X39,X0,X19] :
( c_List_Olist_ONil = X39
| ~ c_in(c_Pair(c_List_Olist_ONil,X39,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olistrel(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f23668,plain,
spl0_2237,
inference(avatar_split_clause,[],[f1016,f23666]) ).
fof(f23666,plain,
( spl0_2237
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_Numeral_Onumber__of(X12,X0) = c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
fof(f1016,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_Numeral_Onumber__of(X12,X0) = c_HOL_Oabs(c_Numeral_Onumber__of(X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f23664,plain,
spl0_2236,
inference(avatar_split_clause,[],[f758,f23662]) ).
fof(f23662,plain,
( spl0_2236
<=> ! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X75),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).
fof(f758,axiom,
! [X34,X75] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X75),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f23660,plain,
spl0_2235,
inference(avatar_split_clause,[],[f694,f23658]) ).
fof(f23658,plain,
( spl0_2235
<=> ! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X9,tc_nat),X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).
fof(f694,axiom,
! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_minus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X9,tc_nat),X50,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f23656,plain,
spl0_2234,
inference(avatar_split_clause,[],[f690,f23654]) ).
fof(f23654,plain,
( spl0_2234
<=> ! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X50,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f690,axiom,
! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(X23,c_minus(X50,X9,tc_nat),tc_nat) = c_minus(c_plus(X23,X50,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f23652,plain,
spl0_2233,
inference(avatar_split_clause,[],[f689,f23650]) ).
fof(f23650,plain,
( spl0_2233
<=> ! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(c_minus(X50,X9,tc_nat),X23,tc_nat) = c_minus(c_plus(X50,X23,tc_nat),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).
fof(f689,axiom,
! [X50,X9,X23] :
( ~ c_lessequals(X9,X50,tc_nat)
| c_plus(c_minus(X50,X9,tc_nat),X23,tc_nat) = c_minus(c_plus(X50,X23,tc_nat),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f23648,plain,
( ~ spl0_33
| spl0_2232
| ~ spl0_1752
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f19617,f19467,f14527,f23646,f3385]) ).
fof(f23646,plain,
( spl0_2232
<=> ! [X0,X1] : c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).
fof(f14527,plain,
( spl0_1752
<=> ! [X16,X12,X35,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X10,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f19617,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X1,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1752
| ~ spl0_2079 ),
inference(resolution,[],[f19468,f14528]) ).
fof(f14528,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16)
| c_lessequals(X10,X35,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1752 ),
inference(avatar_component_clause,[],[f14527]) ).
fof(f23643,plain,
spl0_2231,
inference(avatar_split_clause,[],[f620,f23641]) ).
fof(f620,axiom,
! [X40,X10,X0,X39] :
( c_List_Olist_OCons(X10,X40,X0) != c_List_Orev(X39,X0)
| c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) = X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f23639,plain,
spl0_2230,
inference(avatar_split_clause,[],[f608,f23637]) ).
fof(f23637,plain,
( spl0_2230
<=> ! [X12,X39,X14] :
( c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Oremdups(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).
fof(f608,axiom,
! [X39,X14,X12] :
( c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Oremdups(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f23635,plain,
spl0_2229,
inference(avatar_split_clause,[],[f511,f23633]) ).
fof(f23633,plain,
( spl0_2229
<=> ! [X29,X52,X0,X19] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X29,X52,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).
fof(f511,axiom,
! [X29,X0,X19,X52] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X29,X52,X0),tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f23630,plain,
spl0_2228,
inference(avatar_split_clause,[],[f347,f23628]) ).
fof(f347,axiom,
! [X1] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X1,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f23626,plain,
spl0_2227,
inference(avatar_split_clause,[],[f113,f23624]) ).
fof(f23624,plain,
( spl0_2227
<=> ! [X25,X1,X3] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(X3,X1,tc_nat) = c_div(c_times(X3,X25,tc_nat),c_times(X1,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2227])]) ).
fof(f113,axiom,
! [X3,X1,X25] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(X3,X1,tc_nat) = c_div(c_times(X3,X25,tc_nat),c_times(X1,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f23622,plain,
spl0_2226,
inference(avatar_split_clause,[],[f112,f23620]) ).
fof(f23620,plain,
( spl0_2226
<=> ! [X25,X1,X3] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(c_times(X25,X3,tc_nat),c_times(X25,X1,tc_nat),tc_nat) = c_div(X3,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).
fof(f112,axiom,
! [X3,X1,X25] :
( ~ c_less(c_0,X25,tc_nat)
| c_div(c_times(X25,X3,tc_nat),c_times(X25,X1,tc_nat),tc_nat) = c_div(X3,X1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f23296,plain,
( spl0_2225
| ~ spl0_1253
| ~ spl0_2222 ),
inference(avatar_split_clause,[],[f23090,f22789,f10255,f23294]) ).
fof(f23294,plain,
( spl0_2225
<=> ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f10255,plain,
( spl0_1253
<=> ! [X35] :
( ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X35) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f22789,plain,
( spl0_2222
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).
fof(f23090,plain,
( ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(c_0,X0,tc_IntDef_Oint))
| ~ spl0_1253
| ~ spl0_2222 ),
inference(resolution,[],[f22790,f10256]) ).
fof(f10256,plain,
( ! [X35] :
( ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X35) )
| ~ spl0_1253 ),
inference(avatar_component_clause,[],[f10255]) ).
fof(f22790,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_2222 ),
inference(avatar_component_clause,[],[f22789]) ).
fof(f22966,plain,
( spl0_2224
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2194 ),
inference(avatar_split_clause,[],[f22446,f22442,f19111,f9305,f9280,f22964]) ).
fof(f22964,plain,
( spl0_2224
<=> ! [X10,X40,X0,X12,X39] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X10 = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f22442,plain,
( spl0_2194
<=> ! [X10,X40,X0,X12,X39] :
( X10 = X12
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f22446,plain,
( ! [X40,X10,X0,X39,X12] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X10 = X12 )
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2194 ),
inference(forward_demodulation,[],[f22445,f19137]) ).
fof(f22445,plain,
( ! [X40,X39,X0,X10,X12] :
( c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0)
| X10 = X12 )
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2194 ),
inference(forward_demodulation,[],[f22443,f19137]) ).
fof(f22443,plain,
( ! [X40,X10,X39,X0,X12] :
( X10 = X12
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) )
| ~ spl0_2194 ),
inference(avatar_component_clause,[],[f22442]) ).
fof(f22962,plain,
( spl0_2223
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2193 ),
inference(avatar_split_clause,[],[f22440,f22436,f19111,f9305,f9280,f22960]) ).
fof(f22960,plain,
( spl0_2223
<=> ! [X10,X40,X0,X12,X39] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X39 = X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).
fof(f22436,plain,
( spl0_2193
<=> ! [X40,X0,X12,X10,X39] :
( X39 = X40
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f22440,plain,
( ! [X40,X10,X0,X39,X12] :
( c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0) != c_append(X39,c_List_Oreplicate(c_1,X12,X0),X0)
| X39 = X40 )
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2193 ),
inference(forward_demodulation,[],[f22439,f19137]) ).
fof(f22439,plain,
( ! [X40,X39,X0,X10,X12] :
( c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Oreplicate(c_1,X10,X0),X0)
| X39 = X40 )
| ~ spl0_1131
| ~ spl0_1137
| ~ spl0_2056
| ~ spl0_2193 ),
inference(forward_demodulation,[],[f22437,f19137]) ).
fof(f22437,plain,
( ! [X40,X39,X0,X10,X12] :
( X39 = X40
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) )
| ~ spl0_2193 ),
inference(avatar_component_clause,[],[f22436]) ).
fof(f22791,plain,
( ~ spl0_33
| spl0_2222
| ~ spl0_1749
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f19611,f19467,f14514,f22789,f3385]) ).
fof(f14514,plain,
( spl0_1749
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f19611,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1749
| ~ spl0_2079 ),
inference(resolution,[],[f19468,f14515]) ).
fof(f14515,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16)
| c_lessequals(X12,X10,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1749 ),
inference(avatar_component_clause,[],[f14514]) ).
fof(f22576,plain,
( spl0_2221
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2220 ),
inference(avatar_split_clause,[],[f22572,f22568,f13448,f13139,f8657,f3868,f22574]) ).
fof(f22568,plain,
( spl0_2220
<=> ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,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_2220])]) ).
fof(f22572,plain,
( ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2220 ),
inference(forward_demodulation,[],[f22571,f14217]) ).
fof(f22571,plain,
( ! [X11] : c_plus(X11,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,X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2220 ),
inference(forward_demodulation,[],[f22569,f14217]) ).
fof(f22569,plain,
( ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2220 ),
inference(avatar_component_clause,[],[f22568]) ).
fof(f22570,plain,
spl0_2220,
inference(avatar_split_clause,[],[f3061,f22568]) ).
fof(f22566,plain,
spl0_2219,
inference(avatar_split_clause,[],[f2991,f22564]) ).
fof(f22564,plain,
( spl0_2219
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,X26,X0)
| c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f2991,plain,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,X26,X0)
| c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
inference(definition_unfolding,[],[f1502,f1267]) ).
fof(f1502,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,X26,X0)
| c_in(X25,c_inter(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f22555,plain,
spl0_2218,
inference(avatar_split_clause,[],[f2986,f22553]) ).
fof(f22553,plain,
( spl0_2218
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f2986,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f1036,f1023]) ).
fof(f1036,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f22551,plain,
spl0_2217,
inference(avatar_split_clause,[],[f2985,f22549]) ).
fof(f22549,plain,
( spl0_2217
<=> ! [X0,X12,X10] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f2985,plain,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f1035,f1023]) ).
fof(f1035,axiom,
! [X10,X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(X10,X0) != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f22547,plain,
spl0_2216,
inference(avatar_split_clause,[],[f2940,f22545]) ).
fof(f22545,plain,
( spl0_2216
<=> ! [X11,X0,X23,X39] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(X39,X23,X0) = c_List_Onth(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X23,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f2940,plain,
! [X39,X0,X11,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(X39,X23,X0) = c_List_Onth(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),X23,X0) ),
inference(definition_unfolding,[],[f597,f660]) ).
fof(f597,axiom,
! [X39,X0,X11,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(c_List_Otake(X11,X39,X0),X23,X0) = c_List_Onth(X39,X23,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f22543,plain,
spl0_2215,
inference(avatar_split_clause,[],[f2913,f22541]) ).
fof(f22541,plain,
( spl0_2215
<=> ! [X34,X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).
fof(f2913,plain,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0) ),
inference(definition_unfolding,[],[f1014,f1023]) ).
fof(f1014,axiom,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(X33)),X0) = c_minus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f22539,plain,
spl0_2214,
inference(avatar_split_clause,[],[f1568,f22537]) ).
fof(f22537,plain,
( spl0_2214
<=> ! [X0,X12,X26,X30] :
( ~ c_in(X12,X30,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f1568,axiom,
! [X0,X26,X12,X30] :
( ~ c_in(X12,X30,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f22535,plain,
spl0_2213,
inference(avatar_split_clause,[],[f1541,f22533]) ).
fof(f22533,plain,
( spl0_2213
<=> ! [X0,X30,X2,X26] :
( ~ c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(X26,X2,tc_set(X0))
| c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f1541,axiom,
! [X2,X0,X26,X30] :
( ~ c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(X26,X2,tc_set(X0))
| c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f22531,plain,
spl0_2212,
inference(avatar_split_clause,[],[f1491,f22529]) ).
fof(f22529,plain,
( spl0_2212
<=> ! [X0,X12,X26,X30] :
( c_in(X12,X26,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(X26,c_insert(X12,X30,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f1491,axiom,
! [X0,X26,X12,X30] :
( c_in(X12,X26,X0)
| c_minus(X26,X30,tc_set(X0)) = c_minus(X26,c_insert(X12,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f22527,plain,
spl0_2211,
inference(avatar_split_clause,[],[f1231,f22525]) ).
fof(f22525,plain,
( spl0_2211
<=> ! [X12,X33] :
( c_less(c_0,X12,tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f1231,axiom,
! [X12,X33] :
( c_less(c_0,X12,tc_nat)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f22523,plain,
spl0_2210,
inference(avatar_split_clause,[],[f1223,f22521]) ).
fof(f22521,plain,
( spl0_2210
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f1223,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f22519,plain,
spl0_2209,
inference(avatar_split_clause,[],[f1220,f22517]) ).
fof(f22517,plain,
( spl0_2209
<=> ! [X12,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_Nat_Opower(X12,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f1220,axiom,
! [X0,X11,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Nat_Opower(c_uminus(X12,X0),X11,X0) = c_Nat_Opower(X12,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f22515,plain,
( spl0_2208
| ~ spl0_1253
| ~ spl0_2187 ),
inference(avatar_split_clause,[],[f22463,f22412,f10255,f22513]) ).
fof(f22513,plain,
( spl0_2208
<=> ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f22412,plain,
( spl0_2187
<=> ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f22463,plain,
( ! [X0] : c_0 = c_IntDef_Onat(c_Orderings_Omin(X0,c_0,tc_IntDef_Oint))
| ~ spl0_1253
| ~ spl0_2187 ),
inference(resolution,[],[f22413,f10256]) ).
fof(f22413,plain,
( ! [X0,X1] : c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ spl0_2187 ),
inference(avatar_component_clause,[],[f22412]) ).
fof(f22511,plain,
spl0_2207,
inference(avatar_split_clause,[],[f1217,f22509]) ).
fof(f22509,plain,
( spl0_2207
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f1217,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X33,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f22507,plain,
spl0_2206,
inference(avatar_split_clause,[],[f971,f22505]) ).
fof(f22505,plain,
( spl0_2206
<=> ! [X9,X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).
fof(f971,axiom,
! [X11,X9,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f22503,plain,
spl0_2205,
inference(avatar_split_clause,[],[f968,f22501]) ).
fof(f22501,plain,
( spl0_2205
<=> ! [X9,X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f968,axiom,
! [X11,X9,X24] :
( ~ c_less(X24,X11,tc_nat)
| ~ c_less(c_0,X9,tc_nat)
| c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f22499,plain,
spl0_2204,
inference(avatar_split_clause,[],[f963,f22497]) ).
fof(f22497,plain,
( spl0_2204
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f963,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f22495,plain,
spl0_2203,
inference(avatar_split_clause,[],[f960,f22493]) ).
fof(f22493,plain,
( spl0_2203
<=> ! [X9,X11,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f960,axiom,
! [X11,X9,X24] :
( ~ c_less(c_0,X9,tc_nat)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f22491,plain,
spl0_2202,
inference(avatar_split_clause,[],[f823,f22489]) ).
fof(f22489,plain,
( spl0_2202
<=> ! [X34,X16,X1] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_uminus(X1,X16) != c_Numeral_Onumber__of(X34,X16)
| c_uminus(c_Numeral_Onumber__of(X34,X16),X16) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f823,axiom,
! [X1,X16,X34] :
( ~ class_Numeral_Onumber(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_uminus(X1,X16) != c_Numeral_Onumber__of(X34,X16)
| c_uminus(c_Numeral_Onumber__of(X34,X16),X16) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f22487,plain,
spl0_2201,
inference(avatar_split_clause,[],[f724,f22485]) ).
fof(f22485,plain,
( spl0_2201
<=> ! [X12,X10] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f724,axiom,
! [X10,X12] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f22483,plain,
spl0_2200,
inference(avatar_split_clause,[],[f723,f22481]) ).
fof(f22481,plain,
( spl0_2200
<=> ! [X12,X10] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f723,axiom,
! [X10,X12] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_nat),c_Numeral_Onumber__of(X10,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_nat),c_Numeral_Onumber__of(X12,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f22479,plain,
spl0_2199,
inference(avatar_split_clause,[],[f615,f22477]) ).
fof(f22477,plain,
( spl0_2199
<=> ! [X10,X14,X12,X39] :
( X10 = X12
| c_List_Oremove1(X12,c_List_Olist_OCons(X10,X39,X14),X14) = c_List_Olist_OCons(X10,c_List_Oremove1(X12,X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f615,axiom,
! [X10,X39,X14,X12] :
( X10 = X12
| c_List_Oremove1(X12,c_List_Olist_OCons(X10,X39,X14),X14) = c_List_Olist_OCons(X10,c_List_Oremove1(X12,X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f22475,plain,
spl0_2198,
inference(avatar_split_clause,[],[f598,f22473]) ).
fof(f22473,plain,
( spl0_2198
<=> ! [X50,X9,X23] :
( ~ c_less(c_plus(X23,X9,tc_nat),X50,tc_nat)
| c_plus(X23,X9,tc_nat) = c_List_Onth(c_List_Oupt(X23,X50),X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f598,axiom,
! [X50,X9,X23] :
( ~ c_less(c_plus(X23,X9,tc_nat),X50,tc_nat)
| c_plus(X23,X9,tc_nat) = c_List_Onth(c_List_Oupt(X23,X50),X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f22458,plain,
spl0_2197,
inference(avatar_split_clause,[],[f591,f22456]) ).
fof(f22456,plain,
( spl0_2197
<=> ! [X11,X40,X0,X39] : c_List_Onth(c_append(X39,X40,X0),c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),X0) = c_List_Onth(X40,X11,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f591,axiom,
! [X40,X39,X0,X11] : c_List_Onth(c_append(X39,X40,X0),c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),X0) = c_List_Onth(X40,X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f22454,plain,
spl0_2196,
inference(avatar_split_clause,[],[f524,f22452]) ).
fof(f22452,plain,
( spl0_2196
<=> ! [X51,X14,X56,X3] :
( c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist__inter(X51,X56,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f524,axiom,
! [X51,X3,X56,X14] :
( c_in(X3,c_List_Oset(X56,X14),X14)
| c_List_Olist__inter(c_List_Olist_OCons(X3,X51,X14),X56,X14) = c_List_Olist__inter(X51,X56,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f22450,plain,
spl0_2195,
inference(avatar_split_clause,[],[f493,f22448]) ).
fof(f22448,plain,
( spl0_2195
<=> ! [X39,X0,X40] : c_Nat_Osize(c_append(X39,X40,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f493,axiom,
! [X40,X39,X0] : c_Nat_Osize(c_append(X39,X40,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_Nat_Osize(X40,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f22444,plain,
spl0_2194,
inference(avatar_split_clause,[],[f411,f22442]) ).
fof(f411,axiom,
! [X40,X10,X39,X0,X12] :
( X10 = X12
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f22438,plain,
spl0_2193,
inference(avatar_split_clause,[],[f410,f22436]) ).
fof(f410,axiom,
! [X40,X39,X0,X10,X12] :
( X39 = X40
| c_append(X39,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) != c_append(X40,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f22434,plain,
spl0_2192,
inference(avatar_split_clause,[],[f375,f22432]) ).
fof(f22432,plain,
( spl0_2192
<=> ! [X12,X10] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f375,axiom,
! [X10,X12] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f22430,plain,
spl0_2191,
inference(avatar_split_clause,[],[f374,f22428]) ).
fof(f22428,plain,
( spl0_2191
<=> ! [X12,X10] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f374,axiom,
! [X10,X12] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X12,tc_IntDef_Oint),c_Numeral_Onumber__of(X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X10,tc_IntDef_Oint),c_Numeral_Onumber__of(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f22426,plain,
spl0_2190,
inference(avatar_split_clause,[],[f367,f22424]) ).
fof(f22424,plain,
( spl0_2190
<=> ! [X1,X3] :
( c_0 = X3
| c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f367,axiom,
! [X3,X1] :
( c_0 = X3
| c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f22422,plain,
spl0_2189,
inference(avatar_split_clause,[],[f366,f22420]) ).
fof(f22420,plain,
( spl0_2189
<=> ! [X1,X3] :
( c_0 = X3
| c_div(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f366,axiom,
! [X3,X1] :
( c_0 = X3
| c_div(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_plus(c_div(X1,X3,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f22418,plain,
spl0_2188,
inference(avatar_split_clause,[],[f186,f22416]) ).
fof(f22416,plain,
( spl0_2188
<=> ! [X16,X26] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_lessequals(c_Finite__Set_OMin(X26,X16),c_Finite__Set_OMax(X26,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).
fof(f186,axiom,
! [X26,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X16))
| c_lessequals(c_Finite__Set_OMin(X26,X16),c_Finite__Set_OMax(X26,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f22414,plain,
( ~ spl0_33
| spl0_2187
| ~ spl0_1750
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f19610,f19467,f14518,f22412,f3385]) ).
fof(f14518,plain,
( spl0_1750
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f19610,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint)
| ~ class_Orderings_Olinorder(tc_IntDef_Oint) )
| ~ spl0_1750
| ~ spl0_2079 ),
inference(resolution,[],[f19468,f14519]) ).
fof(f14519,plain,
( ! [X10,X16,X35,X12] :
( ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16)
| c_lessequals(X12,X35,X16)
| ~ class_Orderings_Olinorder(X16) )
| ~ spl0_1750 ),
inference(avatar_component_clause,[],[f14518]) ).
fof(f22410,plain,
spl0_2186,
inference(avatar_split_clause,[],[f182,f22408]) ).
fof(f22408,plain,
( spl0_2186
<=> ! [X6,X0,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f182,axiom,
! [X0,X6,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f22406,plain,
spl0_2185,
inference(avatar_split_clause,[],[f12,f22404]) ).
fof(f22404,plain,
( spl0_2185
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f12,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Otimes(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono_0) ).
fof(f22402,plain,
spl0_2184,
inference(avatar_split_clause,[],[f11,f22400]) ).
fof(f22400,plain,
( spl0_2184
<=> ! [X4,X0,X3,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X4,X2,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f11,axiom,
! [X2,X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X4,X2,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono4_0) ).
fof(f22398,plain,
spl0_2183,
inference(avatar_split_clause,[],[f10,f22396]) ).
fof(f22396,plain,
( spl0_2183
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X2,X4,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f10,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__times(X3,X4,X0),c_times(X2,X4,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__mono3_0) ).
fof(f22394,plain,
spl0_2182,
inference(avatar_split_clause,[],[f6,f22392]) ).
fof(f22392,plain,
( spl0_2182
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f6,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Oplus(X0)
| ~ c_lessequals(X2,X4,tc_set(X0))
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono_0) ).
fof(f22390,plain,
spl0_2181,
inference(avatar_split_clause,[],[f5,f22388]) ).
fof(f22388,plain,
( spl0_2181
<=> ! [X4,X0,X3,X2] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X4,X2,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f5,axiom,
! [X2,X3,X0,X4] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X4,X2,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono4_0) ).
fof(f22386,plain,
spl0_2180,
inference(avatar_split_clause,[],[f4,f22384]) ).
fof(f22384,plain,
( spl0_2180
<=> ! [X4,X0,X3,X2] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X2,X4,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f4,axiom,
! [X2,X3,X0,X4] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X3,X2,X0)
| c_lessequals(c_SetsAndFunctions_Oelt__set__plus(X3,X4,X0),c_plus(X2,X4,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__mono3_0) ).
fof(f22098,plain,
( ~ spl0_965
| spl0_2179
| ~ spl0_1751
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f19302,f19214,f14522,f22096,f8447]) ).
fof(f19214,plain,
( spl0_2067
<=> ! [X0] : c_lessequals(X0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f19302,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X0,X1,t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) )
| ~ spl0_1751
| ~ spl0_2067 ),
inference(resolution,[],[f19215,f14523]) ).
fof(f19215,plain,
( ! [X0] : c_lessequals(X0,X0,t_b)
| ~ spl0_2067 ),
inference(avatar_component_clause,[],[f19214]) ).
fof(f21871,plain,
( ~ spl0_965
| spl0_2178
| ~ spl0_1752
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f19301,f19214,f14527,f21869,f8447]) ).
fof(f19301,plain,
( ! [X0,X1] :
( c_lessequals(X0,c_Orderings_Omax(X1,X0,t_b),t_b)
| ~ class_Orderings_Olinorder(t_b) )
| ~ spl0_1752
| ~ spl0_2067 ),
inference(resolution,[],[f19215,f14528]) ).
fof(f21574,plain,
( ~ spl0_965
| spl0_2177
| ~ spl0_1749
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f19297,f19214,f14514,f21572,f8447]) ).
fof(f19297,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,t_b),X0,t_b)
| ~ class_Orderings_Olinorder(t_b) )
| ~ spl0_1749
| ~ spl0_2067 ),
inference(resolution,[],[f19215,f14515]) ).
fof(f21425,plain,
spl0_2176,
inference(avatar_split_clause,[],[f3219,f21423]) ).
fof(f21423,plain,
( spl0_2176
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f3219,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3016,f1008]) ).
fof(f1008,axiom,
! [X10] : c_Numeral_Obin__add(c_Numeral_OPls,X10) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f3016,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f207,f1023]) ).
fof(f207,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f21421,plain,
spl0_2175,
inference(avatar_split_clause,[],[f3217,f21419]) ).
fof(f21419,plain,
( spl0_2175
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f3217,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3014,f1008]) ).
fof(f3014,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0) ),
inference(definition_unfolding,[],[f219,f1023]) ).
fof(f219,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f21417,plain,
spl0_2174,
inference(avatar_split_clause,[],[f3209,f21415]) ).
fof(f21415,plain,
( spl0_2174
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f3209,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3008,f1008]) ).
fof(f3008,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f206,f1023]) ).
fof(f206,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f21413,plain,
spl0_2173,
inference(avatar_split_clause,[],[f3207,f21411]) ).
fof(f21411,plain,
( spl0_2173
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f3207,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X12),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3006,f1008]) ).
fof(f3006,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X12)),X0),X0) ),
inference(definition_unfolding,[],[f218,f1023]) ).
fof(f218,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X12)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f21409,plain,
spl0_2172,
inference(avatar_split_clause,[],[f3175,f21407]) ).
fof(f21407,plain,
( spl0_2172
<=> ! [X0,X10] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f3175,plain,
! [X10,X0] :
( ~ 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2982,f1050]) ).
fof(f2982,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0)
| ~ 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f230,f1023]) ).
fof(f230,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X10,X0)
| ~ 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f21401,plain,
( spl0_2171
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2169 ),
inference(avatar_split_clause,[],[f21393,f21390,f14768,f10066,f9354,f8934,f8815,f8805,f21399]) ).
fof(f21399,plain,
( spl0_2171
<=> ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).
fof(f21390,plain,
( spl0_2169
<=> ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f21393,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2169 ),
inference(forward_demodulation,[],[f21391,f15806]) ).
fof(f21391,plain,
( ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_2169 ),
inference(avatar_component_clause,[],[f21390]) ).
fof(f21397,plain,
( ~ spl0_965
| spl0_2170
| ~ spl0_1750
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f19296,f19214,f14518,f21395,f8447]) ).
fof(f19296,plain,
( ! [X0,X1] :
( c_lessequals(c_Orderings_Omin(X0,X1,t_b),X1,t_b)
| ~ class_Orderings_Olinorder(t_b) )
| ~ spl0_1750
| ~ spl0_2067 ),
inference(resolution,[],[f19215,f14519]) ).
fof(f21392,plain,
spl0_2169,
inference(avatar_split_clause,[],[f3174,f21390]) ).
fof(f3174,plain,
! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2981,f1050]) ).
fof(f2981,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f234,f1023]) ).
fof(f234,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f21388,plain,
spl0_2168,
inference(avatar_split_clause,[],[f3169,f21386]) ).
fof(f21386,plain,
( spl0_2168
<=> ! [X0,X10] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f3169,plain,
! [X10,X0] :
( 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,X10)),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2978,f1050]) ).
fof(f2978,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0)
| 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,X10)),X0),X0) ),
inference(definition_unfolding,[],[f229,f1023]) ).
fof(f229,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X10,X0)
| 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(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f21380,plain,
( spl0_2167
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2166 ),
inference(avatar_split_clause,[],[f21376,f21373,f14768,f10066,f9354,f8934,f8815,f8805,f21378]) ).
fof(f21378,plain,
( spl0_2167
<=> ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f21373,plain,
( spl0_2166
<=> ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
fof(f21376,plain,
( ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OMin),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2166 ),
inference(forward_demodulation,[],[f21374,f15806]) ).
fof(f21374,plain,
( ! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) )
| ~ spl0_2166 ),
inference(avatar_component_clause,[],[f21373]) ).
fof(f21375,plain,
spl0_2166,
inference(avatar_split_clause,[],[f3168,f21373]) ).
fof(f3168,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2977,f1050]) ).
fof(f2977,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
inference(definition_unfolding,[],[f233,f1023]) ).
fof(f233,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f21371,plain,
( spl0_2165
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2164 ),
inference(avatar_split_clause,[],[f21367,f21364,f13464,f3525,f21369]) ).
fof(f21369,plain,
( spl0_2165
<=> ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f21364,plain,
( spl0_2164
<=> ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f21367,plain,
( ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2164 ),
inference(forward_demodulation,[],[f21365,f14284]) ).
fof(f21365,plain,
( ! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2164 ),
inference(avatar_component_clause,[],[f21364]) ).
fof(f21366,plain,
spl0_2164,
inference(avatar_split_clause,[],[f3139,f21364]) ).
fof(f3139,plain,
! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3138,f1050]) ).
fof(f3138,plain,
! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3137,f1048]) ).
fof(f3137,plain,
! [X34] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1167,f1050]) ).
fof(f1167,axiom,
! [X34] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(f21362,plain,
( spl0_2163
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2162 ),
inference(avatar_split_clause,[],[f21340,f21337,f13464,f3525,f21360]) ).
fof(f21360,plain,
( spl0_2163
<=> ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f21337,plain,
( spl0_2162
<=> ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f21340,plain,
( ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_61
| ~ spl0_1695
| ~ spl0_2162 ),
inference(forward_demodulation,[],[f21338,f14284]) ).
fof(f21338,plain,
( ! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2162 ),
inference(avatar_component_clause,[],[f21337]) ).
fof(f21339,plain,
spl0_2162,
inference(avatar_split_clause,[],[f3135,f21337]) ).
fof(f3135,plain,
! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3134,f1050]) ).
fof(f3134,plain,
! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3133,f1048]) ).
fof(f3133,plain,
! [X34] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1166,f1050]) ).
fof(f1166,axiom,
! [X34] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,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(f21334,plain,
( spl0_2161
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2160 ),
inference(avatar_split_clause,[],[f21330,f21327,f14768,f10066,f9354,f8934,f8815,f8805,f21332]) ).
fof(f21332,plain,
( spl0_2161
<=> ! [X34,X0] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_OMin),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f21327,plain,
( spl0_2160
<=> ! [X34,X0] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f21330,plain,
( ! [X0,X34] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_OMin),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_1026
| ~ spl0_1028
| ~ spl0_1056
| ~ spl0_1149
| ~ spl0_1242
| ~ spl0_1802
| ~ spl0_2160 ),
inference(forward_demodulation,[],[f21328,f15806]) ).
fof(f21328,plain,
( ! [X0,X34] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_2160 ),
inference(avatar_component_clause,[],[f21327]) ).
fof(f21329,plain,
spl0_2160,
inference(avatar_split_clause,[],[f3104,f21327]) ).
fof(f3104,plain,
! [X0,X34] :
( c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f2915,f1050]) ).
fof(f2915,plain,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0) ),
inference(definition_unfolding,[],[f226,f1023]) ).
fof(f226,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f21325,plain,
spl0_2159,
inference(avatar_split_clause,[],[f3103,f21323]) ).
fof(f21323,plain,
( spl0_2159
<=> ! [X0,X33] :
( c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f3103,plain,
! [X0,X33] :
( c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X33)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f2914,f1050]) ).
fof(f2914,plain,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = 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,X33)),X0) ),
inference(definition_unfolding,[],[f225,f1023]) ).
fof(f225,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_minus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X33)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f21321,plain,
spl0_2158,
inference(avatar_split_clause,[],[f3065,f21319]) ).
fof(f21319,plain,
( spl0_2158
<=> ! [X11] : c_plus(X11,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),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f3065,plain,
! [X11] : c_plus(X11,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),X11,tc_nat),
inference(forward_demodulation,[],[f3064,f1050]) ).
fof(f3064,plain,
! [X11] : c_plus(X11,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),X11,tc_nat),
inference(forward_demodulation,[],[f3063,f1048]) ).
fof(f3063,plain,
! [X11] : c_plus(X11,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),X11,tc_nat),
inference(forward_demodulation,[],[f3062,f1050]) ).
fof(f3062,plain,
! [X11] : 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),X11,tc_nat) = c_plus(X11,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2886,f3061]) ).
fof(f2886,plain,
! [X11] : 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),X11,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f775,f1438,f1438]) ).
fof(f775,axiom,
! [X11] : 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),X11,tc_nat) = c_Suc(c_Suc(X11)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f21304,plain,
( spl0_2157
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2156 ),
inference(avatar_split_clause,[],[f21300,f21297,f13448,f13139,f8657,f3868,f21302]) ).
fof(f21302,plain,
( spl0_2157
<=> ! [X34] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).
fof(f21297,plain,
( spl0_2156
<=> ! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f21300,plain,
( ! [X34] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2156 ),
inference(forward_demodulation,[],[f21298,f14217]) ).
fof(f21298,plain,
( ! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) )
| ~ spl0_2156 ),
inference(avatar_component_clause,[],[f21297]) ).
fof(f21299,plain,
spl0_2156,
inference(avatar_split_clause,[],[f2960,f21297]) ).
fof(f2960,plain,
! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f717,f1438]) ).
fof(f717,axiom,
! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X34,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X34),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f21295,plain,
spl0_2155,
inference(avatar_split_clause,[],[f2891,f21293]) ).
fof(f21293,plain,
( spl0_2155
<=> ! [X23,X0,X12,X9] : c_List_Oreplicate(c_Orderings_Omin(X23,X9,tc_nat),X12,X0) = c_List_Osublist(c_List_Oreplicate(X9,X12,X0),c_SetInterval_OlessThan(X23,tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f2891,plain,
! [X0,X9,X12,X23] : c_List_Oreplicate(c_Orderings_Omin(X23,X9,tc_nat),X12,X0) = c_List_Osublist(c_List_Oreplicate(X9,X12,X0),c_SetInterval_OlessThan(X23,tc_nat),X0),
inference(definition_unfolding,[],[f669,f660]) ).
fof(f669,axiom,
! [X0,X9,X12,X23] : c_List_Otake(X23,c_List_Oreplicate(X9,X12,X0),X0) = c_List_Oreplicate(c_Orderings_Omin(X23,X9,tc_nat),X12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f21291,plain,
( spl0_2154
| ~ spl0_1811
| ~ spl0_1982 ),
inference(avatar_split_clause,[],[f21241,f18508,f15367,f21289]) ).
fof(f21289,plain,
( spl0_2154
<=> ! [X0] : c_minus(c_0,c_uminus(X0,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f15367,plain,
( spl0_1811
<=> ! [X0] : c_0 = c_plus(X0,c_uminus(X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f18508,plain,
( spl0_1982
<=> ! [X0,X1] : c_minus(c_plus(X0,X1,t_b),X1,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f21241,plain,
( ! [X0] : c_minus(c_0,c_uminus(X0,t_b),t_b) = X0
| ~ spl0_1811
| ~ spl0_1982 ),
inference(superposition,[],[f18509,f15368]) ).
fof(f15368,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,t_b),t_b)
| ~ spl0_1811 ),
inference(avatar_component_clause,[],[f15367]) ).
fof(f18509,plain,
( ! [X0,X1] : c_minus(c_plus(X0,X1,t_b),X1,t_b) = X0
| ~ spl0_1982 ),
inference(avatar_component_clause,[],[f18508]) ).
fof(f21287,plain,
spl0_2153,
inference(avatar_split_clause,[],[f2889,f21285]) ).
fof(f21285,plain,
( spl0_2153
<=> ! [X0,X11,X39] : c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) = c_Nat_Osize(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f2889,plain,
! [X39,X0,X11] : c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) = c_Nat_Osize(c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0),tc_List_Olist(X0)),
inference(definition_unfolding,[],[f505,f660]) ).
fof(f505,axiom,
! [X39,X0,X11] : c_Nat_Osize(c_List_Otake(X11,X39,X0),tc_List_Olist(X0)) = c_Orderings_Omin(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f21283,plain,
spl0_2152,
inference(avatar_split_clause,[],[f2885,f21281]) ).
fof(f21281,plain,
( spl0_2152
<=> ! [X3,X0,X30] : c_Inter(c_insert(X3,X30,tc_set(X0)),X0) = c_Relation_OImage(c_Relation_Odiag(X3,X0),c_Inter(X30,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f2885,plain,
! [X3,X0,X30] : c_Inter(c_insert(X3,X30,tc_set(X0)),X0) = c_Relation_OImage(c_Relation_Odiag(X3,X0),c_Inter(X30,X0),X0,X0),
inference(definition_unfolding,[],[f1517,f1267]) ).
fof(f1517,axiom,
! [X3,X0,X30] : c_Inter(c_insert(X3,X30,tc_set(X0)),X0) = c_inter(X3,c_Inter(X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f21278,plain,
( spl0_2151
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2150 ),
inference(avatar_split_clause,[],[f21274,f21271,f13448,f13139,f8657,f3868,f21276]) ).
fof(f21276,plain,
( spl0_2151
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f21271,plain,
( spl0_2150
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f21274,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2150 ),
inference(forward_demodulation,[],[f21272,f14217]) ).
fof(f21272,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16)
| ~ spl0_2150 ),
inference(avatar_component_clause,[],[f21271]) ).
fof(f21273,plain,
spl0_2150,
inference(avatar_split_clause,[],[f2884,f21271]) ).
fof(f2884,plain,
! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16),
inference(definition_unfolding,[],[f100,f1438]) ).
fof(f100,axiom,
! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OLeaf(X3,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f21268,plain,
( spl0_2149
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2148 ),
inference(avatar_split_clause,[],[f21264,f21261,f13448,f13139,f8657,f3868,f21266]) ).
fof(f21266,plain,
( spl0_2149
<=> ! [X23,X0,X9,X16] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f21261,plain,
( spl0_2148
<=> ! [X23,X0,X9,X16] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f21264,plain,
( ! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2148 ),
inference(forward_demodulation,[],[f21262,f14217]) ).
fof(f21262,plain,
( ! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16)
| ~ spl0_2148 ),
inference(avatar_component_clause,[],[f21261]) ).
fof(f21263,plain,
spl0_2148,
inference(avatar_split_clause,[],[f2883,f21261]) ).
fof(f2883,plain,
! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16),
inference(definition_unfolding,[],[f101,f1438]) ).
fof(f101,axiom,
! [X0,X9,X16,X23] : c_Datatype__Universe_ONumb(X23,X0,X16) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_ONumb(X23,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f21258,plain,
( spl0_2147
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2146 ),
inference(avatar_split_clause,[],[f21239,f21236,f13448,f13139,f8657,f3868,f21256]) ).
fof(f21256,plain,
( spl0_2147
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f21236,plain,
( spl0_2146
<=> ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f21239,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X9,tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2146 ),
inference(forward_demodulation,[],[f21237,f14217]) ).
fof(f21237,plain,
( ! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16)
| ~ spl0_2146 ),
inference(avatar_component_clause,[],[f21236]) ).
fof(f21238,plain,
spl0_2146,
inference(avatar_split_clause,[],[f2882,f21236]) ).
fof(f2882,plain,
! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16),
inference(definition_unfolding,[],[f97,f1438]) ).
fof(f97,axiom,
! [X3,X0,X9,X16] : c_Datatype__Universe_OAtom(X3,X0,X16) = c_Datatype__Universe_Ontrunc(c_Suc(X9),c_Datatype__Universe_OAtom(X3,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f21234,plain,
spl0_2145,
inference(avatar_split_clause,[],[f2871,f21232]) ).
fof(f21232,plain,
( spl0_2145
<=> ! [X3,X0,X19] : c_in(c_Pair(X3,X3,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f2871,plain,
! [X3,X0,X19] : c_in(c_Pair(X3,X3,X0,X0),c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),tc_prod(X0,X0)),
inference(definition_unfolding,[],[f1741,f1610]) ).
fof(f1741,axiom,
! [X3,X0,X19] : c_in(c_Pair(X3,X3,X0,X0),c_Transitive__Closure_Ortrancl(X19,X0),tc_prod(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f21230,plain,
spl0_2144,
inference(avatar_split_clause,[],[f2869,f21228]) ).
fof(f21228,plain,
( spl0_2144
<=> ! [X0,X19] : c_union(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId,tc_prod(X0,X0)) = c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f2869,plain,
! [X0,X19] : c_union(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId,tc_prod(X0,X0)) = c_Transitive__Closure_Otrancl(c_union(X19,c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1602,f1610]) ).
fof(f1602,axiom,
! [X0,X19] : c_union(c_Transitive__Closure_Otrancl(X19,X0),c_Relation_OId,tc_prod(X0,X0)) = c_Transitive__Closure_Ortrancl(X19,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f21207,plain,
( spl0_2143
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2142 ),
inference(avatar_split_clause,[],[f21203,f21200,f13448,f13139,f8657,f3868,f21205]) ).
fof(f21205,plain,
( spl0_2143
<=> ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f21200,plain,
( spl0_2142
<=> ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f21203,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2142 ),
inference(forward_demodulation,[],[f21201,f14217]) ).
fof(f21201,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2142 ),
inference(avatar_component_clause,[],[f21200]) ).
fof(f21202,plain,
spl0_2142,
inference(avatar_split_clause,[],[f2862,f21200]) ).
fof(f2862,plain,
! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f921,f1438,f1438]) ).
fof(f921,axiom,
! [X11,X24] : c_plus(X24,c_Suc(X11),tc_nat) = c_Suc(c_plus(X24,X11,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f21112,plain,
( spl0_2141
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2140 ),
inference(avatar_split_clause,[],[f21108,f21104,f13448,f13139,f8657,f3868,f21110]) ).
fof(f21110,plain,
( spl0_2141
<=> ! [X11,X24] : c_plus(c_plus(c_1,X24,tc_nat),X11,tc_nat) = c_plus(c_1,c_plus(X24,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f21104,plain,
( spl0_2140
<=> ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f21108,plain,
( ! [X11,X24] : c_plus(c_plus(c_1,X24,tc_nat),X11,tc_nat) = c_plus(c_1,c_plus(X24,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2140 ),
inference(forward_demodulation,[],[f21107,f14217]) ).
fof(f21107,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X24,tc_nat),X11,tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2140 ),
inference(forward_demodulation,[],[f21105,f14217]) ).
fof(f21105,plain,
( ! [X11,X24] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X24,X11,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat)
| ~ spl0_2140 ),
inference(avatar_component_clause,[],[f21104]) ).
fof(f21106,plain,
spl0_2140,
inference(avatar_split_clause,[],[f2861,f21104]) ).
fof(f21046,plain,
( spl0_2139
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2138 ),
inference(avatar_split_clause,[],[f21042,f21038,f13448,f13139,f8657,f3868,f21044]) ).
fof(f21044,plain,
( spl0_2139
<=> ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f21038,plain,
( spl0_2138
<=> ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f21042,plain,
( ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_plus(c_1,X24,tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2138 ),
inference(forward_demodulation,[],[f21041,f14217]) ).
fof(f21041,plain,
( ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2138 ),
inference(forward_demodulation,[],[f21039,f14217]) ).
fof(f21039,plain,
( ! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2138 ),
inference(avatar_component_clause,[],[f21038]) ).
fof(f21040,plain,
spl0_2138,
inference(avatar_split_clause,[],[f2860,f21038]) ).
fof(f2860,plain,
! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f929,f1438,f1438]) ).
fof(f929,axiom,
! [X11,X24] : c_minus(X24,X11,tc_nat) = c_minus(c_Suc(X24),c_Suc(X11),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f21036,plain,
spl0_2137,
inference(avatar_split_clause,[],[f2789,f21034]) ).
fof(f21034,plain,
( spl0_2137
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_plus(X3,X25,X0),X1,X0) = c_minus(X3,c_minus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f2789,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_plus(X3,X25,X0),X1,X0) = c_minus(X3,c_minus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__5_0) ).
fof(f21032,plain,
spl0_2136,
inference(avatar_split_clause,[],[f2788,f21030]) ).
fof(f21030,plain,
( spl0_2136
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_minus(X3,X1,X0),X25,X0) = c_minus(X3,c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f2788,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_minus(X3,X1,X0),X25,X0) = c_minus(X3,c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__4_0) ).
fof(f21028,plain,
spl0_2135,
inference(avatar_split_clause,[],[f2787,f21026]) ).
fof(f21026,plain,
( spl0_2135
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(c_minus(X3,X1,X0),X25,X0) = c_minus(c_plus(X3,X25,X0),X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f2787,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(c_minus(X3,X1,X0),X25,X0) = c_minus(c_plus(X3,X25,X0),X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__3_0) ).
fof(f21024,plain,
spl0_2134,
inference(avatar_split_clause,[],[f2786,f21022]) ).
fof(f21022,plain,
( spl0_2134
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,c_minus(X1,X25,X0),X0) = c_minus(c_plus(X3,X1,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f2786,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,c_minus(X1,X25,X0),X0) = c_minus(c_plus(X3,X1,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__2_0) ).
fof(f21020,plain,
spl0_2133,
inference(avatar_split_clause,[],[f1735,f21018]) ).
fof(f21018,plain,
( spl0_2133
<=> ! [X26,X0,X16,X1,X30] :
( ~ c_in(X1,X30,X0)
| c_in(c_Sum__Type_OInr(X1,X0,X16),c_Sum__Type_OPlus(X26,X30,X16,X0),tc_sum(X16,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f1735,axiom,
! [X0,X1,X26,X16,X30] :
( ~ c_in(X1,X30,X0)
| c_in(c_Sum__Type_OInr(X1,X0,X16),c_Sum__Type_OPlus(X26,X30,X16,X0),tc_sum(X16,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f21016,plain,
spl0_2132,
inference(avatar_split_clause,[],[f1734,f21014]) ).
fof(f21014,plain,
( spl0_2132
<=> ! [X30,X0,X16,X3,X26] :
( ~ c_in(X3,X26,X0)
| c_in(c_Sum__Type_OInl(X3,X0,X16),c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f1734,axiom,
! [X3,X0,X26,X16,X30] :
( ~ c_in(X3,X26,X0)
| c_in(c_Sum__Type_OInl(X3,X0,X16),c_Sum__Type_OPlus(X26,X30,X0,X16),tc_sum(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f21012,plain,
spl0_2131,
inference(avatar_split_clause,[],[f1697,f21010]) ).
fof(f21010,plain,
( spl0_2131
<=> ! [X3,X19,X0,X16,X1] :
( c_in(X1,c_Relation_ORange(X19,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f1697,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(X1,c_Relation_ORange(X19,X0,X16),X16)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f21008,plain,
spl0_2130,
inference(avatar_split_clause,[],[f1693,f21006]) ).
fof(f21006,plain,
( spl0_2130
<=> ! [X1,X0,X16,X19,X26] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Main_OImageE__1(X26,X1,X19,X16,X0),X26,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f1693,axiom,
! [X0,X1,X19,X26,X16] :
( ~ c_in(X1,c_Relation_OImage(X19,X26,X16,X0),X0)
| c_in(c_Main_OImageE__1(X26,X1,X19,X16,X0),X26,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f21003,plain,
spl0_2129,
inference(avatar_split_clause,[],[f1692,f21001]) ).
fof(f21001,plain,
( spl0_2129
<=> ! [X38,X0] :
( ~ c_in(X38,c_Relation_OId,tc_prod(X0,X0))
| c_Pair(c_Main_OIdE__1(X38,X0),c_Main_OIdE__1(X38,X0),X0,X0) = X38 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f1692,axiom,
! [X38,X0] :
( ~ c_in(X38,c_Relation_OId,tc_prod(X0,X0))
| c_Pair(c_Main_OIdE__1(X38,X0),c_Main_OIdE__1(X38,X0),X0,X0) = X38 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f20999,plain,
spl0_2128,
inference(avatar_split_clause,[],[f1691,f20997]) ).
fof(f20997,plain,
( spl0_2128
<=> ! [X19,X0,X3,X16,X1] :
( c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f1691,axiom,
! [X3,X0,X1,X19,X16] :
( c_in(X3,c_Relation_ODomain(X19,X0,X16),X0)
| ~ c_in(c_Pair(X3,X1,X0,X16),X19,tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f20995,plain,
spl0_2127,
inference(avatar_split_clause,[],[f1679,f20993]) ).
fof(f20993,plain,
( spl0_2127
<=> ! [X0,X12,X72,X26] :
( c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f1679,axiom,
! [X72,X0,X26,X12] :
( c_in(X72,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f20991,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1667,f20989]) ).
fof(f20989,plain,
( spl0_2126
<=> ! [X0,X29,X39,X26] :
( c_in(X29,X26,X0)
| ~ c_in(X29,c_List_Oset(X39,X0),X0)
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f1667,axiom,
! [X39,X29,X0,X26] :
( c_in(X29,X26,X0)
| ~ c_in(X29,c_List_Oset(X39,X0),X0)
| ~ c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f20987,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1590,f20985]) ).
fof(f20985,plain,
( spl0_2125
<=> ! [X0,X1,X3,X26] :
( c_lessequals(X26,c_insert(X1,c_emptyset,X0),tc_set(X0))
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f1590,axiom,
! [X3,X0,X1,X26] :
( c_lessequals(X26,c_insert(X1,c_emptyset,X0),tc_set(X0))
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
fof(f20983,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1588,f20981]) ).
fof(f20981,plain,
( spl0_2124
<=> ! [X0,X12,X26] :
( ~ c_lessequals(X26,c_insert(X12,c_emptyset,X0),tc_set(X0))
| c_insert(X12,X26,X0) = c_insert(X12,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f1588,axiom,
! [X0,X26,X12] :
( ~ c_lessequals(X26,c_insert(X12,c_emptyset,X0),tc_set(X0))
| c_insert(X12,X26,X0) = c_insert(X12,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
fof(f20979,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1584,f20977]) ).
fof(f20977,plain,
( spl0_2123
<=> ! [X0,X12,X26,X30] :
( ~ c_in(X12,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f1584,axiom,
! [X0,X26,X12,X30] :
( ~ c_in(X12,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f20975,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1467,f20973]) ).
fof(f20973,plain,
( spl0_2122
<=> ! [X9,X0] :
( ~ class_Orderings_Oorder(X0)
| c_insert(X9,c_emptyset,X0) = c_minus(c_insert(X9,c_emptyset,X0),c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).
fof(f1467,axiom,
! [X0,X9] :
( ~ class_Orderings_Oorder(X0)
| c_insert(X9,c_emptyset,X0) = c_minus(c_insert(X9,c_emptyset,X0),c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f20971,plain,
spl0_2121,
inference(avatar_split_clause,[],[f1459,f20969]) ).
fof(f20969,plain,
( spl0_2121
<=> ! [X24,X11,X0,X50,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X50,X23,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).
fof(f1459,axiom,
! [X50,X0,X11,X24,X23] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X50,X23,X0)
| c_lessequals(c_SetInterval_OatLeastLessThan(X23,X50,X0),c_SetInterval_OatLeastLessThan(X24,X11,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f20967,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1450,f20965]) ).
fof(f20965,plain,
( spl0_2120
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).
fof(f1450,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f20961,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1447,f20959]) ).
fof(f20959,plain,
( spl0_2119
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X36,X0)
| ~ c_less(X72,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).
fof(f1447,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X36,X0)
| ~ c_less(X72,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f20957,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1420,f20955]) ).
fof(f20955,plain,
( spl0_2118
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).
fof(f1420,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_less(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f20953,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1415,f20951]) ).
fof(f20951,plain,
( spl0_2117
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_lessequals(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).
fof(f1415,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X72,X23,X0)
| ~ c_lessequals(X23,X36,X0)
| c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f20949,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1218,f20947]) ).
fof(f20947,plain,
( spl0_2116
<=> ! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X12,c_0,X0)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).
fof(f1218,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X12,c_0,X0)
| ~ c_less(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f20945,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1201,f20943]) ).
fof(f20943,plain,
( spl0_2115
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).
fof(f1201,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f20941,plain,
spl0_2114,
inference(avatar_split_clause,[],[f1199,f20939]) ).
fof(f20939,plain,
( spl0_2114
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_uminus(c_1,X0) = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f1199,axiom,
! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_Parity_Oeven(X12,tc_nat)
| c_uminus(c_1,X0) = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f20937,plain,
spl0_2113,
inference(avatar_split_clause,[],[f1160,f20935]) ).
fof(f20935,plain,
( spl0_2113
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X35,X16)
| ~ c_lessequals(X10,X35,X16)
| c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f1160,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X35,X16)
| ~ c_lessequals(X10,X35,X16)
| c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f20933,plain,
spl0_2112,
inference(avatar_split_clause,[],[f1155,f20931]) ).
fof(f20931,plain,
( spl0_2112
<=> ! [X35,X10,X12,X16] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,X35,X16)
| c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f1155,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| ~ c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,X35,X16)
| c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f20929,plain,
spl0_2111,
inference(avatar_split_clause,[],[f1152,f20927]) ).
fof(f20927,plain,
( spl0_2111
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X35,X12,X0)
| ~ c_less(X35,X10,X0)
| c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f1152,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X35,X12,X0)
| ~ c_less(X35,X10,X0)
| c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f20925,plain,
spl0_2110,
inference(avatar_split_clause,[],[f1149,f20923]) ).
fof(f20923,plain,
( spl0_2110
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X12,X35,X0)
| ~ c_less(X10,X35,X0)
| c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f1149,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_less(X12,X35,X0)
| ~ c_less(X10,X35,X0)
| c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f20919,plain,
spl0_2109,
inference(avatar_split_clause,[],[f1131,f20917]) ).
fof(f20917,plain,
( spl0_2109
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Omeet(X3,X1,X0),X0) = c_LOrder_Ojoin(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f1131,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Omeet(X3,X1,X0),X0) = c_LOrder_Ojoin(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f20915,plain,
spl0_2108,
inference(avatar_split_clause,[],[f1122,f20913]) ).
fof(f20913,plain,
( spl0_2108
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Ojoin(X3,X1,X0),X0) = c_LOrder_Omeet(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f1122,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_uminus(c_LOrder_Ojoin(X3,X1,X0),X0) = c_LOrder_Omeet(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f20911,plain,
spl0_2107,
inference(avatar_split_clause,[],[f1108,f20909]) ).
fof(f20909,plain,
( spl0_2107
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_plus(X3,X1,X0),X0) = c_plus(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f1108,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_plus(X3,X1,X0),X0) = c_plus(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f20907,plain,
spl0_2106,
inference(avatar_split_clause,[],[f737,f20905]) ).
fof(f20905,plain,
( spl0_2106
<=> ! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).
fof(f737,axiom,
! [X34,X75] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f20903,plain,
spl0_2105,
inference(avatar_split_clause,[],[f730,f20901]) ).
fof(f20901,plain,
( spl0_2105
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f730,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_nat) = c_Numeral_Onumber__of(X75,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f20899,plain,
spl0_2104,
inference(avatar_split_clause,[],[f718,f20897]) ).
fof(f20897,plain,
( spl0_2104
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X75,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f718,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X75,tc_nat) = c_plus(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f20895,plain,
spl0_2103,
inference(avatar_split_clause,[],[f715,f20893]) ).
fof(f20893,plain,
( spl0_2103
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_times(X24,X11,tc_nat),X0) = c_times(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f715,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_times(X24,X11,tc_nat),X0) = c_times(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f20891,plain,
spl0_2102,
inference(avatar_split_clause,[],[f703,f20889]) ).
fof(f20889,plain,
( spl0_2102
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_plus(X24,X11,tc_nat),X0) = c_plus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f703,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_NatArith_Oof__nat(c_plus(X24,X11,tc_nat),X0) = c_plus(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f20887,plain,
spl0_2101,
inference(avatar_split_clause,[],[f675,f20885]) ).
fof(f20885,plain,
( spl0_2101
<=> ! [X12,X0,X11] :
( c_0 = X11
| c_List_Otl(c_List_Oreplicate(X11,X12,X0),X0) = c_List_Oreplicate(c_minus(X11,c_1,tc_nat),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).
fof(f675,axiom,
! [X0,X11,X12] :
( c_0 = X11
| c_List_Otl(c_List_Oreplicate(X11,X12,X0),X0) = c_List_Oreplicate(c_minus(X11,c_1,tc_nat),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f20883,plain,
spl0_2100,
inference(avatar_split_clause,[],[f593,f20881]) ).
fof(f20881,plain,
( spl0_2100
<=> ! [X23,X0,X10,X39] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Olist__update(X39,X23,X10,X0),X23,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f593,axiom,
! [X39,X0,X10,X23] :
( ~ c_less(X23,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Onth(c_List_Olist__update(X39,X23,X10,X0),X23,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f20879,plain,
( spl0_2099
| ~ spl0_1306
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f18715,f18246,f10504,f20877]) ).
fof(f20877,plain,
( spl0_2099
<=> ! [X0] : c_Set_Ocontents(c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f10504,plain,
( spl0_1306
<=> ! [X0,X10] : c_Set_Ocontents(c_insert(X10,c_emptyset,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f18715,plain,
( ! [X0] : c_Set_Ocontents(c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) = X0
| ~ spl0_1306
| ~ spl0_1977 ),
inference(superposition,[],[f10505,f18247]) ).
fof(f10505,plain,
( ! [X10,X0] : c_Set_Ocontents(c_insert(X10,c_emptyset,X0),X0) = X10
| ~ spl0_1306 ),
inference(avatar_component_clause,[],[f10504]) ).
fof(f20875,plain,
spl0_2098,
inference(avatar_split_clause,[],[f527,f20873]) ).
fof(f20873,plain,
( spl0_2098
<=> ! [X0,X23,X10] :
( ~ c_less(X23,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X10,X23,c_List_Onth(X10,X23,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).
fof(f527,axiom,
! [X10,X0,X23] :
( ~ c_less(X23,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat)
| c_List_Olist__update(X10,X23,c_List_Onth(X10,X23,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f20871,plain,
spl0_2097,
inference(avatar_split_clause,[],[f486,f20869]) ).
fof(f20869,plain,
( spl0_2097
<=> ! [X0,X11,X39] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(X39,X0) = c_List_Olast(c_List_Odrop(X11,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).
fof(f486,axiom,
! [X39,X0,X11] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_List_Olast(X39,X0) = c_List_Olast(c_List_Odrop(X11,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f20867,plain,
spl0_2096,
inference(avatar_split_clause,[],[f419,f20865]) ).
fof(f20865,plain,
( spl0_2096
<=> ! [X39,X0,X40,X26] :
( c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f419,axiom,
! [X40,X39,X0,X26] :
( c_in(X40,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f20863,plain,
spl0_2095,
inference(avatar_split_clause,[],[f418,f20861]) ).
fof(f20861,plain,
( spl0_2095
<=> ! [X40,X0,X39,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f418,axiom,
! [X40,X39,X0,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| ~ c_in(c_append(X39,X40,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f20859,plain,
spl0_2094,
inference(avatar_split_clause,[],[f311,f20857]) ).
fof(f20857,plain,
( spl0_2094
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_times(X33,X35,tc_IntDef_Oint),X0) = c_times(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f311,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_times(X33,X35,tc_IntDef_Oint),X0) = c_times(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f20855,plain,
spl0_2093,
inference(avatar_split_clause,[],[f297,f20853]) ).
fof(f20853,plain,
( spl0_2093
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_minus(X33,X35,tc_IntDef_Oint),X0) = c_minus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f297,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_minus(X33,X35,tc_IntDef_Oint),X0) = c_minus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f20851,plain,
spl0_2092,
inference(avatar_split_clause,[],[f296,f20849]) ).
fof(f20849,plain,
( spl0_2092
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_plus(X33,X35,tc_IntDef_Oint),X0) = c_plus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f296,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_plus(X33,X35,tc_IntDef_Oint),X0) = c_plus(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f20847,plain,
spl0_2091,
inference(avatar_split_clause,[],[f260,f20845]) ).
fof(f20845,plain,
( spl0_2091
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f260,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f20843,plain,
spl0_2090,
inference(avatar_split_clause,[],[f259,f20841]) ).
fof(f20841,plain,
( spl0_2090
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f259,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_in(X3,c_IntDef_ONats,X0)
| ~ c_in(X1,c_IntDef_ONats,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f20839,plain,
spl0_2089,
inference(avatar_split_clause,[],[f256,f20837]) ).
fof(f20837,plain,
( spl0_2089
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f256,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_times(X3,X1,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f20832,plain,
spl0_2088,
inference(avatar_split_clause,[],[f254,f20830]) ).
fof(f20830,plain,
( spl0_2088
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_minus(X3,X1,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f254,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_minus(X3,X1,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f20828,plain,
spl0_2087,
inference(avatar_split_clause,[],[f253,f20826]) ).
fof(f20826,plain,
( spl0_2087
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f253,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| ~ c_in(X1,c_IntDef_OInts,X0)
| c_in(c_plus(X3,X1,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f20824,plain,
spl0_2086,
inference(avatar_split_clause,[],[f200,f20822]) ).
fof(f20822,plain,
( spl0_2086
<=> ! [X9,X11,X24] :
( ~ c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,X24,tc_nat)
| c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f200,axiom,
! [X11,X9,X24] :
( ~ c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,X24,tc_nat)
| c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f20820,plain,
spl0_2085,
inference(avatar_split_clause,[],[f184,f20818]) ).
fof(f20818,plain,
( spl0_2085
<=> ! [X0,X16,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f184,axiom,
! [X0,X19,X16] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f20816,plain,
spl0_2084,
inference(avatar_split_clause,[],[f183,f20814]) ).
fof(f20814,plain,
( spl0_2084
<=> ! [X0,X16,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| ~ c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f183,axiom,
! [X0,X19,X16] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(tc_prod(X16,X0)))
| ~ c_in(c_Relation_Oconverse(X19,X16,X0),c_Finite__Set_OFinites,tc_set(tc_prod(X0,X16))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f20745,plain,
( ~ spl0_1123
| spl0_2083
| ~ spl0_113
| ~ spl0_1568
| ~ spl0_2043 ),
inference(avatar_split_clause,[],[f20635,f18811,f12742,f3785,f20742,f9247]) ).
fof(f12742,plain,
( spl0_1568
<=> ! [X0] : c_plus(c_0,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f18811,plain,
( spl0_2043
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_minus(X25,X1,X0),X0)
| c_lessequals(c_plus(X3,X1,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f20635,plain,
( c_lessequals(v_k(v_x),v_f(v_x),t_b)
| ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_113
| ~ spl0_1568
| ~ spl0_2043 ),
inference(forward_demodulation,[],[f20613,f12743]) ).
fof(f12743,plain,
( ! [X0] : c_plus(c_0,X0,t_b) = X0
| ~ spl0_1568 ),
inference(avatar_component_clause,[],[f12742]) ).
fof(f20613,plain,
( ~ class_OrderedGroup_Opordered__ab__group__add(t_b)
| c_lessequals(c_plus(c_0,v_k(v_x),t_b),v_f(v_x),t_b)
| ~ spl0_113
| ~ spl0_2043 ),
inference(resolution,[],[f18812,f3787]) ).
fof(f18812,plain,
( ! [X3,X0,X1,X25] :
( ~ c_lessequals(X3,c_minus(X25,X1,X0),X0)
| ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_plus(X3,X1,X0),X25,X0) )
| ~ spl0_2043 ),
inference(avatar_component_clause,[],[f18811]) ).
fof(f20424,plain,
( spl0_2082
| ~ spl0_1801
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f18712,f18246,f14764,f20422]) ).
fof(f20422,plain,
( spl0_2082
<=> ! [X0] : c_Finite__Set_OMax(c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f14764,plain,
( spl0_1801
<=> ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f18712,plain,
( ! [X0] : c_Finite__Set_OMax(c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) = X0
| ~ spl0_1801
| ~ spl0_1977 ),
inference(superposition,[],[f14765,f18247]) ).
fof(f14765,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,t_b),t_b) = X0
| ~ spl0_1801 ),
inference(avatar_component_clause,[],[f14764]) ).
fof(f20231,plain,
( spl0_2081
| ~ spl0_1807
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f18711,f18246,f14841,f20229]) ).
fof(f20229,plain,
( spl0_2081
<=> ! [X0] : c_Finite__Set_OMin(c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f14841,plain,
( spl0_1807
<=> ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,t_b),t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f18711,plain,
( ! [X0] : c_Finite__Set_OMin(c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) = X0
| ~ spl0_1807
| ~ spl0_1977 ),
inference(superposition,[],[f14842,f18247]) ).
fof(f14842,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,t_b),t_b) = X0
| ~ spl0_1807 ),
inference(avatar_component_clause,[],[f14841]) ).
fof(f19799,plain,
( spl0_2080
| ~ spl0_1500
| ~ spl0_2079 ),
inference(avatar_split_clause,[],[f19612,f19467,f12278,f19797]) ).
fof(f12278,plain,
( spl0_1500
<=> ! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f19612,plain,
( ! [X0] : c_less(c_minus(X0,c_1,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1500
| ~ spl0_2079 ),
inference(resolution,[],[f19468,f12279]) ).
fof(f12279,plain,
( ! [X35,X33] :
( ~ c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(X33,X35,tc_IntDef_Oint) )
| ~ spl0_1500 ),
inference(avatar_component_clause,[],[f12278]) ).
fof(f19469,plain,
( ~ spl0_1
| spl0_2079
| ~ spl0_1815
| ~ spl0_2067 ),
inference(avatar_split_clause,[],[f19304,f19214,f15866,f19467,f3226]) ).
fof(f15866,plain,
( spl0_1815
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f19304,plain,
( ! [X0] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(t_b) )
| ~ spl0_1815
| ~ spl0_2067 ),
inference(resolution,[],[f19215,f15867]) ).
fof(f15867,plain,
( ! [X0,X35,X33] :
( ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0)
| c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X0) )
| ~ spl0_1815 ),
inference(avatar_component_clause,[],[f15866]) ).
fof(f19326,plain,
( spl0_2076
| spl0_2078 ),
inference(avatar_split_clause,[],[f3224,f19324,f19284]) ).
fof(f19284,plain,
( spl0_2076
<=> ! [X33] : c_0 != c_Numeral_Onumber__of(X33,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f19324,plain,
( spl0_2078
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| c_less(c_0,c_Nat_Opower(X12,c_0,X0),X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f3224,plain,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_0,X0),X0) ),
inference(inner_rewriting,[],[f1228]) ).
fof(f1228,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f19310,plain,
( ~ spl0_1025
| ~ spl0_2076 ),
inference(avatar_contradiction_clause,[],[f19309]) ).
fof(f19309,plain,
( $false
| ~ spl0_1025
| ~ spl0_2076 ),
inference(trivial_inequality_removal,[],[f19307]) ).
fof(f19307,plain,
( c_0 != c_0
| ~ spl0_1025
| ~ spl0_2076 ),
inference(superposition,[],[f19285,f8802]) ).
fof(f19285,plain,
( ! [X33] : c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| ~ spl0_2076 ),
inference(avatar_component_clause,[],[f19284]) ).
fof(f19289,plain,
( spl0_2076
| spl0_2077 ),
inference(avatar_split_clause,[],[f3223,f19287,f19284]) ).
fof(f19287,plain,
( spl0_2077
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ c_lessequals(c_Nat_Opower(X12,c_0,X0),c_0,X0)
| ~ class_Ring__and__Field_Oordered__idom(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f3223,plain,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_0,X0),c_0,X0) ),
inference(inner_rewriting,[],[f1211]) ).
fof(f1211,axiom,
! [X0,X12,X33] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 != c_Numeral_Onumber__of(X33,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f19254,plain,
( spl0_2075
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1137
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1960
| ~ spl0_2074 ),
inference(avatar_split_clause,[],[f19250,f19246,f17463,f13448,f13139,f9305,f8657,f3868,f19252]) ).
fof(f19252,plain,
( spl0_2075
<=> ! [X10] :
( c_plus(c_1,c_minus(X10,c_1,tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f17463,plain,
( spl0_1960
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_plus(c_1,X72,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f19246,plain,
( spl0_2074
<=> ! [X10] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f19250,plain,
( ! [X10] :
( c_plus(c_1,c_minus(X10,c_1,tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1137
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1960
| ~ spl0_2074 ),
inference(forward_demodulation,[],[f19249,f17466]) ).
fof(f17466,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_1137
| ~ spl0_1960 ),
inference(superposition,[],[f17464,f9306]) ).
fof(f17464,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_plus(c_1,X72,tc_nat),tc_nat)
| ~ spl0_1960 ),
inference(avatar_component_clause,[],[f17463]) ).
fof(f19249,plain,
( ! [X10] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2074 ),
inference(forward_demodulation,[],[f19247,f14217]) ).
fof(f19247,plain,
( ! [X10] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) )
| ~ spl0_2074 ),
inference(avatar_component_clause,[],[f19246]) ).
fof(f19248,plain,
spl0_2074,
inference(avatar_split_clause,[],[f3114,f19246]) ).
fof(f3114,plain,
! [X10] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X10,tc_nat),tc_nat),tc_nat),tc_nat) = X10
| ~ c_less(c_0,X10,tc_nat) ),
inference(forward_demodulation,[],[f2932,f2865]) ).
fof(f2932,plain,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X10 ),
inference(definition_unfolding,[],[f918,f1438,f1438]) ).
fof(f918,axiom,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_Suc(c_minus(X10,c_Suc(c_0),tc_nat)) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f19244,plain,
spl0_2073,
inference(avatar_split_clause,[],[f2963,f19242]) ).
fof(f19242,plain,
( spl0_2073
<=> ! [X0,X30,X2,X26] :
( c_lessequals(X2,X26,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f2963,plain,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X26,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
inference(definition_unfolding,[],[f1503,f1267]) ).
fof(f1503,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X26,tc_set(X0))
| ~ c_lessequals(X2,c_inter(X26,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f19240,plain,
spl0_2072,
inference(avatar_split_clause,[],[f2962,f19238]) ).
fof(f19238,plain,
( spl0_2072
<=> ! [X0,X30,X2,X26] :
( c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f2962,plain,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),tc_set(X0)) ),
inference(definition_unfolding,[],[f1504,f1267]) ).
fof(f1504,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X2,X30,tc_set(X0))
| ~ c_lessequals(X2,c_inter(X26,X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f19236,plain,
spl0_2071,
inference(avatar_split_clause,[],[f2958,f19234]) ).
fof(f19234,plain,
( spl0_2071
<=> ! [X6,X0,X32] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f2958,plain,
! [X0,X6,X32] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
inference(definition_unfolding,[],[f1651,f1267]) ).
fof(f1651,axiom,
! [X0,X6,X32] :
( ~ c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_inter(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f19232,plain,
spl0_2070,
inference(avatar_split_clause,[],[f2957,f19230]) ).
fof(f19230,plain,
( spl0_2070
<=> ! [X6,X0,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f2957,plain,
! [X0,X6,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Relation_OImage(c_Relation_Odiag(X6,X0),X32,X0,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
inference(definition_unfolding,[],[f1652,f1267]) ).
fof(f1652,axiom,
! [X0,X6,X32] :
( ~ c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_inter(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f19226,plain,
spl0_2069,
inference(avatar_split_clause,[],[f2950,f19224]) ).
fof(f19224,plain,
( spl0_2069
<=> ! [X11,X24] :
( c_lessequals(X11,X24,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f2950,plain,
! [X11,X24] :
( c_lessequals(X11,X24,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f913,f1438,f1438]) ).
fof(f913,axiom,
! [X11,X24] :
( c_lessequals(X11,X24,tc_nat)
| ~ c_lessequals(c_Suc(X11),c_Suc(X24),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f19220,plain,
spl0_2068,
inference(avatar_split_clause,[],[f2948,f19218]) ).
fof(f19218,plain,
( spl0_2068
<=> ! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).
fof(f2948,plain,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f915,f1438,f1438]) ).
fof(f915,axiom,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_Suc(X24),c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f19216,plain,
( ~ spl0_1060
| spl0_2067
| ~ spl0_1764
| ~ spl0_2052 ),
inference(avatar_split_clause,[],[f19162,f18913,f14576,f19214,f8979]) ).
fof(f8979,plain,
( spl0_1060
<=> class_Orderings_Oord(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f14576,plain,
( spl0_1764
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f18913,plain,
( spl0_2052
<=> ! [X0] : c_in(X0,c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).
fof(f19162,plain,
( ! [X0] :
( c_lessequals(X0,X0,t_b)
| ~ class_Orderings_Oord(t_b) )
| ~ spl0_1764
| ~ spl0_2052 ),
inference(resolution,[],[f18914,f14577]) ).
fof(f14577,plain,
( ! [X72,X0,X36,X23] :
( ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0)
| c_lessequals(X23,X36,X0)
| ~ class_Orderings_Oord(X0) )
| ~ spl0_1764 ),
inference(avatar_component_clause,[],[f14576]) ).
fof(f18914,plain,
( ! [X0] : c_in(X0,c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b)
| ~ spl0_2052 ),
inference(avatar_component_clause,[],[f18913]) ).
fof(f19212,plain,
spl0_2066,
inference(avatar_split_clause,[],[f2943,f19210]) ).
fof(f19210,plain,
( spl0_2066
<=> ! [X0,X3,X26,X30] :
( ~ c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f2943,plain,
! [X3,X0,X26,X30] :
( ~ c_in(X3,X30,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X3,X26,X0),X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1574,f1267]) ).
fof(f1574,axiom,
! [X3,X0,X26,X30] :
( ~ c_in(X3,X30,X0)
| c_emptyset != c_inter(c_insert(X3,X26,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
fof(f19208,plain,
spl0_2065,
inference(avatar_split_clause,[],[f2941,f19206]) ).
fof(f19206,plain,
( spl0_2065
<=> ! [X0,X30,X1,X26] :
( ~ c_in(X1,X26,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),c_insert(X1,X30,X0),X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f2941,plain,
! [X0,X1,X26,X30] :
( ~ c_in(X1,X26,X0)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X26,X0),c_insert(X1,X30,X0),X0,X0) ),
inference(definition_unfolding,[],[f1558,f1267]) ).
fof(f1558,axiom,
! [X0,X1,X26,X30] :
( ~ c_in(X1,X26,X0)
| c_emptyset != c_inter(X26,c_insert(X1,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
fof(f19202,plain,
spl0_2064,
inference(avatar_split_clause,[],[f2939,f19200]) ).
fof(f19200,plain,
( spl0_2064
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f2939,plain,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f916,f1438,f1438]) ).
fof(f916,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_Suc(X24),c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f19196,plain,
spl0_2063,
inference(avatar_split_clause,[],[f2934,f19194]) ).
fof(f19194,plain,
( spl0_2063
<=> ! [X11,X24] :
( ~ c_lessequals(X11,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f2934,plain,
! [X11,X24] :
( ~ c_lessequals(X11,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f914,f1438,f1438]) ).
fof(f914,axiom,
! [X11,X24] :
( ~ c_lessequals(X11,X24,tc_nat)
| c_lessequals(c_Suc(X11),c_Suc(X24),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f19186,plain,
( spl0_2062
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2061 ),
inference(avatar_split_clause,[],[f19182,f19179,f13448,f13139,f8657,f3868,f19184]) ).
fof(f19184,plain,
( spl0_2062
<=> ! [X24,X14] :
( c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_plus(c_1,X24,tc_nat),X14)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f19179,plain,
( spl0_2061
<=> ! [X24,X14] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f19182,plain,
( ! [X14,X24] :
( c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_plus(c_1,X24,tc_nat),X14)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f19180,f14217]) ).
fof(f19180,plain,
( ! [X14,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X14) )
| ~ spl0_2061 ),
inference(avatar_component_clause,[],[f19179]) ).
fof(f19181,plain,
spl0_2061,
inference(avatar_split_clause,[],[f2919,f19179]) ).
fof(f2919,plain,
! [X14,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X14) ),
inference(definition_unfolding,[],[f696,f1438]) ).
fof(f696,axiom,
! [X14,X24] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X14)
| c_NatArith_Oof__nat(c_Suc(X24),X14) = c_plus(c_NatArith_Oof__nat(X24,X14),c_1,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f19173,plain,
( spl0_2060
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2059 ),
inference(avatar_split_clause,[],[f19169,f19166,f13448,f13139,f8657,f3868,f19171]) ).
fof(f19171,plain,
( spl0_2060
<=> ! [X11,X0,X12,X39] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_plus(c_1,X11,tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f19166,plain,
( spl0_2059
<=> ! [X11,X0,X12,X39] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f19169,plain,
( ! [X39,X0,X11,X12] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_plus(c_1,X11,tc_nat),X0)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2059 ),
inference(forward_demodulation,[],[f19167,f14217]) ).
fof(f19167,plain,
( ! [X39,X0,X11,X12] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0)
| ~ spl0_2059 ),
inference(avatar_component_clause,[],[f19166]) ).
fof(f19168,plain,
spl0_2059,
inference(avatar_split_clause,[],[f2879,f19166]) ).
fof(f2879,plain,
! [X39,X0,X11,X12] : c_List_Onth(X39,X11,X0) = c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0),
inference(definition_unfolding,[],[f587,f1438]) ).
fof(f587,axiom,
! [X39,X0,X11,X12] : c_List_Onth(c_List_Olist_OCons(X12,X39,X0),c_Suc(X11),X0) = c_List_Onth(X39,X11,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f19148,plain,
( spl0_2058
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2057 ),
inference(avatar_split_clause,[],[f19144,f19141,f13448,f13139,f8657,f3868,f19146]) ).
fof(f19146,plain,
( spl0_2058
<=> ! [X11,X0,X12,X39] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_plus(c_1,X11,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f19141,plain,
( spl0_2057
<=> ! [X11,X0,X12,X39] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_List_Olist_OCons(X12,X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f19144,plain,
( ! [X39,X0,X11,X12] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_plus(c_1,X11,tc_nat),c_List_Olist_OCons(X12,X39,X0),X0)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2057 ),
inference(forward_demodulation,[],[f19142,f14217]) ).
fof(f19142,plain,
( ! [X39,X0,X11,X12] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_List_Olist_OCons(X12,X39,X0),X0)
| ~ spl0_2057 ),
inference(avatar_component_clause,[],[f19141]) ).
fof(f19143,plain,
spl0_2057,
inference(avatar_split_clause,[],[f2878,f19141]) ).
fof(f2878,plain,
! [X39,X0,X11,X12] : c_List_Odrop(X11,X39,X0) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),c_List_Olist_OCons(X12,X39,X0),X0),
inference(definition_unfolding,[],[f466,f1438]) ).
fof(f466,axiom,
! [X39,X0,X11,X12] : c_List_Odrop(c_Suc(X11),c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Odrop(X11,X39,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f19113,plain,
( spl0_2056
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2055 ),
inference(avatar_split_clause,[],[f19109,f19106,f13448,f13139,f8657,f3868,f19111]) ).
fof(f19106,plain,
( spl0_2055
<=> ! [X11,X12,X14] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X12,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f19109,plain,
( ! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_plus(c_1,X11,tc_nat),X12,X14)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2055 ),
inference(forward_demodulation,[],[f19107,f14217]) ).
fof(f19107,plain,
( ! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X12,X14)
| ~ spl0_2055 ),
inference(avatar_component_clause,[],[f19106]) ).
fof(f19108,plain,
spl0_2055,
inference(avatar_split_clause,[],[f2877,f19106]) ).
fof(f2877,plain,
! [X11,X14,X12] : c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X12,X14),
inference(definition_unfolding,[],[f617,f1438]) ).
fof(f617,axiom,
! [X11,X14,X12] : c_List_Oreplicate(c_Suc(X11),X12,X14) = c_List_Olist_OCons(X12,c_List_Oreplicate(X11,X12,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f19012,plain,
( spl0_2054
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2053 ),
inference(avatar_split_clause,[],[f19008,f19005,f13448,f13139,f8657,f3868,f19010]) ).
fof(f19010,plain,
( spl0_2054
<=> ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_plus(c_1,X24,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f19005,plain,
( spl0_2053
<=> ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f19008,plain,
( ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_plus(c_1,X24,tc_nat),X11,tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2053 ),
inference(forward_demodulation,[],[f19006,f14217]) ).
fof(f19006,plain,
( ! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat)
| ~ spl0_2053 ),
inference(avatar_component_clause,[],[f19005]) ).
fof(f19007,plain,
spl0_2053,
inference(avatar_split_clause,[],[f2876,f19005]) ).
fof(f2876,plain,
! [X11,X24] : c_plus(X11,c_times(X24,X11,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),X11,tc_nat),
inference(definition_unfolding,[],[f993,f1438]) ).
fof(f993,axiom,
! [X11,X24] : c_times(c_Suc(X24),X11,tc_nat) = c_plus(X11,c_times(X24,X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f18915,plain,
( spl0_2052
| ~ spl0_1229
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f18717,f18246,f10008,f18913]) ).
fof(f10008,plain,
( spl0_1229
<=> ! [X0,X12,X26] : c_in(X12,c_insert(X12,X26,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f18717,plain,
( ! [X0] : c_in(X0,c_SetInterval_OatLeastAtMost(X0,X0,t_b),t_b)
| ~ spl0_1229
| ~ spl0_1977 ),
inference(superposition,[],[f10009,f18247]) ).
fof(f10009,plain,
( ! [X0,X26,X12] : c_in(X12,c_insert(X12,X26,X0),X0)
| ~ spl0_1229 ),
inference(avatar_component_clause,[],[f10008]) ).
fof(f18911,plain,
( spl0_2051
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2050 ),
inference(avatar_split_clause,[],[f18907,f18904,f13448,f13139,f8657,f3868,f18909]) ).
fof(f18909,plain,
( spl0_2051
<=> ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f18904,plain,
( spl0_2050
<=> ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f18907,plain,
( ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2050 ),
inference(forward_demodulation,[],[f18905,f14217]) ).
fof(f18905,plain,
( ! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2050 ),
inference(avatar_component_clause,[],[f18904]) ).
fof(f18906,plain,
spl0_2050,
inference(avatar_split_clause,[],[f2875,f18904]) ).
fof(f2875,plain,
! [X11,X24] : c_plus(X24,c_times(X24,X11,tc_nat),tc_nat) = c_times(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f951,f1438]) ).
fof(f951,axiom,
! [X11,X24] : c_times(X24,c_Suc(X11),tc_nat) = c_plus(X24,c_times(X24,X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f18855,plain,
( spl0_2049
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2048 ),
inference(avatar_split_clause,[],[f18851,f18848,f13448,f13139,f8657,f3868,f18853]) ).
fof(f18853,plain,
( spl0_2049
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f18848,plain,
( spl0_2048
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f18851,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2048 ),
inference(forward_demodulation,[],[f18849,f14217]) ).
fof(f18849,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat)
| ~ spl0_2048 ),
inference(avatar_component_clause,[],[f18848]) ).
fof(f18850,plain,
spl0_2048,
inference(avatar_split_clause,[],[f2874,f18848]) ).
fof(f2874,plain,
! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1239,f1438]) ).
fof(f1239,axiom,
! [X38,X11] : c_Nat_Opower(X38,c_Suc(X11),tc_nat) = c_times(X38,c_Nat_Opower(X38,X11,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f18831,plain,
( spl0_2047
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2046 ),
inference(avatar_split_clause,[],[f18827,f18824,f13448,f13139,f8657,f3868,f18829]) ).
fof(f18829,plain,
( spl0_2047
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f18824,plain,
( spl0_2046
<=> ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f18827,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_plus(c_1,X11,tc_nat),tc_IntDef_Oint)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_2046 ),
inference(forward_demodulation,[],[f18825,f14217]) ).
fof(f18825,plain,
( ! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_2046 ),
inference(avatar_component_clause,[],[f18824]) ).
fof(f18826,plain,
spl0_2046,
inference(avatar_split_clause,[],[f2873,f18824]) ).
fof(f2873,plain,
! [X38,X11] : c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X38,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f359,f1438]) ).
fof(f359,axiom,
! [X38,X11] : c_Nat_Opower(X38,c_Suc(X11),tc_IntDef_Oint) = c_times(X38,c_Nat_Opower(X38,X11,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f18822,plain,
spl0_2045,
inference(avatar_split_clause,[],[f2872,f18820]) ).
fof(f18820,plain,
( spl0_2045
<=> ! [X0,X30,X26] : c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) = c_minus(X26,c_uminus(X30,tc_set(X0)),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f2872,plain,
! [X0,X26,X30] : c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) = c_minus(X26,c_uminus(X30,tc_set(X0)),tc_set(X0)),
inference(definition_unfolding,[],[f1480,f1267]) ).
fof(f1480,axiom,
! [X0,X26,X30] : c_inter(X26,X30,X0) = c_minus(X26,c_uminus(X30,tc_set(X0)),tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f18818,plain,
spl0_2044,
inference(avatar_split_clause,[],[f2797,f18816]) ).
fof(f18816,plain,
( spl0_2044
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_plus(X3,X1,X0),X25,X0)
| c_lessequals(X3,c_minus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f2797,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_plus(X3,X1,X0),X25,X0)
| c_lessequals(X3,c_minus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_1) ).
fof(f18813,plain,
spl0_2043,
inference(avatar_split_clause,[],[f2796,f18811]) ).
fof(f2796,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_minus(X25,X1,X0),X0)
| c_lessequals(c_plus(X3,X1,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__9_0) ).
fof(f18809,plain,
spl0_2042,
inference(avatar_split_clause,[],[f2795,f18807]) ).
fof(f18807,plain,
( spl0_2042
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_plus(X25,X1,X0),X0)
| c_lessequals(c_minus(X3,X1,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f2795,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_plus(X25,X1,X0),X0)
| c_lessequals(c_minus(X3,X1,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_1) ).
fof(f18805,plain,
spl0_2041,
inference(avatar_split_clause,[],[f2794,f18803]) ).
fof(f2794,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_minus(X3,X1,X0),X25,X0)
| c_lessequals(X3,c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__8_0) ).
fof(f18801,plain,
spl0_2040,
inference(avatar_split_clause,[],[f2793,f18799]) ).
fof(f18799,plain,
( spl0_2040
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_plus(X3,X1,X0),X25,X0)
| c_less(X3,c_minus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f2793,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_plus(X3,X1,X0),X25,X0)
| c_less(X3,c_minus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__7_1) ).
fof(f18797,plain,
spl0_2039,
inference(avatar_split_clause,[],[f2792,f18795]) ).
fof(f18795,plain,
( spl0_2039
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_minus(X25,X1,X0),X0)
| c_less(c_plus(X3,X1,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f2792,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_minus(X25,X1,X0),X0)
| c_less(c_plus(X3,X1,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__7_0) ).
fof(f18793,plain,
spl0_2038,
inference(avatar_split_clause,[],[f2791,f18791]) ).
fof(f18791,plain,
( spl0_2038
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_plus(X25,X1,X0),X0)
| c_less(c_minus(X3,X1,X0),X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f2791,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_plus(X25,X1,X0),X0)
| c_less(c_minus(X3,X1,X0),X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__6_1) ).
fof(f18789,plain,
spl0_2037,
inference(avatar_split_clause,[],[f2790,f18787]) ).
fof(f2790,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_minus(X3,X1,X0),X25,X0)
| c_less(X3,c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__6_0) ).
fof(f18785,plain,
spl0_2036,
inference(avatar_split_clause,[],[f1702,f18783]) ).
fof(f18783,plain,
( spl0_2036
<=> ! [X0,X3,X26] :
( ~ c_in(X3,X26,X0)
| c_in(c_Pair(X3,X3,X0,X0),c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f1702,axiom,
! [X3,X0,X26] :
( ~ c_in(X3,X26,X0)
| c_in(c_Pair(X3,X3,X0,X0),c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f18781,plain,
spl0_2035,
inference(avatar_split_clause,[],[f1668,f18779]) ).
fof(f18779,plain,
( spl0_2035
<=> ! [X0,X39,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_Main_Oin__listsI__1(X26,X39,X0),c_List_Oset(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f1668,axiom,
! [X39,X0,X26] :
( c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0))
| c_in(c_Main_Oin__listsI__1(X26,X39,X0),c_List_Oset(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f18777,plain,
spl0_2034,
inference(avatar_split_clause,[],[f1569,f18775]) ).
fof(f18775,plain,
( spl0_2034
<=> ! [X0,X3,X26] : c_insert(X3,X26,X0) = c_insert(X3,c_minus(X26,c_insert(X3,c_emptyset,X0),tc_set(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f1569,axiom,
! [X3,X0,X26] : c_insert(X3,X26,X0) = c_insert(X3,c_minus(X26,c_insert(X3,c_emptyset,X0),tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f18773,plain,
( spl0_2033
| ~ spl0_1170
| ~ spl0_1977 ),
inference(avatar_split_clause,[],[f18716,f18246,f9441,f18771]) ).
fof(f18771,plain,
( spl0_2033
<=> ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).
fof(f18716,plain,
( ! [X0] : c_emptyset != c_SetInterval_OatLeastAtMost(X0,X0,t_b)
| ~ spl0_1170
| ~ spl0_1977 ),
inference(superposition,[],[f9442,f18247]) ).
fof(f18769,plain,
spl0_2032,
inference(avatar_split_clause,[],[f1544,f18767]) ).
fof(f18767,plain,
( spl0_2032
<=> ! [X0,X30,X26] : c_Union(c_union(X26,X30,tc_set(X0)),X0) = c_union(c_Union(X26,X0),c_Union(X30,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f1544,axiom,
! [X0,X26,X30] : c_Union(c_union(X26,X30,tc_set(X0)),X0) = c_union(c_Union(X26,X0),c_Union(X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f18765,plain,
spl0_2031,
inference(avatar_split_clause,[],[f1490,f18763]) ).
fof(f18763,plain,
( spl0_2031
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f1490,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f18761,plain,
spl0_2030,
inference(avatar_split_clause,[],[f1479,f18759]) ).
fof(f18759,plain,
( spl0_2030
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f1479,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f18757,plain,
spl0_2029,
inference(avatar_split_clause,[],[f1478,f18755]) ).
fof(f18755,plain,
( spl0_2029
<=> ! [X0,X30,X26] :
( c_lessequals(X30,X26,tc_set(X0))
| ~ c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f1478,axiom,
! [X0,X26,X30] :
( c_lessequals(X30,X26,tc_set(X0))
| ~ c_lessequals(c_uminus(X26,tc_set(X0)),c_uminus(X30,tc_set(X0)),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f18753,plain,
spl0_2028,
inference(avatar_split_clause,[],[f1468,f18751]) ).
fof(f18751,plain,
( spl0_2028
<=> ! [X0,X30,X26] : c_uminus(c_minus(X26,X30,tc_set(X0)),tc_set(X0)) = c_union(c_uminus(X26,tc_set(X0)),X30,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f1468,axiom,
! [X0,X26,X30] : c_uminus(c_minus(X26,X30,tc_set(X0)),tc_set(X0)) = c_union(c_uminus(X26,tc_set(X0)),X30,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f18749,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1254,f18747]) ).
fof(f18747,plain,
( spl0_2027
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f1254,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f18745,plain,
spl0_2026,
inference(avatar_split_clause,[],[f1253,f18743]) ).
fof(f18743,plain,
( spl0_2026
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f1253,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f18741,plain,
spl0_2025,
inference(avatar_split_clause,[],[f1088,f18739]) ).
fof(f18739,plain,
( spl0_2025
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f1088,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f18737,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1087,f18735]) ).
fof(f18735,plain,
( spl0_2024
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f1087,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f18733,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1086,f18731]) ).
fof(f18731,plain,
( spl0_2023
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f1086,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f18710,plain,
spl0_2022,
inference(avatar_split_clause,[],[f1085,f18708]) ).
fof(f18708,plain,
( spl0_2022
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f1085,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f18706,plain,
spl0_2021,
inference(avatar_split_clause,[],[f1083,f18704]) ).
fof(f18704,plain,
( spl0_2021
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f1083,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f18702,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1082,f18700]) ).
fof(f18700,plain,
( spl0_2020
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f1082,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X3,X25,X0),c_plus(X1,X25,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f18698,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1081,f18696]) ).
fof(f18696,plain,
( spl0_2019
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f1081,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f18694,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1080,f18692]) ).
fof(f18692,plain,
( spl0_2018
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f1080,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_plus(X25,X3,X0),c_plus(X25,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f18690,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1040,f18688]) ).
fof(f18688,plain,
( spl0_2017
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f1040,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f18686,plain,
spl0_2016,
inference(avatar_split_clause,[],[f1039,f18684]) ).
fof(f18684,plain,
( spl0_2016
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f1039,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f18682,plain,
spl0_2015,
inference(avatar_split_clause,[],[f1032,f18680]) ).
fof(f18680,plain,
( spl0_2015
<=> ! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f1032,axiom,
! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f18678,plain,
spl0_2014,
inference(avatar_split_clause,[],[f1031,f18676]) ).
fof(f18676,plain,
( spl0_2014
<=> ! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f1031,axiom,
! [X0,X12,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X33,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X33,X12),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f18674,plain,
spl0_2013,
inference(avatar_split_clause,[],[f1013,f18672]) ).
fof(f1013,axiom,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X34,X33),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f18661,plain,
spl0_2012,
inference(avatar_split_clause,[],[f1010,f18659]) ).
fof(f1010,axiom,
! [X0,X34,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,X33),X0) = c_plus(c_Numeral_Onumber__of(X34,X0),c_Numeral_Onumber__of(X33,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f18657,plain,
spl0_2011,
inference(avatar_split_clause,[],[f865,f18655]) ).
fof(f18655,plain,
( spl0_2011
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(c_1,X16),X3,X16)
| c_less(c_uminus(X3,X16),c_1,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f865,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(c_1,X16),X3,X16)
| c_less(c_uminus(X3,X16),c_1,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f18653,plain,
spl0_2010,
inference(avatar_split_clause,[],[f864,f18651]) ).
fof(f18651,plain,
( spl0_2010
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(X3,X16),c_1,X16)
| c_less(c_uminus(c_1,X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f864,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_uminus(X3,X16),c_1,X16)
| c_less(c_uminus(c_1,X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f18649,plain,
spl0_2009,
inference(avatar_split_clause,[],[f861,f18647]) ).
fof(f18647,plain,
( spl0_2009
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(c_1,X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_1,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f861,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(c_1,X16),X3,X16)
| c_lessequals(c_uminus(X3,X16),c_1,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f18645,plain,
spl0_2008,
inference(avatar_split_clause,[],[f860,f18643]) ).
fof(f18643,plain,
( spl0_2008
<=> ! [X16,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_1,X16)
| c_lessequals(c_uminus(c_1,X16),X3,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f860,axiom,
! [X3,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_uminus(X3,X16),c_1,X16)
| c_lessequals(c_uminus(c_1,X16),X3,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f18641,plain,
spl0_2007,
inference(avatar_split_clause,[],[f854,f18639]) ).
fof(f18639,plain,
( spl0_2007
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(X1,c_uminus(c_1,X16),X16)
| c_less(c_1,c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f854,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(X1,c_uminus(c_1,X16),X16)
| c_less(c_1,c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f18637,plain,
spl0_2006,
inference(avatar_split_clause,[],[f853,f18635]) ).
fof(f18635,plain,
( spl0_2006
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_1,c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f853,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_less(c_1,c_uminus(X1,X16),X16)
| c_less(X1,c_uminus(c_1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f18633,plain,
spl0_2005,
inference(avatar_split_clause,[],[f838,f18631]) ).
fof(f18631,plain,
( spl0_2005
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(X1,c_uminus(c_1,X16),X16)
| c_lessequals(c_1,c_uminus(X1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f838,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(X1,c_uminus(c_1,X16),X16)
| c_lessequals(c_1,c_uminus(X1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f18629,plain,
spl0_2004,
inference(avatar_split_clause,[],[f837,f18627]) ).
fof(f18627,plain,
( spl0_2004
<=> ! [X16,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_1,c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_1,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f837,axiom,
! [X1,X16] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X16)
| ~ class_HOL_Oone(X16)
| ~ c_lessequals(c_1,c_uminus(X1,X16),X16)
| c_lessequals(X1,c_uminus(c_1,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f18625,plain,
spl0_2003,
inference(avatar_split_clause,[],[f763,f18623]) ).
fof(f18623,plain,
( spl0_2003
<=> ! [X34,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,X0) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f763,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,X0) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f18610,plain,
spl0_2002,
inference(avatar_split_clause,[],[f674,f18608]) ).
fof(f18608,plain,
( spl0_2002
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Otl(c_append(X39,X40,X0),X0) = c_append(c_List_Otl(X39,X0),X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f674,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Otl(c_append(X39,X40,X0),X0) = c_append(c_List_Otl(X39,X0),X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f18606,plain,
spl0_2001,
inference(avatar_split_clause,[],[f658,f18604]) ).
fof(f18604,plain,
( spl0_2001
<=> ! [X0,X12,X26] :
( ~ c_in(c_0,X26,tc_nat)
| c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f658,axiom,
! [X0,X26,X12] :
( ~ c_in(c_0,X26,tc_nat)
| c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f18601,plain,
spl0_2000,
inference(avatar_split_clause,[],[f621,f18599]) ).
fof(f18599,plain,
( spl0_2000
<=> ! [X0,X40,X10] : c_List_Olist_OCons(X10,X40,X0) = c_List_Orev(c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f621,axiom,
! [X40,X10,X0] : c_List_Olist_OCons(X10,X40,X0) = c_List_Orev(c_append(c_List_Orev(X40,X0),c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f18597,plain,
spl0_1999,
inference(avatar_split_clause,[],[f618,f18595]) ).
fof(f18595,plain,
( spl0_1999
<=> ! [X12,X39,X14] : c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f618,axiom,
! [X39,X14,X12] : c_List_Orev(c_List_Olist_OCons(X12,X39,X14),X14) = c_append(c_List_Orev(X39,X14),c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f18593,plain,
spl0_1998,
inference(avatar_split_clause,[],[f607,f18591]) ).
fof(f18591,plain,
( spl0_1998
<=> ! [X12,X39,X14] :
( ~ c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Oremdups(X39,X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f607,axiom,
! [X39,X14,X12] :
( ~ c_in(X12,c_List_Oset(X39,X14),X14)
| c_List_Oremdups(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Oremdups(X39,X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f18589,plain,
spl0_1997,
inference(avatar_split_clause,[],[f595,f18587]) ).
fof(f18587,plain,
( spl0_1997
<=> ! [X0,X11,X39] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_in(c_List_Onth(X39,X11,X0),c_List_Oset(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f595,axiom,
! [X39,X0,X11] :
( ~ c_less(X11,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat)
| c_in(c_List_Onth(X39,X11,X0),c_List_Oset(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f18585,plain,
spl0_1996,
inference(avatar_split_clause,[],[f594,f18583]) ).
fof(f18583,plain,
( spl0_1996
<=> ! [X0,X12,X50,X23,X39] :
( X23 = X50
| c_List_Onth(c_List_Olist__update(X39,X23,X12,X0),X50,X0) = c_List_Onth(X39,X50,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f594,axiom,
! [X50,X39,X0,X12,X23] :
( X23 = X50
| c_List_Onth(c_List_Olist__update(X39,X23,X12,X0),X50,X0) = c_List_Onth(X39,X50,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f18581,plain,
spl0_1995,
inference(avatar_split_clause,[],[f512,f18579]) ).
fof(f18579,plain,
( spl0_1995
<=> ! [X0,X12,X19] : ~ c_in(c_Pair(X12,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f512,axiom,
! [X0,X19,X12] : ~ c_in(c_Pair(X12,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olexord(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f18577,plain,
spl0_1994,
inference(avatar_split_clause,[],[f499,f18575]) ).
fof(f18575,plain,
( spl0_1994
<=> ! [X0,X39] :
( c_List_Oremdups(X39,X0) = X39
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f499,axiom,
! [X39,X0] :
( c_List_Oremdups(X39,X0) = X39
| c_Nat_Osize(X39,tc_List_Olist(X0)) != c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f18573,plain,
spl0_1993,
inference(avatar_split_clause,[],[f439,f18571]) ).
fof(f18571,plain,
( spl0_1993
<=> ! [X39,X0,X40] : c_List_Oconcat(c_append(X39,X40,tc_List_Olist(X0)),X0) = c_append(c_List_Oconcat(X39,X0),c_List_Oconcat(X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f439,axiom,
! [X40,X39,X0] : c_List_Oconcat(c_append(X39,X40,tc_List_Olist(X0)),X0) = c_append(c_List_Oconcat(X39,X0),c_List_Oconcat(X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f18550,plain,
spl0_1992,
inference(avatar_split_clause,[],[f432,f18548]) ).
fof(f18548,plain,
( spl0_1992
<=> ! [X12,X39,X14] :
( c_List_Olist_ONil = X39
| c_List_Obutlast(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Obutlast(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f432,axiom,
! [X39,X14,X12] :
( c_List_Olist_ONil = X39
| c_List_Obutlast(c_List_Olist_OCons(X12,X39,X14),X14) = c_List_Olist_OCons(X12,c_List_Obutlast(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f18546,plain,
spl0_1991,
inference(avatar_split_clause,[],[f413,f18544]) ).
fof(f18544,plain,
( spl0_1991
<=> ! [X0,X10] :
( c_List_Olist_ONil = X10
| c_append(c_List_Obutlast(X10,X0),c_List_Olist_OCons(c_List_Olast(X10,X0),c_List_Olist_ONil,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f413,axiom,
! [X10,X0] :
( c_List_Olist_ONil = X10
| c_append(c_List_Obutlast(X10,X0),c_List_Olist_OCons(c_List_Olast(X10,X0),c_List_Olist_ONil,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f18542,plain,
spl0_1990,
inference(avatar_split_clause,[],[f409,f18540]) ).
fof(f18540,plain,
( spl0_1990
<=> ! [X0,X40,X19] : ~ c_in(c_Pair(c_List_Olist_ONil,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f409,axiom,
! [X40,X0,X19] : ~ c_in(c_Pair(c_List_Olist_ONil,X40,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f18538,plain,
spl0_1989,
inference(avatar_split_clause,[],[f401,f18536]) ).
fof(f18536,plain,
( spl0_1989
<=> ! [X29,X41,X0] :
( c_List_Olist_ONil = X29
| c_List_Olist_ONil != c_List_Oconcat(X41,X0)
| ~ c_in(X29,c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).
fof(f401,axiom,
! [X41,X29,X0] :
( c_List_Olist_ONil = X29
| c_List_Olist_ONil != c_List_Oconcat(X41,X0)
| ~ c_in(X29,c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
fof(f18534,plain,
spl0_1988,
inference(avatar_split_clause,[],[f400,f18532]) ).
fof(f18532,plain,
( spl0_1988
<=> ! [X0,X39,X19] : ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f400,axiom,
! [X39,X0,X19] : ~ c_in(c_Pair(X39,c_List_Olist_ONil,tc_List_Olist(X0),tc_List_Olist(X0)),c_List_Olex(X19,X0),tc_prod(tc_List_Olist(X0),tc_List_Olist(X0))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f18530,plain,
spl0_1987,
inference(avatar_split_clause,[],[f205,f18528]) ).
fof(f18528,plain,
( spl0_1987
<=> ! [X0,X11] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f205,axiom,
! [X0,X11] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f18526,plain,
spl0_1986,
inference(avatar_split_clause,[],[f197,f18524]) ).
fof(f18524,plain,
( spl0_1986
<=> ! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X11,X24,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f197,axiom,
! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X11,X24,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f18522,plain,
spl0_1985,
inference(avatar_split_clause,[],[f196,f18520]) ).
fof(f18520,plain,
( spl0_1985
<=> ! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X24,X11,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f196,axiom,
! [X11,X24] : c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,c_plus(X24,X11,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f18518,plain,
spl0_1984,
inference(avatar_split_clause,[],[f195,f18516]) ).
fof(f18516,plain,
( spl0_1984
<=> ! [X11,X24] : c_GCD_Ogcd(c_Pair(c_plus(X24,X11,tc_nat),X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f195,axiom,
! [X11,X24] : c_GCD_Ogcd(c_Pair(c_plus(X24,X11,tc_nat),X11,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f18514,plain,
spl0_1983,
inference(avatar_split_clause,[],[f166,f18512]) ).
fof(f18512,plain,
( spl0_1983
<=> ! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMin(X26,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f166,axiom,
! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMin(X26,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f18510,plain,
( spl0_1982
| ~ spl0_1009
| ~ spl0_1555 ),
inference(avatar_split_clause,[],[f12923,f12508,f8725,f18508]) ).
fof(f12508,plain,
( spl0_1555
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_plus(X3,X1,X0),X1,X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f12923,plain,
( ! [X0,X1] : c_minus(c_plus(X0,X1,t_b),X1,t_b) = X0
| ~ spl0_1009
| ~ spl0_1555 ),
inference(resolution,[],[f12509,f8727]) ).
fof(f8727,plain,
( class_OrderedGroup_Oab__group__add(t_b)
| ~ spl0_1009 ),
inference(avatar_component_clause,[],[f8725]) ).
fof(f12509,plain,
( ! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_plus(X3,X1,X0),X1,X0) = X3 )
| ~ spl0_1555 ),
inference(avatar_component_clause,[],[f12508]) ).
fof(f18506,plain,
spl0_1981,
inference(avatar_split_clause,[],[f151,f18504]) ).
fof(f18504,plain,
( spl0_1981
<=> ! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMax(X26,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f151,axiom,
! [X0,X26] :
( ~ class_Orderings_Olinorder(X0)
| c_emptyset = X26
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Finite__Set_OMax(X26,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f18502,plain,
spl0_1980,
inference(avatar_split_clause,[],[f7,f18500]) ).
fof(f18500,plain,
( spl0_1980
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_times(X3,X1,X0),c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ class_HOL_Otimes(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_times(X3,X1,X0),c_SetsAndFunctions_Oelt__set__times(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__times__intro2_0) ).
fof(f18498,plain,
spl0_1979,
inference(avatar_split_clause,[],[f1,f18496]) ).
fof(f18496,plain,
( spl0_1979
<=> ! [X0,X3,X2,X1] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_plus(X3,X1,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ class_HOL_Oplus(X0)
| ~ c_in(X1,X2,X0)
| c_in(c_plus(X3,X1,X0),c_SetsAndFunctions_Oelt__set__plus(X3,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__plus__intro2_0) ).
fof(f18432,plain,
( spl0_1978
| ~ spl0_1009
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f12920,f12504,f8725,f18430]) ).
fof(f18430,plain,
( spl0_1978
<=> ! [X0,X1] : c_plus(c_minus(X0,X1,t_b),X1,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f12504,plain,
( spl0_1554
<=> ! [X25,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(c_minus(X25,X1,X0),X1,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f12920,plain,
( ! [X0,X1] : c_plus(c_minus(X0,X1,t_b),X1,t_b) = X0
| ~ spl0_1009
| ~ spl0_1554 ),
inference(resolution,[],[f12505,f8727]) ).
fof(f12505,plain,
( ! [X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(c_minus(X25,X1,X0),X1,X0) = X25 )
| ~ spl0_1554 ),
inference(avatar_component_clause,[],[f12504]) ).
fof(f18248,plain,
( spl0_1977
| ~ spl0_1059
| ~ spl0_1544 ),
inference(avatar_split_clause,[],[f12891,f12464,f8960,f18246]) ).
fof(f12464,plain,
( spl0_1544
<=> ! [X0,X3] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_OatLeastAtMost(X3,X3,X0) = c_insert(X3,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f12891,plain,
( ! [X0] : c_insert(X0,c_emptyset,t_b) = c_SetInterval_OatLeastAtMost(X0,X0,t_b)
| ~ spl0_1059
| ~ spl0_1544 ),
inference(resolution,[],[f12465,f8962]) ).
fof(f8962,plain,
( class_Orderings_Oorder(t_b)
| ~ spl0_1059 ),
inference(avatar_component_clause,[],[f8960]) ).
fof(f12465,plain,
( ! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_OatLeastAtMost(X3,X3,X0) = c_insert(X3,c_emptyset,X0) )
| ~ spl0_1544 ),
inference(avatar_component_clause,[],[f12464]) ).
fof(f18122,plain,
( spl0_1976
| ~ spl0_1069
| ~ spl0_1533 ),
inference(avatar_split_clause,[],[f12766,f12420,f9023,f18120]) ).
fof(f18120,plain,
( spl0_1976
<=> ! [X0] : c_HOL_Oabs(X0,t_b) = c_HOL_Oabs(c_uminus(X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f12420,plain,
( spl0_1533
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f12766,plain,
( ! [X0] : c_HOL_Oabs(X0,t_b) = c_HOL_Oabs(c_uminus(X0,t_b),t_b)
| ~ spl0_1069
| ~ spl0_1533 ),
inference(resolution,[],[f12421,f9025]) ).
fof(f9025,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1069 ),
inference(avatar_component_clause,[],[f9023]) ).
fof(f12421,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_uminus(X3,X0),X0) )
| ~ spl0_1533 ),
inference(avatar_component_clause,[],[f12420]) ).
fof(f17961,plain,
( spl0_1975
| ~ spl0_1059
| ~ spl0_1650
| ~ spl0_1974 ),
inference(avatar_split_clause,[],[f17715,f17551,f13280,f8960,f17958]) ).
fof(f17958,plain,
( spl0_1975
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f13280,plain,
( spl0_1650
<=> ! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(X24,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f17551,plain,
( spl0_1974
<=> c_less(c_0,c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f17715,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OatLeastAtMost(c_1,c_0,t_b)
| ~ spl0_1650
| ~ spl0_1974 ),
inference(resolution,[],[f17553,f13281]) ).
fof(f13281,plain,
( ! [X0,X11,X24] :
( ~ c_less(X11,X24,X0)
| ~ class_Orderings_Oorder(X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(X24,X11,X0) )
| ~ spl0_1650 ),
inference(avatar_component_clause,[],[f13280]) ).
fof(f17553,plain,
( c_less(c_0,c_1,t_b)
| ~ spl0_1974 ),
inference(avatar_component_clause,[],[f17551]) ).
fof(f17554,plain,
( spl0_1974
| ~ spl0_965
| ~ spl0_1472
| spl0_1956 ),
inference(avatar_split_clause,[],[f17509,f17424,f11911,f8447,f17551]) ).
fof(f17509,plain,
( ~ class_Orderings_Olinorder(t_b)
| c_less(c_0,c_1,t_b)
| ~ spl0_1472
| spl0_1956 ),
inference(resolution,[],[f17426,f11912]) ).
fof(f17426,plain,
( ~ c_lessequals(c_1,c_0,t_b)
| spl0_1956 ),
inference(avatar_component_clause,[],[f17424]) ).
fof(f17549,plain,
spl0_1973,
inference(avatar_split_clause,[],[f3222,f17547]) ).
fof(f17547,plain,
( spl0_1973
<=> ! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f3222,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3221,f1009]) ).
fof(f1009,axiom,
! [X10] : c_Numeral_Obin__add(X10,c_Numeral_OPls) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3221,plain,
! [X0,X12] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3018,f2813]) ).
fof(f2813,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f1020,f1023]) ).
fof(f1020,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(f3018,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f211,f1023]) ).
fof(f211,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f17545,plain,
spl0_1972,
inference(avatar_split_clause,[],[f3215,f17543]) ).
fof(f17543,plain,
( spl0_1972
<=> ! [X0,X10] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f3215,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3214,f1009]) ).
fof(f3214,plain,
! [X10,X0] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3012,f2813]) ).
fof(f3012,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f215,f1023]) ).
fof(f215,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f17541,plain,
spl0_1971,
inference(avatar_split_clause,[],[f3212,f17539]) ).
fof(f17539,plain,
( spl0_1971
<=> ! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f3212,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3211,f1009]) ).
fof(f3211,plain,
! [X0,X12] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0) ),
inference(forward_demodulation,[],[f3010,f2813]) ).
fof(f3010,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f210,f1023]) ).
fof(f210,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_Numeral_Onumber__of(X12,X0),c_0,X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f17537,plain,
spl0_1970,
inference(avatar_split_clause,[],[f3205,f17535]) ).
fof(f17535,plain,
( spl0_1970
<=> ! [X0,X10] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f3205,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X10,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3204,f1009]) ).
fof(f3204,plain,
! [X10,X0] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0) ),
inference(forward_demodulation,[],[f3004,f2813]) ).
fof(f3004,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f214,f1023]) ).
fof(f214,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X10,X0),X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X10,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f17533,plain,
spl0_1969,
inference(avatar_split_clause,[],[f3186,f17531]) ).
fof(f17531,plain,
( spl0_1969
<=> ! [X11,X24] :
( c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f3186,plain,
! [X11,X24] :
( c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ),
inference(forward_demodulation,[],[f2990,f2814]) ).
fof(f2990,plain,
! [X11,X24] :
( ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X24,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f991,f1438]) ).
fof(f991,axiom,
! [X11,X24] :
( ~ c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f17529,plain,
spl0_1968,
inference(avatar_split_clause,[],[f3102,f17527]) ).
fof(f17527,plain,
( spl0_1968
<=> ! [X34,X0] :
( c_plus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f3102,plain,
! [X0,X34] :
( c_plus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f224,f1050]) ).
fof(f224,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_Numeral_Onumber__of(X34,X0),c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X34,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f17525,plain,
spl0_1967,
inference(avatar_split_clause,[],[f3101,f17523]) ).
fof(f17523,plain,
( spl0_1967
<=> ! [X0,X33] :
( c_plus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X33),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f3101,plain,
! [X0,X33] :
( c_plus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X33),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f223,f1050]) ).
fof(f223,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_1,c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X33),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f17521,plain,
spl0_1966,
inference(avatar_split_clause,[],[f3074,f17519]) ).
fof(f17519,plain,
( spl0_1966
<=> ! [X0,X19] : c_List_Olistset(c_List_Olist_ONil,X0) = c_Relation_OImage(c_List_Olistrel(X19,X0),c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f3074,plain,
! [X0,X19] : c_List_Olistset(c_List_Olist_ONil,X0) = c_Relation_OImage(c_List_Olistrel(X19,X0),c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0),tc_List_Olist(X0)),
inference(forward_demodulation,[],[f530,f533]) ).
fof(f533,axiom,
! [X14] : c_List_Olistset(c_List_Olist_ONil,X14) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X14)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f530,axiom,
! [X0,X19] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X0)) = c_Relation_OImage(c_List_Olistrel(X19,X0),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X0)),tc_List_Olist(X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f17517,plain,
spl0_1965,
inference(avatar_split_clause,[],[f3071,f17515]) ).
fof(f17515,plain,
( spl0_1965
<=> ! [X0,X55,X3] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f3071,plain,
! [X3,X0,X55] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_1,tc_nat),
inference(forward_demodulation,[],[f2895,f2814]) ).
fof(f2895,plain,
! [X3,X0,X55] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f521,f1438]) ).
fof(f521,axiom,
! [X3,X0,X55] : c_Nat_Osize(c_List_Olist_OCons(X3,X55,X0),tc_List_Olist(X0)) = c_plus(c_Nat_Osize(X55,tc_List_Olist(X0)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f17513,plain,
spl0_1964,
inference(avatar_split_clause,[],[f3067,f17511]) ).
fof(f17511,plain,
( spl0_1964
<=> ! [X3,X0,X30,X2] : c_union(c_insert(X3,X30,X0),X2,X0) = c_union(X30,c_insert(X3,X2,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f3067,plain,
! [X2,X3,X0,X30] : c_union(c_insert(X3,X30,X0),X2,X0) = c_union(X30,c_insert(X3,X2,X0),X0),
inference(forward_demodulation,[],[f1537,f1538]) ).
fof(f1538,axiom,
! [X3,X0,X26,X30] : c_union(X26,c_insert(X3,X30,X0),X0) = c_insert(X3,c_union(X26,X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f1537,axiom,
! [X2,X3,X0,X30] : c_union(c_insert(X3,X30,X0),X2,X0) = c_insert(X3,c_union(X30,X2,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f17508,plain,
spl0_1963,
inference(avatar_split_clause,[],[f2972,f17506]) ).
fof(f17506,plain,
( spl0_1963
<=> ! [X0,X11,X10] :
( c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f2972,plain,
! [X10,X0,X11] :
( c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X11,tc_nat) ),
inference(definition_unfolding,[],[f664,f660]) ).
fof(f664,axiom,
! [X10,X0,X11] :
( c_List_Otake(X11,X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f17488,plain,
( spl0_1962
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1961 ),
inference(avatar_split_clause,[],[f17484,f17481,f13448,f13139,f8657,f3868,f17486]) ).
fof(f17486,plain,
( spl0_1962
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_plus(c_1,X36,tc_nat),X72,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f17481,plain,
( spl0_1961
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),X72,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f17484,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_plus(c_1,X36,tc_nat),X72,tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1961 ),
inference(forward_demodulation,[],[f17482,f14217]) ).
fof(f17482,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),X72,tc_nat)
| ~ spl0_1961 ),
inference(avatar_component_clause,[],[f17481]) ).
fof(f17483,plain,
spl0_1961,
inference(avatar_split_clause,[],[f2866,f17481]) ).
fof(f17465,plain,
( spl0_1960
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1959 ),
inference(avatar_split_clause,[],[f17461,f17458,f13448,f13139,f8657,f3868,f17463]) ).
fof(f17458,plain,
( spl0_1959
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Finite__Set_Ocard(c_SetInterval_OatMost(X72,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f17461,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_plus(c_1,X72,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1959 ),
inference(forward_demodulation,[],[f17459,f14217]) ).
fof(f17459,plain,
( ! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,c_Finite__Set_Ocard(c_SetInterval_OatMost(X72,tc_nat),tc_nat),tc_nat)
| ~ spl0_1959 ),
inference(avatar_component_clause,[],[f17458]) ).
fof(f17460,plain,
spl0_1959,
inference(avatar_split_clause,[],[f2865,f17458]) ).
fof(f17436,plain,
( spl0_1958
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1957 ),
inference(avatar_split_clause,[],[f17432,f17429,f13448,f13139,f8657,f3868,f17434]) ).
fof(f17434,plain,
( spl0_1958
<=> ! [X0,X11,X39] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_plus(c_1,X11,tc_nat),X39,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f17429,plain,
( spl0_1957
<=> ! [X0,X11,X39] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X39,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f17432,plain,
( ! [X39,X0,X11] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_plus(c_1,X11,tc_nat),X39,X0)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1957 ),
inference(forward_demodulation,[],[f17430,f14217]) ).
fof(f17430,plain,
( ! [X39,X0,X11] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X39,X0)
| ~ spl0_1957 ),
inference(avatar_component_clause,[],[f17429]) ).
fof(f17431,plain,
spl0_1957,
inference(avatar_split_clause,[],[f2864,f17429]) ).
fof(f2864,plain,
! [X39,X0,X11] : c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X39,X0),
inference(definition_unfolding,[],[f632,f1438]) ).
fof(f632,axiom,
! [X39,X0,X11] : c_List_Orotate(c_Suc(X11),X39,X0) = c_List_Orotate1(c_List_Orotate(X11,X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f17427,plain,
( ~ spl0_1069
| spl0_116
| ~ spl0_1956
| ~ spl0_1427
| ~ spl0_1532 ),
inference(avatar_split_clause,[],[f12762,f12416,f11725,f17424,f3800,f9023]) ).
fof(f3800,plain,
( spl0_116
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f11725,plain,
( spl0_1427
<=> c_1 = c_HOL_Oabs(c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f12416,plain,
( spl0_1532
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| ~ c_lessequals(c_HOL_Oabs(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f12762,plain,
( ~ c_lessequals(c_1,c_0,t_b)
| c_0 = c_1
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1427
| ~ spl0_1532 ),
inference(superposition,[],[f12417,f11727]) ).
fof(f11727,plain,
( c_1 = c_HOL_Oabs(c_1,t_b)
| ~ spl0_1427 ),
inference(avatar_component_clause,[],[f11725]) ).
fof(f12417,plain,
( ! [X3,X0] :
( ~ c_lessequals(c_HOL_Oabs(X3,X0),c_0,X0)
| c_0 = X3
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1532 ),
inference(avatar_component_clause,[],[f12416]) ).
fof(f17422,plain,
spl0_1955,
inference(avatar_split_clause,[],[f1748,f17420]) ).
fof(f17420,plain,
( spl0_1955
<=> ! [X0,X85,X16,X86] :
( ~ c_Wellfounded__Recursion_Owf(X85,X16)
| ~ c_Wellfounded__Recursion_Owf(X86,X0)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X86,X85,X0,X16),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f1748,axiom,
! [X0,X86,X16,X85] :
( ~ c_Wellfounded__Recursion_Owf(X85,X16)
| ~ c_Wellfounded__Recursion_Owf(X86,X0)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X86,X85,X0,X16),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f17418,plain,
spl0_1954,
inference(avatar_split_clause,[],[f1746,f17416]) ).
fof(f17416,plain,
( spl0_1954
<=> ! [X0,X84,X16,X83] :
( ~ c_Relation_Otrans(X83,X16)
| ~ c_Relation_Otrans(X84,X0)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X84,X83,X0,X16),tc_prod(X0,X16)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f1746,axiom,
! [X83,X0,X16,X84] :
( ~ c_Relation_Otrans(X83,X16)
| ~ c_Relation_Otrans(X84,X0)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X84,X83,X0,X16),tc_prod(X0,X16)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f17414,plain,
spl0_1953,
inference(avatar_split_clause,[],[f1701,f17412]) ).
fof(f17412,plain,
( spl0_1953
<=> ! [X25,X0,X26] :
( c_in(c_Main_OdiagE__1(X26,X25,X0),X26,X0)
| ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f1701,axiom,
! [X0,X26,X25] :
( c_in(c_Main_OdiagE__1(X26,X25,X0),X26,X0)
| ~ c_in(X25,c_Relation_Odiag(X26,X0),tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f17410,plain,
spl0_1952,
inference(avatar_split_clause,[],[f1616,f17408]) ).
fof(f17408,plain,
( spl0_1952
<=> ! [X0,X12,X19,X10] :
( c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f1616,axiom,
! [X10,X0,X19,X12] :
( c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f17406,plain,
spl0_1951,
inference(avatar_split_clause,[],[f1613,f17404]) ).
fof(f17404,plain,
( spl0_1951
<=> ! [X0,X12,X19,X10] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f1613,axiom,
! [X10,X0,X19,X12] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X10,X12,X0,X0),X19,tc_prod(X0,X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f17402,plain,
spl0_1950,
inference(avatar_split_clause,[],[f1551,f17400]) ).
fof(f17400,plain,
( spl0_1950
<=> ! [X0,X29,X2,X26] :
( ~ c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| c_in(X26,c_Union(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f1551,axiom,
! [X2,X29,X0,X26] :
( ~ c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| c_in(X26,c_Union(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f17398,plain,
spl0_1949,
inference(avatar_split_clause,[],[f1538,f17396]) ).
fof(f17396,plain,
( spl0_1949
<=> ! [X0,X3,X26,X30] : c_union(X26,c_insert(X3,X30,X0),X0) = c_insert(X3,c_union(X26,X30,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f17394,plain,
spl0_1948,
inference(avatar_split_clause,[],[f1534,f17392]) ).
fof(f17392,plain,
( spl0_1948
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_in(X25,c_union(X26,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f1534,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_in(X25,c_union(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f17390,plain,
spl0_1947,
inference(avatar_split_clause,[],[f1514,f17388]) ).
fof(f17388,plain,
( spl0_1947
<=> ! [X0,X29,X2,X26] :
( c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| ~ c_in(X26,c_Inter(X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f1514,axiom,
! [X2,X29,X0,X26] :
( c_in(X26,X29,X0)
| ~ c_in(X29,X2,tc_set(X0))
| ~ c_in(X26,c_Inter(X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f17386,plain,
spl0_1946,
inference(avatar_split_clause,[],[f1487,f17384]) ).
fof(f17384,plain,
( spl0_1946
<=> ! [X0,X30,X26] : c_minus(X26,X30,tc_set(X0)) = c_minus(c_minus(X26,X30,tc_set(X0)),X30,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f1487,axiom,
! [X0,X26,X30] : c_minus(X26,X30,tc_set(X0)) = c_minus(c_minus(X26,X30,tc_set(X0)),X30,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f17382,plain,
( spl0_1945
| ~ spl0_1069
| ~ spl0_1530 ),
inference(avatar_split_clause,[],[f12758,f12408,f9023,f17380]) ).
fof(f17380,plain,
( spl0_1945
<=> ! [X0] : c_HOL_Oabs(X0,t_b) = c_HOL_Oabs(c_HOL_Oabs(X0,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f12408,plain,
( spl0_1530
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_HOL_Oabs(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f12758,plain,
( ! [X0] : c_HOL_Oabs(X0,t_b) = c_HOL_Oabs(c_HOL_Oabs(X0,t_b),t_b)
| ~ spl0_1069
| ~ spl0_1530 ),
inference(resolution,[],[f12409,f9025]) ).
fof(f12409,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_HOL_Oabs(X3,X0),X0) )
| ~ spl0_1530 ),
inference(avatar_component_clause,[],[f12408]) ).
fof(f17378,plain,
spl0_1944,
inference(avatar_split_clause,[],[f1466,f17376]) ).
fof(f17376,plain,
( spl0_1944
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f1466,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f17374,plain,
spl0_1943,
inference(avatar_split_clause,[],[f1465,f17372]) ).
fof(f17372,plain,
( spl0_1943
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f1465,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OlessThan(X12,X0),c_SetInterval_OlessThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f17370,plain,
spl0_1942,
inference(avatar_split_clause,[],[f1455,f17368]) ).
fof(f17368,plain,
( spl0_1942
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f1455,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f17366,plain,
spl0_1941,
inference(avatar_split_clause,[],[f1454,f17364]) ).
fof(f17364,plain,
( spl0_1941
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f1454,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X12,X0),c_SetInterval_OgreaterThan(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f17362,plain,
spl0_1940,
inference(avatar_split_clause,[],[f1442,f17360]) ).
fof(f17360,plain,
( spl0_1940
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,c_plus(X72,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f1442,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,c_plus(X72,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f17358,plain,
spl0_1939,
inference(avatar_split_clause,[],[f1435,f17356]) ).
fof(f17356,plain,
( spl0_1939
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X36,X72,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f1435,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X36,X72,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f17354,plain,
spl0_1938,
inference(avatar_split_clause,[],[f1433,f17352]) ).
fof(f17352,plain,
( spl0_1938
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f1433,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X12,X10,X0)
| c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f17350,plain,
spl0_1937,
inference(avatar_split_clause,[],[f1432,f17348]) ).
fof(f17348,plain,
( spl0_1937
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f1432,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X10,X0)
| ~ c_lessequals(c_SetInterval_OatMost(X12,X0),c_SetInterval_OatMost(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f17346,plain,
spl0_1936,
inference(avatar_split_clause,[],[f1427,f17344]) ).
fof(f17344,plain,
( spl0_1936
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f1427,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X10,X12,X0)
| c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f17342,plain,
spl0_1935,
inference(avatar_split_clause,[],[f1426,f17340]) ).
fof(f17340,plain,
( spl0_1935
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f1426,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X10,X12,X0)
| ~ c_lessequals(c_SetInterval_OatLeast(X12,X0),c_SetInterval_OatLeast(X10,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f17338,plain,
( spl0_1934
| ~ spl0_938
| ~ spl0_1502 ),
inference(avatar_split_clause,[],[f12602,f12287,f7778,f17336]) ).
fof(f7778,plain,
( spl0_938
<=> class_Ring__and__Field_Ocomm__ring__1(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f12287,plain,
( spl0_1502
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_NatArith_Oof__nat(X11,X0) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X11,tc_IntDef_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f12602,plain,
( ! [X0] : c_NatArith_Oof__nat(X0,t_b) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X0,tc_IntDef_Oint),t_b)
| ~ spl0_938
| ~ spl0_1502 ),
inference(resolution,[],[f12288,f7780]) ).
fof(f7780,plain,
( class_Ring__and__Field_Ocomm__ring__1(t_b)
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f7778]) ).
fof(f12288,plain,
( ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_NatArith_Oof__nat(X11,X0) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X11,tc_IntDef_Oint),X0) )
| ~ spl0_1502 ),
inference(avatar_component_clause,[],[f12287]) ).
fof(f17334,plain,
spl0_1933,
inference(avatar_split_clause,[],[f1384,f17332]) ).
fof(f17332,plain,
( spl0_1933
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_uminus(c_times(X3,X1,X0),X0) = c_times(X3,c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f1384,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_uminus(c_times(X3,X1,X0),X0) = c_times(X3,c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f17330,plain,
spl0_1932,
inference(avatar_split_clause,[],[f1383,f17328]) ).
fof(f17328,plain,
( spl0_1932
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(c_uminus(X3,X0),X1,X0) = c_uminus(c_times(X3,X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f1383,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(c_uminus(X3,X0),X1,X0) = c_uminus(c_times(X3,X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f17326,plain,
spl0_1931,
inference(avatar_split_clause,[],[f1361,f17324]) ).
fof(f17324,plain,
( spl0_1931
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(X3,X1,X0) = c_times(c_uminus(X3,X0),c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f1361,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oring(X0)
| c_times(X3,X1,X0) = c_times(c_uminus(X3,X0),c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f17322,plain,
spl0_1930,
inference(avatar_split_clause,[],[f1206,f17320]) ).
fof(f17320,plain,
( spl0_1930
<=> ! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f1206,axiom,
! [X0,X33] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Numeral_Onumber__of(X33,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X33,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f17318,plain,
spl0_1929,
inference(avatar_split_clause,[],[f1200,f17316]) ).
fof(f17316,plain,
( spl0_1929
<=> ! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f1200,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Power_Orecpower(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f17314,plain,
spl0_1928,
inference(avatar_split_clause,[],[f1198,f17312]) ).
fof(f17312,plain,
( spl0_1928
<=> ! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f1198,axiom,
! [X0,X12] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X0),X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f17310,plain,
spl0_1927,
inference(avatar_split_clause,[],[f1103,f17308]) ).
fof(f17308,plain,
( spl0_1927
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f1103,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f17306,plain,
spl0_1926,
inference(avatar_split_clause,[],[f1102,f17304]) ).
fof(f17304,plain,
( spl0_1926
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f1102,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ class_Orderings_Olinorder(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f17302,plain,
spl0_1925,
inference(avatar_split_clause,[],[f974,f17300]) ).
fof(f17300,plain,
( spl0_1925
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f974,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f17298,plain,
spl0_1924,
inference(avatar_split_clause,[],[f954,f17296]) ).
fof(f17296,plain,
( spl0_1924
<=> ! [X9,X11,X24] :
( X11 = X24
| c_0 = X9
| c_times(X11,X9,tc_nat) != c_times(X24,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f954,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_0 = X9
| c_times(X11,X9,tc_nat) != c_times(X24,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f17292,plain,
spl0_1923,
inference(avatar_split_clause,[],[f952,f17290]) ).
fof(f17290,plain,
( spl0_1923
<=> ! [X9,X11,X24] :
( X11 = X24
| c_0 = X9
| c_times(X9,X11,tc_nat) != c_times(X9,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f952,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_0 = X9
| c_times(X9,X11,tc_nat) != c_times(X9,X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f17288,plain,
spl0_1922,
inference(avatar_split_clause,[],[f931,f17286]) ).
fof(f17286,plain,
( spl0_1922
<=> ! [X9,X50,X23] : c_minus(c_minus(X23,X50,tc_nat),X9,tc_nat) = c_minus(X23,c_plus(X50,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f17284,plain,
spl0_1921,
inference(avatar_split_clause,[],[f922,f17282]) ).
fof(f17282,plain,
( spl0_1921
<=> ! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f922,axiom,
! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f17280,plain,
spl0_1920,
inference(avatar_split_clause,[],[f757,f17278]) ).
fof(f17278,plain,
( spl0_1920
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f757,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f17276,plain,
spl0_1919,
inference(avatar_split_clause,[],[f754,f17274]) ).
fof(f17274,plain,
( spl0_1919
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f754,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f17272,plain,
spl0_1918,
inference(avatar_split_clause,[],[f725,f17270]) ).
fof(f17270,plain,
( spl0_1918
<=> ! [X34] :
( c_0 != c_Numeral_Onumber__of(X34,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f725,axiom,
! [X34] :
( c_0 != c_Numeral_Onumber__of(X34,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_0) ).
fof(f17268,plain,
spl0_1917,
inference(avatar_split_clause,[],[f721,f17266]) ).
fof(f17266,plain,
( spl0_1917
<=> ! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f721,axiom,
! [X34,X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X34,tc_nat),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f17264,plain,
spl0_1916,
inference(avatar_split_clause,[],[f695,f17262]) ).
fof(f17262,plain,
( spl0_1916
<=> ! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X24,X11,tc_nat),X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f695,axiom,
! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X24,X11,tc_nat),X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f17260,plain,
spl0_1915,
inference(avatar_split_clause,[],[f643,f17258]) ).
fof(f17258,plain,
( spl0_1915
<=> ! [X39,X0,X40] : c_List_Oset(c_append(X39,X40,X0),X0) = c_union(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f643,axiom,
! [X40,X39,X0] : c_List_Oset(c_append(X39,X40,X0),X0) = c_union(c_List_Oset(X39,X0),c_List_Oset(X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f17256,plain,
spl0_1914,
inference(avatar_split_clause,[],[f633,f17254]) ).
fof(f17254,plain,
( spl0_1914
<=> ! [X0,X11,X10] :
( c_List_Orotate(X11,X10,X0) = X10
| c_0 != c_Divides_Oop_Amod(X11,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f633,axiom,
! [X10,X0,X11] :
( c_List_Orotate(X11,X10,X0) = X10
| c_0 != c_Divides_Oop_Amod(X11,c_Nat_Osize(X10,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f17252,plain,
( spl0_1913
| ~ spl0_1059
| ~ spl0_2
| ~ spl0_1661 ),
inference(avatar_split_clause,[],[f13983,f13325,f3231,f8960,f17250]) ).
fof(f17250,plain,
( spl0_1913
<=> ! [X0] : c_emptyset = c_SetInterval_OgreaterThanAtMost(v_k(X0),c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f13983,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(v_k(X0),c_0,t_b) )
| ~ spl0_2
| ~ spl0_1661 ),
inference(resolution,[],[f13326,f3232]) ).
fof(f17248,plain,
spl0_1912,
inference(avatar_split_clause,[],[f619,f17246]) ).
fof(f17246,plain,
( spl0_1912
<=> ! [X40,X0,X39] : c_List_Orev(c_append(X39,X40,X0),X0) = c_append(c_List_Orev(X40,X0),c_List_Orev(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f619,axiom,
! [X40,X39,X0] : c_List_Orev(c_append(X39,X40,X0),X0) = c_append(c_List_Orev(X40,X0),c_List_Orev(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f17244,plain,
spl0_1911,
inference(avatar_split_clause,[],[f602,f17242]) ).
fof(f17242,plain,
( spl0_1911
<=> ! [X40,X14,X12,X39] : c_append(c_List_Olist_OCons(X12,X39,X14),X40,X14) = c_List_Olist_OCons(X12,c_append(X39,X40,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f602,axiom,
! [X40,X39,X14,X12] : c_append(c_List_Olist_OCons(X12,X39,X14),X40,X14) = c_List_Olist_OCons(X12,c_append(X39,X40,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f17240,plain,
spl0_1910,
inference(avatar_split_clause,[],[f590,f17238]) ).
fof(f17238,plain,
( spl0_1910
<=> ! [X40,X0,X10,X39] : c_List_Onth(c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f590,axiom,
! [X40,X39,X10,X0] : c_List_Onth(c_append(X39,c_List_Olist_OCons(X10,X40,X0),X0),c_Nat_Osize(X39,tc_List_Olist(X0)),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f17236,plain,
spl0_1909,
inference(avatar_split_clause,[],[f585,f17234]) ).
fof(f17234,plain,
( spl0_1909
<=> ! [X49,X0,X12,X39] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Osublist(X39,X49,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f585,axiom,
! [X39,X0,X49,X12] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Osublist(X39,X49,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f17232,plain,
spl0_1908,
inference(avatar_split_clause,[],[f584,f17230]) ).
fof(f17230,plain,
( spl0_1908
<=> ! [X10,X0,X12,X39] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Oremove1(X10,X39,X0),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f584,axiom,
! [X39,X0,X10,X12] :
( c_in(X12,c_List_Oset(X39,X0),X0)
| ~ c_in(X12,c_List_Oset(c_List_Oremove1(X10,X39,X0),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f17228,plain,
spl0_1907,
inference(avatar_split_clause,[],[f495,f17226]) ).
fof(f17226,plain,
( spl0_1907
<=> ! [X0,X11,X39] : c_Nat_Osize(c_List_Odrop(X11,X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f495,axiom,
! [X39,X0,X11] : c_Nat_Osize(c_List_Odrop(X11,X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f17224,plain,
spl0_1906,
inference(avatar_split_clause,[],[f471,f17222]) ).
fof(f17222,plain,
( spl0_1906
<=> ! [X23,X0,X12,X9] : c_List_Odrop(X23,c_List_Oreplicate(X9,X12,X0),X0) = c_List_Oreplicate(c_minus(X9,X23,tc_nat),X12,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f471,axiom,
! [X0,X9,X12,X23] : c_List_Odrop(X23,c_List_Oreplicate(X9,X12,X0),X0) = c_List_Oreplicate(c_minus(X9,X23,tc_nat),X12,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f17220,plain,
spl0_1905,
inference(avatar_split_clause,[],[f468,f17218]) ).
fof(f17218,plain,
( spl0_1905
<=> ! [X24,X11,X0,X39] : c_List_Odrop(X11,c_List_Odrop(X24,X39,X0),X0) = c_List_Odrop(c_plus(X11,X24,tc_nat),X39,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f468,axiom,
! [X39,X0,X11,X24] : c_List_Odrop(X11,c_List_Odrop(X24,X39,X0),X0) = c_List_Odrop(c_plus(X11,X24,tc_nat),X39,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f17216,plain,
spl0_1904,
inference(avatar_split_clause,[],[f448,f17214]) ).
fof(f17214,plain,
( spl0_1904
<=> ! [X12,X39,X14] :
( ~ c_List_Odistinct(X39,X14)
| c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| c_in(X12,c_List_Oset(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f448,axiom,
! [X39,X14,X12] :
( ~ c_List_Odistinct(X39,X14)
| c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| c_in(X12,c_List_Oset(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f17212,plain,
spl0_1903,
inference(avatar_split_clause,[],[f441,f17210]) ).
fof(f17210,plain,
( spl0_1903
<=> ! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f441,axiom,
! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f17206,plain,
spl0_1902,
inference(avatar_split_clause,[],[f412,f17204]) ).
fof(f17204,plain,
( spl0_1902
<=> ! [X42,X40,X0,X39] : c_append(c_append(X39,X40,X0),X42,X0) = c_append(X39,c_append(X40,X42,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f412,axiom,
! [X40,X39,X0,X42] : c_append(c_append(X39,X40,X0),X42,X0) = c_append(X39,c_append(X40,X42,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f17202,plain,
spl0_1901,
inference(avatar_split_clause,[],[f402,f17200]) ).
fof(f17200,plain,
( spl0_1901
<=> ! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_ONil__eq__concat__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f402,axiom,
! [X41,X0] :
( c_List_Olist_ONil = c_List_Oconcat(X41,X0)
| c_in(c_Main_ONil__eq__concat__conv__1(X41,X0),c_List_Oset(X41,tc_List_Olist(X0)),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f17198,plain,
spl0_1900,
inference(avatar_split_clause,[],[f389,f17196]) ).
fof(f17196,plain,
( spl0_1900
<=> ! [X1,X3] : c_Divides_Oop_Amod(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f389,axiom,
! [X3,X1] : c_Divides_Oop_Amod(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f17194,plain,
spl0_1899,
inference(avatar_split_clause,[],[f133,f17192]) ).
fof(f17192,plain,
( spl0_1899
<=> ! [X9,X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f133,axiom,
! [X11,X9,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X11,X9,tc_nat),tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f17190,plain,
spl0_1898,
inference(avatar_split_clause,[],[f131,f17188]) ).
fof(f17188,plain,
( spl0_1898
<=> ! [X9,X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f131,axiom,
! [X11,X9,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,c_times(X9,X11,tc_nat),tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f17186,plain,
spl0_1897,
inference(avatar_split_clause,[],[f111,f17184]) ).
fof(f17184,plain,
( spl0_1897
<=> ! [X11,X24] :
( ~ c_less(c_1,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_div(X24,X11,tc_nat),X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f111,axiom,
! [X11,X24] :
( ~ c_less(c_1,X11,tc_nat)
| ~ c_less(c_0,X24,tc_nat)
| c_less(c_div(X24,X11,tc_nat),X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f17167,plain,
( spl0_1896
| ~ spl0_1059
| ~ spl0_2
| ~ spl0_1651 ),
inference(avatar_split_clause,[],[f13936,f13284,f3231,f8960,f17165]) ).
fof(f17165,plain,
( spl0_1896
<=> ! [X0] : c_emptyset = c_SetInterval_OatLeastLessThan(v_k(X0),c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f13936,plain,
( ! [X0] :
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OatLeastLessThan(v_k(X0),c_0,t_b) )
| ~ spl0_2
| ~ spl0_1651 ),
inference(resolution,[],[f13285,f3232]) ).
fof(f16846,plain,
( spl0_1895
| ~ spl0_1102
| ~ spl0_2
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f12864,f12444,f3231,f9158,f16844]) ).
fof(f16844,plain,
( spl0_1895
<=> ! [X0] : v_k(X0) = c_OrderedGroup_Opprt(v_k(X0),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f12864,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| v_k(X0) = c_OrderedGroup_Opprt(v_k(X0),t_b) )
| ~ spl0_2
| ~ spl0_1539 ),
inference(resolution,[],[f12445,f3232]) ).
fof(f16580,plain,
( ~ spl0_1069
| spl0_1894
| ~ spl0_1278
| ~ spl0_1893 ),
inference(avatar_split_clause,[],[f16469,f16316,f10378,f16578,f9023]) ).
fof(f16578,plain,
( spl0_1894
<=> ! [X0] : ~ c_less(v_k(X0),c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f10378,plain,
( spl0_1278
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_HOL_Oabs(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f16316,plain,
( spl0_1893
<=> ! [X0] : v_k(X0) = c_HOL_Oabs(v_k(X0),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f16469,plain,
( ! [X0] :
( ~ c_less(v_k(X0),c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b) )
| ~ spl0_1278
| ~ spl0_1893 ),
inference(superposition,[],[f10379,f16317]) ).
fof(f16317,plain,
( ! [X0] : v_k(X0) = c_HOL_Oabs(v_k(X0),t_b)
| ~ spl0_1893 ),
inference(avatar_component_clause,[],[f16316]) ).
fof(f10379,plain,
( ! [X3,X0] :
( ~ c_less(c_HOL_Oabs(X3,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1278 ),
inference(avatar_component_clause,[],[f10378]) ).
fof(f16318,plain,
( spl0_1893
| ~ spl0_1069
| ~ spl0_2
| ~ spl0_1534 ),
inference(avatar_split_clause,[],[f12782,f12424,f3231,f9023,f16316]) ).
fof(f12782,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| v_k(X0) = c_HOL_Oabs(v_k(X0),t_b) )
| ~ spl0_2
| ~ spl0_1534 ),
inference(resolution,[],[f12425,f3232]) ).
fof(f16191,plain,
spl0_1892,
inference(avatar_split_clause,[],[f3178,f16189]) ).
fof(f16189,plain,
( spl0_1892
<=> ! [X0,X10] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f3178,plain,
! [X10,X0] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2984,f1008]) ).
fof(f2984,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f228,f1023]) ).
fof(f228,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X10,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f16187,plain,
spl0_1891,
inference(avatar_split_clause,[],[f3173,f16185]) ).
fof(f16185,plain,
( spl0_1891
<=> ! [X0,X10] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f3173,plain,
! [X10,X0] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X10),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0) ),
inference(forward_demodulation,[],[f2980,f1008]) ).
fof(f2980,plain,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X10)),X0),X0) ),
inference(definition_unfolding,[],[f227,f1023]) ).
fof(f227,axiom,
! [X10,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X10,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X10)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f16183,plain,
spl0_1890,
inference(avatar_split_clause,[],[f3066,f16181]) ).
fof(f16181,plain,
( spl0_1890
<=> ! [X75] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f3066,plain,
! [X75] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2888,f2814]) ).
fof(f2888,plain,
! [X75] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,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(X75,tc_nat),tc_nat),
inference(definition_unfolding,[],[f764,f1438]) ).
fof(f764,axiom,
! [X75] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f16179,plain,
spl0_1889,
inference(avatar_split_clause,[],[f2989,f16177]) ).
fof(f16177,plain,
( spl0_1889
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil = X39
| c_0 = X11
| c_List_Olist_ONil != c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f2989,plain,
! [X39,X0,X11] :
( c_List_Olist_ONil = X39
| c_0 = X11
| c_List_Olist_ONil != c_List_Osublist(X39,c_SetInterval_OlessThan(X11,tc_nat),X0) ),
inference(definition_unfolding,[],[f666,f660]) ).
fof(f666,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil = X39
| c_0 = X11
| c_List_Olist_ONil != c_List_Otake(X11,X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f16172,plain,
( spl0_1888
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1887 ),
inference(avatar_split_clause,[],[f16168,f16165,f13448,f13139,f8657,f3868,f16170]) ).
fof(f16170,plain,
( spl0_1888
<=> ! [X34] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f16165,plain,
( spl0_1887
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f16168,plain,
( ! [X34] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1887 ),
inference(forward_demodulation,[],[f16166,f14217]) ).
fof(f16166,plain,
( ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1887 ),
inference(avatar_component_clause,[],[f16165]) ).
fof(f16167,plain,
spl0_1887,
inference(avatar_split_clause,[],[f2955,f16165]) ).
fof(f2955,plain,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X34,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f716,f1438]) ).
fof(f716,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X34,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f16163,plain,
spl0_1886,
inference(avatar_split_clause,[],[f2953,f16161]) ).
fof(f16161,plain,
( spl0_1886
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X30,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f2953,plain,
! [X0,X26,X25,X30] :
( c_in(X25,X30,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
inference(definition_unfolding,[],[f1501,f1267]) ).
fof(f1501,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X30,X0)
| ~ c_in(X25,c_inter(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f16159,plain,
spl0_1885,
inference(avatar_split_clause,[],[f2952,f16157]) ).
fof(f16157,plain,
( spl0_1885
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f2952,plain,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0),X0) ),
inference(definition_unfolding,[],[f1500,f1267]) ).
fof(f1500,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_inter(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f16155,plain,
spl0_1884,
inference(avatar_split_clause,[],[f2922,f16153]) ).
fof(f16153,plain,
( spl0_1884
<=> ! [X11,X24] :
( X11 = X24
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f2922,plain,
! [X11,X24] :
( X11 = X24
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f911,f1438,f1438]) ).
fof(f911,axiom,
! [X11,X24] :
( X11 = X24
| c_Suc(X11) != c_Suc(X24) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f16151,plain,
spl0_1883,
inference(avatar_split_clause,[],[f2870,f16149]) ).
fof(f16149,plain,
( spl0_1883
<=> ! [X0,X11,X10] : c_append(c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Odrop(X11,X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f2870,plain,
! [X10,X0,X11] : c_append(c_List_Osublist(X10,c_SetInterval_OlessThan(X11,tc_nat),X0),c_List_Odrop(X11,X10,X0),X0) = X10,
inference(definition_unfolding,[],[f429,f660]) ).
fof(f429,axiom,
! [X10,X0,X11] : c_append(c_List_Otake(X11,X10,X0),c_List_Odrop(X11,X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f16147,plain,
spl0_1882,
inference(avatar_split_clause,[],[f2803,f16145]) ).
fof(f2803,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X12,X10,X0)
| ~ c_lessequals(X10,X35,X0)
| c_lessequals(X12,X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oorder__trans_0) ).
fof(f16143,plain,
spl0_1881,
inference(avatar_split_clause,[],[f1720,f16141]) ).
fof(f16141,plain,
( spl0_1881
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnionE__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f1720,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnionE__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f16139,plain,
spl0_1880,
inference(avatar_split_clause,[],[f1717,f16137]) ).
fof(f16137,plain,
( spl0_1880
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInterI__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f1717,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInterI__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f16135,plain,
spl0_1879,
inference(avatar_split_clause,[],[f1680,f16133]) ).
fof(f16133,plain,
( spl0_1879
<=> ! [X0,X12,X26,X72] :
( c_in(X12,X26,X0)
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f1680,axiom,
! [X72,X0,X26,X12] :
( c_in(X12,X26,X0)
| ~ c_in(c_List_Olist_OCons(X12,X72,X0),c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f16131,plain,
spl0_1878,
inference(avatar_split_clause,[],[f1669,f16129]) ).
fof(f16129,plain,
( spl0_1878
<=> ! [X0,X39,X26] :
( ~ c_in(c_Main_Oin__listsI__1(X26,X39,X0),X26,X0)
| c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f1669,axiom,
! [X39,X0,X26] :
( ~ c_in(c_Main_Oin__listsI__1(X26,X39,X0),X26,X0)
| c_in(X39,c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f16127,plain,
spl0_1877,
inference(avatar_split_clause,[],[f1664,f16125]) ).
fof(f16125,plain,
( spl0_1877
<=> ! [X24,X78] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_IntDef_Oint)
| c_times(X78,c_Main_Ozmod__eq__0D__dest__1(X78,X24),tc_IntDef_Oint) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f1664,axiom,
! [X78,X24] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_IntDef_Oint)
| c_times(X78,c_Main_Ozmod__eq__0D__dest__1(X78,X24),tc_IntDef_Oint) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f16123,plain,
spl0_1876,
inference(avatar_split_clause,[],[f1648,f16121]) ).
fof(f16121,plain,
( spl0_1876
<=> ! [X24,X78] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_nat)
| c_times(X78,c_Main_Omod__eq__0D__dest__1(X78,X24),tc_nat) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f1648,axiom,
! [X78,X24] :
( c_0 != c_Divides_Oop_Amod(X24,X78,tc_nat)
| c_times(X78,c_Main_Omod__eq__0D__dest__1(X78,X24),tc_nat) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f16119,plain,
spl0_1875,
inference(avatar_split_clause,[],[f1621,f16117]) ).
fof(f16117,plain,
( spl0_1875
<=> ! [X12,X10] :
( ~ c_less(X12,X10,tc_nat)
| c_in(c_Pair(X12,X10,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f1621,axiom,
! [X10,X12] :
( ~ c_less(X12,X10,tc_nat)
| c_in(c_Pair(X12,X10,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(f16115,plain,
( spl0_1873
| ~ spl0_1874
| ~ spl0_1
| ~ spl0_1495 ),
inference(avatar_split_clause,[],[f12579,f12257,f3226,f16112,f16108]) ).
fof(f16108,plain,
( spl0_1873
<=> c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,t_b),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f16112,plain,
( spl0_1874
<=> class_Numeral_Onumber__ring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f12257,plain,
( spl0_1495
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f12579,plain,
( ~ class_Numeral_Onumber__ring(t_b)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,t_b),t_b)
| ~ spl0_1
| ~ spl0_1495 ),
inference(resolution,[],[f12258,f3228]) ).
fof(f3228,plain,
( class_Ring__and__Field_Oordered__idom(t_b)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f3226]) ).
fof(f12258,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) )
| ~ spl0_1495 ),
inference(avatar_component_clause,[],[f12257]) ).
fof(f16106,plain,
spl0_1872,
inference(avatar_split_clause,[],[f1620,f16104]) ).
fof(f16104,plain,
( spl0_1872
<=> ! [X12,X10] :
( c_less(X12,X10,tc_nat)
| ~ c_in(c_Pair(X12,X10,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f1620,axiom,
! [X10,X12] :
( c_less(X12,X10,tc_nat)
| ~ c_in(c_Pair(X12,X10,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(f16102,plain,
spl0_1871,
inference(avatar_split_clause,[],[f1577,f16100]) ).
fof(f16100,plain,
( spl0_1871
<=> ! [X0,X3,X1,X26] :
( X1 = X3
| c_in(X3,X26,X0)
| ~ c_in(X3,c_insert(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f1577,axiom,
! [X3,X0,X1,X26] :
( X1 = X3
| c_in(X3,X26,X0)
| ~ c_in(X3,c_insert(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f16098,plain,
spl0_1870,
inference(avatar_split_clause,[],[f1552,f16096]) ).
fof(f16096,plain,
( spl0_1870
<=> ! [X3,X0,X30] : c_Union(c_insert(X3,X30,tc_set(X0)),X0) = c_union(X3,c_Union(X30,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f1552,axiom,
! [X3,X0,X30] : c_Union(c_insert(X3,X30,tc_set(X0)),X0) = c_union(X3,c_Union(X30,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f16094,plain,
spl0_1869,
inference(avatar_split_clause,[],[f1549,f16092]) ).
fof(f16092,plain,
( spl0_1869
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnion__iff__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f1549,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(c_Main_OUnion__iff__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f16090,plain,
spl0_1868,
inference(avatar_split_clause,[],[f1515,f16088]) ).
fof(f16088,plain,
( spl0_1868
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInter__iff__1(X26,X2,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f1515,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| c_in(c_Main_OInter__iff__1(X26,X2,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f16086,plain,
spl0_1867,
inference(avatar_split_clause,[],[f1382,f16084]) ).
fof(f16084,plain,
( spl0_1867
<=> ! [X0,X1,X3] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_0 = X3
| c_0 = X1
| c_times(X3,X1,X0) != c_0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f1382,axiom,
! [X3,X0,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X0)
| c_0 = X3
| c_0 = X1
| c_times(X3,X1,X0) != c_0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f16082,plain,
spl0_1866,
inference(avatar_split_clause,[],[f1366,f16080]) ).
fof(f16080,plain,
( spl0_1866
<=> ! [X25,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X1
| c_0 = X25
| c_times(X1,X25,X0) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f1366,axiom,
! [X0,X1,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X1
| c_0 = X25
| c_times(X1,X25,X0) != X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
fof(f16078,plain,
spl0_1865,
inference(avatar_split_clause,[],[f1362,f16076]) ).
fof(f16076,plain,
( spl0_1865
<=> ! [X25,X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X1
| c_0 = X25
| c_times(X25,X1,X0) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f1362,axiom,
! [X0,X1,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = X1
| c_0 = X25
| c_times(X25,X1,X0) != X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
fof(f16074,plain,
spl0_1864,
inference(avatar_split_clause,[],[f1257,f16072]) ).
fof(f16072,plain,
( spl0_1864
<=> ! [X15,X3,X0,X16,X76,X1] :
( X1 = X76
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f1257,axiom,
! [X3,X0,X1,X76,X16,X15] :
( X1 = X76
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f16070,plain,
spl0_1863,
inference(avatar_split_clause,[],[f1256,f16068]) ).
fof(f16068,plain,
( spl0_1863
<=> ! [X15,X0,X16,X76,X3,X1] :
( X3 = X15
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f1256,axiom,
! [X3,X0,X1,X16,X76,X15] :
( X3 = X15
| c_Pair(X3,X1,X0,X16) != c_Pair(X15,X76,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f16064,plain,
spl0_1862,
inference(avatar_split_clause,[],[f1243,f16062]) ).
fof(f16062,plain,
( spl0_1862
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f1243,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f16060,plain,
spl0_1861,
inference(avatar_split_clause,[],[f1242,f16058]) ).
fof(f16058,plain,
( spl0_1861
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X11,tc_nat)
| c_0 != c_Nat_Opower(X3,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f1242,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X11,tc_nat)
| c_0 != c_Nat_Opower(X3,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f16056,plain,
spl0_1860,
inference(avatar_split_clause,[],[f1162,f16054]) ).
fof(f16054,plain,
( spl0_1860
<=> ! [X16,X12,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X12,X10,X16) = c_Orderings_Omax(X12,c_Orderings_Omax(X12,X10,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f1162,axiom,
! [X10,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X12,X10,X16) = c_Orderings_Omax(X12,c_Orderings_Omax(X12,X10,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f16052,plain,
spl0_1859,
inference(avatar_split_clause,[],[f1157,f16050]) ).
fof(f16050,plain,
( spl0_1859
<=> ! [X16,X12,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X12,X10,X16) = c_Orderings_Omin(X12,c_Orderings_Omin(X12,X10,X16),X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f1157,axiom,
! [X10,X16,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X12,X10,X16) = c_Orderings_Omin(X12,c_Orderings_Omin(X12,X10,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f16048,plain,
spl0_1858,
inference(avatar_split_clause,[],[f1140,f16046]) ).
fof(f16046,plain,
( spl0_1858
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Opprt(X3,X0),c_OrderedGroup_Opprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f1140,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Opprt(X3,X0),c_OrderedGroup_Opprt(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f16044,plain,
spl0_1857,
inference(avatar_split_clause,[],[f1136,f16042]) ).
fof(f16042,plain,
( spl0_1857
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_OrderedGroup_Onprt(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f1136,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_OrderedGroup_Onprt(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f16040,plain,
spl0_1856,
inference(avatar_split_clause,[],[f1130,f16038]) ).
fof(f16038,plain,
( spl0_1856
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f1130,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f16036,plain,
spl0_1855,
inference(avatar_split_clause,[],[f1129,f16034]) ).
fof(f16034,plain,
( spl0_1855
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f1129,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f16032,plain,
spl0_1854,
inference(avatar_split_clause,[],[f1126,f16030]) ).
fof(f16030,plain,
( spl0_1854
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f1126,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f16028,plain,
spl0_1853,
inference(avatar_split_clause,[],[f1125,f16026]) ).
fof(f16026,plain,
( spl0_1853
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f1125,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_uminus(X1,X0),c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f16024,plain,
( spl0_1852
| ~ spl0_1059
| ~ spl0_1654
| ~ spl0_1661 ),
inference(avatar_split_clause,[],[f13986,f13325,f13296,f8960,f16021]) ).
fof(f16021,plain,
( spl0_1852
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f13986,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_1,c_0,t_b)
| ~ spl0_1654
| ~ spl0_1661 ),
inference(resolution,[],[f13326,f13298]) ).
fof(f16019,plain,
spl0_1851,
inference(avatar_split_clause,[],[f1089,f16017]) ).
fof(f16017,plain,
( spl0_1851
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X25,X3,X0) != c_plus(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f1089,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X25,X3,X0) != c_plus(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f16015,plain,
spl0_1850,
inference(avatar_split_clause,[],[f1084,f16013]) ).
fof(f16013,plain,
( spl0_1850
<=> ! [X0,X3,X25,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X3,X1,X0) != c_plus(X3,X25,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f1084,axiom,
! [X3,X0,X1,X25] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X0)
| X1 = X25
| c_plus(X3,X1,X0) != c_plus(X3,X25,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f16011,plain,
spl0_1849,
inference(avatar_split_clause,[],[f1005,f16009]) ).
fof(f16009,plain,
( spl0_1849
<=> ! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(X33)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f1005,axiom,
! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,c_Numeral_Obin__succ(X33)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f16007,plain,
spl0_1848,
inference(avatar_split_clause,[],[f979,f16005]) ).
fof(f16005,plain,
( spl0_1848
<=> ! [X9,X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f979,axiom,
! [X11,X9,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f16003,plain,
spl0_1847,
inference(avatar_split_clause,[],[f978,f16001]) ).
fof(f16001,plain,
( spl0_1847
<=> ! [X9,X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f978,axiom,
! [X11,X9,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f15999,plain,
spl0_1846,
inference(avatar_split_clause,[],[f977,f15997]) ).
fof(f15997,plain,
( spl0_1846
<=> ! [X9,X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f977,axiom,
! [X11,X9,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f15995,plain,
spl0_1845,
inference(avatar_split_clause,[],[f976,f15993]) ).
fof(f15993,plain,
( spl0_1845
<=> ! [X9,X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f976,axiom,
! [X11,X9,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_plus(X9,X24,tc_nat),c_plus(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f15991,plain,
spl0_1844,
inference(avatar_split_clause,[],[f970,f15989]) ).
fof(f15989,plain,
( spl0_1844
<=> ! [X9,X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f970,axiom,
! [X11,X9,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f15987,plain,
spl0_1843,
inference(avatar_split_clause,[],[f969,f15985]) ).
fof(f15985,plain,
( spl0_1843
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f969,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f15983,plain,
spl0_1842,
inference(avatar_split_clause,[],[f967,f15981]) ).
fof(f15981,plain,
( spl0_1842
<=> ! [X9,X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f967,axiom,
! [X11,X9,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f15977,plain,
spl0_1841,
inference(avatar_split_clause,[],[f966,f15975]) ).
fof(f15975,plain,
( spl0_1841
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f966,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| ~ c_less(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f15973,plain,
spl0_1840,
inference(avatar_split_clause,[],[f965,f15971]) ).
fof(f15971,plain,
( spl0_1840
<=> ! [X9,X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f965,axiom,
! [X11,X9,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f15969,plain,
spl0_1839,
inference(avatar_split_clause,[],[f964,f15967]) ).
fof(f15967,plain,
( spl0_1839
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f964,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X24,X9,tc_nat),c_times(X11,X9,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f15965,plain,
spl0_1838,
inference(avatar_split_clause,[],[f962,f15963]) ).
fof(f15963,plain,
( spl0_1838
<=> ! [X9,X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f962,axiom,
! [X11,X9,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f15961,plain,
spl0_1837,
inference(avatar_split_clause,[],[f961,f15959]) ).
fof(f15959,plain,
( spl0_1837
<=> ! [X9,X11,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f961,axiom,
! [X11,X9,X24] :
( c_less(c_0,X9,tc_nat)
| c_lessequals(c_times(X9,X24,tc_nat),c_times(X9,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f15957,plain,
spl0_1836,
inference(avatar_split_clause,[],[f821,f15955]) ).
fof(f15955,plain,
( spl0_1836
<=> ! [X16,X1] :
( ~ class_HOL_Oone(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_1 != c_uminus(X1,X16)
| c_uminus(c_1,X16) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f821,axiom,
! [X1,X16] :
( ~ class_HOL_Oone(X16)
| ~ class_OrderedGroup_Oab__group__add(X16)
| c_1 != c_uminus(X1,X16)
| c_uminus(c_1,X16) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f15953,plain,
spl0_1835,
inference(avatar_split_clause,[],[f762,f15951]) ).
fof(f15951,plain,
( spl0_1835
<=> ! [X34,X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f762,axiom,
! [X0,X34] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X34,tc_nat),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f15949,plain,
spl0_1834,
inference(avatar_split_clause,[],[f714,f15947]) ).
fof(f15947,plain,
( spl0_1834
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X24,X11,tc_nat)
| c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f714,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(X24,X11,tc_nat)
| c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f15945,plain,
spl0_1833,
inference(avatar_split_clause,[],[f713,f15943]) ).
fof(f15943,plain,
( spl0_1833
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(X24,X11,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f713,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(X24,X11,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f15941,plain,
spl0_1832,
inference(avatar_split_clause,[],[f711,f15939]) ).
fof(f15939,plain,
( spl0_1832
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f711,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f15937,plain,
( spl0_1831
| ~ spl0_1059
| ~ spl0_1651
| ~ spl0_1654 ),
inference(avatar_split_clause,[],[f13939,f13296,f13284,f8960,f15934]) ).
fof(f15934,plain,
( spl0_1831
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f13939,plain,
( ~ class_Orderings_Oorder(t_b)
| c_emptyset = c_SetInterval_OatLeastLessThan(c_1,c_0,t_b)
| ~ spl0_1651
| ~ spl0_1654 ),
inference(resolution,[],[f13285,f13298]) ).
fof(f15932,plain,
spl0_1830,
inference(avatar_split_clause,[],[f710,f15930]) ).
fof(f15930,plain,
( spl0_1830
<=> ! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f710,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f15928,plain,
spl0_1829,
inference(avatar_split_clause,[],[f654,f15926]) ).
fof(f15926,plain,
( spl0_1829
<=> ! [X0,X12,X39] :
( c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = X39
| c_List_Orev(X39,X0) != c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f654,axiom,
! [X39,X0,X12] :
( c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = X39
| c_List_Orev(X39,X0) != c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).
fof(f15924,plain,
spl0_1828,
inference(avatar_split_clause,[],[f650,f15922]) ).
fof(f15922,plain,
( spl0_1828
<=> ! [X12,X0,X11] :
( c_0 = X11
| c_insert(X12,c_emptyset,X0) = c_List_Oset(c_List_Oreplicate(X11,X12,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f650,axiom,
! [X0,X11,X12] :
( c_0 = X11
| c_insert(X12,c_emptyset,X0) = c_List_Oset(c_List_Oreplicate(X11,X12,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f15920,plain,
spl0_1827,
inference(avatar_split_clause,[],[f604,f15918]) ).
fof(f15918,plain,
( spl0_1827
<=> ! [X10,X40,X14,X12] :
( X10 = X12
| c_List_Oop_Amem(X12,X40,X14)
| ~ c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f604,axiom,
! [X40,X10,X14,X12] :
( X10 = X12
| c_List_Oop_Amem(X12,X40,X14)
| ~ c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f15916,plain,
spl0_1826,
inference(avatar_split_clause,[],[f534,f15914]) ).
fof(f15914,plain,
( spl0_1826
<=> ! [X57,X14,X26] : c_List_Olistset(c_List_Olist_OCons(X26,X57,tc_set(X14)),X14) = c_List_Oset__Cons(X26,c_List_Olistset(X57,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f534,axiom,
! [X57,X26,X14] : c_List_Olistset(c_List_Olist_OCons(X26,X57,tc_set(X14)),X14) = c_List_Oset__Cons(X26,c_List_Olistset(X57,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f15912,plain,
spl0_1825,
inference(avatar_split_clause,[],[f526,f15910]) ).
fof(f15910,plain,
( spl0_1825
<=> ! [X23,X0,X12,X10] :
( ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X23,tc_nat)
| c_List_Olist__update(X10,X23,X12,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f526,axiom,
! [X10,X0,X12,X23] :
( ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),X23,tc_nat)
| c_List_Olist__update(X10,X23,X12,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f15908,plain,
spl0_1824,
inference(avatar_split_clause,[],[f506,f15906]) ).
fof(f15906,plain,
( spl0_1824
<=> ! [X0,X39] : c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f506,axiom,
! [X39,X0] : c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f15904,plain,
spl0_1823,
inference(avatar_split_clause,[],[f494,f15902]) ).
fof(f15902,plain,
( spl0_1823
<=> ! [X0,X39] : c_Nat_Osize(c_List_Obutlast(X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f494,axiom,
! [X39,X0] : c_Nat_Osize(c_List_Obutlast(X39,X0),tc_List_Olist(X0)) = c_minus(c_Nat_Osize(X39,tc_List_Olist(X0)),c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f15900,plain,
spl0_1822,
inference(avatar_split_clause,[],[f490,f15898]) ).
fof(f15898,plain,
( spl0_1822
<=> ! [X50,X23] :
( ~ c_less(X23,X50,tc_nat)
| c_List_Olast(c_List_Oupt(X23,X50),tc_nat) = c_minus(X50,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f490,axiom,
! [X50,X23] :
( ~ c_less(X23,X50,tc_nat)
| c_List_Olast(c_List_Oupt(X23,X50),tc_nat) = c_minus(X50,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f15896,plain,
spl0_1821,
inference(avatar_split_clause,[],[f438,f15894]) ).
fof(f15894,plain,
( spl0_1821
<=> ! [X12,X39,X14] : c_List_Oconcat(c_List_Olist_OCons(X12,X39,tc_List_Olist(X14)),X14) = c_append(X12,c_List_Oconcat(X39,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f438,axiom,
! [X39,X14,X12] : c_List_Oconcat(c_List_Olist_OCons(X12,X39,tc_List_Olist(X14)),X14) = c_append(X12,c_List_Oconcat(X39,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f15888,plain,
spl0_1820,
inference(avatar_split_clause,[],[f350,f15886]) ).
fof(f15886,plain,
( spl0_1820
<=> ! [X37,X19] : c_IntDiv_OnegateSnd(c_Pair(X37,X19,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X37,c_uminus(X19,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f15884,plain,
spl0_1819,
inference(avatar_split_clause,[],[f325,f15882]) ).
fof(f15882,plain,
( spl0_1819
<=> ! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f325,axiom,
! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f15880,plain,
spl0_1818,
inference(avatar_split_clause,[],[f309,f15878]) ).
fof(f15878,plain,
( spl0_1818
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f309,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,X35,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f15876,plain,
spl0_1817,
inference(avatar_split_clause,[],[f308,f15874]) ).
fof(f15874,plain,
( spl0_1817
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f308,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f15872,plain,
spl0_1816,
inference(avatar_split_clause,[],[f305,f15870]) ).
fof(f15870,plain,
( spl0_1816
<=> ! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f305,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f15868,plain,
spl0_1815,
inference(avatar_split_clause,[],[f304,f15866]) ).
fof(f304,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f15864,plain,
spl0_1814,
inference(avatar_split_clause,[],[f175,f15862]) ).
fof(f15862,plain,
( spl0_1814
<=> ! [X0,X30,X31] :
( ~ c_in(X30,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X30,X31,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f175,axiom,
! [X31,X0,X30] :
( ~ c_in(X30,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_minus(X30,X31,tc_set(X0)),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f15860,plain,
spl0_1813,
inference(avatar_split_clause,[],[f92,f15858]) ).
fof(f15858,plain,
( spl0_1813
<=> ! [X18,X0,X21,X16,X17,X22] :
( X18 = X22
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f92,axiom,
! [X21,X0,X18,X16,X17,X22] :
( X18 = X22
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f15856,plain,
spl0_1812,
inference(avatar_split_clause,[],[f91,f15854]) ).
fof(f15854,plain,
( spl0_1812
<=> ! [X17,X0,X18,X22,X16,X21] :
( X17 = X21
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f91,axiom,
! [X21,X0,X18,X16,X17,X22] :
( X17 = X21
| c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OScons(X21,X22,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f15369,plain,
( spl0_1811
| ~ spl0_1009
| ~ spl0_1454 ),
inference(avatar_split_clause,[],[f12158,f11837,f8725,f15367]) ).
fof(f11837,plain,
( spl0_1454
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(X3,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f12158,plain,
( ! [X0] : c_0 = c_plus(X0,c_uminus(X0,t_b),t_b)
| ~ spl0_1009
| ~ spl0_1454 ),
inference(resolution,[],[f11838,f8727]) ).
fof(f11838,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(X3,c_uminus(X3,X0),X0) )
| ~ spl0_1454 ),
inference(avatar_component_clause,[],[f11837]) ).
fof(f15260,plain,
( spl0_1810
| ~ spl0_1009
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f12141,f11821,f8725,f15258]) ).
fof(f15258,plain,
( spl0_1810
<=> ! [X0] : c_uminus(X0,t_b) = c_minus(c_0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f12141,plain,
( ! [X0] : c_uminus(X0,t_b) = c_minus(c_0,X0,t_b)
| ~ spl0_1009
| ~ spl0_1450 ),
inference(resolution,[],[f11822,f8727]) ).
fof(f15047,plain,
( spl0_1809
| ~ spl0_1009
| ~ spl0_1448 ),
inference(avatar_split_clause,[],[f12135,f11813,f8725,f15045]) ).
fof(f15045,plain,
( spl0_1809
<=> ! [X0] : c_0 = c_plus(c_uminus(X0,t_b),X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f11813,plain,
( spl0_1448
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(c_uminus(X3,X0),X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f12135,plain,
( ! [X0] : c_0 = c_plus(c_uminus(X0,t_b),X0,t_b)
| ~ spl0_1009
| ~ spl0_1448 ),
inference(resolution,[],[f11814,f8727]) ).
fof(f11814,plain,
( ! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(c_uminus(X3,X0),X3,X0) )
| ~ spl0_1448 ),
inference(avatar_component_clause,[],[f11813]) ).
fof(f14920,plain,
( spl0_1808
| ~ spl0_938
| ~ spl0_1423 ),
inference(avatar_split_clause,[],[f12026,f11709,f7778,f14918]) ).
fof(f11709,plain,
( spl0_1423
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_IntDef_Oint(X11),X0) = c_NatArith_Oof__nat(X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f12026,plain,
( ! [X0] : c_IntDef_Oof__int(c_IntDef_Oint(X0),t_b) = c_NatArith_Oof__nat(X0,t_b)
| ~ spl0_938
| ~ spl0_1423 ),
inference(resolution,[],[f11710,f7780]) ).
fof(f11710,plain,
( ! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_IntDef_Oint(X11),X0) = c_NatArith_Oof__nat(X11,X0) )
| ~ spl0_1423 ),
inference(avatar_component_clause,[],[f11709]) ).
fof(f14843,plain,
( spl0_1807
| ~ spl0_965
| ~ spl0_1418 ),
inference(avatar_split_clause,[],[f12012,f11689,f8447,f14841]) ).
fof(f11689,plain,
( spl0_1418
<=> ! [X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMin(c_insert(X10,c_emptyset,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f12012,plain,
( ! [X0] : c_Finite__Set_OMin(c_insert(X0,c_emptyset,t_b),t_b) = X0
| ~ spl0_965
| ~ spl0_1418 ),
inference(resolution,[],[f11690,f8449]) ).
fof(f11690,plain,
( ! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMin(c_insert(X10,c_emptyset,X0),X0) = X10 )
| ~ spl0_1418 ),
inference(avatar_component_clause,[],[f11689]) ).
fof(f14786,plain,
spl0_1806,
inference(avatar_split_clause,[],[f3132,f14784]) ).
fof(f14784,plain,
( spl0_1806
<=> ! [X75] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f3132,plain,
! [X75] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X75,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2956,f2814]) ).
fof(f2956,plain,
! [X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,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(X75,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f765,f1438,f1438]) ).
fof(f765,axiom,
! [X75] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X75,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X75,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f14782,plain,
spl0_1805,
inference(avatar_split_clause,[],[f3115,f14780]) ).
fof(f14780,plain,
( spl0_1805
<=> ! [X11,X23] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X23,X11,tc_nat),tc_nat),X11,tc_nat)
| ~ c_less(c_0,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f3115,plain,
! [X11,X23] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X23,X11,tc_nat),tc_nat),X11,tc_nat)
| ~ c_less(c_0,X11,tc_nat) ),
inference(forward_demodulation,[],[f2933,f2865]) ).
fof(f2933,plain,
! [X11,X23] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X23,tc_nat),tc_nat),tc_nat),X11,tc_nat) ),
inference(definition_unfolding,[],[f930,f1438]) ).
fof(f930,axiom,
! [X11,X23] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_minus(X11,c_Suc(X23),tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f14778,plain,
spl0_1804,
inference(avatar_split_clause,[],[f3070,f14776]) ).
fof(f14776,plain,
( spl0_1804
<=> ! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f3070,plain,
! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f3069,f1050]) ).
fof(f3069,plain,
! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f3068,f1048]) ).
fof(f3068,plain,
! [X10] : c_div(c_plus(X10,X10,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X10,
inference(forward_demodulation,[],[f777,f1050]) ).
fof(f777,axiom,
! [X10] : c_div(c_plus(X10,X10,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) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f14774,plain,
spl0_1803,
inference(avatar_split_clause,[],[f3058,f14772]) ).
fof(f14772,plain,
( spl0_1803
<=> ! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),X33) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33),X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f3058,plain,
! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),X33) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33),X33),
inference(forward_demodulation,[],[f1022,f1021]) ).
fof(f1021,axiom,
! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33) = c_Numeral_OBit(c_Numeral_Obin__mult(X34,X33),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f1022,axiom,
! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),X33) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X34,X33),c_Numeral_Obit_OB0),X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f14770,plain,
spl0_1802,
inference(avatar_split_clause,[],[f3055,f14768]) ).
fof(f3055,plain,
! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X33)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2856,f2829]) ).
fof(f2829,plain,
! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin),
inference(definition_unfolding,[],[f1006,f1007]) ).
fof(f1007,axiom,
! [X33] : c_Numeral_Obin__pred(X33) = c_Numeral_Obin__add(X33,c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f1006,axiom,
! [X33] : c_Numeral_Obin__add(c_Numeral_OMin,X33) = c_Numeral_Obin__pred(X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2856,plain,
! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X33),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f1018,f1023,f1007,f1023]) ).
fof(f1018,axiom,
! [X33] : c_Numeral_Obin__minus(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X33)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f14766,plain,
( spl0_1801
| ~ spl0_965
| ~ spl0_1417 ),
inference(avatar_split_clause,[],[f12009,f11685,f8447,f14764]) ).
fof(f11685,plain,
( spl0_1417
<=> ! [X0,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMax(c_insert(X10,c_emptyset,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f12009,plain,
( ! [X0] : c_Finite__Set_OMax(c_insert(X0,c_emptyset,t_b),t_b) = X0
| ~ spl0_965
| ~ spl0_1417 ),
inference(resolution,[],[f11686,f8449]) ).
fof(f11686,plain,
( ! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMax(c_insert(X10,c_emptyset,X0),X0) = X10 )
| ~ spl0_1417 ),
inference(avatar_component_clause,[],[f11685]) ).
fof(f14762,plain,
spl0_1800,
inference(avatar_split_clause,[],[f2966,f14760]) ).
fof(f14760,plain,
( spl0_1800
<=> ! [X34] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f2966,plain,
! [X34] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f747,f1023]) ).
fof(f747,axiom,
! [X34] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X34),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f14758,plain,
spl0_1799,
inference(avatar_split_clause,[],[f2964,f14756]) ).
fof(f14756,plain,
( spl0_1799
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f2964,plain,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f748,f1023]) ).
fof(f748,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X34),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X34,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f14726,plain,
( spl0_1798
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1797 ),
inference(avatar_split_clause,[],[f14722,f14719,f13448,f13139,f8657,f3868,f14724]) ).
fof(f14724,plain,
( spl0_1798
<=> ! [X50,X23] :
( c_List_Olist_ONil = c_List_Oupt(X23,c_plus(c_1,X50,tc_nat))
| c_lessequals(X23,X50,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f14719,plain,
( spl0_1797
<=> ! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f14722,plain,
( ! [X50,X23] :
( c_List_Olist_ONil = c_List_Oupt(X23,c_plus(c_1,X50,tc_nat))
| c_lessequals(X23,X50,tc_nat) )
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1797 ),
inference(forward_demodulation,[],[f14720,f14217]) ).
fof(f14720,plain,
( ! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) )
| ~ spl0_1797 ),
inference(avatar_component_clause,[],[f14719]) ).
fof(f14721,plain,
spl0_1797,
inference(avatar_split_clause,[],[f2951,f14719]) ).
fof(f2951,plain,
! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Finite__Set_Ocard(c_SetInterval_OatMost(X50,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f677,f1438]) ).
fof(f677,axiom,
! [X50,X23] :
( c_lessequals(X23,X50,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,c_Suc(X50)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f14717,plain,
spl0_1796,
inference(avatar_split_clause,[],[f2912,f14715]) ).
fof(f2912,plain,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X33),X0) ),
inference(definition_unfolding,[],[f1011,f1023]) ).
fof(f1011,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(c_Numeral_Onumber__of(X33,X0),X0) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X33),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f14709,plain,
( spl0_1795
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1794 ),
inference(avatar_split_clause,[],[f14705,f14702,f13448,f13139,f8657,f3868,f14707]) ).
fof(f14707,plain,
( spl0_1795
<=> ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_plus(c_1,X24,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f14702,plain,
( spl0_1794
<=> ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f14705,plain,
( ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_plus(c_1,X24,tc_nat),tc_nat)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1794 ),
inference(forward_demodulation,[],[f14703,f14217]) ).
fof(f14703,plain,
( ! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat)
| ~ spl0_1794 ),
inference(avatar_component_clause,[],[f14702]) ).
fof(f14704,plain,
spl0_1794,
inference(avatar_split_clause,[],[f2857,f14702]) ).
fof(f2857,plain,
! [X24] : c_insert(X24,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1421,f1438]) ).
fof(f1421,axiom,
! [X24] : c_SetInterval_OatLeastLessThan(X24,c_Suc(X24),tc_nat) = c_insert(X24,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f14700,plain,
spl0_1793,
inference(avatar_split_clause,[],[f2855,f14698]) ).
fof(f14698,plain,
( spl0_1793
<=> ! [X0,X30,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_minus(X30,X26,tc_set(X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f2855,plain,
! [X0,X26,X30] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_minus(X30,X26,tc_set(X0)),X0,X0),
inference(definition_unfolding,[],[f1483,f1267]) ).
fof(f1483,axiom,
! [X0,X26,X30] : c_emptyset = c_inter(X26,c_minus(X30,X26,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f14695,plain,
spl0_1792,
inference(avatar_split_clause,[],[f2844,f14693]) ).
fof(f14693,plain,
( spl0_1792
<=> ! [X77,X0] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f2844,plain,
! [X0,X77] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0),
inference(definition_unfolding,[],[f1600,f1610]) ).
fof(f1600,axiom,
! [X0,X77] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X77,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f14691,plain,
spl0_1791,
inference(avatar_split_clause,[],[f2843,f14689]) ).
fof(f14689,plain,
( spl0_1791
<=> ! [X77,X0] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f2843,plain,
! [X0,X77] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X77,c_Relation_OId,tc_prod(X0,X0)),X0),X0,X0),
inference(definition_unfolding,[],[f1601,f1610]) ).
fof(f1601,axiom,
! [X0,X77] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X77,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f14684,plain,
( spl0_1790
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1789 ),
inference(avatar_split_clause,[],[f14680,f14677,f13448,f13139,f8657,f3868,f14682]) ).
fof(f14682,plain,
( spl0_1790
<=> ! [X11] : c_plus(c_1,X11,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f14677,plain,
( spl0_1789
<=> ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f14680,plain,
( ! [X11] : c_plus(c_1,X11,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X11,tc_nat),X11)
| ~ spl0_131
| ~ spl0_994
| ~ spl0_1615
| ~ spl0_1691
| ~ spl0_1789 ),
inference(forward_demodulation,[],[f14678,f14217]) ).
fof(f14678,plain,
( ! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X11)
| ~ spl0_1789 ),
inference(avatar_component_clause,[],[f14677]) ).
fof(f14679,plain,
spl0_1789,
inference(avatar_split_clause,[],[f2839,f14677]) ).
fof(f2839,plain,
! [X11] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X11),
inference(definition_unfolding,[],[f57,f1438,f1438]) ).
fof(f57,axiom,
! [X11] : c_Suc(X11) = c_Binomial_Obinomial(c_Suc(X11),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f14675,plain,
spl0_1788,
inference(avatar_split_clause,[],[f2785,f14673]) ).
fof(f14673,plain,
( spl0_1788
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X3,X1,X0) = c_plus(X3,c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f2785,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X3,X1,X0) = c_plus(X3,c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__1_0) ).
fof(f14671,plain,
spl0_1787,
inference(avatar_split_clause,[],[f1732,f14669]) ).
fof(f14669,plain,
( spl0_1787
<=> ! [X0,X30,X26] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(X30,X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f1732,axiom,
! [X0,X26,X30] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(X30,X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f14667,plain,
spl0_1786,
inference(avatar_split_clause,[],[f1729,f14665]) ).
fof(f14665,plain,
( spl0_1786
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f1729,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X26,X0)
| c_in(X25,X30,X0)
| ~ c_lessequals(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f14663,plain,
spl0_1785,
inference(avatar_split_clause,[],[f1725,f14661]) ).
fof(f14661,plain,
( spl0_1785
<=> ! [X0,X30,X26] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_less(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f1725,axiom,
! [X0,X26,X30] :
( X26 = X30
| ~ c_lessequals(X26,X30,tc_set(X0))
| c_less(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f14659,plain,
spl0_1784,
inference(avatar_split_clause,[],[f1721,f14657]) ).
fof(f14657,plain,
( spl0_1784
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnionE__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f1721,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnionE__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f14655,plain,
( spl0_1783
| ~ spl0_1102
| ~ spl0_2
| ~ spl0_1536 ),
inference(avatar_split_clause,[],[f12808,f12432,f3231,f9158,f14653]) ).
fof(f14653,plain,
( spl0_1783
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(v_k(X0),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f12808,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Onprt(v_k(X0),t_b) )
| ~ spl0_2
| ~ spl0_1536 ),
inference(resolution,[],[f12433,f3232]) ).
fof(f14651,plain,
spl0_1782,
inference(avatar_split_clause,[],[f1718,f14649]) ).
fof(f14649,plain,
( spl0_1782
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInterI__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f1718,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInterI__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f14647,plain,
spl0_1781,
inference(avatar_split_clause,[],[f1650,f14645]) ).
fof(f14645,plain,
( spl0_1781
<=> ! [X0,X3,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f1650,axiom,
! [X3,X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f14643,plain,
spl0_1780,
inference(avatar_split_clause,[],[f1619,f14641]) ).
fof(f1619,axiom,
! [X3,X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| ~ c_in(c_Pair(X3,X3,X0,X0),X19,tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f14639,plain,
spl0_1779,
inference(avatar_split_clause,[],[f1583,f14637]) ).
fof(f14637,plain,
( spl0_1779
<=> ! [X0,X12,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f1583,axiom,
! [X0,X26,X12,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f14635,plain,
spl0_1778,
inference(avatar_split_clause,[],[f1550,f14633]) ).
fof(f14633,plain,
( spl0_1778
<=> ! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnion__iff__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f1550,axiom,
! [X2,X0,X26] :
( ~ c_in(X26,c_Union(X2,X0),X0)
| c_in(X26,c_Main_OUnion__iff__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f14631,plain,
spl0_1777,
inference(avatar_split_clause,[],[f1546,f14629]) ).
fof(f14629,plain,
( spl0_1777
<=> ! [X29,X0,X26] :
( c_emptyset = X29
| c_emptyset != c_Union(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f1546,axiom,
! [X29,X0,X26] :
( c_emptyset = X29
| c_emptyset != c_Union(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f14627,plain,
spl0_1776,
inference(avatar_split_clause,[],[f1540,f14625]) ).
fof(f14625,plain,
( spl0_1776
<=> ! [X2,X0,X30,X26] :
( c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f1540,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X30,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f14623,plain,
spl0_1775,
inference(avatar_split_clause,[],[f1539,f14621]) ).
fof(f14621,plain,
( spl0_1775
<=> ! [X0,X30,X2,X26] :
( c_lessequals(X26,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f1539,axiom,
! [X2,X0,X26,X30] :
( c_lessequals(X26,X2,tc_set(X0))
| ~ c_lessequals(c_union(X26,X30,X0),X2,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f14619,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1525,f14617]) ).
fof(f14617,plain,
( spl0_1774
<=> ! [X0,X30,X26] : c_union(X26,X30,X0) = c_union(X26,c_minus(X30,X26,tc_set(X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f1525,axiom,
! [X0,X26,X30] : c_union(X26,X30,X0) = c_union(X26,c_minus(X30,X26,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f14615,plain,
spl0_1773,
inference(avatar_split_clause,[],[f1524,f14613]) ).
fof(f14613,plain,
( spl0_1773
<=> ! [X0,X30,X26] : c_union(c_minus(X30,X26,tc_set(X0)),X26,X0) = c_union(X30,X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f1524,axiom,
! [X0,X26,X30] : c_union(c_minus(X30,X26,tc_set(X0)),X26,X0) = c_union(X30,X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f14610,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1516,f14608]) ).
fof(f14608,plain,
( spl0_1772
<=> ! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInter__iff__1(X26,X2,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f1516,axiom,
! [X2,X0,X26] :
( c_in(X26,c_Inter(X2,X0),X0)
| ~ c_in(X26,c_Main_OInter__iff__1(X26,X2,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f14606,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1507,f14604]) ).
fof(f14604,plain,
( spl0_1771
<=> ! [X29,X0,X26] :
( c_UNIV = X29
| c_UNIV != c_Inter(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f1507,axiom,
! [X29,X0,X26] :
( c_UNIV = X29
| c_UNIV != c_Inter(X26,X0)
| ~ c_in(X29,X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_0) ).
fof(f14602,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1449,f14600]) ).
fof(f14600,plain,
( spl0_1770
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f1449,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f14598,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1448,f14596]) ).
fof(f14596,plain,
( spl0_1769
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f1448,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f14594,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1446,f14592]) ).
fof(f14592,plain,
( spl0_1768
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f1446,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f14590,plain,
spl0_1767,
inference(avatar_split_clause,[],[f1445,f14588]) ).
fof(f14588,plain,
( spl0_1767
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f1445,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThanAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f14586,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1419,f14584]) ).
fof(f14584,plain,
( spl0_1766
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f1419,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f14582,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1418,f14580]) ).
fof(f14580,plain,
( spl0_1765
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f1418,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastLessThan(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f14578,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1414,f14576]) ).
fof(f1414,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X36,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f14574,plain,
spl0_1763,
inference(avatar_split_clause,[],[f1413,f14572]) ).
fof(f14572,plain,
( spl0_1763
<=> ! [X23,X0,X36,X72] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f1413,axiom,
! [X72,X0,X36,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X72,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeastAtMost(X72,X36,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f14570,plain,
( spl0_1762
| ~ spl0_1102
| ~ spl0_1536
| ~ spl0_1654 ),
inference(avatar_split_clause,[],[f13341,f13296,f12432,f9158,f14567]) ).
fof(f14567,plain,
( spl0_1762
<=> c_0 = c_OrderedGroup_Onprt(c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f13341,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_0 = c_OrderedGroup_Onprt(c_1,t_b)
| ~ spl0_1536
| ~ spl0_1654 ),
inference(resolution,[],[f13298,f12433]) ).
fof(f14565,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1281,f14563]) ).
fof(f14563,plain,
( spl0_1761
<=> ! [X0,X1,X3] :
( X1 = X3
| ~ c_in(c_Pair(X3,X1,X0,X0),c_Relation_OId,tc_prod(X0,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f1281,axiom,
! [X3,X0,X1] :
( X1 = X3
| ~ c_in(c_Pair(X3,X1,X0,X0),c_Relation_OId,tc_prod(X0,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f14561,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1261,f14559]) ).
fof(f1261,axiom,
! [X0,X16,X35] : c_Pair(c_Main_Osurj__pair__1(X35,X0,X16),c_Main_Osurj__pair__2(X35,X0,X16),X0,X16) = X35,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f14557,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1259,f14555]) ).
fof(f14555,plain,
( spl0_1759
<=> ! [X16,X0,X10] : c_Pair(c_fst(X10,X0,X16),c_snd(X10,X0,X16),X0,X16) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f1259,axiom,
! [X10,X0,X16] : c_Pair(c_fst(X10,X0,X16),c_snd(X10,X0,X16),X0,X16) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f14553,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1255,f14551]) ).
fof(f14551,plain,
( spl0_1758
<=> ! [X0,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1255,axiom,
! [X3,X0] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f14549,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1252,f14547]) ).
fof(f14547,plain,
( spl0_1757
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1252,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,X0),X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f14545,plain,
spl0_1756,
inference(avatar_split_clause,[],[f1241,f14543]) ).
fof(f14543,plain,
( spl0_1756
<=> ! [X0,X11,X3] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_0 != c_Nat_Opower(X3,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f1241,axiom,
! [X3,X0,X11] :
( ~ class_Power_Orecpower(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X3
| c_0 != c_Nat_Opower(X3,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f14541,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1233,f14539]) ).
fof(f14539,plain,
( spl0_1755
<=> ! [X12,X33] :
( ~ c_less(c_0,X12,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f1233,axiom,
! [X12,X33] :
( ~ c_less(c_0,X12,tc_nat)
| c_less(c_0,c_Nat_Opower(X12,c_Numeral_Onumber__of(X33,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f14537,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1189,f14535]) ).
fof(f14535,plain,
( spl0_1754
<=> ! [X11,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_less(c_0,X11,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f1189,axiom,
! [X11,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_less(c_0,X11,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f14533,plain,
spl0_1753,
inference(avatar_split_clause,[],[f1176,f14531]) ).
fof(f14531,plain,
( spl0_1753
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_less(c_0,X10,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f1176,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_less(c_0,X10,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f14529,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1159,f14527]) ).
fof(f1159,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X10,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f14524,plain,
spl0_1751,
inference(avatar_split_clause,[],[f1158,f14522]) ).
fof(f1158,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(c_Orderings_Omax(X12,X10,X16),X35,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f14520,plain,
spl0_1750,
inference(avatar_split_clause,[],[f1154,f14518]) ).
fof(f1154,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X35,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f14516,plain,
spl0_1749,
inference(avatar_split_clause,[],[f1153,f14514]) ).
fof(f1153,axiom,
! [X10,X16,X35,X12] :
( ~ class_Orderings_Olinorder(X16)
| c_lessequals(X12,X10,X16)
| ~ c_lessequals(X12,c_Orderings_Omin(X10,X35,X16),X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f14512,plain,
spl0_1748,
inference(avatar_split_clause,[],[f1151,f14510]) ).
fof(f14510,plain,
( spl0_1748
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X10,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f1151,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X10,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f14508,plain,
spl0_1747,
inference(avatar_split_clause,[],[f1150,f14506]) ).
fof(f14506,plain,
( spl0_1747
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X12,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f1150,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X35,X12,X0)
| ~ c_less(X35,c_Orderings_Omin(X12,X10,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f14504,plain,
spl0_1746,
inference(avatar_split_clause,[],[f1148,f14502]) ).
fof(f14502,plain,
( spl0_1746
<=> ! [X0,X12,X35,X10] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X10,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f1148,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X10,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f14500,plain,
spl0_1745,
inference(avatar_split_clause,[],[f1147,f14498]) ).
fof(f14498,plain,
( spl0_1745
<=> ! [X35,X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X12,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f1147,axiom,
! [X10,X0,X35,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_less(X12,X35,X0)
| ~ c_less(c_Orderings_Omax(X12,X10,X0),X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f14496,plain,
spl0_1744,
inference(avatar_split_clause,[],[f1143,f14494]) ).
fof(f14494,plain,
( spl0_1744
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_0,c_plus(X3,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f1143,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_0,c_plus(X3,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f14492,plain,
spl0_1743,
inference(avatar_split_clause,[],[f1142,f14490]) ).
fof(f14490,plain,
( spl0_1743
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_0,c_plus(X3,X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f1142,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_0,c_plus(X3,X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f14488,plain,
spl0_1742,
inference(avatar_split_clause,[],[f1109,f14486]) ).
fof(f14486,plain,
( spl0_1742
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X3,X1,X0),X0) = c_minus(X1,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f1109,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_minus(X3,X1,X0),X0) = c_minus(X1,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f14484,plain,
( spl0_1741
| ~ spl0_1102
| ~ spl0_1539
| ~ spl0_1654 ),
inference(avatar_split_clause,[],[f13340,f13296,f12444,f9158,f14481]) ).
fof(f14481,plain,
( spl0_1741
<=> c_1 = c_OrderedGroup_Opprt(c_1,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f13340,plain,
( ~ class_OrderedGroup_Olordered__ab__group(t_b)
| c_1 = c_OrderedGroup_Opprt(c_1,t_b)
| ~ spl0_1539
| ~ spl0_1654 ),
inference(resolution,[],[f13298,f12445]) ).
fof(f14479,plain,
spl0_1740,
inference(avatar_split_clause,[],[f1106,f14477]) ).
fof(f14477,plain,
( spl0_1740
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Omeet(X3,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f1106,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Omeet(X3,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f14475,plain,
spl0_1739,
inference(avatar_split_clause,[],[f1104,f14473]) ).
fof(f14473,plain,
( spl0_1739
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Ojoin(X3,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f1104,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = X3
| c_0 != c_LOrder_Ojoin(X3,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f14471,plain,
spl0_1738,
inference(avatar_split_clause,[],[f1101,f14469]) ).
fof(f14469,plain,
( spl0_1738
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f1101,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f14467,plain,
spl0_1737,
inference(avatar_split_clause,[],[f1100,f14465]) ).
fof(f14465,plain,
( spl0_1737
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_plus(X3,X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f1100,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_plus(X3,X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f14463,plain,
spl0_1736,
inference(avatar_split_clause,[],[f1098,f14461]) ).
fof(f14461,plain,
( spl0_1736
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,X1,X0) = c_minus(X3,c_uminus(X1,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f1098,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(X3,X1,X0) = c_minus(X3,c_uminus(X1,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f14459,plain,
spl0_1735,
inference(avatar_split_clause,[],[f1097,f14457]) ).
fof(f1097,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,X1,X0)
| c_less(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f14455,plain,
spl0_1734,
inference(avatar_split_clause,[],[f1096,f14453]) ).
fof(f1096,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,X1,X0)
| ~ c_less(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f14451,plain,
spl0_1733,
inference(avatar_split_clause,[],[f1095,f14449]) ).
fof(f14449,plain,
( spl0_1733
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f1095,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,X1,X0)
| c_lessequals(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f14447,plain,
spl0_1732,
inference(avatar_split_clause,[],[f1094,f14445]) ).
fof(f14445,plain,
( spl0_1732
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_minus(X3,X1,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f1094,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,X1,X0)
| ~ c_lessequals(c_minus(X3,X1,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f14443,plain,
spl0_1731,
inference(avatar_split_clause,[],[f1078,f14441]) ).
fof(f14441,plain,
( spl0_1731
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_uminus(X3,X0) = c_HOL_Oabs(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f1078,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_uminus(X3,X0) = c_HOL_Oabs(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f14426,plain,
spl0_1730,
inference(avatar_split_clause,[],[f1004,f14424]) ).
fof(f14424,plain,
( spl0_1730
<=> ! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f1004,axiom,
! [X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB1),c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f14422,plain,
spl0_1729,
inference(avatar_split_clause,[],[f1003,f14420]) ).
fof(f14420,plain,
( spl0_1729
<=> ! [X34,X33,X10] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),c_Numeral_OBit(X33,X10)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f1003,axiom,
! [X10,X34,X33] : c_Numeral_Obin__add(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),c_Numeral_OBit(X33,X10)) = c_Numeral_OBit(c_Numeral_Obin__add(X34,X33),X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f14418,plain,
spl0_1728,
inference(avatar_split_clause,[],[f939,f14416]) ).
fof(f14416,plain,
( spl0_1728
<=> ! [X11,X10] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(X11,c_minus(X10,X11,tc_nat),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f939,axiom,
! [X10,X11] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(X11,c_minus(X10,X11,tc_nat),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f14414,plain,
spl0_1727,
inference(avatar_split_clause,[],[f938,f14412]) ).
fof(f14412,plain,
( spl0_1727
<=> ! [X11,X10] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(c_minus(X10,X11,tc_nat),X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f938,axiom,
! [X10,X11] :
( ~ c_lessequals(X11,X10,tc_nat)
| c_plus(c_minus(X10,X11,tc_nat),X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f14410,plain,
spl0_1726,
inference(avatar_split_clause,[],[f746,f14408]) ).
fof(f14408,plain,
( spl0_1726
<=> ! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f746,axiom,
! [X34] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X34,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f14406,plain,
spl0_1725,
inference(avatar_split_clause,[],[f693,f14404]) ).
fof(f14404,plain,
( spl0_1725
<=> ! [X11,X10] :
( ~ c_lessequals(X10,X11,tc_nat)
| c_minus(X11,c_minus(X11,X10,tc_nat),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f693,axiom,
! [X10,X11] :
( ~ c_lessequals(X10,X11,tc_nat)
| c_minus(X11,c_minus(X11,X10,tc_nat),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f14402,plain,
spl0_1724,
inference(avatar_split_clause,[],[f659,f14400]) ).
fof(f14400,plain,
( spl0_1724
<=> ! [X0,X12,X26] :
( c_in(c_0,X26,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f659,axiom,
! [X0,X26,X12] :
( c_in(c_0,X26,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f14398,plain,
spl0_1723,
inference(avatar_split_clause,[],[f642,f14396]) ).
fof(f14396,plain,
( spl0_1723
<=> ! [X12,X39,X14] : c_List_Oset(c_List_Olist_OCons(X12,X39,X14),X14) = c_insert(X12,c_List_Oset(X39,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f642,axiom,
! [X39,X14,X12] : c_List_Oset(c_List_Olist_OCons(X12,X39,X14),X14) = c_insert(X12,c_List_Oset(X39,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f14394,plain,
spl0_1722,
inference(avatar_split_clause,[],[f636,f14392]) ).
fof(f14392,plain,
( spl0_1722
<=> ! [X0,X11,X10] :
( c_List_Orotate(X11,X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f636,axiom,
! [X10,X0,X11] :
( c_List_Orotate(X11,X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f14390,plain,
spl0_1721,
inference(avatar_split_clause,[],[f596,f14388]) ).
fof(f14388,plain,
( spl0_1721
<=> ! [X10,X11,X0,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(c_List_Oreplicate(X11,X10,X0),X23,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f596,axiom,
! [X10,X0,X11,X23] :
( ~ c_less(X23,X11,tc_nat)
| c_List_Onth(c_List_Oreplicate(X11,X10,X0),X23,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f14386,plain,
( spl0_1720
| ~ spl0_1009
| ~ spl0_1373 ),
inference(avatar_split_clause,[],[f11504,f11108,f8725,f14384]) ).
fof(f11108,plain,
( spl0_1373
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f11504,plain,
( ! [X0] : c_uminus(c_uminus(X0,t_b),t_b) = X0
| ~ spl0_1009
| ~ spl0_1373 ),
inference(resolution,[],[f11109,f8727]) ).
fof(f11109,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X10,X0),X0) = X10 )
| ~ spl0_1373 ),
inference(avatar_component_clause,[],[f11108]) ).
fof(f14382,plain,
spl0_1719,
inference(avatar_split_clause,[],[f498,f14380]) ).
fof(f14380,plain,
( spl0_1719
<=> ! [X23,X0,X12,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Olist__update(X39,X23,X12,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f498,axiom,
! [X39,X0,X12,X23] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Olist__update(X39,X23,X12,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f14378,plain,
spl0_1718,
inference(avatar_split_clause,[],[f485,f14376]) ).
fof(f14376,plain,
( spl0_1718
<=> ! [X39,X0,X40] :
( c_List_Olist_ONil = X40
| c_List_Olast(c_append(X39,X40,X0),X0) = c_List_Olast(X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f485,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X40
| c_List_Olast(c_append(X39,X40,X0),X0) = c_List_Olast(X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f14374,plain,
spl0_1717,
inference(avatar_split_clause,[],[f483,f14372]) ).
fof(f14372,plain,
( spl0_1717
<=> ! [X0,X12,X39] :
( c_List_Olist_ONil = X39
| c_List_Olast(c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olast(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f483,axiom,
! [X39,X0,X12] :
( c_List_Olist_ONil = X39
| c_List_Olast(c_List_Olist_OCons(X12,X39,X0),X0) = c_List_Olast(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f14370,plain,
spl0_1716,
inference(avatar_split_clause,[],[f475,f14368]) ).
fof(f14368,plain,
( spl0_1716
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Ohd(c_append(X39,X40,X0),X0) = c_List_Ohd(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f475,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Ohd(c_append(X39,X40,X0),X0) = c_List_Ohd(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f14366,plain,
spl0_1715,
inference(avatar_split_clause,[],[f474,f14364]) ).
fof(f14364,plain,
( spl0_1715
<=> ! [X0,X10] :
( c_List_Olist_ONil = X10
| c_List_Olist_OCons(c_List_Ohd(X10,X0),c_List_Otl(X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f474,axiom,
! [X10,X0] :
( c_List_Olist_ONil = X10
| c_List_Olist_OCons(c_List_Ohd(X10,X0),c_List_Otl(X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f14362,plain,
spl0_1714,
inference(avatar_split_clause,[],[f472,f14360]) ).
fof(f14360,plain,
( spl0_1714
<=> ! [X50,X24,X23] : c_List_Odrop(X24,c_List_Oupt(X23,X50),tc_nat) = c_List_Oupt(c_plus(X23,X24,tc_nat),X50) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f472,axiom,
! [X50,X24,X23] : c_List_Odrop(X24,c_List_Oupt(X23,X50),tc_nat) = c_List_Oupt(c_plus(X23,X24,tc_nat),X50),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f14358,plain,
spl0_1713,
inference(avatar_split_clause,[],[f470,f14356]) ).
fof(f14356,plain,
( spl0_1713
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil = c_List_Odrop(X11,X39,X0)
| ~ c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f470,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil = c_List_Odrop(X11,X39,X0)
| ~ c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f14354,plain,
spl0_1712,
inference(avatar_split_clause,[],[f469,f14352]) ).
fof(f14352,plain,
( spl0_1712
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil != c_List_Odrop(X11,X39,X0)
| c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f469,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil != c_List_Odrop(X11,X39,X0)
| c_lessequals(c_Nat_Osize(X39,tc_List_Olist(X0)),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f14350,plain,
spl0_1711,
inference(avatar_split_clause,[],[f369,f14348]) ).
fof(f14348,plain,
( spl0_1711
<=> ! [X1,X3] : c_div(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X3,X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f369,axiom,
! [X3,X1] : c_div(c_uminus(X3,tc_IntDef_Oint),c_uminus(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X3,X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f14346,plain,
spl0_1710,
inference(avatar_split_clause,[],[f310,f14344]) ).
fof(f14344,plain,
( spl0_1710
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_uminus(X35,tc_IntDef_Oint),X0) = c_uminus(c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f310,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_uminus(X35,tc_IntDef_Oint),X0) = c_uminus(c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f14335,plain,
spl0_1709,
inference(avatar_split_clause,[],[f199,f14333]) ).
fof(f14333,plain,
( spl0_1709
<=> ! [X9,X11,X24] :
( c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f199,axiom,
! [X11,X9,X24] :
( c_Divides_Oop_Advd(X9,X11,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f14331,plain,
spl0_1708,
inference(avatar_split_clause,[],[f198,f14329]) ).
fof(f14329,plain,
( spl0_1708
<=> ! [X9,X11,X24] :
( c_Divides_Oop_Advd(X9,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f198,axiom,
! [X11,X9,X24] :
( c_Divides_Oop_Advd(X9,X24,tc_nat)
| ~ c_Divides_Oop_Advd(X9,c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f14327,plain,
spl0_1707,
inference(avatar_split_clause,[],[f185,f14325]) ).
fof(f14325,plain,
( spl0_1707
<=> ! [X0,X3,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f185,axiom,
! [X3,X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_insert(X3,X26,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f14323,plain,
spl0_1706,
inference(avatar_split_clause,[],[f181,f14321]) ).
fof(f14321,plain,
( spl0_1706
<=> ! [X6,X0,X32] :
( c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f181,axiom,
! [X0,X6,X32] :
( c_in(X32,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f14319,plain,
spl0_1705,
inference(avatar_split_clause,[],[f180,f14317]) ).
fof(f14317,plain,
( spl0_1705
<=> ! [X6,X0,X32] :
( c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f180,axiom,
! [X0,X6,X32] :
( c_in(X6,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_union(X6,X32,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f14315,plain,
spl0_1704,
inference(avatar_split_clause,[],[f179,f14313]) ).
fof(f14313,plain,
( spl0_1704
<=> ! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f179,axiom,
! [X0,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f14311,plain,
spl0_1703,
inference(avatar_split_clause,[],[f178,f14309]) ).
fof(f14309,plain,
( spl0_1703
<=> ! [X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f178,axiom,
! [X0,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X0))
| ~ c_in(c_Pow(X26,X0),c_Finite__Set_OFinites,tc_set(tc_set(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f14307,plain,
spl0_1702,
inference(avatar_split_clause,[],[f170,f14305]) ).
fof(f14305,plain,
( spl0_1702
<=> ! [X0,X26] :
( c_emptyset = X26
| c_0 != c_Finite__Set_Ocard(X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f170,axiom,
! [X0,X26] :
( c_emptyset = X26
| c_0 != c_Finite__Set_Ocard(X26,X0)
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f14303,plain,
spl0_1701,
inference(avatar_split_clause,[],[f117,f14301]) ).
fof(f14301,plain,
( spl0_1701
<=> ! [X11,X10] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X10,X11,tc_nat),X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f117,axiom,
! [X10,X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X10,X11,tc_nat),X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f14299,plain,
spl0_1700,
inference(avatar_split_clause,[],[f115,f14297]) ).
fof(f14297,plain,
( spl0_1700
<=> ! [X11,X10] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X11,X10,tc_nat),X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f115,axiom,
! [X10,X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_div(c_times(X11,X10,tc_nat),X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f14295,plain,
( ~ spl0_1069
| spl0_1699
| ~ spl0_1277
| ~ spl0_1479 ),
inference(avatar_split_clause,[],[f12181,f11941,f10374,f14292,f9023]) ).
fof(f14292,plain,
( spl0_1699
<=> c_lessequals(c_0,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f10374,plain,
( spl0_1277
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f11941,plain,
( spl0_1479
<=> c_0 = c_HOL_Oabs(c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f12181,plain,
( c_lessequals(c_0,c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1277
| ~ spl0_1479 ),
inference(superposition,[],[f10375,f11943]) ).
fof(f11943,plain,
( c_0 = c_HOL_Oabs(c_0,t_b)
| ~ spl0_1479 ),
inference(avatar_component_clause,[],[f11941]) ).
fof(f10375,plain,
( ! [X0] :
( c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1277 ),
inference(avatar_component_clause,[],[f10374]) ).
fof(f14085,plain,
( ~ spl0_1069
| ~ spl0_1698
| ~ spl0_1287
| ~ spl0_1479 ),
inference(avatar_split_clause,[],[f12180,f11941,f10416,f14082,f9023]) ).
fof(f10416,plain,
( spl0_1287
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f12180,plain,
( ~ c_less(c_0,c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1287
| ~ spl0_1479 ),
inference(superposition,[],[f10417,f11943]) ).
fof(f10417,plain,
( ! [X0] :
( ~ c_less(c_0,c_HOL_Oabs(c_0,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1287 ),
inference(avatar_component_clause,[],[f10416]) ).
fof(f13474,plain,
spl0_1697,
inference(avatar_split_clause,[],[f3177,f13472]) ).
fof(f13472,plain,
( spl0_1697
<=> ! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f3177,plain,
! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f3176,f1009]) ).
fof(f3176,plain,
! [X0,X12] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2983,f2813]) ).
fof(f2983,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f232,f1023]) ).
fof(f232,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(X12,X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f13470,plain,
spl0_1696,
inference(avatar_split_clause,[],[f3107,f13468]) ).
fof(f13468,plain,
( spl0_1696
<=> ! [X0] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X0)
| ~ class_Power_Orecpower(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f3107,plain,
! [X0] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X0)
| ~ class_Power_Orecpower(X0) ),
inference(forward_demodulation,[],[f3106,f1050]) ).
fof(f3106,plain,
! [X0] :
( 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),X0)
| ~ class_Power_Orecpower(X0) ),
inference(forward_demodulation,[],[f3105,f1048]) ).
fof(f3105,plain,
! [X0] :
( 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),X0)
| ~ class_Power_Orecpower(X0) ),
inference(forward_demodulation,[],[f772,f1050]) ).
fof(f772,axiom,
! [X0] :
( ~ class_Power_Orecpower(X0)
| 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),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f13466,plain,
spl0_1695,
inference(avatar_split_clause,[],[f3100,f13464]) ).
fof(f3100,plain,
! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f3099,f1050]) ).
fof(f3099,plain,
! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f3098,f1048]) ).
fof(f3098,plain,
! [X0] :
( c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f222,f1050]) ).
fof(f222,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_plus(c_1,c_1,X0) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f13462,plain,
spl0_1694,
inference(avatar_split_clause,[],[f2924,f13460]) ).
fof(f13460,plain,
( spl0_1694
<=> ! [X0,X30,X26] :
( c_UNIV = X30
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f2924,plain,
! [X0,X26,X30] :
( c_UNIV = X30
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1493,f1267]) ).
fof(f1493,axiom,
! [X0,X26,X30] :
( c_UNIV = X30
| c_UNIV != c_inter(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f13458,plain,
spl0_1693,
inference(avatar_split_clause,[],[f2923,f13456]) ).
fof(f13456,plain,
( spl0_1693
<=> ! [X0,X30,X26] :
( c_UNIV = X26
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f2923,plain,
! [X0,X26,X30] :
( c_UNIV = X26
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X26,X0),X30,X0,X0) ),
inference(definition_unfolding,[],[f1492,f1267]) ).
fof(f1492,axiom,
! [X0,X26,X30] :
( c_UNIV = X26
| c_UNIV != c_inter(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f13454,plain,
spl0_1692,
inference(avatar_split_clause,[],[f2918,f13452]) ).
fof(f13452,plain,
( spl0_1692
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f2918,plain,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),X0) ),
inference(definition_unfolding,[],[f1240,f1438]) ).
fof(f1240,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_0 = c_Nat_Opower(c_0,c_Suc(X11),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f13450,plain,
spl0_1691,
inference(avatar_split_clause,[],[f2850,f13448]) ).
fof(f2850,plain,
! [X24] : c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f266,f1438]) ).
fof(f266,axiom,
! [X24] : c_IntDef_Oint(c_Suc(X24)) = c_plus(c_1,c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f13446,plain,
spl0_1690,
inference(avatar_split_clause,[],[f2847,f13444]) ).
fof(f13444,plain,
( spl0_1690
<=> ! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),X26,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f2847,plain,
! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X26,tc_set(X0)),X0),X26,X0,X0),
inference(definition_unfolding,[],[f1472,f1267]) ).
fof(f1472,axiom,
! [X0,X26] : c_emptyset = c_inter(c_uminus(X26,tc_set(X0)),X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f13442,plain,
spl0_1689,
inference(avatar_split_clause,[],[f2846,f13440]) ).
fof(f13440,plain,
( spl0_1689
<=> ! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_uminus(X26,tc_set(X0)),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f2846,plain,
! [X0,X26] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X26,X0),c_uminus(X26,tc_set(X0)),X0,X0),
inference(definition_unfolding,[],[f1473,f1267]) ).
fof(f1473,axiom,
! [X0,X26] : c_emptyset = c_inter(X26,c_uminus(X26,tc_set(X0)),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f13438,plain,
spl0_1688,
inference(avatar_split_clause,[],[f1731,f13436]) ).
fof(f13436,plain,
( spl0_1688
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(c_Main_OsubsetI__1(X26,X30,X0),X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f1731,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(c_Main_OsubsetI__1(X26,X30,X0),X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f13434,plain,
spl0_1687,
inference(avatar_split_clause,[],[f1730,f13432]) ).
fof(f13432,plain,
( spl0_1687
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| c_in(c_Main_OsubsetI__1(X26,X30,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f1730,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| c_in(c_Main_OsubsetI__1(X26,X30,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f13430,plain,
spl0_1686,
inference(avatar_split_clause,[],[f1670,f13428]) ).
fof(f13428,plain,
( spl0_1686
<=> ! [X0,X39] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f1670,axiom,
! [X39,X0] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X39,X0),tc_List_Olist(X0)),c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f13426,plain,
spl0_1685,
inference(avatar_split_clause,[],[f1623,f13424]) ).
fof(f13424,plain,
( spl0_1685
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Datatype__Universe_ONumb(X12,X0,X16) != c_Datatype__Universe_ONumb(X10,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f1623,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Datatype__Universe_ONumb(X12,X0,X16) != c_Datatype__Universe_ONumb(X10,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f13422,plain,
spl0_1684,
inference(avatar_split_clause,[],[f1622,f13420]) ).
fof(f13420,plain,
( spl0_1684
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Datatype__Universe_OLeaf(X12,X0,X16) != c_Datatype__Universe_OLeaf(X10,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f1622,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Datatype__Universe_OLeaf(X12,X0,X16) != c_Datatype__Universe_OLeaf(X10,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f13418,plain,
spl0_1683,
inference(avatar_split_clause,[],[f1597,f13416]) ).
fof(f13416,plain,
( spl0_1683
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Sum__Type_OInr(X12,X16,X0) != c_Sum__Type_OInr(X10,X16,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f1597,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Sum__Type_OInr(X12,X16,X0) != c_Sum__Type_OInr(X10,X16,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f13414,plain,
spl0_1682,
inference(avatar_split_clause,[],[f1595,f13412]) ).
fof(f13412,plain,
( spl0_1682
<=> ! [X10,X0,X12,X16] :
( X10 = X12
| c_Sum__Type_OInl(X12,X0,X16) != c_Sum__Type_OInl(X10,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f1595,axiom,
! [X10,X0,X16,X12] :
( X10 = X12
| c_Sum__Type_OInl(X12,X0,X16) != c_Sum__Type_OInl(X10,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f13410,plain,
spl0_1681,
inference(avatar_split_clause,[],[f1589,f13408]) ).
fof(f13408,plain,
( spl0_1681
<=> ! [X0,X3,X1,X26] :
( X1 = X3
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f1589,axiom,
! [X3,X0,X1,X26] :
( X1 = X3
| c_insert(X3,X26,X0) != c_insert(X1,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
fof(f13406,plain,
spl0_1680,
inference(avatar_split_clause,[],[f1582,f13404]) ).
fof(f13404,plain,
( spl0_1680
<=> ! [X0,X12,X26,X30] :
( c_in(X12,X30,X0)
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f1582,axiom,
! [X0,X26,X12,X30] :
( c_in(X12,X30,X0)
| ~ c_lessequals(c_insert(X12,X26,X0),X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f13402,plain,
spl0_1679,
inference(avatar_split_clause,[],[f1570,f13400]) ).
fof(f13400,plain,
( spl0_1679
<=> ! [X0,X12,X26] : c_insert(X12,X26,X0) = c_insert(X12,c_insert(X12,X26,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f1570,axiom,
! [X0,X26,X12] : c_insert(X12,X26,X0) = c_insert(X12,c_insert(X12,X26,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f13398,plain,
spl0_1678,
inference(avatar_split_clause,[],[f1564,f13396]) ).
fof(f13396,plain,
( spl0_1678
<=> ! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_Oempty__Union__conv__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f1564,axiom,
! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_Oempty__Union__conv__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f13394,plain,
spl0_1677,
inference(avatar_split_clause,[],[f1547,f13392]) ).
fof(f13392,plain,
( spl0_1677
<=> ! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_OUnion__empty__conv__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f1547,axiom,
! [X0,X26] :
( c_emptyset = c_Union(X26,X0)
| c_in(c_Main_OUnion__empty__conv__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f13390,plain,
spl0_1676,
inference(avatar_split_clause,[],[f1522,f13388]) ).
fof(f13388,plain,
( spl0_1676
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_in(X26,c_Pow(X30,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f1522,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_in(X26,c_Pow(X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f13386,plain,
spl0_1675,
inference(avatar_split_clause,[],[f1521,f13384]) ).
fof(f13384,plain,
( spl0_1675
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(X26,c_Pow(X30,X0),tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f1521,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| ~ c_in(X26,c_Pow(X30,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f13382,plain,
spl0_1674,
inference(avatar_split_clause,[],[f1511,f13380]) ).
fof(f13380,plain,
( spl0_1674
<=> ! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__2__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f1511,axiom,
! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__2__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f13378,plain,
spl0_1673,
inference(avatar_split_clause,[],[f1508,f13376]) ).
fof(f13376,plain,
( spl0_1673
<=> ! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__1__1(X26,X0),X26,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f1508,axiom,
! [X0,X26] :
( c_UNIV = c_Inter(X26,X0)
| c_in(c_Main_OInter__UNIV__conv__1__1(X26,X0),X26,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f13374,plain,
spl0_1672,
inference(avatar_split_clause,[],[f1489,f13372]) ).
fof(f13372,plain,
( spl0_1672
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f1489,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f13370,plain,
spl0_1671,
inference(avatar_split_clause,[],[f1488,f13368]) ).
fof(f13368,plain,
( spl0_1671
<=> ! [X0,X30,X25,X26] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f1488,axiom,
! [X0,X26,X25,X30] :
( c_in(X25,X26,X0)
| ~ c_in(X25,c_minus(X26,X30,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f13366,plain,
spl0_1670,
inference(avatar_split_clause,[],[f1486,f13364]) ).
fof(f13364,plain,
( spl0_1670
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_emptyset = c_minus(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f1486,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X26,X30,tc_set(X0))
| c_emptyset = c_minus(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f13362,plain,
spl0_1669,
inference(avatar_split_clause,[],[f1485,f13360]) ).
fof(f13360,plain,
( spl0_1669
<=> ! [X0,X30,X26] :
( c_lessequals(X26,X30,tc_set(X0))
| c_emptyset != c_minus(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f1485,axiom,
! [X0,X26,X30] :
( c_lessequals(X26,X30,tc_set(X0))
| c_emptyset != c_minus(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f13358,plain,
spl0_1668,
inference(avatar_split_clause,[],[f1475,f13356]) ).
fof(f13356,plain,
( spl0_1668
<=> ! [X0,X30,X26] :
( X26 = X30
| c_uminus(X26,tc_set(X0)) != c_uminus(X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f1475,axiom,
! [X0,X26,X30] :
( X26 = X30
| c_uminus(X26,tc_set(X0)) != c_uminus(X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f13354,plain,
spl0_1667,
inference(avatar_split_clause,[],[f1464,f13352]) ).
fof(f13352,plain,
( spl0_1667
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X23,X9,X0)
| c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f1464,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X23,X9,X0)
| c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f13350,plain,
spl0_1666,
inference(avatar_split_clause,[],[f1463,f13348]) ).
fof(f13348,plain,
( spl0_1666
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f1463,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OlessThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f13346,plain,
spl0_1665,
inference(avatar_split_clause,[],[f1462,f13344]) ).
fof(f13344,plain,
( spl0_1665
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OlessThan(X12,X0) != c_SetInterval_OlessThan(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f1462,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OlessThan(X12,X0) != c_SetInterval_OlessThan(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f13339,plain,
spl0_1664,
inference(avatar_split_clause,[],[f1453,f13337]) ).
fof(f13337,plain,
( spl0_1664
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X9,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f1453,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_less(X9,X23,X0)
| c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f13335,plain,
spl0_1663,
inference(avatar_split_clause,[],[f1452,f13333]) ).
fof(f13333,plain,
( spl0_1663
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f1452,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_less(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OgreaterThan(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f13331,plain,
spl0_1662,
inference(avatar_split_clause,[],[f1451,f13329]) ).
fof(f13329,plain,
( spl0_1662
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OgreaterThan(X12,X0) != c_SetInterval_OgreaterThan(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f1451,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OgreaterThan(X12,X0) != c_SetInterval_OgreaterThan(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f13327,plain,
spl0_1661,
inference(avatar_split_clause,[],[f1444,f13325]) ).
fof(f1444,axiom,
! [X72,X0,X9] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X72,X9,X0)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X72,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f13323,plain,
spl0_1660,
inference(avatar_split_clause,[],[f1440,f13321]) ).
fof(f13321,plain,
( spl0_1660
<=> ! [X36,X72] : c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f1440,axiom,
! [X72,X36] : c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f13319,plain,
spl0_1659,
inference(avatar_split_clause,[],[f1437,f13317]) ).
fof(f13317,plain,
( spl0_1659
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f1437,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X36,X72,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f13315,plain,
spl0_1658,
inference(avatar_split_clause,[],[f1431,f13313]) ).
fof(f13313,plain,
( spl0_1658
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X9,X0)
| c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f1431,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X23,X9,X0)
| c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f13311,plain,
spl0_1657,
inference(avatar_split_clause,[],[f1430,f13309]) ).
fof(f13309,plain,
( spl0_1657
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f1430,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X23,X9,X0)
| ~ c_in(X23,c_SetInterval_OatMost(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f13307,plain,
spl0_1656,
inference(avatar_split_clause,[],[f1429,f13305]) ).
fof(f13305,plain,
( spl0_1656
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatMost(X12,X0) != c_SetInterval_OatMost(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f1429,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatMost(X12,X0) != c_SetInterval_OatMost(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f13303,plain,
spl0_1655,
inference(avatar_split_clause,[],[f1425,f13301]) ).
fof(f13301,plain,
( spl0_1655
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X9,X23,X0)
| c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f1425,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| ~ c_lessequals(X9,X23,X0)
| c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f13299,plain,
( ~ spl0_1069
| spl0_1654
| ~ spl0_1276
| ~ spl0_1427 ),
inference(avatar_split_clause,[],[f11811,f11725,f10370,f13296,f9023]) ).
fof(f10370,plain,
( spl0_1276
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f11811,plain,
( c_lessequals(c_0,c_1,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1276
| ~ spl0_1427 ),
inference(superposition,[],[f10371,f11727]) ).
fof(f10371,plain,
( ! [X3,X0] :
( c_lessequals(c_0,c_HOL_Oabs(X3,X0),X0)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X0) )
| ~ spl0_1276 ),
inference(avatar_component_clause,[],[f10370]) ).
fof(f13294,plain,
spl0_1653,
inference(avatar_split_clause,[],[f1424,f13292]) ).
fof(f13292,plain,
( spl0_1653
<=> ! [X9,X0,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f1424,axiom,
! [X0,X9,X23] :
( ~ class_Orderings_Oord(X0)
| c_lessequals(X9,X23,X0)
| ~ c_in(X23,c_SetInterval_OatLeast(X9,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f13290,plain,
spl0_1652,
inference(avatar_split_clause,[],[f1423,f13288]) ).
fof(f13288,plain,
( spl0_1652
<=> ! [X0,X12,X10] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatLeast(X12,X0) != c_SetInterval_OatLeast(X10,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f1423,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| X10 = X12
| c_SetInterval_OatLeast(X12,X0) != c_SetInterval_OatLeast(X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f13286,plain,
spl0_1651,
inference(avatar_split_clause,[],[f1417,f13284]) ).
fof(f1417,axiom,
! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_lessequals(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastLessThan(X24,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f13282,plain,
spl0_1650,
inference(avatar_split_clause,[],[f1412,f13280]) ).
fof(f1412,axiom,
! [X0,X11,X24] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X11,X24,X0)
| c_emptyset = c_SetInterval_OatLeastAtMost(X24,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f13278,plain,
spl0_1649,
inference(avatar_split_clause,[],[f1411,f13276]) ).
fof(f1411,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatLeast(X9,X0) = c_uminus(c_SetInterval_OlessThan(X9,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f13274,plain,
spl0_1648,
inference(avatar_split_clause,[],[f1410,f13272]) ).
fof(f1410,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_SetInterval_OatMost(X9,X0) = c_uminus(c_SetInterval_OgreaterThan(X9,X0),tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f13270,plain,
spl0_1647,
inference(avatar_split_clause,[],[f1409,f13268]) ).
fof(f1409,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatMost(X9,X0),tc_set(X0)) = c_SetInterval_OgreaterThan(X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f13266,plain,
spl0_1646,
inference(avatar_split_clause,[],[f1408,f13264]) ).
fof(f1408,axiom,
! [X0,X9] :
( ~ class_Orderings_Olinorder(X0)
| c_uminus(c_SetInterval_OatLeast(X9,X0),tc_set(X0)) = c_SetInterval_OlessThan(X9,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f13262,plain,
spl0_1645,
inference(avatar_split_clause,[],[f1196,f13260]) ).
fof(f13260,plain,
( spl0_1645
<=> ! [X12,X10] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f1196,axiom,
! [X10,X12] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f13258,plain,
spl0_1644,
inference(avatar_split_clause,[],[f1195,f13256]) ).
fof(f13256,plain,
( spl0_1644
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f1195,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f13254,plain,
spl0_1643,
inference(avatar_split_clause,[],[f1194,f13252]) ).
fof(f13252,plain,
( spl0_1643
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f1194,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f13250,plain,
spl0_1642,
inference(avatar_split_clause,[],[f1193,f13248]) ).
fof(f13248,plain,
( spl0_1642
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f1193,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f13246,plain,
spl0_1641,
inference(avatar_split_clause,[],[f1190,f13244]) ).
fof(f13244,plain,
( spl0_1641
<=> ! [X12,X10] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f1190,axiom,
! [X10,X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f13242,plain,
spl0_1640,
inference(avatar_split_clause,[],[f1183,f13240]) ).
fof(f13240,plain,
( spl0_1640
<=> ! [X12,X10] :
( c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f1183,axiom,
! [X10,X12] :
( c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f13238,plain,
spl0_1639,
inference(avatar_split_clause,[],[f1182,f13236]) ).
fof(f13236,plain,
( spl0_1639
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f1182,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f13234,plain,
spl0_1638,
inference(avatar_split_clause,[],[f1181,f13232]) ).
fof(f13232,plain,
( spl0_1638
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f1181,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f13230,plain,
spl0_1637,
inference(avatar_split_clause,[],[f1180,f13228]) ).
fof(f13228,plain,
( spl0_1637
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f1180,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_plus(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f13226,plain,
spl0_1636,
inference(avatar_split_clause,[],[f1177,f13224]) ).
fof(f13224,plain,
( spl0_1636
<=> ! [X12,X10] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f1177,axiom,
! [X10,X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(X10,tc_nat)
| ~ c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f13222,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1171,f13220]) ).
fof(f13220,plain,
( spl0_1635
<=> ! [X12,X10] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f1171,axiom,
! [X10,X12] :
( c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f13218,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1170,f13216]) ).
fof(f13216,plain,
( spl0_1634
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f1170,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f13214,plain,
( ~ spl0_1069
| ~ spl0_1633
| ~ spl0_1278
| ~ spl0_1427 ),
inference(avatar_split_clause,[],[f11810,f11725,f10378,f13211,f9023]) ).
fof(f13211,plain,
( spl0_1633
<=> c_less(c_1,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f11810,plain,
( ~ c_less(c_1,c_0,t_b)
| ~ class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1278
| ~ spl0_1427 ),
inference(superposition,[],[f10379,f11727]) ).
fof(f13209,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1169,f13207]) ).
fof(f13207,plain,
( spl0_1632
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f1169,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(X10,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f13205,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1168,f13203]) ).
fof(f13203,plain,
( spl0_1631
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f1168,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f13201,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1128,f13199]) ).
fof(f13199,plain,
( spl0_1630
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_0,X3,X0)
| c_less(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f1128,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(c_0,X3,X0)
| c_less(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f13197,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1127,f13195]) ).
fof(f13195,plain,
( spl0_1629
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(c_0,X3,X0)
| ~ c_less(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f1127,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(c_0,X3,X0)
| ~ c_less(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f13193,plain,
spl0_1628,
inference(avatar_split_clause,[],[f1124,f13191]) ).
fof(f13191,plain,
( spl0_1628
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f1124,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(c_0,X3,X0)
| c_lessequals(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f13189,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1123,f13187]) ).
fof(f13187,plain,
( spl0_1627
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_uminus(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f1123,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(c_0,X3,X0)
| ~ c_lessequals(c_uminus(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f13185,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1121,f13183]) ).
fof(f13183,plain,
( spl0_1626
<=> ! [X0,X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_uminus(X3,X0) != c_uminus(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f1121,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_uminus(X3,X0) != c_uminus(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f13181,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1118,f13179]) ).
fof(f13179,plain,
( spl0_1625
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f1118,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_less(X3,c_0,X0)
| c_less(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f13177,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1117,f13175]) ).
fof(f13175,plain,
( spl0_1624
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f1117,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_less(X3,c_0,X0)
| ~ c_less(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f13173,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1116,f13171]) ).
fof(f13171,plain,
( spl0_1623
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f1116,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| ~ c_lessequals(X3,c_0,X0)
| c_lessequals(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f13169,plain,
( spl0_1622
| ~ spl0_1179
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f11587,f10568,f9526,f13167]) ).
fof(f13167,plain,
( spl0_1622
<=> ! [X0] : c_SetsAndFunctions_Oelt__set__times(c_1,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f9526,plain,
( spl0_1179
<=> class_OrderedGroup_Ocomm__monoid__mult(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f10568,plain,
( spl0_1320
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_SetsAndFunctions_Oelt__set__times(c_1,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f11587,plain,
( ! [X0] : c_SetsAndFunctions_Oelt__set__times(c_1,X0,t_b) = X0
| ~ spl0_1179
| ~ spl0_1320 ),
inference(resolution,[],[f9528,f10569]) ).
fof(f10569,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_SetsAndFunctions_Oelt__set__times(c_1,X10,X0) = X10 )
| ~ spl0_1320 ),
inference(avatar_component_clause,[],[f10568]) ).
fof(f9528,plain,
( class_OrderedGroup_Ocomm__monoid__mult(t_b)
| ~ spl0_1179 ),
inference(avatar_component_clause,[],[f9526]) ).
fof(f13165,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1115,f13163]) ).
fof(f13163,plain,
( spl0_1621
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_0,c_uminus(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f1115,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X0)
| c_lessequals(X3,c_0,X0)
| ~ c_lessequals(c_0,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f13161,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1061,f13159]) ).
fof(f13159,plain,
( spl0_1620
<=> ! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(X35,X0) = c_times(X35,c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f1061,axiom,
! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_uminus(X35,X0) = c_times(X35,c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f13157,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1060,f13155]) ).
fof(f13155,plain,
( spl0_1619
<=> ! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X35,X0) = c_uminus(X35,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f1060,axiom,
! [X0,X35] :
( ~ class_Numeral_Onumber__ring(X0)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X35,X0) = c_uminus(X35,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f13153,plain,
spl0_1618,
inference(avatar_split_clause,[],[f980,f13151]) ).
fof(f13151,plain,
( spl0_1618
<=> ! [X9,X11,X24] :
( X11 = X24
| c_plus(X24,X9,tc_nat) != c_plus(X11,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f980,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_plus(X24,X9,tc_nat) != c_plus(X11,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f13149,plain,
spl0_1617,
inference(avatar_split_clause,[],[f975,f13147]) ).
fof(f13147,plain,
( spl0_1617
<=> ! [X9,X11,X24] :
( X11 = X24
| c_plus(X9,X24,tc_nat) != c_plus(X9,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f975,axiom,
! [X11,X9,X24] :
( X11 = X24
| c_plus(X9,X24,tc_nat) != c_plus(X9,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f13145,plain,
spl0_1616,
inference(avatar_split_clause,[],[f959,f13143]) ).
fof(f13143,plain,
( spl0_1616
<=> ! [X11,X24] :
( c_0 = X24
| c_0 = X11
| c_0 != c_times(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f959,axiom,
! [X11,X24] :
( c_0 = X24
| c_0 = X11
| c_0 != c_times(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f13141,plain,
spl0_1615,
inference(avatar_split_clause,[],[f744,f13139]) ).
fof(f744,axiom,
! [X11,X24] : c_IntDef_Oint(c_plus(X24,X11,tc_nat)) = c_plus(c_IntDef_Oint(X24),c_IntDef_Oint(X11),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(f13137,plain,
spl0_1614,
inference(avatar_split_clause,[],[f707,f13135]) ).
fof(f707,axiom,
! [X0,X11,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| X11 = X24
| c_NatArith_Oof__nat(X11,X0) != c_NatArith_Oof__nat(X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f13133,plain,
spl0_1613,
inference(avatar_split_clause,[],[f701,f13131]) ).
fof(f13131,plain,
( spl0_1613
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f701,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f13129,plain,
spl0_1612,
inference(avatar_split_clause,[],[f700,f13127]) ).
fof(f13127,plain,
( spl0_1612
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f700,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f13125,plain,
( spl0_1611
| ~ spl0_954
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f10805,f10572,f8190,f13123]) ).
fof(f13123,plain,
( spl0_1611
<=> ! [X0] : c_SetsAndFunctions_Oelt__set__plus(c_0,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f8190,plain,
( spl0_954
<=> class_OrderedGroup_Ocomm__monoid__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f10572,plain,
( spl0_1321
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_SetsAndFunctions_Oelt__set__plus(c_0,X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f10805,plain,
( ! [X0] : c_SetsAndFunctions_Oelt__set__plus(c_0,X0,t_b) = X0
| ~ spl0_954
| ~ spl0_1321 ),
inference(resolution,[],[f10573,f8192]) ).
fof(f8192,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ spl0_954 ),
inference(avatar_component_clause,[],[f8190]) ).
fof(f10573,plain,
( ! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_SetsAndFunctions_Oelt__set__plus(c_0,X10,X0) = X10 )
| ~ spl0_1321 ),
inference(avatar_component_clause,[],[f10572]) ).
fof(f13121,plain,
spl0_1610,
inference(avatar_split_clause,[],[f678,f13119]) ).
fof(f13119,plain,
( spl0_1610
<=> ! [X50,X23] :
( c_0 = X50
| c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X23,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f678,axiom,
! [X50,X23] :
( c_0 = X50
| c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X23,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f13117,plain,
spl0_1609,
inference(avatar_split_clause,[],[f637,f13115]) ).
fof(f13115,plain,
( spl0_1609
<=> ! [X42,X40,X0,X39] :
( X40 = X42
| c_append(X39,X40,X0) != c_append(X39,X42,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f637,axiom,
! [X40,X39,X0,X42] :
( X40 = X42
| c_append(X39,X40,X0) != c_append(X39,X42,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f13113,plain,
spl0_1608,
inference(avatar_split_clause,[],[f631,f13111]) ).
fof(f13111,plain,
( spl0_1608
<=> ! [X0,X10] :
( c_List_Orotate1(X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f631,axiom,
! [X10,X0] :
( c_List_Orotate1(X10,X0) = X10
| ~ c_lessequals(c_Nat_Osize(X10,tc_List_Olist(X0)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f13109,plain,
spl0_1607,
inference(avatar_split_clause,[],[f520,f13107]) ).
fof(f13107,plain,
( spl0_1607
<=> ! [X55,X54,X0,X3,X15] :
( X54 = X55
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f520,axiom,
! [X3,X0,X54,X55,X15] :
( X54 = X55
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f13105,plain,
spl0_1606,
inference(avatar_split_clause,[],[f519,f13103]) ).
fof(f13103,plain,
( spl0_1606
<=> ! [X55,X54,X0,X3,X15] :
( X3 = X15
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f519,axiom,
! [X3,X0,X54,X55,X15] :
( X3 = X15
| c_List_Olist_OCons(X15,X54,X0) != c_List_Olist_OCons(X3,X55,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f13101,plain,
spl0_1605,
inference(avatar_split_clause,[],[f504,f13099]) ).
fof(f13099,plain,
( spl0_1605
<=> ! [X0,X11,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate(X11,X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f504,axiom,
! [X39,X0,X11] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate(X11,X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f13097,plain,
spl0_1604,
inference(avatar_split_clause,[],[f446,f13095]) ).
fof(f13095,plain,
( spl0_1604
<=> ! [X12,X39,X14] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| ~ c_in(X12,c_List_Oset(X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f446,axiom,
! [X39,X14,X12] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14)
| ~ c_in(X12,c_List_Oset(X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f13093,plain,
spl0_1603,
inference(avatar_split_clause,[],[f424,f13091]) ).
fof(f13091,plain,
( spl0_1603
<=> ! [X42,X40,X0,X39] :
( X40 = X42
| c_append(X40,X39,X0) != c_append(X42,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f424,axiom,
! [X40,X39,X0,X42] :
( X40 = X42
| c_append(X40,X39,X0) != c_append(X42,X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f13089,plain,
spl0_1602,
inference(avatar_split_clause,[],[f387,f13087]) ).
fof(f13087,plain,
( spl0_1602
<=> ! [X1,X3] : c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f387,axiom,
! [X3,X1] : c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X1,X3,tc_IntDef_Oint),X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f13085,plain,
spl0_1601,
inference(avatar_split_clause,[],[f386,f13083]) ).
fof(f13083,plain,
( spl0_1601
<=> ! [X1,X3] : c_Divides_Oop_Amod(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f386,axiom,
! [X3,X1] : c_Divides_Oop_Amod(c_plus(X3,X1,tc_IntDef_Oint),X3,tc_IntDef_Oint) = c_Divides_Oop_Amod(X1,X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f13081,plain,
( spl0_1600
| ~ spl0_965
| ~ spl0_1289 ),
inference(avatar_split_clause,[],[f10752,f10424,f8447,f13079]) ).
fof(f13079,plain,
( spl0_1600
<=> ! [X0] : c_Orderings_Omax(X0,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f10424,plain,
( spl0_1289
<=> ! [X16,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X10,X10,X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f10752,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,t_b) = X0
| ~ spl0_965
| ~ spl0_1289 ),
inference(resolution,[],[f10425,f8449]) ).
fof(f10425,plain,
( ! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X10,X10,X16) = X10 )
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f10424]) ).
fof(f13077,plain,
spl0_1599,
inference(avatar_split_clause,[],[f379,f13075]) ).
fof(f13075,plain,
( spl0_1599
<=> ! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f379,axiom,
! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f13072,plain,
( spl0_1598
| ~ spl0_132
| ~ spl0_1189
| ~ spl0_1597 ),
inference(avatar_split_clause,[],[f13068,f13065,f9843,f3873,f13070]) ).
fof(f13070,plain,
( spl0_1598
<=> ! [X11] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f13065,plain,
( spl0_1597
<=> ! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f13068,plain,
( ! [X11] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X11 )
| ~ spl0_132
| ~ spl0_1189
| ~ spl0_1597 ),
inference(forward_demodulation,[],[f13066,f10085]) ).
fof(f13066,plain,
( ! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1597 ),
inference(avatar_component_clause,[],[f13065]) ).
fof(f13067,plain,
spl0_1597,
inference(avatar_split_clause,[],[f378,f13065]) ).
fof(f378,axiom,
! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f13063,plain,
spl0_1596,
inference(avatar_split_clause,[],[f371,f13061]) ).
fof(f13061,plain,
( spl0_1596
<=> ! [X1,X10] :
( c_0 = X1
| c_div(c_times(X1,X10,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f371,axiom,
! [X10,X1] :
( c_0 = X1
| c_div(c_times(X1,X10,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f13059,plain,
spl0_1595,
inference(avatar_split_clause,[],[f370,f13057]) ).
fof(f13057,plain,
( spl0_1595
<=> ! [X1,X10] :
( c_0 = X1
| c_div(c_times(X10,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f370,axiom,
! [X10,X1] :
( c_0 = X1
| c_div(c_times(X10,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f13055,plain,
spl0_1594,
inference(avatar_split_clause,[],[f351,f13053]) ).
fof(f13053,plain,
( spl0_1594
<=> ! [X1] : c_IntDiv_OposDivAlg(c_Pair(c_0,X1,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_1594])]) ).
fof(f351,axiom,
! [X1] : c_IntDiv_OposDivAlg(c_Pair(c_0,X1,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(f13051,plain,
spl0_1593,
inference(avatar_split_clause,[],[f336,f13049]) ).
fof(f13049,plain,
( spl0_1593
<=> ! [X1,X3] : c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f336,axiom,
! [X3,X1] : c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f13047,plain,
spl0_1592,
inference(avatar_split_clause,[],[f307,f13045]) ).
fof(f13045,plain,
( spl0_1592
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f307,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(X33,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f13043,plain,
spl0_1591,
inference(avatar_split_clause,[],[f306,f13041]) ).
fof(f13041,plain,
( spl0_1591
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f306,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(X33,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f13039,plain,
( spl0_1590
| ~ spl0_965
| ~ spl0_1288 ),
inference(avatar_split_clause,[],[f10749,f10420,f8447,f13037]) ).
fof(f13037,plain,
( spl0_1590
<=> ! [X0] : c_Orderings_Omin(X0,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f10420,plain,
( spl0_1288
<=> ! [X16,X10] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X10,X10,X16) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f10749,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,t_b) = X0
| ~ spl0_965
| ~ spl0_1288 ),
inference(resolution,[],[f10421,f8449]) ).
fof(f10421,plain,
( ! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X10,X10,X16) = X10 )
| ~ spl0_1288 ),
inference(avatar_component_clause,[],[f10420]) ).
fof(f13035,plain,
spl0_1589,
inference(avatar_split_clause,[],[f303,f13033]) ).
fof(f303,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(X33,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f13031,plain,
spl0_1588,
inference(avatar_split_clause,[],[f302,f13029]) ).
fof(f13029,plain,
( spl0_1588
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f302,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(X33,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X33,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f13027,plain,
spl0_1587,
inference(avatar_split_clause,[],[f300,f13025]) ).
fof(f300,axiom,
! [X0,X35,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| X33 = X35
| c_IntDef_Oof__int(X35,X0) != c_IntDef_Oof__int(X33,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f13023,plain,
spl0_1586,
inference(avatar_split_clause,[],[f294,f13021]) ).
fof(f13021,plain,
( spl0_1586
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f294,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f13019,plain,
spl0_1585,
inference(avatar_split_clause,[],[f293,f13017]) ).
fof(f13017,plain,
( spl0_1585
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f293,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f13015,plain,
spl0_1584,
inference(avatar_split_clause,[],[f292,f13013]) ).
fof(f13013,plain,
( spl0_1584
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f292,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f13011,plain,
spl0_1583,
inference(avatar_split_clause,[],[f291,f13009]) ).
fof(f13009,plain,
( spl0_1583
<=> ! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f291,axiom,
! [X0,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_lessequals(c_0,X35,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X35,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f13007,plain,
spl0_1582,
inference(avatar_split_clause,[],[f255,f13005]) ).
fof(f13005,plain,
( spl0_1582
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| c_in(c_uminus(X3,X0),c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f255,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| ~ c_in(X3,c_IntDef_OInts,X0)
| c_in(c_uminus(X3,X0),c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f13003,plain,
spl0_1581,
inference(avatar_split_clause,[],[f250,f13001]) ).
fof(f13001,plain,
( spl0_1581
<=> ! [X10] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X10)) = X10
| ~ c_in(X10,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f250,axiom,
! [X10] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X10)) = X10
| ~ c_in(X10,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(f12999,plain,
spl0_1580,
inference(avatar_split_clause,[],[f236,f12997]) ).
fof(f12997,plain,
( spl0_1580
<=> ! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f236,axiom,
! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f12995,plain,
( spl0_1579
| ~ spl0_942
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f10743,f10404,f7878,f12993]) ).
fof(f12993,plain,
( spl0_1579
<=> ! [X0] : c_times(X0,c_1,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f7878,plain,
( spl0_942
<=> class_OrderedGroup_Omonoid__mult(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f10743,plain,
( ! [X0] : c_times(X0,c_1,t_b) = X0
| ~ spl0_942
| ~ spl0_1284 ),
inference(resolution,[],[f10405,f7880]) ).
fof(f7880,plain,
( class_OrderedGroup_Omonoid__mult(t_b)
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f7878]) ).
fof(f12991,plain,
spl0_1578,
inference(avatar_split_clause,[],[f235,f12989]) ).
fof(f12989,plain,
( spl0_1578
<=> ! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X34,tc_IntDef_Oint)) = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f235,axiom,
! [X34,X24] :
( c_IntDef_Oint(X24) != c_Numeral_Onumber__of(X34,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X34,tc_IntDef_Oint)) = X24 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f12987,plain,
spl0_1577,
inference(avatar_split_clause,[],[f137,f12985]) ).
fof(f12985,plain,
( spl0_1577
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f137,axiom,
! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f12983,plain,
spl0_1576,
inference(avatar_split_clause,[],[f127,f12981]) ).
fof(f12981,plain,
( spl0_1576
<=> ! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f127,axiom,
! [X11,X24] : c_Divides_Oop_Amod(X24,X11,tc_nat) = c_Divides_Oop_Amod(c_plus(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f12979,plain,
spl0_1575,
inference(avatar_split_clause,[],[f126,f12977]) ).
fof(f12977,plain,
( spl0_1575
<=> ! [X11,X24] : c_Divides_Oop_Amod(c_plus(X11,X24,tc_nat),X11,tc_nat) = c_Divides_Oop_Amod(X24,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f126,axiom,
! [X11,X24] : c_Divides_Oop_Amod(c_plus(X11,X24,tc_nat),X11,tc_nat) = c_Divides_Oop_Amod(X24,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f12975,plain,
spl0_1574,
inference(avatar_split_clause,[],[f85,f12973]) ).
fof(f12973,plain,
( spl0_1574
<=> ! [X18,X17,X0,X16] :
( X17 = X18
| c_Datatype__Universe_OIn1(X18,X0,X16) != c_Datatype__Universe_OIn1(X17,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f85,axiom,
! [X0,X18,X16,X17] :
( X17 = X18
| c_Datatype__Universe_OIn1(X18,X0,X16) != c_Datatype__Universe_OIn1(X17,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f12971,plain,
spl0_1573,
inference(avatar_split_clause,[],[f83,f12969]) ).
fof(f12969,plain,
( spl0_1573
<=> ! [X18,X17,X0,X16] :
( X17 = X18
| c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn0(X18,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f83,axiom,
! [X0,X18,X16,X17] :
( X17 = X18
| c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn0(X18,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f12967,plain,
spl0_1572,
inference(avatar_split_clause,[],[f79,f12965]) ).
fof(f12965,plain,
( spl0_1572
<=> ! [X3,X0,X16,X1] :
( X1 = X3
| c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OAtom(X1,X0,X16) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f79,axiom,
! [X3,X0,X1,X16] :
( X1 = X3
| c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OAtom(X1,X0,X16) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f12955,plain,
( spl0_1571
| ~ spl0_942
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f10738,f10398,f7878,f12953]) ).
fof(f12953,plain,
( spl0_1571
<=> ! [X0] : c_times(c_1,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f10738,plain,
( ! [X0] : c_times(c_1,X0,t_b) = X0
| ~ spl0_942
| ~ spl0_1283 ),
inference(resolution,[],[f10399,f7880]) ).
fof(f12908,plain,
( spl0_1570
| ~ spl0_1009
| ~ spl0_1282 ),
inference(avatar_split_clause,[],[f10721,f10394,f8725,f12906]) ).
fof(f10721,plain,
( ! [X0] : c_0 = c_minus(X0,X0,t_b)
| ~ spl0_1009
| ~ spl0_1282 ),
inference(resolution,[],[f10395,f8727]) ).
fof(f12848,plain,
( spl0_1569
| ~ spl0_1009
| ~ spl0_1281 ),
inference(avatar_split_clause,[],[f10718,f10390,f8725,f12846]) ).
fof(f12846,plain,
( spl0_1569
<=> ! [X0] : c_minus(X0,c_0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f10718,plain,
( ! [X0] : c_minus(X0,c_0,t_b) = X0
| ~ spl0_1009
| ~ spl0_1281 ),
inference(resolution,[],[f10391,f8727]) ).
fof(f12744,plain,
( spl0_1568
| ~ spl0_954
| ~ spl0_1280 ),
inference(avatar_split_clause,[],[f10715,f10386,f8190,f12742]) ).
fof(f10715,plain,
( ! [X0] : c_plus(c_0,X0,t_b) = X0
| ~ spl0_954
| ~ spl0_1280 ),
inference(resolution,[],[f10387,f8192]) ).
fof(f12684,plain,
( spl0_1567
| ~ spl0_954
| ~ spl0_1279 ),
inference(avatar_split_clause,[],[f10710,f10382,f8190,f12682]) ).
fof(f12682,plain,
( spl0_1567
<=> ! [X0] : c_plus(X0,c_0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f10710,plain,
( ! [X0] : c_plus(X0,c_0,t_b) = X0
| ~ spl0_954
| ~ spl0_1279 ),
inference(resolution,[],[f10383,f8192]) ).
fof(f12643,plain,
( spl0_1566
| ~ spl0_968
| ~ spl0_1258 ),
inference(avatar_split_clause,[],[f10646,f10289,f8546,f12641]) ).
fof(f12641,plain,
( spl0_1566
<=> ! [X0] : c_LOrder_Omeet(X0,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f8546,plain,
( spl0_968
<=> class_LOrder_Omeet__semilorder(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f10646,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,t_b) = X0
| ~ spl0_968
| ~ spl0_1258 ),
inference(resolution,[],[f10290,f8548]) ).
fof(f8548,plain,
( class_LOrder_Omeet__semilorder(t_b)
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8546]) ).
fof(f12591,plain,
( spl0_1565
| ~ spl0_967
| ~ spl0_1257 ),
inference(avatar_split_clause,[],[f10643,f10285,f8497,f12589]) ).
fof(f12589,plain,
( spl0_1565
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,t_b) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f8497,plain,
( spl0_967
<=> class_LOrder_Ojoin__semilorder(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f10643,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,t_b) = X0
| ~ spl0_967
| ~ spl0_1257 ),
inference(resolution,[],[f10286,f8499]) ).
fof(f8499,plain,
( class_LOrder_Ojoin__semilorder(t_b)
| ~ spl0_967 ),
inference(avatar_component_clause,[],[f8497]) ).
fof(f12585,plain,
( spl0_1564
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_1496 ),
inference(avatar_split_clause,[],[f12264,f12261,f11072,f3525,f12583]) ).
fof(f12583,plain,
( spl0_1564
<=> ! [X0] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f12261,plain,
( spl0_1496
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f12264,plain,
( ! [X0] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X0)
| ~ class_Numeral_Onumber__ring(X0) )
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_1496 ),
inference(forward_demodulation,[],[f12262,f11495]) ).
fof(f12262,plain,
( ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0) )
| ~ spl0_1496 ),
inference(avatar_component_clause,[],[f12261]) ).
fof(f12548,plain,
spl0_1563,
inference(avatar_split_clause,[],[f3124,f12546]) ).
fof(f12546,plain,
( spl0_1563
<=> ! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f3124,plain,
! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X11,tc_nat) ),
inference(forward_demodulation,[],[f2947,f2814]) ).
fof(f2947,plain,
! [X11,X24] :
( c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X24,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f990,f1438]) ).
fof(f990,axiom,
! [X11,X24] :
( c_lessequals(c_1,X11,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f12544,plain,
spl0_1562,
inference(avatar_split_clause,[],[f3123,f12542]) ).
fof(f12542,plain,
( spl0_1562
<=> ! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f3123,plain,
! [X11,X24] :
( ~ c_lessequals(c_1,c_times(X24,X11,tc_nat),tc_nat)
| c_lessequals(c_1,X24,tc_nat) ),
inference(forward_demodulation,[],[f2946,f2814]) ).
fof(f2946,plain,
! [X11,X24] :
( c_lessequals(c_1,X24,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X24,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f989,f1438]) ).
fof(f989,axiom,
! [X11,X24] :
( c_lessequals(c_1,X24,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f12540,plain,
spl0_1561,
inference(avatar_split_clause,[],[f3120,f12538]) ).
fof(f12538,plain,
( spl0_1561
<=> ! [X11,X23] :
( c_lessequals(c_1,c_Nat_Opower(X23,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X23,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f3120,plain,
! [X11,X23] :
( c_lessequals(c_1,c_Nat_Opower(X23,X11,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X23,tc_nat) ),
inference(forward_demodulation,[],[f2938,f2814]) ).
fof(f2938,plain,
! [X11,X23] :
( ~ c_lessequals(c_1,X23,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X23,X11,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1234,f1438]) ).
fof(f1234,axiom,
! [X11,X23] :
( ~ c_lessequals(c_1,X23,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X23,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f12536,plain,
spl0_1560,
inference(avatar_split_clause,[],[f3054,f12534]) ).
fof(f12534,plain,
( spl0_1560
<=> ! [X11,X24] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f3054,plain,
! [X11,X24] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2854,f2850]) ).
fof(f2854,plain,
! [X11,X24] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1659,f1438]) ).
fof(f1659,axiom,
! [X11,X24] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X11)),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f12532,plain,
spl0_1559,
inference(avatar_split_clause,[],[f3050,f12530]) ).
fof(f12530,plain,
( spl0_1559
<=> ! [X33] : c_Numeral_OBit(c_Numeral_Obin__add(X33,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f3050,plain,
! [X33] : c_Numeral_OBit(c_Numeral_Obin__add(X33,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2852,f2829]) ).
fof(f2852,plain,
! [X33] : c_Numeral_Obin__add(c_Numeral_OBit(X33,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X33,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f1025,f1007,f1007]) ).
fof(f1025,axiom,
! [X33] : c_Numeral_Obin__pred(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X33),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f12528,plain,
spl0_1558,
inference(avatar_split_clause,[],[f2853,f12526]) ).
fof(f12526,plain,
( spl0_1558
<=> ! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X33),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f2853,plain,
! [X33] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X33),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f1017,f1023,f1023]) ).
fof(f1017,axiom,
! [X33] : c_Numeral_Obin__minus(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X33),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f12519,plain,
( spl0_1557
| ~ spl0_1556 ),
inference(avatar_split_clause,[],[f12515,f12512,f12517]) ).
fof(f12517,plain,
( spl0_1557
<=> ! [X11] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f12512,plain,
( spl0_1556
<=> ! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f12515,plain,
( ! [X11] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1556 ),
inference(forward_demodulation,[],[f12513,f2850]) ).
fof(f12513,plain,
( ! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f12512]) ).
fof(f12514,plain,
spl0_1556,
inference(avatar_split_clause,[],[f2842,f12512]) ).
fof(f2842,plain,
! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f288,f1438]) ).
fof(f288,axiom,
! [X11] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X11)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f12510,plain,
spl0_1555,
inference(avatar_split_clause,[],[f2784,f12508]) ).
fof(f2784,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(c_plus(X3,X1,X0),X1,X0) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__11_1) ).
fof(f12506,plain,
spl0_1554,
inference(avatar_split_clause,[],[f2783,f12504]) ).
fof(f2783,axiom,
! [X0,X1,X25] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_plus(c_minus(X25,X1,X0),X1,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocompare__rls__11_0) ).
fof(f12502,plain,
spl0_1553,
inference(avatar_split_clause,[],[f1609,f12500]) ).
fof(f12500,plain,
( spl0_1553
<=> ! [X0,X19] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ORange(X19,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1609,axiom,
! [X0,X19] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ORange(X19,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f12498,plain,
spl0_1552,
inference(avatar_split_clause,[],[f1607,f12496]) ).
fof(f12496,plain,
( spl0_1552
<=> ! [X0,X19] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ODomain(X19,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f1607,axiom,
! [X0,X19] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X19,X0),X0,X0) = c_Relation_ODomain(X19,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f12494,plain,
spl0_1551,
inference(avatar_split_clause,[],[f1579,f12492]) ).
fof(f12492,plain,
( spl0_1551
<=> ! [X0,X3,X1,X26] :
( ~ c_in(X3,X26,X0)
| c_in(X3,c_insert(X1,X26,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f1579,axiom,
! [X3,X0,X1,X26] :
( ~ c_in(X3,X26,X0)
| c_in(X3,c_insert(X1,X26,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f12490,plain,
spl0_1550,
inference(avatar_split_clause,[],[f1536,f12488]) ).
fof(f12488,plain,
( spl0_1550
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X30,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f1536,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X30,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f12486,plain,
spl0_1549,
inference(avatar_split_clause,[],[f1535,f12484]) ).
fof(f12484,plain,
( spl0_1549
<=> ! [X0,X30,X25,X26] :
( ~ c_in(X25,X26,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f1535,axiom,
! [X0,X26,X25,X30] :
( ~ c_in(X25,X26,X0)
| c_in(X25,c_union(X26,X30,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f12482,plain,
spl0_1548,
inference(avatar_split_clause,[],[f1477,f12480]) ).
fof(f12480,plain,
( spl0_1548
<=> ! [X25,X0,X26] :
( c_in(X25,X26,X0)
| c_in(X25,c_uminus(X26,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f1477,axiom,
! [X0,X26,X25] :
( c_in(X25,X26,X0)
| c_in(X25,c_uminus(X26,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f12478,plain,
spl0_1547,
inference(avatar_split_clause,[],[f1476,f12476]) ).
fof(f12476,plain,
( spl0_1547
<=> ! [X25,X0,X26] :
( ~ c_in(X25,X26,X0)
| ~ c_in(X25,c_uminus(X26,tc_set(X0)),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f1476,axiom,
! [X0,X26,X25] :
( ~ c_in(X25,X26,X0)
| ~ c_in(X25,c_uminus(X26,tc_set(X0)),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f12474,plain,
spl0_1546,
inference(avatar_split_clause,[],[f1439,f12472]) ).
fof(f12472,plain,
( spl0_1546
<=> ! [X36,X72] : c_minus(X36,X72,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f1439,axiom,
! [X72,X36] : c_minus(X36,X72,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f12470,plain,
spl0_1545,
inference(avatar_split_clause,[],[f1436,f12468]) ).
fof(f12468,plain,
( spl0_1545
<=> ! [X36,X72] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,X72,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f1436,axiom,
! [X72,X36] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),tc_nat) = c_minus(X36,X72,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f12466,plain,
spl0_1544,
inference(avatar_split_clause,[],[f1416,f12464]) ).
fof(f1416,axiom,
! [X3,X0] :
( ~ class_Orderings_Oorder(X0)
| c_SetInterval_OatLeastAtMost(X3,X3,X0) = c_insert(X3,c_emptyset,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f12462,plain,
spl0_1543,
inference(avatar_split_clause,[],[f1165,f12460]) ).
fof(f12460,plain,
( spl0_1543
<=> ! [X34] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f1165,axiom,
! [X34] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,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(f12458,plain,
( spl0_1542
| ~ spl0_1
| ~ spl0_1301 ),
inference(avatar_split_clause,[],[f10773,f10474,f3226,f12456]) ).
fof(f12456,plain,
( spl0_1542
<=> ! [X0] : c_0 = c_times(X0,c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f10474,plain,
( spl0_1301
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(X1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f10773,plain,
( ! [X0] : c_0 = c_times(X0,c_0,t_b)
| ~ spl0_1
| ~ spl0_1301 ),
inference(resolution,[],[f10475,f3228]) ).
fof(f10475,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(X1,c_0,X0) )
| ~ spl0_1301 ),
inference(avatar_component_clause,[],[f10474]) ).
fof(f12454,plain,
spl0_1541,
inference(avatar_split_clause,[],[f1164,f12452]) ).
fof(f12452,plain,
( spl0_1541
<=> ! [X34] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f1164,axiom,
! [X34] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X34,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X34,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(f12450,plain,
spl0_1540,
inference(avatar_split_clause,[],[f1146,f12448]) ).
fof(f12448,plain,
( spl0_1540
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_less(c_0,c_HOL_Oabs(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f1146,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_less(c_0,c_HOL_Oabs(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f12446,plain,
spl0_1539,
inference(avatar_split_clause,[],[f1139,f12444]) ).
fof(f1139,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_OrderedGroup_Opprt(X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f12442,plain,
spl0_1538,
inference(avatar_split_clause,[],[f1138,f12440]) ).
fof(f1138,axiom,
! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X12,c_0,X0)
| c_0 = c_OrderedGroup_Opprt(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f12438,plain,
spl0_1537,
inference(avatar_split_clause,[],[f1134,f12436]) ).
fof(f12436,plain,
( spl0_1537
<=> ! [X0,X10] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X10,c_0,X0)
| c_OrderedGroup_Onprt(X10,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f1134,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(X10,c_0,X0)
| c_OrderedGroup_Onprt(X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f12434,plain,
spl0_1536,
inference(avatar_split_clause,[],[f1133,f12432]) ).
fof(f1133,axiom,
! [X0,X12] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| ~ c_lessequals(c_0,X12,X0)
| c_0 = c_OrderedGroup_Onprt(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f12430,plain,
spl0_1535,
inference(avatar_split_clause,[],[f1093,f12428]) ).
fof(f1093,axiom,
! [X3,X0,X1] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| X1 = X3
| c_0 != c_minus(X3,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f12426,plain,
spl0_1534,
inference(avatar_split_clause,[],[f1077,f12424]) ).
fof(f1077,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_lessequals(c_0,X10,X0)
| c_HOL_Oabs(X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f12422,plain,
spl0_1533,
inference(avatar_split_clause,[],[f1075,f12420]) ).
fof(f1075,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f12418,plain,
spl0_1532,
inference(avatar_split_clause,[],[f1073,f12416]) ).
fof(f1073,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| ~ c_lessequals(c_HOL_Oabs(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f12414,plain,
( spl0_1531
| ~ spl0_1
| ~ spl0_1299 ),
inference(avatar_split_clause,[],[f10769,f10466,f3226,f12412]) ).
fof(f12412,plain,
( spl0_1531
<=> ! [X0] : c_0 = c_times(c_0,X0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f10466,plain,
( spl0_1299
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(c_0,X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f10769,plain,
( ! [X0] : c_0 = c_times(c_0,X0,t_b)
| ~ spl0_1
| ~ spl0_1299 ),
inference(resolution,[],[f10467,f3228]) ).
fof(f10467,plain,
( ! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(c_0,X1,X0) )
| ~ spl0_1299 ),
inference(avatar_component_clause,[],[f10466]) ).
fof(f12410,plain,
spl0_1530,
inference(avatar_split_clause,[],[f1072,f12408]) ).
fof(f1072,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_HOL_Oabs(X3,X0) = c_HOL_Oabs(c_HOL_Oabs(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f12406,plain,
spl0_1529,
inference(avatar_split_clause,[],[f1041,f12404]) ).
fof(f12404,plain,
( spl0_1529
<=> ! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f1041,axiom,
! [X0,X33] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f12402,plain,
spl0_1528,
inference(avatar_split_clause,[],[f1021,f12400]) ).
fof(f12400,plain,
( spl0_1528
<=> ! [X34,X33] : c_Numeral_Obin__mult(c_Numeral_OBit(X34,c_Numeral_Obit_OB0),X33) = c_Numeral_OBit(c_Numeral_Obin__mult(X34,X33),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f12398,plain,
spl0_1527,
inference(avatar_split_clause,[],[f998,f12396]) ).
fof(f12396,plain,
( spl0_1527
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f998,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f12394,plain,
spl0_1526,
inference(avatar_split_clause,[],[f997,f12392]) ).
fof(f12392,plain,
( spl0_1526
<=> ! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f997,axiom,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_0,c_minus(X11,X24,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f12390,plain,
spl0_1525,
inference(avatar_split_clause,[],[f973,f12388]) ).
fof(f12388,plain,
( spl0_1525
<=> ! [X11,X24] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f973,axiom,
! [X11,X24] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f12386,plain,
spl0_1524,
inference(avatar_split_clause,[],[f972,f12384]) ).
fof(f12384,plain,
( spl0_1524
<=> ! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f972,axiom,
! [X11,X24] :
( c_less(c_0,X24,tc_nat)
| ~ c_less(c_0,c_times(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f12382,plain,
spl0_1523,
inference(avatar_split_clause,[],[f924,f12380]) ).
fof(f12380,plain,
( spl0_1523
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f924,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f12378,plain,
spl0_1522,
inference(avatar_split_clause,[],[f923,f12376]) ).
fof(f12376,plain,
( spl0_1522
<=> ! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f923,axiom,
! [X11,X24] :
( ~ c_less(c_0,X24,tc_nat)
| c_less(c_0,c_plus(X24,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f12374,plain,
spl0_1521,
inference(avatar_split_clause,[],[f745,f12372]) ).
fof(f12372,plain,
( spl0_1521
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f745,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X34,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f12366,plain,
spl0_1520,
inference(avatar_split_clause,[],[f708,f12364]) ).
fof(f12364,plain,
( spl0_1520
<=> ! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X24
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f708,axiom,
! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X24
| ~ c_lessequals(c_NatArith_Oof__nat(X24,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f12362,plain,
spl0_1519,
inference(avatar_split_clause,[],[f628,f12360]) ).
fof(f12360,plain,
( spl0_1519
<=> ! [X0,X12] : c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f628,axiom,
! [X0,X12] : c_List_Olist_OCons(X12,c_List_Olist_ONil,X0) = c_List_Orev(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f12358,plain,
spl0_1518,
inference(avatar_split_clause,[],[f625,f12356]) ).
fof(f12356,plain,
( spl0_1518
<=> ! [X11,X0,X12] : c_List_Oreplicate(X11,X12,X0) = c_List_Orev(c_List_Oreplicate(X11,X12,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f625,axiom,
! [X0,X11,X12] : c_List_Oreplicate(X11,X12,X0) = c_List_Orev(c_List_Oreplicate(X11,X12,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f12354,plain,
spl0_1517,
inference(avatar_split_clause,[],[f606,f12352]) ).
fof(f12352,plain,
( spl0_1517
<=> ! [X10,X40,X14,X12] :
( ~ c_List_Oop_Amem(X12,X40,X14)
| c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f606,axiom,
! [X40,X10,X14,X12] :
( ~ c_List_Oop_Amem(X12,X40,X14)
| c_List_Oop_Amem(X12,c_List_Olist_OCons(X10,X40,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f12350,plain,
spl0_1516,
inference(avatar_split_clause,[],[f507,f12348]) ).
fof(f12348,plain,
( spl0_1516
<=> ! [X50,X23] : c_Nat_Osize(c_List_Oupt(X23,X50),tc_List_Olist(tc_nat)) = c_minus(X50,X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f507,axiom,
! [X50,X23] : c_Nat_Osize(c_List_Oupt(X23,X50),tc_List_Olist(tc_nat)) = c_minus(X50,X23,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f12346,plain,
spl0_1515,
inference(avatar_split_clause,[],[f503,f12344]) ).
fof(f12344,plain,
( spl0_1515
<=> ! [X0,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate1(X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f503,axiom,
! [X39,X0] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orotate1(X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f12342,plain,
spl0_1514,
inference(avatar_split_clause,[],[f502,f12340]) ).
fof(f12340,plain,
( spl0_1514
<=> ! [X0,X39] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orev(X39,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f502,axiom,
! [X39,X0] : c_Nat_Osize(X39,tc_List_Olist(X0)) = c_Nat_Osize(c_List_Orev(X39,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f12338,plain,
spl0_1513,
inference(avatar_split_clause,[],[f489,f12336]) ).
fof(f12336,plain,
( spl0_1513
<=> ! [X0,X39,X10] : c_List_Olast(c_append(X39,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f489,axiom,
! [X39,X10,X0] : c_List_Olast(c_append(X39,c_List_Olist_OCons(X10,c_List_Olist_ONil,X0),X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f12334,plain,
spl0_1512,
inference(avatar_split_clause,[],[f488,f12332]) ).
fof(f12332,plain,
( spl0_1512
<=> ! [X0,X11,X10] :
( c_0 = X11
| c_List_Olast(c_List_Oreplicate(X11,X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f488,axiom,
! [X10,X0,X11] :
( c_0 = X11
| c_List_Olast(c_List_Oreplicate(X11,X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f12330,plain,
spl0_1511,
inference(avatar_split_clause,[],[f487,f12328]) ).
fof(f12328,plain,
( spl0_1511
<=> ! [X0,X51] :
( c_List_Olist_ONil = X51
| c_in(c_List_Olast(X51,X0),c_List_Oset(X51,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f487,axiom,
! [X51,X0] :
( c_List_Olist_ONil = X51
| c_in(c_List_Olast(X51,X0),c_List_Oset(X51,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f12321,plain,
spl0_1510,
inference(avatar_split_clause,[],[f478,f12319]) ).
fof(f12319,plain,
( spl0_1510
<=> ! [X50,X10] :
( ~ c_less(X10,X50,tc_nat)
| c_List_Ohd(c_List_Oupt(X10,X50),tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f478,axiom,
! [X50,X10] :
( ~ c_less(X10,X50,tc_nat)
| c_List_Ohd(c_List_Oupt(X10,X50),tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f12317,plain,
spl0_1509,
inference(avatar_split_clause,[],[f477,f12315]) ).
fof(f12315,plain,
( spl0_1509
<=> ! [X0,X11,X10] :
( c_0 = X11
| c_List_Ohd(c_List_Oreplicate(X11,X10,X0),X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f477,axiom,
! [X10,X0,X11] :
( c_0 = X11
| c_List_Ohd(c_List_Oreplicate(X11,X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f12313,plain,
spl0_1508,
inference(avatar_split_clause,[],[f476,f12311]) ).
fof(f12311,plain,
( spl0_1508
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_in(c_List_Ohd(X39,X0),c_List_Oset(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f476,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_in(c_List_Ohd(X39,X0),c_List_Oset(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f12309,plain,
spl0_1507,
inference(avatar_split_clause,[],[f433,f12307]) ).
fof(f12307,plain,
( spl0_1507
<=> ! [X0,X12,X10] : c_List_Obutlast(c_append(X10,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f433,axiom,
! [X10,X0,X12] : c_List_Obutlast(c_append(X10,c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f12305,plain,
spl0_1506,
inference(avatar_split_clause,[],[f357,f12303]) ).
fof(f12303,plain,
( spl0_1506
<=> ! [X1,X3] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f357,axiom,
! [X3,X1] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f12301,plain,
spl0_1505,
inference(avatar_split_clause,[],[f356,f12299]) ).
fof(f12299,plain,
( spl0_1505
<=> ! [X1,X3] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f356,axiom,
! [X3,X1] :
( ~ c_less(c_0,X1,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f12297,plain,
spl0_1504,
inference(avatar_split_clause,[],[f349,f12295]) ).
fof(f12295,plain,
( spl0_1504
<=> ! [X1,X3] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f349,axiom,
! [X3,X1] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f12293,plain,
spl0_1503,
inference(avatar_split_clause,[],[f348,f12291]) ).
fof(f12291,plain,
( spl0_1503
<=> ! [X1,X3] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_less(X1,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f348,axiom,
! [X3,X1] :
( ~ c_less(X1,c_0,tc_IntDef_Oint)
| c_less(X1,c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f12289,plain,
spl0_1502,
inference(avatar_split_clause,[],[f312,f12287]) ).
fof(f312,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_NatArith_Oof__nat(X11,X0) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X11,tc_IntDef_Oint),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f12285,plain,
spl0_1501,
inference(avatar_split_clause,[],[f248,f12283]) ).
fof(f248,axiom,
! [X35,X33] :
( ~ c_less(X33,X35,tc_IntDef_Oint)
| c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f12280,plain,
spl0_1500,
inference(avatar_split_clause,[],[f247,f12278]) ).
fof(f247,axiom,
! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_lessequals(X33,c_minus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f12276,plain,
spl0_1499,
inference(avatar_split_clause,[],[f246,f12274]) ).
fof(f246,axiom,
! [X35,X33] :
( ~ c_lessequals(X33,X35,tc_IntDef_Oint)
| c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f12272,plain,
spl0_1498,
inference(avatar_split_clause,[],[f245,f12270]) ).
fof(f12270,plain,
( spl0_1498
<=> ! [X35,X33] :
( c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f245,axiom,
! [X35,X33] :
( c_lessequals(X33,X35,tc_IntDef_Oint)
| ~ c_less(X33,c_plus(X35,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f12268,plain,
spl0_1497,
inference(avatar_split_clause,[],[f242,f12266]) ).
fof(f12266,plain,
( spl0_1497
<=> ! [X35,X33] : c_plus(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X35,X33,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f242,axiom,
! [X35,X33] : c_plus(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X35,X33,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(f12263,plain,
spl0_1496,
inference(avatar_split_clause,[],[f239,f12261]) ).
fof(f239,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f12259,plain,
spl0_1495,
inference(avatar_split_clause,[],[f204,f12257]) ).
fof(f204,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f12255,plain,
spl0_1494,
inference(avatar_split_clause,[],[f201,f12253]) ).
fof(f12253,plain,
( spl0_1494
<=> ! [X11,X10] : c_GCD_Ogcd(c_Pair(X10,c_times(X10,X11,tc_nat),tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f201,axiom,
! [X10,X11] : c_GCD_Ogcd(c_Pair(X10,c_times(X10,X11,tc_nat),tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f12251,plain,
spl0_1493,
inference(avatar_split_clause,[],[f130,f12249]) ).
fof(f12249,plain,
( spl0_1493
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f130,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f12247,plain,
spl0_1492,
inference(avatar_split_clause,[],[f128,f12245]) ).
fof(f12245,plain,
( spl0_1492
<=> ! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f128,axiom,
! [X11,X24] :
( ~ c_less(c_0,X11,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f12243,plain,
spl0_1491,
inference(avatar_split_clause,[],[f72,f12241]) ).
fof(f12241,plain,
( spl0_1491
<=> ! [X16,X0,X1,X3] : c_0 = c_Nat_Osize(c_Pair(X3,X1,X0,X16),tc_prod(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f72,axiom,
! [X3,X0,X1,X16] : c_0 = c_Nat_Osize(c_Pair(X3,X1,X0,X16),tc_prod(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f12238,plain,
spl0_1490,
inference(avatar_split_clause,[],[f60,f12236]) ).
fof(f12236,plain,
( spl0_1490
<=> ! [X13,X0,X12] :
( c_Datatype_Ooption_OSome(X12,X0) = X13
| ~ c_in(X12,c_Datatype_Oo2s(X13,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f60,axiom,
! [X0,X12,X13] :
( c_Datatype_Ooption_OSome(X12,X0) = X13
| ~ c_in(X12,c_Datatype_Oo2s(X13,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f12098,plain,
( spl0_1489
| ~ spl0_1167
| ~ spl0_1202 ),
inference(avatar_split_clause,[],[f11531,f9896,f9428,f12095]) ).
fof(f9428,plain,
( spl0_1167
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f11531,plain,
( c_1 = c_NatArith_Oof__nat(c_1,t_b)
| ~ spl0_1167
| ~ spl0_1202 ),
inference(resolution,[],[f9430,f9897]) ).
fof(f9430,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(t_b)
| ~ spl0_1167 ),
inference(avatar_component_clause,[],[f9428]) ).
fof(f12082,plain,
( spl0_1488
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_1433 ),
inference(avatar_split_clause,[],[f11753,f11750,f11072,f3525,f12080]) ).
fof(f12080,plain,
( spl0_1488
<=> ! [X3] : c_uminus(X3,tc_IntDef_Oint) = c_div(X3,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f11750,plain,
( spl0_1433
<=> ! [X3] : c_div(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f11753,plain,
( ! [X3] : c_uminus(X3,tc_IntDef_Oint) = c_div(X3,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_61
| ~ spl0_1369
| ~ spl0_1433 ),
inference(forward_demodulation,[],[f11751,f11495]) ).
fof(f11751,plain,
( ! [X3] : c_div(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X3,tc_IntDef_Oint)
| ~ spl0_1433 ),
inference(avatar_component_clause,[],[f11750]) ).
fof(f12062,plain,
( spl0_1487
| ~ spl0_1134
| ~ spl0_1201 ),
inference(avatar_split_clause,[],[f11412,f9892,f9292,f12059]) ).
fof(f12059,plain,
( spl0_1487
<=> c_0 = c_NatArith_Oof__nat(c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f11412,plain,
( c_0 = c_NatArith_Oof__nat(c_0,t_b)
| ~ spl0_1134
| ~ spl0_1201 ),
inference(resolution,[],[f9294,f9893]) ).
fof(f9294,plain,
( class_Ring__and__Field_Oordered__semidom(t_b)
| ~ spl0_1134 ),
inference(avatar_component_clause,[],[f9292]) ).
fof(f12017,plain,
( spl0_1486
| ~ spl0_1102
| ~ spl0_1219 ),
inference(avatar_split_clause,[],[f11284,f9968,f9158,f12014]) ).
fof(f12014,plain,
( spl0_1486
<=> c_0 = c_OrderedGroup_Opprt(c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f11284,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,t_b)
| ~ spl0_1102
| ~ spl0_1219 ),
inference(resolution,[],[f9160,f9969]) ).
fof(f9160,plain,
( class_OrderedGroup_Olordered__ab__group(t_b)
| ~ spl0_1102 ),
inference(avatar_component_clause,[],[f9158]) ).
fof(f11986,plain,
( spl0_1485
| ~ spl0_1102
| ~ spl0_1218 ),
inference(avatar_split_clause,[],[f11283,f9964,f9158,f11983]) ).
fof(f11983,plain,
( spl0_1485
<=> c_0 = c_OrderedGroup_Onprt(c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f11283,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,t_b)
| ~ spl0_1102
| ~ spl0_1218 ),
inference(resolution,[],[f9160,f9965]) ).
fof(f11967,plain,
spl0_1484,
inference(avatar_split_clause,[],[f3172,f11965]) ).
fof(f11965,plain,
( spl0_1484
<=> ! [X0,X12] :
( c_IntDef_Oiszero(c_0,X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f3172,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_0,X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ),
inference(inner_rewriting,[],[f3171]) ).
fof(f3171,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X12,X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f3170,f1009]) ).
fof(f3170,plain,
! [X0,X12] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_OPls),X0),X0)
| ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0) ),
inference(forward_demodulation,[],[f2979,f2813]) ).
fof(f2979,plain,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X0),X0) ),
inference(definition_unfolding,[],[f231,f1023]) ).
fof(f231,axiom,
! [X0,X12] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 != c_Numeral_Onumber__of(X12,X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X12,c_Numeral_Obin__minus(c_Numeral_OPls)),X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f11963,plain,
spl0_1483,
inference(avatar_split_clause,[],[f3057,f11961]) ).
fof(f11961,plain,
( spl0_1483
<=> ! [X16,X0,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f3057,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2859,f2814]) ).
fof(f2859,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f103,f1438]) ).
fof(f103,axiom,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f11959,plain,
spl0_1482,
inference(avatar_split_clause,[],[f3056,f11957]) ).
fof(f11957,plain,
( spl0_1482
<=> ! [X16,X0,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f3056,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
inference(forward_demodulation,[],[f2858,f2814]) ).
fof(f2858,plain,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
inference(definition_unfolding,[],[f104,f1438]) ).
fof(f104,axiom,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X17,X0,X16),X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f11955,plain,
spl0_1481,
inference(avatar_split_clause,[],[f2930,f11953]) ).
fof(f11953,plain,
( spl0_1481
<=> ! [X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f2930,plain,
! [X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1173,f1438]) ).
fof(f1173,axiom,
! [X12] :
( c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_Suc(X12),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f11951,plain,
spl0_1480,
inference(avatar_split_clause,[],[f2920,f11949]) ).
fof(f11949,plain,
( spl0_1480
<=> ! [X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f2920,plain,
! [X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X12,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1172,f1438]) ).
fof(f1172,axiom,
! [X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X12),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f11944,plain,
( spl0_1479
| ~ spl0_1069
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f11106,f9952,f9023,f11941]) ).
fof(f9952,plain,
( spl0_1216
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f11106,plain,
( c_0 = c_HOL_Oabs(c_0,t_b)
| ~ spl0_1069
| ~ spl0_1216 ),
inference(resolution,[],[f9025,f9953]) ).
fof(f9953,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) )
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f9952]) ).
fof(f11939,plain,
( spl0_1478
| ~ spl0_1477 ),
inference(avatar_split_clause,[],[f11935,f11932,f11937]) ).
fof(f11932,plain,
( spl0_1477
<=> ! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f11935,plain,
( ! [X11] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X11),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1477 ),
inference(forward_demodulation,[],[f11933,f2850]) ).
fof(f11933,plain,
( ! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1477 ),
inference(avatar_component_clause,[],[f11932]) ).
fof(f11934,plain,
spl0_1477,
inference(avatar_split_clause,[],[f2841,f11932]) ).
fof(f2841,plain,
! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f282,f1438]) ).
fof(f282,axiom,
! [X11] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X11)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f11930,plain,
( spl0_1476
| ~ spl0_1168
| ~ spl0_1475 ),
inference(avatar_split_clause,[],[f11926,f11923,f9433,f11928]) ).
fof(f11928,plain,
( spl0_1476
<=> ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f9433,plain,
( spl0_1168
<=> ! [X0,X10] : c_union(c_emptyset,X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f11923,plain,
( spl0_1475
<=> ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X0,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f11926,plain,
( ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X0)
| ~ spl0_1168
| ~ spl0_1475 ),
inference(forward_demodulation,[],[f11924,f9434]) ).
fof(f9434,plain,
( ! [X10,X0] : c_union(c_emptyset,X10,X0) = X10
| ~ spl0_1168 ),
inference(avatar_component_clause,[],[f9433]) ).
fof(f11924,plain,
( ! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X0,X0)),X0)
| ~ spl0_1475 ),
inference(avatar_component_clause,[],[f11923]) ).
fof(f11925,plain,
spl0_1475,
inference(avatar_split_clause,[],[f2815,f11923]) ).
fof(f2815,plain,
! [X0] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X0,X0)),X0),
inference(definition_unfolding,[],[f1603,f1610]) ).
fof(f1603,axiom,
! [X0] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f11921,plain,
spl0_1474,
inference(avatar_split_clause,[],[f2804,f11919]) ).
fof(f2804,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X12,X10,X0)
| c_lessequals(X12,X10,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__imp__le_0) ).
fof(f11917,plain,
spl0_1473,
inference(avatar_split_clause,[],[f2802,f11915]) ).
fof(f2802,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| ~ c_lessequals(X12,X10,X0)
| ~ c_less(X10,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_1) ).
fof(f11913,plain,
spl0_1472,
inference(avatar_split_clause,[],[f2801,f11911]) ).
fof(f2801,axiom,
! [X10,X0,X12] :
( ~ class_Orderings_Olinorder(X0)
| c_lessequals(X12,X10,X0)
| c_less(X10,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Olinorder__not__le_0) ).
fof(f11909,plain,
spl0_1471,
inference(avatar_split_clause,[],[f1726,f11907]) ).
fof(f1726,axiom,
! [X3,X0,X1] :
( X1 = X3
| ~ c_in(X1,c_insert(X3,c_emptyset,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f11905,plain,
spl0_1470,
inference(avatar_split_clause,[],[f1724,f11903]) ).
fof(f11903,plain,
( spl0_1470
<=> ! [X0,X30,X26] :
( ~ c_less(X26,X30,tc_set(X0))
| c_lessequals(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f1724,axiom,
! [X0,X26,X30] :
( ~ c_less(X26,X30,tc_set(X0))
| c_lessequals(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f11901,plain,
( spl0_1469
| ~ spl0_1009
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f10632,f9956,f8725,f11898]) ).
fof(f11898,plain,
( spl0_1469
<=> c_0 = c_uminus(c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f9956,plain,
( spl0_1217
<=> ! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_uminus(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f10632,plain,
( c_0 = c_uminus(c_0,t_b)
| ~ spl0_1009
| ~ spl0_1217 ),
inference(resolution,[],[f8727,f9957]) ).
fof(f9957,plain,
( ! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_uminus(c_0,X0) )
| ~ spl0_1217 ),
inference(avatar_component_clause,[],[f9956]) ).
fof(f11896,plain,
spl0_1468,
inference(avatar_split_clause,[],[f1723,f11894]) ).
fof(f11894,plain,
( spl0_1468
<=> ! [X0,X30,X26] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| ~ c_less(X26,X30,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f1723,axiom,
! [X0,X26,X30] :
( ~ c_lessequals(X30,X26,tc_set(X0))
| ~ c_less(X26,X30,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f11892,plain,
spl0_1467,
inference(avatar_split_clause,[],[f1565,f11890]) ).
fof(f11890,plain,
( spl0_1467
<=> ! [X0,X26] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f1565,axiom,
! [X0,X26] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f11888,plain,
spl0_1466,
inference(avatar_split_clause,[],[f1548,f11886]) ).
fof(f11886,plain,
( spl0_1466
<=> ! [X0,X26] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f1548,axiom,
! [X0,X26] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X26,X0)
| c_emptyset = c_Union(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f11884,plain,
spl0_1465,
inference(avatar_split_clause,[],[f1512,f11882]) ).
fof(f11882,plain,
( spl0_1465
<=> ! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f1512,axiom,
! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f11880,plain,
spl0_1464,
inference(avatar_split_clause,[],[f1509,f11878]) ).
fof(f11878,plain,
( spl0_1464
<=> ! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f1509,axiom,
! [X0,X26] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X26,X0)
| c_UNIV = c_Inter(X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f11876,plain,
spl0_1463,
inference(avatar_split_clause,[],[f1282,f11874]) ).
fof(f1282,axiom,
! [X0,X12] : c_in(c_Pair(X12,X12,X0,X0),c_Relation_OId,tc_prod(X0,X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f11872,plain,
spl0_1462,
inference(avatar_split_clause,[],[f1277,f11870]) ).
fof(f11870,plain,
( spl0_1462
<=> ! [X0,X26] : c_Relation_Odiag(X26,X0) = c_Relation_Oconverse(c_Relation_Odiag(X26,X0),X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f1277,axiom,
! [X0,X26] : c_Relation_Odiag(X26,X0) = c_Relation_Oconverse(c_Relation_Odiag(X26,X0),X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f11868,plain,
spl0_1461,
inference(avatar_split_clause,[],[f1260,f11866]) ).
fof(f1260,axiom,
! [X3,X10,X0,X16] : c_snd(c_Pair(X3,X10,X16,X0),X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f11864,plain,
spl0_1460,
inference(avatar_split_clause,[],[f1258,f11862]) ).
fof(f1258,axiom,
! [X10,X0,X1,X16] : c_fst(c_Pair(X10,X1,X0,X16),X0,X16) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f11860,plain,
spl0_1459,
inference(avatar_split_clause,[],[f1236,f11858]) ).
fof(f11858,plain,
( spl0_1459
<=> ! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(X12,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f1236,axiom,
! [X11,X12] :
( c_0 = X12
| c_less(c_0,c_Nat_Opower(X12,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f11856,plain,
( spl0_1458
| ~ spl0_938
| ~ spl0_1193 ),
inference(avatar_split_clause,[],[f10094,f9859,f7778,f11853]) ).
fof(f10094,plain,
( c_1 = c_IntDef_Oof__int(c_1,t_b)
| ~ spl0_938
| ~ spl0_1193 ),
inference(resolution,[],[f9860,f7780]) ).
fof(f11851,plain,
spl0_1457,
inference(avatar_split_clause,[],[f1235,f11849]) ).
fof(f11849,plain,
( spl0_1457
<=> ! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f1235,axiom,
! [X11] :
( c_0 = X11
| ~ c_less(c_0,c_Nat_Opower(c_0,X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f11847,plain,
spl0_1456,
inference(avatar_split_clause,[],[f1188,f11845]) ).
fof(f11845,plain,
( spl0_1456
<=> ! [X12,X11] :
( c_less(c_0,X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f1188,axiom,
! [X11,X12] :
( c_less(c_0,X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f11843,plain,
spl0_1455,
inference(avatar_split_clause,[],[f1175,f11841]) ).
fof(f11841,plain,
( spl0_1455
<=> ! [X12,X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f1175,axiom,
! [X10,X12] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f11839,plain,
spl0_1454,
inference(avatar_split_clause,[],[f1141,f11837]) ).
fof(f1141,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(X3,c_uminus(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f11835,plain,
spl0_1453,
inference(avatar_split_clause,[],[f1113,f11833]) ).
fof(f1113,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = X3
| c_0 != c_uminus(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
fof(f11831,plain,
spl0_1452,
inference(avatar_split_clause,[],[f1107,f11829]) ).
fof(f11829,plain,
( spl0_1452
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f1107,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f11827,plain,
spl0_1451,
inference(avatar_split_clause,[],[f1105,f11825]) ).
fof(f11825,plain,
( spl0_1451
<=> ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f1105,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f11823,plain,
spl0_1450,
inference(avatar_split_clause,[],[f1091,f11821]) ).
fof(f1091,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(X3,X0) = c_minus(c_0,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f11819,plain,
spl0_1449,
inference(avatar_split_clause,[],[f1069,f11817]) ).
fof(f11817,plain,
( spl0_1449
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_0 != c_HOL_Oabs(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f1069,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = X3
| c_0 != c_HOL_Oabs(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f11815,plain,
spl0_1448,
inference(avatar_split_clause,[],[f1065,f11813]) ).
fof(f1065,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_plus(c_uminus(X3,X0),X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f11809,plain,
spl0_1447,
inference(avatar_split_clause,[],[f933,f11807]) ).
fof(f11807,plain,
( spl0_1447
<=> ! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_0 = c_minus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f933,axiom,
! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_0 = c_minus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f11805,plain,
spl0_1446,
inference(avatar_split_clause,[],[f932,f11803]) ).
fof(f11803,plain,
( spl0_1446
<=> ! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| c_0 != c_minus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f932,axiom,
! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| c_0 != c_minus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f11801,plain,
spl0_1445,
inference(avatar_split_clause,[],[f743,f11799]) ).
fof(f11799,plain,
( spl0_1445
<=> ! [X34] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f743,axiom,
! [X34] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f11797,plain,
spl0_1444,
inference(avatar_split_clause,[],[f726,f11795]) ).
fof(f11795,plain,
( spl0_1444
<=> ! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f726,axiom,
! [X34] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X34,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X34,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f11793,plain,
spl0_1443,
inference(avatar_split_clause,[],[f705,f11791]) ).
fof(f11791,plain,
( spl0_1443
<=> ! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X24
| c_0 != c_NatArith_Oof__nat(X24,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f705,axiom,
! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = X24
| c_0 != c_NatArith_Oof__nat(X24,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
fof(f11789,plain,
spl0_1442,
inference(avatar_split_clause,[],[f653,f11787]) ).
fof(f11787,plain,
( spl0_1442
<=> ! [X0,X11,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate(X11,X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f653,axiom,
! [X39,X0,X11] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate(X11,X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f11785,plain,
spl0_1441,
inference(avatar_split_clause,[],[f624,f11783]) ).
fof(f11783,plain,
( spl0_1441
<=> ! [X39,X0,X40] :
( X39 = X40
| c_List_Orev(X39,X0) != c_List_Orev(X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f624,axiom,
! [X40,X39,X0] :
( X39 = X40
| c_List_Orev(X39,X0) != c_List_Orev(X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f11781,plain,
spl0_1440,
inference(avatar_split_clause,[],[f497,f11779]) ).
fof(f11779,plain,
( spl0_1440
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_less(c_0,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f497,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_less(c_0,c_Nat_Osize(X39,tc_List_Olist(X0)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f11777,plain,
spl0_1439,
inference(avatar_split_clause,[],[f442,f11775]) ).
fof(f11775,plain,
( spl0_1439
<=> ! [X41,X0] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f442,axiom,
! [X41,X0] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f11773,plain,
spl0_1438,
inference(avatar_split_clause,[],[f435,f11771]) ).
fof(f11771,plain,
( spl0_1438
<=> ! [X45,X48,X46,X47] :
( X46 = X48
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f435,axiom,
! [X48,X46,X47,X45] :
( X46 = X48
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f11769,plain,
spl0_1437,
inference(avatar_split_clause,[],[f434,f11767]) ).
fof(f11767,plain,
( spl0_1437
<=> ! [X48,X47,X46,X45] :
( X45 = X47
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f434,axiom,
! [X48,X46,X47,X45] :
( X45 = X47
| c_List_Ochar_OChar(X45,X46) != c_List_Ochar_OChar(X47,X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f11765,plain,
spl0_1436,
inference(avatar_split_clause,[],[f403,f11763]) ).
fof(f11763,plain,
( spl0_1436
<=> ! [X41,X0] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f403,axiom,
! [X41,X0] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X41,X0)
| c_List_Olist_ONil = c_List_Oconcat(X41,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f11761,plain,
spl0_1435,
inference(avatar_split_clause,[],[f382,f11759]) ).
fof(f11759,plain,
( spl0_1435
<=> ! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f382,axiom,
! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f11757,plain,
spl0_1434,
inference(avatar_split_clause,[],[f381,f11755]) ).
fof(f11755,plain,
( spl0_1434
<=> ! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f381,axiom,
! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X35,tc_IntDef_Oint),X33,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f11752,plain,
spl0_1433,
inference(avatar_split_clause,[],[f361,f11750]) ).
fof(f361,axiom,
! [X3] : c_div(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f11748,plain,
spl0_1432,
inference(avatar_split_clause,[],[f334,f11746]) ).
fof(f11746,plain,
( spl0_1432
<=> ! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f334,axiom,
! [X35,X33] :
( ~ c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f11744,plain,
spl0_1431,
inference(avatar_split_clause,[],[f333,f11742]) ).
fof(f11742,plain,
( spl0_1431
<=> ! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f333,axiom,
! [X35,X33] :
( c_Divides_Oop_Advd(X35,X33,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X35,c_uminus(X33,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f11740,plain,
spl0_1430,
inference(avatar_split_clause,[],[f324,f11738]) ).
fof(f11738,plain,
( spl0_1430
<=> ! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f324,axiom,
! [X35,X33] :
( c_less(X33,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f11736,plain,
spl0_1429,
inference(avatar_split_clause,[],[f323,f11734]) ).
fof(f11734,plain,
( spl0_1429
<=> ! [X35,X33] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f323,axiom,
! [X35,X33] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X33),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f11732,plain,
spl0_1428,
inference(avatar_split_clause,[],[f322,f11730]) ).
fof(f11730,plain,
( spl0_1428
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f322,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f11728,plain,
( spl0_1427
| ~ spl0_1
| ~ spl0_1222 ),
inference(avatar_split_clause,[],[f10131,f9980,f3226,f11725]) ).
fof(f9980,plain,
( spl0_1222
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f10131,plain,
( c_1 = c_HOL_Oabs(c_1,t_b)
| ~ spl0_1
| ~ spl0_1222 ),
inference(resolution,[],[f9981,f3228]) ).
fof(f9981,plain,
( ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_1,X0) )
| ~ spl0_1222 ),
inference(avatar_component_clause,[],[f9980]) ).
fof(f11723,plain,
spl0_1426,
inference(avatar_split_clause,[],[f321,f11721]) ).
fof(f11721,plain,
( spl0_1426
<=> ! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f321,axiom,
! [X11,X24] :
( c_less(X24,X11,tc_nat)
| ~ c_less(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f11719,plain,
spl0_1425,
inference(avatar_split_clause,[],[f320,f11717]) ).
fof(f11717,plain,
( spl0_1425
<=> ! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f320,axiom,
! [X11,X24] :
( ~ c_lessequals(X24,X11,tc_nat)
| c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f11715,plain,
spl0_1424,
inference(avatar_split_clause,[],[f319,f11713]) ).
fof(f11713,plain,
( spl0_1424
<=> ! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f319,axiom,
! [X11,X24] :
( c_lessequals(X24,X11,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X24),c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f11711,plain,
spl0_1423,
inference(avatar_split_clause,[],[f301,f11709]) ).
fof(f301,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_IntDef_Oof__int(c_IntDef_Oint(X11),X0) = c_NatArith_Oof__nat(X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f11707,plain,
spl0_1422,
inference(avatar_split_clause,[],[f298,f11705]) ).
fof(f11705,plain,
( spl0_1422
<=> ! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X33
| c_0 != c_IntDef_Oof__int(X33,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f298,axiom,
! [X0,X33] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = X33
| c_0 != c_IntDef_Oof__int(X33,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
fof(f11703,plain,
spl0_1421,
inference(avatar_split_clause,[],[f284,f11701]) ).
fof(f11701,plain,
( spl0_1421
<=> ! [X11,X24] :
( c_0 = X24
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f284,axiom,
! [X11,X24] :
( c_0 = X24
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f11699,plain,
spl0_1420,
inference(avatar_split_clause,[],[f283,f11697]) ).
fof(f11697,plain,
( spl0_1420
<=> ! [X11,X24] :
( c_0 = X11
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f283,axiom,
! [X11,X24] :
( c_0 = X11
| c_IntDef_Oint(X24) != c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f11695,plain,
spl0_1419,
inference(avatar_split_clause,[],[f173,f11693]) ).
fof(f173,axiom,
! [X0,X26] :
( c_0 = c_Finite__Set_Ocard(X26,X0)
| c_in(X26,c_Finite__Set_OFinites,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f11691,plain,
spl0_1418,
inference(avatar_split_clause,[],[f169,f11689]) ).
fof(f169,axiom,
! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMin(c_insert(X10,c_emptyset,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f11687,plain,
spl0_1417,
inference(avatar_split_clause,[],[f159,f11685]) ).
fof(f159,axiom,
! [X10,X0] :
( ~ class_Orderings_Olinorder(X0)
| c_Finite__Set_OMax(c_insert(X10,c_emptyset,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f11683,plain,
( spl0_1416
| ~ spl0_1
| ~ spl0_1192 ),
inference(avatar_split_clause,[],[f10091,f9855,f3226,f11680]) ).
fof(f11680,plain,
( spl0_1416
<=> c_0 = c_IntDef_Oof__int(c_0,t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f10091,plain,
( c_0 = c_IntDef_Oof__int(c_0,t_b)
| ~ spl0_1
| ~ spl0_1192 ),
inference(resolution,[],[f9856,f3228]) ).
fof(f11678,plain,
spl0_1415,
inference(avatar_split_clause,[],[f129,f11676]) ).
fof(f11676,plain,
( spl0_1415
<=> ! [X11,X10] :
( ~ c_less(X10,X11,tc_nat)
| c_Divides_Oop_Amod(X10,X11,tc_nat) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f129,axiom,
! [X10,X11] :
( ~ c_less(X10,X11,tc_nat)
| c_Divides_Oop_Amod(X10,X11,tc_nat) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f11674,plain,
spl0_1414,
inference(avatar_split_clause,[],[f118,f11672]) ).
fof(f11672,plain,
( spl0_1414
<=> ! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_1 = c_div(X11,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f118,axiom,
! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_1 = c_div(X11,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f11670,plain,
spl0_1413,
inference(avatar_split_clause,[],[f110,f11668]) ).
fof(f11668,plain,
( spl0_1413
<=> ! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_0 = c_div(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f110,axiom,
! [X11,X24] :
( ~ c_less(X24,X11,tc_nat)
| c_0 = c_div(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f11666,plain,
spl0_1412,
inference(avatar_split_clause,[],[f95,f11664]) ).
fof(f11664,plain,
( spl0_1412
<=> ! [X18,X0,X9,X17,X16] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f95,axiom,
! [X0,X18,X9,X16,X17] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb_0) ).
fof(f11662,plain,
spl0_1411,
inference(avatar_split_clause,[],[f94,f11660]) ).
fof(f11660,plain,
( spl0_1411
<=> ! [X18,X0,X16,X17,X3] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OLeaf(X3,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f94,axiom,
! [X3,X0,X18,X16,X17] : c_Datatype__Universe_OScons(X17,X18,X0,X16) != c_Datatype__Universe_OLeaf(X3,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf_0) ).
fof(f11658,plain,
spl0_1410,
inference(avatar_split_clause,[],[f80,f11656]) ).
fof(f11656,plain,
( spl0_1410
<=> ! [X18,X0,X16,X17,X3] : c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OScons(X17,X18,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f80,axiom,
! [X3,X0,X18,X16,X17] : c_Datatype__Universe_OAtom(X3,X0,X16) != c_Datatype__Universe_OScons(X17,X18,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f11654,plain,
spl0_1409,
inference(avatar_split_clause,[],[f74,f11652]) ).
fof(f11652,plain,
( spl0_1409
<=> ! [X16,X0,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X1,X16,X0),tc_sum(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f74,axiom,
! [X0,X1,X16] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X1,X16,X0),tc_sum(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f11650,plain,
spl0_1408,
inference(avatar_split_clause,[],[f73,f11648]) ).
fof(f11648,plain,
( spl0_1408
<=> ! [X16,X0,X3] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X3,X0,X16),tc_sum(X0,X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f73,axiom,
! [X3,X0,X16] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X3,X0,X16),tc_sum(X0,X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f11646,plain,
spl0_1407,
inference(avatar_split_clause,[],[f69,f11644]) ).
fof(f11644,plain,
( spl0_1407
<=> ! [X0,X3,X15] :
( X3 = X15
| c_Datatype_Ooption_OSome(X15,X0) != c_Datatype_Ooption_OSome(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f69,axiom,
! [X3,X0,X15] :
( X3 = X15
| c_Datatype_Ooption_OSome(X15,X0) != c_Datatype_Ooption_OSome(X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f11642,plain,
spl0_1406,
inference(avatar_split_clause,[],[f64,f11640]) ).
fof(f11640,plain,
( spl0_1406
<=> ! [X12,X14] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X14),X14) = c_insert(X12,c_emptyset,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f64,axiom,
! [X14,X12] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X14),X14) = c_insert(X12,c_emptyset,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f11622,plain,
spl0_1405,
inference(avatar_split_clause,[],[f63,f11620]) ).
fof(f11620,plain,
( spl0_1405
<=> ! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X12,X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f63,axiom,
! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X12,X0),X0) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f11618,plain,
spl0_1404,
inference(avatar_split_clause,[],[f62,f11616]) ).
fof(f11616,plain,
( spl0_1404
<=> ! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X12,X0),X0) = X12 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f62,axiom,
! [X0,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X12,X0),X0) = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f11288,plain,
spl0_1403,
inference(avatar_split_clause,[],[f3125,f11286]) ).
fof(f11286,plain,
( spl0_1403
<=> ! [X35] :
( ~ c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| c_less(c_1,X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f3125,plain,
! [X35] :
( ~ c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| c_less(c_1,X35,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2949,f2814]) ).
fof(f2949,plain,
! [X35] :
( c_less(c_1,X35,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X35),tc_nat) ),
inference(definition_unfolding,[],[f240,f1438]) ).
fof(f240,axiom,
! [X35] :
( c_less(c_1,X35,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f11264,plain,
spl0_1402,
inference(avatar_split_clause,[],[f3113,f11262]) ).
fof(f11262,plain,
( spl0_1402
<=> ! [X35] :
( c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| ~ c_less(c_1,X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f3113,plain,
! [X35] :
( c_less(c_1,c_IntDef_Onat(X35),tc_nat)
| ~ c_less(c_1,X35,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2931,f2814]) ).
fof(f2931,plain,
! [X35] :
( ~ c_less(c_1,X35,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X35),tc_nat) ),
inference(definition_unfolding,[],[f241,f1438]) ).
fof(f241,axiom,
! [X35] :
( ~ c_less(c_1,X35,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f11260,plain,
spl0_1401,
inference(avatar_split_clause,[],[f3109,f11258]) ).
fof(f11258,plain,
( spl0_1401
<=> ! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f3109,plain,
! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X11 ),
inference(forward_demodulation,[],[f2926,f2814]) ).
fof(f2926,plain,
! [X11,X24] :
( c_1 = X11
| c_times(X24,X11,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f957,f1438]) ).
fof(f957,axiom,
! [X11,X24] :
( c_1 = X11
| c_Suc(c_0) != c_times(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
fof(f11256,plain,
spl0_1400,
inference(avatar_split_clause,[],[f3108,f11254]) ).
fof(f11254,plain,
( spl0_1400
<=> ! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f3108,plain,
! [X11,X24] :
( c_1 != c_times(X24,X11,tc_nat)
| c_1 = X24 ),
inference(forward_demodulation,[],[f2925,f2814]) ).
fof(f2925,plain,
! [X11,X24] :
( c_1 = X24
| c_times(X24,X11,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f986,f1438]) ).
fof(f986,axiom,
! [X11,X24] :
( c_1 = X24
| c_Suc(c_0) != c_times(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
fof(f11252,plain,
spl0_1399,
inference(avatar_split_clause,[],[f2845,f11250]) ).
fof(f11250,plain,
( spl0_1399
<=> ! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f2845,plain,
! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X33,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f1026,f1007]) ).
fof(f1026,axiom,
! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f11248,plain,
spl0_1398,
inference(avatar_split_clause,[],[f2834,f11246]) ).
fof(f11246,plain,
( spl0_1398
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_Odiag(X10,X0),X10,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f2834,plain,
! [X10,X0] : c_Relation_OImage(c_Relation_Odiag(X10,X0),X10,X0,X0) = X10,
inference(definition_unfolding,[],[f1497,f1267]) ).
fof(f1497,axiom,
! [X10,X0] : c_inter(X10,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f11244,plain,
spl0_1397,
inference(avatar_split_clause,[],[f2833,f11242]) ).
fof(f11242,plain,
( spl0_1397
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X0),X10,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f2833,plain,
! [X10,X0] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X0),X10,X0,X0) = X10,
inference(definition_unfolding,[],[f1495,f1267]) ).
fof(f1495,axiom,
! [X10,X0] : c_inter(c_UNIV,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f11240,plain,
spl0_1396,
inference(avatar_split_clause,[],[f2832,f11238]) ).
fof(f11238,plain,
( spl0_1396
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_Odiag(X10,X0),c_UNIV,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f2832,plain,
! [X10,X0] : c_Relation_OImage(c_Relation_Odiag(X10,X0),c_UNIV,X0,X0) = X10,
inference(definition_unfolding,[],[f1496,f1267]) ).
fof(f1496,axiom,
! [X10,X0] : c_inter(X10,c_UNIV,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f11236,plain,
spl0_1395,
inference(avatar_split_clause,[],[f2826,f11234]) ).
fof(f11234,plain,
( spl0_1395
<=> ! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f2826,plain,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f54,f1438]) ).
fof(f54,axiom,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f11232,plain,
spl0_1394,
inference(avatar_split_clause,[],[f1684,f11230]) ).
fof(f11230,plain,
( spl0_1394
<=> ! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X19,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f1684,axiom,
! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X19,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f11228,plain,
spl0_1393,
inference(avatar_split_clause,[],[f1683,f11226]) ).
fof(f11226,plain,
( spl0_1393
<=> ! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X19,X0),tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f1683,axiom,
! [X0,X19] :
( ~ c_Wellfounded__Recursion_Owf(X19,X0)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X19,X0),tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f11205,plain,
spl0_1392,
inference(avatar_split_clause,[],[f1656,f11203]) ).
fof(f11203,plain,
( spl0_1392
<=> ! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f1656,axiom,
! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f11201,plain,
spl0_1391,
inference(avatar_split_clause,[],[f1655,f11199]) ).
fof(f11199,plain,
( spl0_1391
<=> ! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f1655,axiom,
! [X11,X24] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X24,X11,tc_nat,tc_nat)),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f11197,plain,
spl0_1390,
inference(avatar_split_clause,[],[f1612,f11195]) ).
fof(f11195,plain,
( spl0_1390
<=> ! [X0,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f1612,axiom,
! [X0,X19] :
( ~ c_Wellfounded__Recursion_Oacyclic(X19,X0)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f11193,plain,
spl0_1389,
inference(avatar_split_clause,[],[f1611,f11191]) ).
fof(f11191,plain,
( spl0_1389
<=> ! [X0,X19] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f1611,axiom,
! [X0,X19] :
( c_Wellfounded__Recursion_Oacyclic(X19,X0)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X19,X0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f11189,plain,
spl0_1388,
inference(avatar_split_clause,[],[f1596,f11187]) ).
fof(f11187,plain,
( spl0_1388
<=> ! [X0,X1,X16,X3] : c_Sum__Type_OInl(X3,X0,X16) != c_Sum__Type_OInr(X1,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f1596,axiom,
! [X3,X0,X1,X16] : c_Sum__Type_OInl(X3,X0,X16) != c_Sum__Type_OInr(X1,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr_0) ).
fof(f11185,plain,
spl0_1387,
inference(avatar_split_clause,[],[f1561,f11183]) ).
fof(f11183,plain,
( spl0_1387
<=> ! [X0,X10] : c_uminus(c_uminus(X10,tc_set(X0)),tc_set(X0)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f1561,axiom,
! [X10,X0] : c_uminus(c_uminus(X10,tc_set(X0)),tc_set(X0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f11181,plain,
spl0_1386,
inference(avatar_split_clause,[],[f1553,f11179]) ).
fof(f11179,plain,
( spl0_1386
<=> ! [X0,X26] :
( c_emptyset = X26
| c_in(c_Main_Oall__not__in__conv__1(X26,X0),X26,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f1553,axiom,
! [X0,X26] :
( c_emptyset = X26
| c_in(c_Main_Oall__not__in__conv__1(X26,X0),X26,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f11177,plain,
spl0_1385,
inference(avatar_split_clause,[],[f1530,f11175]) ).
fof(f11175,plain,
( spl0_1385
<=> ! [X0,X30,X26] :
( c_emptyset = X30
| c_emptyset != c_union(X26,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f1530,axiom,
! [X0,X26,X30] :
( c_emptyset = X30
| c_emptyset != c_union(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f11173,plain,
spl0_1384,
inference(avatar_split_clause,[],[f1529,f11171]) ).
fof(f11171,plain,
( spl0_1384
<=> ! [X0,X30,X26] :
( c_emptyset = X26
| c_emptyset != c_union(X26,X30,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f1529,axiom,
! [X0,X26,X30] :
( c_emptyset = X26
| c_emptyset != c_union(X26,X30,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f11169,plain,
spl0_1383,
inference(avatar_split_clause,[],[f1520,f11167]) ).
fof(f1520,axiom,
! [X0] : c_Pow(c_emptyset,X0) = c_insert(c_emptyset,c_emptyset,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f11146,plain,
spl0_1382,
inference(avatar_split_clause,[],[f1284,f11144]) ).
fof(f11144,plain,
( spl0_1382
<=> ! [X77,X14] : c_Relation_OId = c_Nat_Opower(X77,c_0,tc_set(tc_prod(X14,X14))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f1284,axiom,
! [X14,X77] : c_Relation_OId = c_Nat_Opower(X77,c_0,tc_set(tc_prod(X14,X14))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f11142,plain,
spl0_1381,
inference(avatar_split_clause,[],[f1283,f11140]) ).
fof(f11140,plain,
( spl0_1381
<=> ! [X0,X10] : c_Nat_Opower(X10,c_1,tc_set(tc_prod(X0,X0))) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f1283,axiom,
! [X10,X0] : c_Nat_Opower(X10,c_1,tc_set(tc_prod(X0,X0))) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f11138,plain,
spl0_1380,
inference(avatar_split_clause,[],[f1276,f11136]) ).
fof(f11136,plain,
( spl0_1380
<=> ! [X0,X16,X10] : c_Relation_Oconverse(c_Relation_Oconverse(X10,X0,X16),X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f1276,axiom,
! [X10,X0,X16] : c_Relation_Oconverse(c_Relation_Oconverse(X10,X0,X16),X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f11134,plain,
spl0_1379,
inference(avatar_split_clause,[],[f1192,f11132]) ).
fof(f11132,plain,
( spl0_1379
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f1192,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f11130,plain,
spl0_1378,
inference(avatar_split_clause,[],[f1191,f11128]) ).
fof(f11128,plain,
( spl0_1378
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f1191,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X12,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f11126,plain,
spl0_1377,
inference(avatar_split_clause,[],[f1187,f11124]) ).
fof(f11124,plain,
( spl0_1377
<=> ! [X11,X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f1187,axiom,
! [X11,X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f11122,plain,
spl0_1376,
inference(avatar_split_clause,[],[f1179,f11120]) ).
fof(f11120,plain,
( spl0_1376
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f1179,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X10,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f11118,plain,
spl0_1375,
inference(avatar_split_clause,[],[f1178,f11116]) ).
fof(f11116,plain,
( spl0_1375
<=> ! [X12,X10] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f1178,axiom,
! [X10,X12] :
( ~ c_Parity_Oeven(X12,tc_nat)
| c_Parity_Oeven(c_times(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f11114,plain,
spl0_1374,
inference(avatar_split_clause,[],[f1174,f11112]) ).
fof(f11112,plain,
( spl0_1374
<=> ! [X12,X10] :
( c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f1174,axiom,
! [X10,X12] :
( c_Parity_Oeven(X12,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X12,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f11110,plain,
spl0_1373,
inference(avatar_split_clause,[],[f1110,f11108]) ).
fof(f1110,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_uminus(c_uminus(X10,X0),X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f11086,plain,
spl0_1372,
inference(avatar_split_clause,[],[f1048,f11084]) ).
fof(f11084,plain,
( spl0_1372
<=> ! [X33] : c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X33),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f11082,plain,
spl0_1371,
inference(avatar_split_clause,[],[f1044,f11080]) ).
fof(f11080,plain,
( spl0_1371
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f1044,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f11078,plain,
spl0_1370,
inference(avatar_split_clause,[],[f1030,f11076]) ).
fof(f11076,plain,
( spl0_1370
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f1030,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ class_Ring__and__Field_Oordered__idom(X0)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f11074,plain,
spl0_1369,
inference(avatar_split_clause,[],[f1012,f11072]) ).
fof(f1012,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_Numeral_Onumber__of(c_Numeral_OMin,X0) = c_uminus(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f11070,plain,
spl0_1368,
inference(avatar_split_clause,[],[f926,f11068]) ).
fof(f11068,plain,
( spl0_1368
<=> ! [X11,X24] :
( c_0 = X11
| c_0 != c_plus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f926,axiom,
! [X11,X24] :
( c_0 = X11
| c_0 != c_plus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f11066,plain,
spl0_1367,
inference(avatar_split_clause,[],[f925,f11064]) ).
fof(f11064,plain,
( spl0_1367
<=> ! [X11,X24] :
( c_0 = X24
| c_0 != c_plus(X24,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f925,axiom,
! [X11,X24] :
( c_0 = X24
| c_0 != c_plus(X24,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f11062,plain,
spl0_1366,
inference(avatar_split_clause,[],[f680,f11060]) ).
fof(f11060,plain,
( spl0_1366
<=> ! [X50,X23] :
( ~ c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f680,axiom,
! [X50,X23] :
( ~ c_lessequals(X50,X23,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X23,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f11058,plain,
spl0_1365,
inference(avatar_split_clause,[],[f652,f11056]) ).
fof(f11056,plain,
( spl0_1365
<=> ! [X0,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate1(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f652,axiom,
! [X39,X0] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orotate1(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f11054,plain,
spl0_1364,
inference(avatar_split_clause,[],[f651,f11052]) ).
fof(f11052,plain,
( spl0_1364
<=> ! [X0,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orev(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f651,axiom,
! [X39,X0] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Orev(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f11050,plain,
spl0_1363,
inference(avatar_split_clause,[],[f648,f11048]) ).
fof(f11048,plain,
( spl0_1363
<=> ! [X0,X39] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Oremdups(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f648,axiom,
! [X39,X0] : c_List_Oset(X39,X0) = c_List_Oset(c_List_Oremdups(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f11046,plain,
spl0_1362,
inference(avatar_split_clause,[],[f634,f11044]) ).
fof(f11044,plain,
( spl0_1362
<=> ! [X0,X11,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate(X11,X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f634,axiom,
! [X39,X0,X11] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate(X11,X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f11042,plain,
spl0_1361,
inference(avatar_split_clause,[],[f614,f11040]) ).
fof(f11040,plain,
( spl0_1361
<=> ! [X0,X12,X39] : c_List_Oremove1(X12,c_List_Olist_OCons(X12,X39,X0),X0) = X39 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f614,axiom,
! [X39,X0,X12] : c_List_Oremove1(X12,c_List_Olist_OCons(X12,X39,X0),X0) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f11038,plain,
spl0_1360,
inference(avatar_split_clause,[],[f586,f11036]) ).
fof(f11036,plain,
( spl0_1360
<=> ! [X0,X39,X10] : c_List_Onth(c_List_Olist_OCons(X10,X39,X0),c_0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f586,axiom,
! [X10,X39,X0] : c_List_Onth(c_List_Olist_OCons(X10,X39,X0),c_0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f11034,plain,
spl0_1359,
inference(avatar_split_clause,[],[f533,f11032]) ).
fof(f11030,plain,
spl0_1358,
inference(avatar_split_clause,[],[f501,f11028]) ).
fof(f11028,plain,
( spl0_1358
<=> ! [X0,X12,X10] : c_Nat_Osize(c_List_Oreplicate(X10,X12,X0),tc_List_Olist(X0)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f501,axiom,
! [X10,X0,X12] : c_Nat_Osize(c_List_Oreplicate(X10,X12,X0),tc_List_Olist(X0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f11026,plain,
spl0_1357,
inference(avatar_split_clause,[],[f491,f11024]) ).
fof(f11024,plain,
( spl0_1357
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_0 != c_Nat_Osize(X39,tc_List_Olist(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f491,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_0 != c_Nat_Osize(X39,tc_List_Olist(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f11022,plain,
spl0_1356,
inference(avatar_split_clause,[],[f459,f11020]) ).
fof(f11020,plain,
( spl0_1356
<=> ! [X0,X39,X49] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Osublist(X39,X49,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f459,axiom,
! [X39,X0,X49] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Osublist(X39,X49,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f11018,plain,
spl0_1355,
inference(avatar_split_clause,[],[f458,f11016]) ).
fof(f11016,plain,
( spl0_1355
<=> ! [X0,X11,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f458,axiom,
! [X39,X0,X11] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f11014,plain,
spl0_1354,
inference(avatar_split_clause,[],[f457,f11012]) ).
fof(f11012,plain,
( spl0_1354
<=> ! [X0,X11,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f457,axiom,
! [X39,X0,X11] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate(X11,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f11010,plain,
spl0_1353,
inference(avatar_split_clause,[],[f454,f11008]) ).
fof(f11008,plain,
( spl0_1353
<=> ! [X0,X12,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Oremove1(X12,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f454,axiom,
! [X39,X0,X12] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Oremove1(X12,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f10983,plain,
spl0_1352,
inference(avatar_split_clause,[],[f453,f10981]) ).
fof(f10981,plain,
( spl0_1352
<=> ! [X0,X39,X23] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Odrop(X23,X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f453,axiom,
! [X39,X0,X23] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Odrop(X23,X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f10979,plain,
spl0_1351,
inference(avatar_split_clause,[],[f450,f10977]) ).
fof(f10977,plain,
( spl0_1351
<=> ! [X39,X0,X40] :
( c_List_Odistinct(X40,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f450,axiom,
! [X40,X39,X0] :
( c_List_Odistinct(X40,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f10975,plain,
spl0_1350,
inference(avatar_split_clause,[],[f449,f10973]) ).
fof(f10973,plain,
( spl0_1350
<=> ! [X40,X0,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f449,axiom,
! [X40,X39,X0] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_append(X39,X40,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f10971,plain,
spl0_1349,
inference(avatar_split_clause,[],[f447,f10969]) ).
fof(f10969,plain,
( spl0_1349
<=> ! [X12,X39,X14] :
( c_List_Odistinct(X39,X14)
| ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f447,axiom,
! [X39,X14,X12] :
( c_List_Odistinct(X39,X14)
| ~ c_List_Odistinct(c_List_Olist_OCons(X12,X39,X14),X14) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f10967,plain,
spl0_1348,
inference(avatar_split_clause,[],[f427,f10965]) ).
fof(f10965,plain,
( spl0_1348
<=> ! [X39,X0,X40] :
( c_List_Olist_ONil = X40
| c_append(X39,X40,X0) != X39 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f427,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X40
| c_append(X39,X40,X0) != X39 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f10963,plain,
spl0_1347,
inference(avatar_split_clause,[],[f425,f10961]) ).
fof(f10961,plain,
( spl0_1347
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_append(X39,X40,X0) != X40 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f425,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_append(X39,X40,X0) != X40 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv2_0) ).
fof(f10959,plain,
spl0_1346,
inference(avatar_split_clause,[],[f422,f10957]) ).
fof(f10957,plain,
( spl0_1346
<=> ! [X39,X0,X40] :
( c_List_Olist_ONil = X40
| c_List_Olist_ONil != c_append(X39,X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f422,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X40
| c_List_Olist_ONil != c_append(X39,X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
fof(f10955,plain,
spl0_1345,
inference(avatar_split_clause,[],[f404,f10953]) ).
fof(f10953,plain,
( spl0_1345
<=> ! [X40,X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_append(X39,X40,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f404,axiom,
! [X40,X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_append(X39,X40,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).
fof(f10951,plain,
spl0_1344,
inference(avatar_split_clause,[],[f391,f10949]) ).
fof(f10949,plain,
( spl0_1344
<=> ! [X1,X3] : c_0 = c_Divides_Oop_Amod(c_times(X1,X3,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f391,axiom,
! [X3,X1] : c_0 = c_Divides_Oop_Amod(c_times(X1,X3,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f10947,plain,
spl0_1343,
inference(avatar_split_clause,[],[f390,f10945]) ).
fof(f10945,plain,
( spl0_1343
<=> ! [X1,X3] : c_0 = c_Divides_Oop_Amod(c_times(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f390,axiom,
! [X3,X1] : c_0 = c_Divides_Oop_Amod(c_times(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f10912,plain,
spl0_1342,
inference(avatar_split_clause,[],[f377,f10910]) ).
fof(f10910,plain,
( spl0_1342
<=> ! [X12,X11] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f377,axiom,
! [X11,X12] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),X11,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f10908,plain,
spl0_1341,
inference(avatar_split_clause,[],[f365,f10906]) ).
fof(f10906,plain,
( spl0_1341
<=> ! [X3] :
( c_0 = X3
| c_1 = c_div(X3,X3,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f365,axiom,
! [X3] :
( c_0 = X3
| c_1 = c_div(X3,X3,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f10904,plain,
spl0_1340,
inference(avatar_split_clause,[],[f335,f10902]) ).
fof(f10902,plain,
( spl0_1340
<=> ! [X1,X3] : c_0 = c_div(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f335,axiom,
! [X3,X1] : c_0 = c_div(c_Divides_Oop_Amod(X3,X1,tc_IntDef_Oint),X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f10900,plain,
spl0_1339,
inference(avatar_split_clause,[],[f317,f10898]) ).
fof(f10898,plain,
( spl0_1339
<=> ! [X35] :
( ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f317,axiom,
! [X35] :
( ~ c_less(c_0,X35,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f10896,plain,
spl0_1338,
inference(avatar_split_clause,[],[f316,f10894]) ).
fof(f10894,plain,
( spl0_1338
<=> ! [X35] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X35),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f316,axiom,
! [X35] :
( c_less(c_0,X35,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X35),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f10892,plain,
spl0_1337,
inference(avatar_split_clause,[],[f315,f10890]) ).
fof(f10890,plain,
( spl0_1337
<=> ! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f315,axiom,
! [X11] :
( ~ c_less(c_0,X11,tc_nat)
| c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f10888,plain,
spl0_1336,
inference(avatar_split_clause,[],[f314,f10886]) ).
fof(f10886,plain,
( spl0_1336
<=> ! [X11] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f314,axiom,
! [X11] :
( c_less(c_0,X11,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f10884,plain,
spl0_1335,
inference(avatar_split_clause,[],[f274,f10882]) ).
fof(f10882,plain,
( spl0_1335
<=> ! [X35] :
( c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X35)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f274,axiom,
! [X35] :
( c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X35)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f10880,plain,
spl0_1334,
inference(avatar_split_clause,[],[f273,f10878]) ).
fof(f10878,plain,
( spl0_1334
<=> ! [X35] :
( ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X35)) = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f273,axiom,
! [X35] :
( ~ c_lessequals(c_0,X35,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X35)) = X35 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f10876,plain,
spl0_1333,
inference(avatar_split_clause,[],[f243,f10874]) ).
fof(f10874,plain,
( spl0_1333
<=> ! [X35] :
( c_0 = X35
| ~ c_less(c_HOL_Oabs(X35,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f243,axiom,
! [X35] :
( c_0 = X35
| ~ c_less(c_HOL_Oabs(X35,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f10835,plain,
spl0_1332,
inference(avatar_split_clause,[],[f138,f10833]) ).
fof(f10833,plain,
( spl0_1332
<=> ! [X0,X19,X26] :
( c_emptyset = X26
| c_emptyset != c_Equiv__Relations_Oquotient(X26,X19,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f138,axiom,
! [X0,X19,X26] :
( c_emptyset = X26
| c_emptyset != c_Equiv__Relations_Oquotient(X26,X19,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
fof(f10831,plain,
spl0_1331,
inference(avatar_split_clause,[],[f136,f10829]) ).
fof(f10829,plain,
( spl0_1331
<=> ! [X11,X24] : c_0 = c_div(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f136,axiom,
! [X11,X24] : c_0 = c_div(c_Divides_Oop_Amod(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f10827,plain,
spl0_1330,
inference(avatar_split_clause,[],[f134,f10825]) ).
fof(f10825,plain,
( spl0_1330
<=> ! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X24,X11,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f134,axiom,
! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X24,X11,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f10823,plain,
spl0_1329,
inference(avatar_split_clause,[],[f132,f10821]) ).
fof(f10821,plain,
( spl0_1329
<=> ! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X11,X24,tc_nat),X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f132,axiom,
! [X11,X24] : c_0 = c_Divides_Oop_Amod(c_times(X11,X24,tc_nat),X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f10819,plain,
spl0_1328,
inference(avatar_split_clause,[],[f89,f10817]) ).
fof(f10817,plain,
( spl0_1328
<=> ! [X9,X16,X0,X3] : c_Datatype__Universe_OLeaf(X3,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f89,axiom,
! [X3,X0,X9,X16] : c_Datatype__Universe_OLeaf(X3,X0,X16) != c_Datatype__Universe_ONumb(X9,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f10815,plain,
spl0_1327,
inference(avatar_split_clause,[],[f84,f10813]) ).
fof(f10813,plain,
( spl0_1327
<=> ! [X18,X16,X0,X17] : c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn1(X18,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f84,axiom,
! [X0,X18,X16,X17] : c_Datatype__Universe_OIn0(X17,X0,X16) != c_Datatype__Universe_OIn1(X18,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f10615,plain,
spl0_1326,
inference(avatar_split_clause,[],[f3097,f10613]) ).
fof(f10613,plain,
( spl0_1326
<=> ! [X0] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ class_Numeral_Onumber__ring(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f3097,plain,
! [X0] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ class_Numeral_Onumber__ring(X0) ),
inference(forward_demodulation,[],[f1064,f1050]) ).
fof(f1064,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f10611,plain,
spl0_1325,
inference(avatar_split_clause,[],[f3049,f10609]) ).
fof(f10609,plain,
( spl0_1325
<=> ! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X24,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f3049,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X24,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2849,f2814]) ).
fof(f2849,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X24,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f194,f1438]) ).
fof(f194,axiom,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X24,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f10607,plain,
spl0_1324,
inference(avatar_split_clause,[],[f3048,f10605]) ).
fof(f10605,plain,
( spl0_1324
<=> ! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f3048,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2848,f2814]) ).
fof(f2848,plain,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f193,f1438]) ).
fof(f193,axiom,
! [X24] : c_1 = c_GCD_Ogcd(c_Pair(X24,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f10582,plain,
spl0_1323,
inference(avatar_split_clause,[],[f2820,f10580]) ).
fof(f10580,plain,
( spl0_1323
<=> ! [X11] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f2820,plain,
! [X11] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1688,f1438]) ).
fof(f1688,axiom,
! [X11] : c_less(c_0,c_Suc(X11),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f10578,plain,
spl0_1322,
inference(avatar_split_clause,[],[f2819,f10576]) ).
fof(f10576,plain,
( spl0_1322
<=> ! [X11] : c_less(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f2819,plain,
! [X11] : c_less(X11,c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1686,f1438]) ).
fof(f1686,axiom,
! [X11] : c_less(X11,c_Suc(X11),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f10574,plain,
spl0_1321,
inference(avatar_split_clause,[],[f2799,f10572]) ).
fof(f2799,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_SetsAndFunctions_Oelt__set__plus(c_0,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__zero__plus_0) ).
fof(f10570,plain,
spl0_1320,
inference(avatar_split_clause,[],[f2798,f10568]) ).
fof(f2798,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X0)
| c_SetsAndFunctions_Oelt__set__times(c_1,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetsAndFunctions_Oset__one__times_0) ).
fof(f10566,plain,
spl0_1319,
inference(avatar_split_clause,[],[f1873,f10564]) ).
fof(f10564,plain,
( spl0_1319
<=> ! [X7,X8] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_sum(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f1873,axiom,
! [X8,X7] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_sum(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f10562,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1867,f10560]) ).
fof(f10560,plain,
( spl0_1318
<=> ! [X7,X8] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_prod(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1867,axiom,
! [X8,X7] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_prod(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f10558,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1817,f10556]) ).
fof(f10556,plain,
( spl0_1317
<=> ! [X7,X8] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1817,axiom,
! [X8,X7] :
( ~ class_Finite__Set_Ofinite(X7)
| ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f10554,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1715,f10552]) ).
fof(f10552,plain,
( spl0_1316
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f1715,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,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(f10550,plain,
spl0_1315,
inference(avatar_split_clause,[],[f1714,f10548]) ).
fof(f10548,plain,
( spl0_1315
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f1714,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f10546,plain,
spl0_1314,
inference(avatar_split_clause,[],[f1713,f10544]) ).
fof(f10544,plain,
( spl0_1314
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f1713,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,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(f10534,plain,
spl0_1313,
inference(avatar_split_clause,[],[f1712,f10532]) ).
fof(f10532,plain,
( spl0_1313
<=> ! [X36,X72] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1712,axiom,
! [X72,X36] : c_in(c_SetInterval_OgreaterThanAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f10530,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1710,f10528]) ).
fof(f10528,plain,
( spl0_1312
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1710,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,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(f10526,plain,
spl0_1311,
inference(avatar_split_clause,[],[f1709,f10524]) ).
fof(f10524,plain,
( spl0_1311
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f1709,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastLessThan(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f10522,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1708,f10520]) ).
fof(f10520,plain,
( spl0_1310
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f1708,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,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(f10518,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1707,f10516]) ).
fof(f10516,plain,
( spl0_1309
<=> ! [X36,X72] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1707,axiom,
! [X72,X36] : c_in(c_SetInterval_OatLeastAtMost(X72,X36,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f10514,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1658,f10512]) ).
fof(f10512,plain,
( spl0_1308
<=> ! [X11,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1658,axiom,
! [X11,X24] : c_lessequals(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint),c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f10510,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1593,f10508]) ).
fof(f10508,plain,
( spl0_1307
<=> ! [X0,X26] :
( c_emptyset = X26
| ~ c_lessequals(X26,c_emptyset,tc_set(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1593,axiom,
! [X0,X26] :
( c_emptyset = X26
| ~ c_lessequals(X26,c_emptyset,tc_set(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f10506,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1554,f10504]) ).
fof(f1554,axiom,
! [X10,X0] : c_Set_Ocontents(c_insert(X10,c_emptyset,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f10502,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1428,f10499]) ).
fof(f1428,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(f10497,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1386,f10495]) ).
fof(f10495,plain,
( spl0_1304
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(X3,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1386,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(X3,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f10484,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1385,f10482]) ).
fof(f10482,plain,
( spl0_1303
<=> ! [X0,X3] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(c_0,X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1385,axiom,
! [X3,X0] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X0)
| c_0 = c_times(c_0,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f10480,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1368,f10478]) ).
fof(f10478,plain,
( spl0_1302
<=> ! [X25,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(c_1,X25,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1368,axiom,
! [X0,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(c_1,X25,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f10476,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1367,f10474]) ).
fof(f1367,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(X1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f10472,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1364,f10470]) ).
fof(f10470,plain,
( spl0_1300
<=> ! [X25,X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(X25,c_1,X0) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1364,axiom,
! [X0,X25] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_times(X25,c_1,X0) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f10468,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1363,f10466]) ).
fof(f1363,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_times(c_0,X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f10464,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1273,f10462]) ).
fof(f10462,plain,
( spl0_1298
<=> ! [X0,X10] : c_Relation_ORange(c_Relation_Odiag(X10,X0),X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1273,axiom,
! [X10,X0] : c_Relation_ORange(c_Relation_Odiag(X10,X0),X0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f10460,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1271,f10458]) ).
fof(f10458,plain,
( spl0_1297
<=> ! [X0,X16,X10] : c_Relation_Orel__comp(X10,c_Relation_OId,X0,X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1271,axiom,
! [X10,X0,X16] : c_Relation_Orel__comp(X10,c_Relation_OId,X0,X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f10456,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1265,f10454]) ).
fof(f10454,plain,
( spl0_1296
<=> ! [X0,X16,X10] : c_Relation_Orel__comp(c_Relation_OId,X10,X16,X16,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1265,axiom,
! [X10,X0,X16] : c_Relation_Orel__comp(c_Relation_OId,X10,X16,X16,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f10452,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1263,f10450]) ).
fof(f10450,plain,
( spl0_1295
<=> ! [X0,X10] : c_Relation_ODomain(c_Relation_Odiag(X10,X0),X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1263,axiom,
! [X10,X0] : c_Relation_ODomain(c_Relation_Odiag(X10,X0),X0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f10448,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1251,f10446]) ).
fof(f10446,plain,
( spl0_1294
<=> ! [X0,X3] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(X3,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1251,axiom,
! [X3,X0] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(X3,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f10442,plain,
spl0_1293,
inference(avatar_split_clause,[],[f1248,f10440]) ).
fof(f10440,plain,
( spl0_1293
<=> ! [X0,X10] :
( ~ class_Power_Orecpower(X0)
| c_Nat_Opower(X10,c_1,X0) = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f1248,axiom,
! [X10,X0] :
( ~ class_Power_Orecpower(X0)
| c_Nat_Opower(X10,c_1,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f10438,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1247,f10436]) ).
fof(f10436,plain,
( spl0_1292
<=> ! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(c_1,X11,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f1247,axiom,
! [X0,X11] :
( ~ class_Power_Orecpower(X0)
| c_1 = c_Nat_Opower(c_1,X11,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f10434,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1186,f10432]) ).
fof(f10432,plain,
( spl0_1291
<=> ! [X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1186,axiom,
! [X12] :
( ~ c_Parity_Oeven(X12,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f10430,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1185,f10428]) ).
fof(f10428,plain,
( spl0_1290
<=> ! [X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1185,axiom,
! [X12] :
( c_Parity_Oeven(X12,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X12,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f10426,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1161,f10424]) ).
fof(f1161,axiom,
! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omax(X10,X10,X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f10422,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1156,f10420]) ).
fof(f1156,axiom,
! [X10,X16] :
( ~ class_Orderings_Olinorder(X16)
| c_Orderings_Omin(X10,X10,X16) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f10418,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1145,f10416]) ).
fof(f1145,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f10414,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1144,f10412]) ).
fof(f10412,plain,
( spl0_1286
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X3,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1144,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f10410,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1135,f10408]) ).
fof(f10408,plain,
( spl0_1285
<=> ! [X0,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1135,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_lessequals(c_OrderedGroup_Onprt(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f10406,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1112,f10404]) ).
fof(f1112,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(X10,c_1,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f10400,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1111,f10398]) ).
fof(f1111,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Omonoid__mult(X0)
| c_times(c_1,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f10396,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1099,f10394]) ).
fof(f1099,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_minus(X3,X3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f10392,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1092,f10390]) ).
fof(f1092,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_minus(X10,c_0,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f10388,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1090,f10386]) ).
fof(f1090,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(c_0,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f10384,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1079,f10382]) ).
fof(f1079,axiom,
! [X10,X0] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X0)
| c_plus(X10,c_0,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f10380,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1076,f10378]) ).
fof(f1076,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| ~ c_less(c_HOL_Oabs(X3,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f10376,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1074,f10374]) ).
fof(f1074,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_HOL_Oabs(c_0,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f10372,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1071,f10370]) ).
fof(f1071,axiom,
! [X3,X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_lessequals(c_0,c_HOL_Oabs(X3,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f10368,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1047,f10366]) ).
fof(f1047,axiom,
! [X33] : c_Numeral_OBit(X33,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X33,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f10364,plain,
spl0_1274,
inference(avatar_split_clause,[],[f759,f10362]) ).
fof(f10362,plain,
( spl0_1274
<=> ! [X33] : c_IntDef_Onat(c_Numeral_Onumber__of(X33,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X33,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f759,axiom,
! [X33] : c_IntDef_Onat(c_Numeral_Onumber__of(X33,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X33,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f10356,plain,
spl0_1273,
inference(avatar_split_clause,[],[f712,f10354]) ).
fof(f10354,plain,
( spl0_1273
<=> ! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f712,axiom,
! [X0,X24] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_NatArith_Oof__nat(X24,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f10352,plain,
spl0_1272,
inference(avatar_split_clause,[],[f709,f10350]) ).
fof(f10350,plain,
( spl0_1272
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_NatArith_Oof__nat(c_0,X0),c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f709,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_NatArith_Oof__nat(c_0,X0),c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f10348,plain,
spl0_1271,
inference(avatar_split_clause,[],[f699,f10346]) ).
fof(f10346,plain,
( spl0_1271
<=> ! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_NatArith_Oof__nat(X11,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f699,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_NatArith_Oof__nat(X11,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f10344,plain,
spl0_1270,
inference(avatar_split_clause,[],[f673,f10342]) ).
fof(f10342,plain,
( spl0_1270
<=> ! [X12,X14,X10] : c_List_Otl(c_List_Olist_OCons(X12,X10,X14),X14) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f673,axiom,
! [X10,X14,X12] : c_List_Otl(c_List_Olist_OCons(X12,X10,X14),X14) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f10340,plain,
spl0_1269,
inference(avatar_split_clause,[],[f646,f10338]) ).
fof(f10338,plain,
( spl0_1269
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_emptyset != c_List_Oset(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f646,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_emptyset != c_List_Oset(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).
fof(f10336,plain,
spl0_1268,
inference(avatar_split_clause,[],[f629,f10334]) ).
fof(f10334,plain,
( spl0_1268
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate1(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f629,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orotate1(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f10332,plain,
spl0_1267,
inference(avatar_split_clause,[],[f622,f10330]) ).
fof(f10330,plain,
( spl0_1267
<=> ! [X0,X39] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orev(X39,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f622,axiom,
! [X39,X0] :
( c_List_Olist_ONil = X39
| c_List_Olist_ONil != c_List_Orev(X39,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_0) ).
fof(f10328,plain,
spl0_1266,
inference(avatar_split_clause,[],[f611,f10326]) ).
fof(f10326,plain,
( spl0_1266
<=> ! [X0,X12] :
( c_List_Olist_ONil = X12
| c_List_Olist_ONil != c_List_Oremdups(X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f611,axiom,
! [X0,X12] :
( c_List_Olist_ONil = X12
| c_List_Olist_ONil != c_List_Oremdups(X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f10324,plain,
spl0_1265,
inference(avatar_split_clause,[],[f482,f10322]) ).
fof(f10322,plain,
( spl0_1265
<=> ! [X0,X12] : c_List_Olast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) = X12 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f482,axiom,
! [X0,X12] : c_List_Olast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X0),X0) = X12,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f10320,plain,
spl0_1264,
inference(avatar_split_clause,[],[f473,f10318]) ).
fof(f10318,plain,
( spl0_1264
<=> ! [X0,X39,X10] : c_List_Ohd(c_List_Olist_OCons(X10,X39,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f473,axiom,
! [X10,X39,X0] : c_List_Ohd(c_List_Olist_OCons(X10,X39,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f10311,plain,
spl0_1263,
inference(avatar_split_clause,[],[f456,f10309]) ).
fof(f10309,plain,
( spl0_1263
<=> ! [X0,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orev(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f456,axiom,
! [X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orev(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f10307,plain,
spl0_1262,
inference(avatar_split_clause,[],[f455,f10305]) ).
fof(f10305,plain,
( spl0_1262
<=> ! [X0,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orev(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f455,axiom,
! [X39,X0] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orev(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f10303,plain,
spl0_1261,
inference(avatar_split_clause,[],[f444,f10301]) ).
fof(f10301,plain,
( spl0_1261
<=> ! [X0,X39] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f444,axiom,
! [X39,X0] :
( ~ c_List_Odistinct(X39,X0)
| c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f10299,plain,
spl0_1260,
inference(avatar_split_clause,[],[f443,f10297]) ).
fof(f10297,plain,
( spl0_1260
<=> ! [X0,X39] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f443,axiom,
! [X39,X0] :
( c_List_Odistinct(X39,X0)
| ~ c_List_Odistinct(c_List_Orotate1(X39,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f10295,plain,
spl0_1259,
inference(avatar_split_clause,[],[f431,f10293]) ).
fof(f10293,plain,
( spl0_1259
<=> ! [X12,X14] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f431,axiom,
! [X14,X12] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X12,c_List_Olist_ONil,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f10291,plain,
spl0_1258,
inference(avatar_split_clause,[],[f393,f10289]) ).
fof(f393,axiom,
! [X10,X0] :
( ~ class_LOrder_Omeet__semilorder(X0)
| c_LOrder_Omeet(X10,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f10287,plain,
spl0_1257,
inference(avatar_split_clause,[],[f392,f10285]) ).
fof(f392,axiom,
! [X10,X0] :
( ~ class_LOrder_Ojoin__semilorder(X0)
| c_LOrder_Ojoin(X10,X10,X0) = X10 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f10283,plain,
spl0_1256,
inference(avatar_split_clause,[],[f384,f10281]) ).
fof(f10281,plain,
( spl0_1256
<=> ! [X3] : c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f384,axiom,
! [X3] : c_0 = c_Divides_Oop_Amod(X3,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(f10279,plain,
spl0_1255,
inference(avatar_split_clause,[],[f313,f10277]) ).
fof(f313,axiom,
! [X0,X11] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_NatArith_Oof__nat(X11,X0),c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f10275,plain,
spl0_1254,
inference(avatar_split_clause,[],[f286,f10273]) ).
fof(f10273,plain,
( spl0_1254
<=> ! [X11,X24] : ~ c_less(c_IntDef_Oint(X11),c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f286,axiom,
! [X11,X24] : ~ c_less(c_IntDef_Oint(X11),c_uminus(c_IntDef_Oint(X24),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f10257,plain,
spl0_1253,
inference(avatar_split_clause,[],[f279,f10255]) ).
fof(f279,axiom,
! [X35] :
( ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X35) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f10253,plain,
spl0_1252,
inference(avatar_split_clause,[],[f270,f10251]) ).
fof(f10251,plain,
( spl0_1252
<=> ! [X11] :
( c_0 = X11
| ~ c_lessequals(c_IntDef_Oint(X11),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f270,axiom,
! [X11] :
( c_0 = X11
| ~ c_lessequals(c_IntDef_Oint(X11),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f10249,plain,
spl0_1251,
inference(avatar_split_clause,[],[f269,f10247]) ).
fof(f10247,plain,
( spl0_1251
<=> ! [X11,X24] :
( X11 = X24
| c_IntDef_Oint(X24) != c_IntDef_Oint(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f269,axiom,
! [X11,X24] :
( X11 = X24
| c_IntDef_Oint(X24) != c_IntDef_Oint(X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f10245,plain,
spl0_1250,
inference(avatar_split_clause,[],[f202,f10243]) ).
fof(f10243,plain,
( spl0_1250
<=> ! [X10] : c_GCD_Ogcd(c_Pair(X10,X10,tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f202,axiom,
! [X10] : c_GCD_Ogcd(c_Pair(X10,X10,tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f10241,plain,
spl0_1249,
inference(avatar_split_clause,[],[f192,f10239]) ).
fof(f10239,plain,
( spl0_1249
<=> ! [X10] : c_GCD_Ogcd(c_Pair(c_0,X10,tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f192,axiom,
! [X10] : c_GCD_Ogcd(c_Pair(c_0,X10,tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f10237,plain,
spl0_1248,
inference(avatar_split_clause,[],[f191,f10235]) ).
fof(f10235,plain,
( spl0_1248
<=> ! [X10] : c_GCD_Ogcd(c_Pair(X10,c_0,tc_nat,tc_nat)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f191,axiom,
! [X10] : c_GCD_Ogcd(c_Pair(X10,c_0,tc_nat,tc_nat)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f10233,plain,
spl0_1247,
inference(avatar_split_clause,[],[f71,f10231]) ).
fof(f10231,plain,
( spl0_1247
<=> ! [X0,X3] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X3,X0),tc_Datatype_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f71,axiom,
! [X3,X0] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X3,X0),tc_Datatype_Ooption(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f10229,plain,
spl0_1246,
inference(avatar_split_clause,[],[f65,f10227]) ).
fof(f10227,plain,
( spl0_1246
<=> ! [X13,X0] :
( c_Datatype_Ooption_ONone = X13
| c_Datatype_Oo2s(X13,X0) != c_emptyset ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f65,axiom,
! [X0,X13] :
( c_Datatype_Ooption_ONone = X13
| c_Datatype_Oo2s(X13,X0) != c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f10224,plain,
spl0_1245,
inference(avatar_split_clause,[],[f61,f10222]) ).
fof(f10222,plain,
( spl0_1245
<=> ! [X0,X12] : c_in(X12,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X0),X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f61,axiom,
! [X0,X12] : c_in(X12,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X12,X0),X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f10076,plain,
spl0_1244,
inference(avatar_split_clause,[],[f3122,f10074]) ).
fof(f10074,plain,
( spl0_1244
<=> ! [X24] :
( ~ c_Divides_Oop_Advd(X24,c_1,tc_nat)
| c_1 = X24 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f3122,plain,
! [X24] :
( ~ c_Divides_Oop_Advd(X24,c_1,tc_nat)
| c_1 = X24 ),
inference(forward_demodulation,[],[f3121,f2814]) ).
fof(f3121,plain,
! [X24] :
( c_1 = X24
| ~ c_Divides_Oop_Advd(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2945,f2814]) ).
fof(f2945,plain,
! [X24] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X24
| ~ c_Divides_Oop_Advd(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f121,f1438,f1438]) ).
fof(f121,axiom,
! [X24] :
( c_Suc(c_0) = X24
| ~ c_Divides_Oop_Advd(X24,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f10072,plain,
spl0_1243,
inference(avatar_split_clause,[],[f3036,f10070]) ).
fof(f10070,plain,
( spl0_1243
<=> ! [X0,X30] : c_emptyset = c_Relation_OImage(c_emptyset,X30,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f3036,plain,
! [X0,X30] : c_emptyset = c_Relation_OImage(c_emptyset,X30,X0,X0),
inference(forward_demodulation,[],[f2825,f1280]) ).
fof(f1280,axiom,
! [X0] : c_emptyset = c_Relation_Odiag(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2825,plain,
! [X0,X30] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X0),X30,X0,X0),
inference(definition_unfolding,[],[f1498,f1267]) ).
fof(f1498,axiom,
! [X0,X30] : c_emptyset = c_inter(c_emptyset,X30,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f10068,plain,
spl0_1242,
inference(avatar_split_clause,[],[f2829,f10066]) ).
fof(f10064,plain,
spl0_1241,
inference(avatar_split_clause,[],[f2827,f10061]) ).
fof(f2827,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f1027,f1007]) ).
fof(f1027,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(f10059,plain,
spl0_1240,
inference(avatar_split_clause,[],[f2814,f10056]) ).
fof(f10056,plain,
( spl0_1240
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f10054,plain,
spl0_1239,
inference(avatar_split_clause,[],[f2810,f10052]) ).
fof(f10052,plain,
( spl0_1239
<=> ! [X24] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f2810,plain,
! [X24] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X24,tc_nat),tc_nat),
inference(definition_unfolding,[],[f917,f1438]) ).
fof(f917,axiom,
! [X24] : c_0 != c_Suc(X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
fof(f10050,plain,
spl0_1238,
inference(avatar_split_clause,[],[f1716,f10048]) ).
fof(f10048,plain,
( spl0_1238
<=> ! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f1716,axiom,
! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f10042,plain,
spl0_1237,
inference(avatar_split_clause,[],[f1711,f10040]) ).
fof(f10040,plain,
( spl0_1237
<=> ! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f1711,axiom,
! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f10038,plain,
spl0_1236,
inference(avatar_split_clause,[],[f1682,f10036]) ).
fof(f10036,plain,
( spl0_1236
<=> ! [X0,X26] : c_in(c_List_Olist_ONil,c_List_Olists(X26,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f1682,axiom,
! [X0,X26] : c_in(c_List_Olist_ONil,c_List_Olists(X26,X0),tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f10034,plain,
spl0_1235,
inference(avatar_split_clause,[],[f1666,f10032]) ).
fof(f10032,plain,
( spl0_1235
<=> ! [X0,X39] : c_in(c_List_Oset(X39,X0),c_Finite__Set_OFinites,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f1666,axiom,
! [X39,X0] : c_in(c_List_Oset(X39,X0),c_Finite__Set_OFinites,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f10030,plain,
spl0_1234,
inference(avatar_split_clause,[],[f1663,f10028]) ).
fof(f1663,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f10026,plain,
spl0_1233,
inference(avatar_split_clause,[],[f1662,f10024]) ).
fof(f1662,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f10022,plain,
spl0_1232,
inference(avatar_split_clause,[],[f1647,f10020]) ).
fof(f10020,plain,
( spl0_1232
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f1647,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X24,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f10018,plain,
spl0_1231,
inference(avatar_split_clause,[],[f1646,f10016]) ).
fof(f10016,plain,
( spl0_1231
<=> ! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f1646,axiom,
! [X9,X24] : c_Divides_Oop_Advd(X9,c_times(X9,X24,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f10014,plain,
spl0_1230,
inference(avatar_split_clause,[],[f1599,f10012]) ).
fof(f10012,plain,
( spl0_1230
<=> ! [X16,X0] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f1599,axiom,
! [X0,X16] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f10010,plain,
spl0_1229,
inference(avatar_split_clause,[],[f1578,f10008]) ).
fof(f1578,axiom,
! [X0,X26,X12] : c_in(X12,c_insert(X12,X26,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f10006,plain,
spl0_1228,
inference(avatar_split_clause,[],[f1562,f10004]) ).
fof(f10004,plain,
( spl0_1228
<=> ! [X0,X26] : c_emptyset = c_minus(c_emptyset,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f1562,axiom,
! [X0,X26] : c_emptyset = c_minus(c_emptyset,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f10002,plain,
spl0_1227,
inference(avatar_split_clause,[],[f1542,f10000]) ).
fof(f10000,plain,
( spl0_1227
<=> ! [X0,X10] : c_Union(c_Pow(X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f1542,axiom,
! [X10,X0] : c_Union(c_Pow(X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f9998,plain,
spl0_1226,
inference(avatar_split_clause,[],[f1484,f9996]) ).
fof(f9996,plain,
( spl0_1226
<=> ! [X0,X10] : c_minus(X10,c_emptyset,tc_set(X0)) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f1484,axiom,
! [X10,X0] : c_minus(X10,c_emptyset,tc_set(X0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f9994,plain,
spl0_1225,
inference(avatar_split_clause,[],[f1482,f9992]) ).
fof(f1482,axiom,
! [X0,X26] : c_emptyset = c_minus(X26,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f9990,plain,
spl0_1224,
inference(avatar_split_clause,[],[f1481,f9988]) ).
fof(f9988,plain,
( spl0_1224
<=> ! [X0,X26] : c_emptyset = c_minus(X26,c_UNIV,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f1481,axiom,
! [X0,X26] : c_emptyset = c_minus(X26,c_UNIV,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f9986,plain,
spl0_1223,
inference(avatar_split_clause,[],[f1443,f9984]) ).
fof(f9984,plain,
( spl0_1223
<=> ! [X10] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X10,tc_nat),tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f1443,axiom,
! [X10] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X10,tc_nat),tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f9982,plain,
spl0_1222,
inference(avatar_split_clause,[],[f1288,f9980]) ).
fof(f1288,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_1 = c_HOL_Oabs(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f9978,plain,
spl0_1221,
inference(avatar_split_clause,[],[f1268,f9976]) ).
fof(f9976,plain,
( spl0_1221
<=> ! [X77,X0,X16] : c_emptyset = c_Relation_OImage(X77,c_emptyset,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f1268,axiom,
! [X0,X16,X77] : c_emptyset = c_Relation_OImage(X77,c_emptyset,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f9974,plain,
spl0_1220,
inference(avatar_split_clause,[],[f1266,f9972]) ).
fof(f9972,plain,
( spl0_1220
<=> ! [X0,X10] : c_Relation_OImage(c_Relation_OId,X10,X0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f1266,axiom,
! [X10,X0] : c_Relation_OImage(c_Relation_OId,X10,X0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f9970,plain,
spl0_1219,
inference(avatar_split_clause,[],[f1137,f9968]) ).
fof(f1137,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Opprt(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f9966,plain,
spl0_1218,
inference(avatar_split_clause,[],[f1132,f9964]) ).
fof(f1132,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(X0)
| c_0 = c_OrderedGroup_Onprt(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f9958,plain,
spl0_1217,
inference(avatar_split_clause,[],[f1120,f9956]) ).
fof(f1120,axiom,
! [X0] :
( ~ class_OrderedGroup_Oab__group__add(X0)
| c_0 = c_uminus(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
fof(f9954,plain,
spl0_1216,
inference(avatar_split_clause,[],[f1070,f9952]) ).
fof(f1070,axiom,
! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X0)
| c_0 = c_HOL_Oabs(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f9950,plain,
spl0_1215,
inference(avatar_split_clause,[],[f1063,f9948]) ).
fof(f1063,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f9946,plain,
spl0_1214,
inference(avatar_split_clause,[],[f1056,f9944]) ).
fof(f9944,plain,
( spl0_1214
<=> ! [X0,X28,X10] : c_Numeral_Obit_Obit__rec(X28,X10,c_Numeral_Obit_OB1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f1056,axiom,
! [X28,X10,X0] : c_Numeral_Obit_Obit__rec(X28,X10,c_Numeral_Obit_OB1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f9942,plain,
spl0_1213,
inference(avatar_split_clause,[],[f1055,f9940]) ).
fof(f9940,plain,
( spl0_1213
<=> ! [X0,X27,X10] : c_Numeral_Obit_Obit__rec(X10,X27,c_Numeral_Obit_OB0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f1055,axiom,
! [X10,X0,X27] : c_Numeral_Obit_Obit__rec(X10,X27,c_Numeral_Obit_OB0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f9938,plain,
spl0_1212,
inference(avatar_split_clause,[],[f1052,f9936]) ).
fof(f9936,plain,
( spl0_1212
<=> ! [X0,X28,X10] : c_Numeral_Obit_Obit__case(X28,X10,c_Numeral_Obit_OB1,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f1052,axiom,
! [X28,X10,X0] : c_Numeral_Obit_Obit__case(X28,X10,c_Numeral_Obit_OB1,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f9934,plain,
spl0_1211,
inference(avatar_split_clause,[],[f1051,f9932]) ).
fof(f9932,plain,
( spl0_1211
<=> ! [X0,X27,X10] : c_Numeral_Obit_Obit__case(X10,X27,c_Numeral_Obit_OB0,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f1051,axiom,
! [X10,X0,X27] : c_Numeral_Obit_Obit__case(X10,X27,c_Numeral_Obit_OB0,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f9930,plain,
spl0_1210,
inference(avatar_split_clause,[],[f1038,f9928]) ).
fof(f9928,plain,
( spl0_1210
<=> ! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f1038,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f9926,plain,
spl0_1209,
inference(avatar_split_clause,[],[f1037,f9924]) ).
fof(f1037,axiom,
! [X0] :
( ~ class_Numeral_Onumber__ring(X0)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X0),X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f9922,plain,
spl0_1208,
inference(avatar_split_clause,[],[f983,f9920]) ).
fof(f9920,plain,
( spl0_1208
<=> ! [X11] :
( c_0 = X11
| c_less(c_0,X11,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f983,axiom,
! [X11] :
( c_0 = X11
| c_less(c_0,X11,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f9918,plain,
spl0_1207,
inference(avatar_split_clause,[],[f982,f9916]) ).
fof(f9916,plain,
( spl0_1207
<=> ! [X50,X23] : ~ c_less(c_plus(X50,X23,tc_nat),X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f982,axiom,
! [X50,X23] : ~ c_less(c_plus(X50,X23,tc_nat),X23,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f9914,plain,
spl0_1206,
inference(avatar_split_clause,[],[f981,f9912]) ).
fof(f9912,plain,
( spl0_1206
<=> ! [X50,X23] : ~ c_less(c_plus(X23,X50,tc_nat),X23,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f981,axiom,
! [X50,X23] : ~ c_less(c_plus(X23,X50,tc_nat),X23,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f9910,plain,
spl0_1205,
inference(avatar_split_clause,[],[f942,f9908]) ).
fof(f9908,plain,
( spl0_1205
<=> ! [X11] :
( c_0 = X11
| ~ c_less(X11,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f942,axiom,
! [X11] :
( c_0 = X11
| ~ c_less(X11,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f9906,plain,
spl0_1204,
inference(avatar_split_clause,[],[f936,f9904]) ).
fof(f9904,plain,
( spl0_1204
<=> ! [X23] :
( c_0 = X23
| ~ c_lessequals(X23,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f936,axiom,
! [X23] :
( c_0 = X23
| ~ c_lessequals(X23,c_0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f9902,plain,
spl0_1203,
inference(avatar_split_clause,[],[f934,f9900]) ).
fof(f9900,plain,
( spl0_1203
<=> ! [X11,X24] : c_lessequals(c_minus(X24,X11,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f934,axiom,
! [X11,X24] : c_lessequals(c_minus(X24,X11,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f9898,plain,
spl0_1202,
inference(avatar_split_clause,[],[f702,f9896]) ).
fof(f702,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_1 = c_NatArith_Oof__nat(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f9894,plain,
spl0_1201,
inference(avatar_split_clause,[],[f698,f9892]) ).
fof(f698,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_0 = c_NatArith_Oof__nat(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
fof(f9890,plain,
spl0_1200,
inference(avatar_split_clause,[],[f684,f9888]) ).
fof(f9888,plain,
( spl0_1200
<=> ! [X16,X0,X40] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X40,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f684,axiom,
! [X40,X0,X16] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X40,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f9886,plain,
spl0_1199,
inference(avatar_split_clause,[],[f682,f9884]) ).
fof(f9884,plain,
( spl0_1199
<=> ! [X39,X14,X74] : c_List_Olist_ONil = c_List_Ozip(X39,c_List_Olist_ONil,X14,X74) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f682,axiom,
! [X39,X14,X74] : c_List_Olist_ONil = c_List_Ozip(X39,c_List_Olist_ONil,X14,X74),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f9882,plain,
spl0_1198,
inference(avatar_split_clause,[],[f626,f9880]) ).
fof(f9880,plain,
( spl0_1198
<=> ! [X0,X10] : c_List_Orev(c_List_Orev(X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f626,axiom,
! [X10,X0] : c_List_Orev(c_List_Orev(X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f9877,plain,
spl0_1197,
inference(avatar_split_clause,[],[f605,f9875]) ).
fof(f9875,plain,
( spl0_1197
<=> ! [X0,X12,X40] : c_List_Oop_Amem(X12,c_List_Olist_OCons(X12,X40,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f605,axiom,
! [X40,X0,X12] : c_List_Oop_Amem(X12,c_List_Olist_OCons(X12,X40,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f9873,plain,
spl0_1196,
inference(avatar_split_clause,[],[f525,f9871]) ).
fof(f9871,plain,
( spl0_1196
<=> ! [X34,X23,X14] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X23,X34,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f525,axiom,
! [X14,X34,X23] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X23,X34,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f9869,plain,
spl0_1195,
inference(avatar_split_clause,[],[f436,f9867]) ).
fof(f9867,plain,
( spl0_1195
<=> ! [X45,X46] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X45,X46),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f436,axiom,
! [X46,X45] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X45,X46),tc_List_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f9865,plain,
spl0_1194,
inference(avatar_split_clause,[],[f372,f9863]) ).
fof(f372,axiom,
! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f9861,plain,
spl0_1193,
inference(avatar_split_clause,[],[f295,f9859]) ).
fof(f295,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_1 = c_IntDef_Oof__int(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f9857,plain,
spl0_1192,
inference(avatar_split_clause,[],[f290,f9855]) ).
fof(f290,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| c_0 = c_IntDef_Oof__int(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
fof(f9853,plain,
spl0_1191,
inference(avatar_split_clause,[],[f281,f9851]) ).
fof(f281,axiom,
! [X11] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X11),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f9849,plain,
spl0_1190,
inference(avatar_split_clause,[],[f267,f9847]) ).
fof(f9847,plain,
( spl0_1190
<=> ! [X11] :
( c_0 = X11
| c_0 != c_IntDef_Oint(X11) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f267,axiom,
! [X11] :
( c_0 = X11
| c_0 != c_IntDef_Oint(X11) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f9845,plain,
spl0_1189,
inference(avatar_split_clause,[],[f261,f9843]) ).
fof(f261,axiom,
! [X24] : c_IntDef_Oint(X24) = c_HOL_Oabs(c_IntDef_Oint(X24),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f9841,plain,
spl0_1188,
inference(avatar_split_clause,[],[f147,f9839]) ).
fof(f9839,plain,
( spl0_1188
<=> ! [X0,X28,X10] : c_Extraction_Osumbool_Osumbool__rec(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f147,axiom,
! [X28,X10,X0] : c_Extraction_Osumbool_Osumbool__rec(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f9832,plain,
spl0_1187,
inference(avatar_split_clause,[],[f146,f9830]) ).
fof(f9830,plain,
( spl0_1187
<=> ! [X0,X27,X10] : c_Extraction_Osumbool_Osumbool__rec(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f146,axiom,
! [X10,X0,X27] : c_Extraction_Osumbool_Osumbool__rec(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f9828,plain,
spl0_1186,
inference(avatar_split_clause,[],[f143,f9826]) ).
fof(f9826,plain,
( spl0_1186
<=> ! [X0,X28,X10] : c_Extraction_Osumbool_Osumbool__case(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f143,axiom,
! [X28,X10,X0] : c_Extraction_Osumbool_Osumbool__case(X28,X10,c_Extraction_Osumbool_ORight,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f9824,plain,
spl0_1185,
inference(avatar_split_clause,[],[f142,f9822]) ).
fof(f9822,plain,
( spl0_1185
<=> ! [X0,X27,X10] : c_Extraction_Osumbool_Osumbool__case(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f142,axiom,
! [X10,X0,X27] : c_Extraction_Osumbool_Osumbool__case(X10,X27,c_Extraction_Osumbool_OLeft,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f9820,plain,
spl0_1184,
inference(avatar_split_clause,[],[f119,f9818]) ).
fof(f9818,plain,
( spl0_1184
<=> ! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f119,axiom,
! [X24] :
( c_0 = X24
| ~ c_Divides_Oop_Advd(c_0,X24,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f9816,plain,
spl0_1183,
inference(avatar_split_clause,[],[f109,f9814]) ).
fof(f109,axiom,
! [X11,X24] : c_lessequals(c_div(X24,X11,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f9812,plain,
spl0_1182,
inference(avatar_split_clause,[],[f96,f9810]) ).
fof(f9810,plain,
( spl0_1182
<=> ! [X16,X0,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X17,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f96,axiom,
! [X0,X16,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X17,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f9808,plain,
spl0_1181,
inference(avatar_split_clause,[],[f75,f9806]) ).
fof(f9806,plain,
( spl0_1181
<=> ! [X0,X10] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X10,X0),X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f75,axiom,
! [X10,X0] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X10,X0),X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f9651,plain,
( spl0_1180
| ~ spl0_1
| ~ spl0_650 ),
inference(avatar_split_clause,[],[f7896,f5949,f3226,f9648]) ).
fof(f9648,plain,
( spl0_1180
<=> class_Ring__and__Field_Osemiring__1__cancel(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f5949,plain,
( spl0_650
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f7896,plain,
( class_Ring__and__Field_Osemiring__1__cancel(t_b)
| ~ spl0_1
| ~ spl0_650 ),
inference(resolution,[],[f5950,f3228]) ).
fof(f5950,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) )
| ~ spl0_650 ),
inference(avatar_component_clause,[],[f5949]) ).
fof(f9529,plain,
( spl0_1179
| ~ spl0_1
| ~ spl0_649 ),
inference(avatar_split_clause,[],[f7894,f5945,f3226,f9526]) ).
fof(f5945,plain,
( spl0_649
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f7894,plain,
( class_OrderedGroup_Ocomm__monoid__mult(t_b)
| ~ spl0_1
| ~ spl0_649 ),
inference(resolution,[],[f5946,f3228]) ).
fof(f5946,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) )
| ~ spl0_649 ),
inference(avatar_component_clause,[],[f5945]) ).
fof(f9479,plain,
( spl0_1178
| ~ spl0_1
| ~ spl0_648 ),
inference(avatar_split_clause,[],[f7892,f5941,f3226,f9476]) ).
fof(f9476,plain,
( spl0_1178
<=> class_Ring__and__Field_Ocomm__semiring__1(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f5941,plain,
( spl0_648
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f7892,plain,
( class_Ring__and__Field_Ocomm__semiring__1(t_b)
| ~ spl0_1
| ~ spl0_648 ),
inference(resolution,[],[f5942,f3228]) ).
fof(f5942,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) )
| ~ spl0_648 ),
inference(avatar_component_clause,[],[f5941]) ).
fof(f9474,plain,
spl0_1177,
inference(avatar_split_clause,[],[f3046,f9472]) ).
fof(f3046,plain,
! [X10] : c_div(X10,c_1,tc_nat) = X10,
inference(forward_demodulation,[],[f2840,f2814]) ).
fof(f2840,plain,
! [X10] : c_div(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X10,
inference(definition_unfolding,[],[f108,f1438]) ).
fof(f108,axiom,
! [X10] : c_div(X10,c_Suc(c_0),tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f9470,plain,
spl0_1176,
inference(avatar_split_clause,[],[f3044,f9467]) ).
fof(f9467,plain,
( spl0_1176
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f3044,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2837,f2814]) ).
fof(f2837,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,[],[f988,f1438]) ).
fof(f988,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(f9465,plain,
spl0_1175,
inference(avatar_split_clause,[],[f3042,f9463]) ).
fof(f9463,plain,
( spl0_1175
<=> ! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f3042,plain,
! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_1,tc_nat),
inference(forward_demodulation,[],[f2836,f2814]) ).
fof(f2836,plain,
! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f125,f1438]) ).
fof(f125,axiom,
! [X24] : c_0 = c_Divides_Oop_Amod(X24,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f9461,plain,
spl0_1174,
inference(avatar_split_clause,[],[f3041,f9458]) ).
fof(f9458,plain,
( spl0_1174
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f3041,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f761,f1050]) ).
fof(f761,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(f9456,plain,
spl0_1173,
inference(avatar_split_clause,[],[f3039,f9454]) ).
fof(f9454,plain,
( spl0_1173
<=> ! [X14,X10] : c_append(c_List_Olist_ONil,X10,X14) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f3039,plain,
! [X10,X14] : c_append(c_List_Olist_ONil,X10,X14) = X10,
inference(forward_demodulation,[],[f2831,f408]) ).
fof(f408,axiom,
! [X0] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
fof(f2831,plain,
! [X10,X14] : c_append(c_List_Orev(c_List_Olist_ONil,X14),X10,X14) = X10,
inference(definition_unfolding,[],[f480,f479]) ).
fof(f480,axiom,
! [X10,X14] : c_List_Oitrev(c_List_Olist_ONil,X10,X14) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f9452,plain,
spl0_1172,
inference(avatar_split_clause,[],[f3037,f9449]) ).
fof(f9449,plain,
( spl0_1172
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f3037,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2828,f1050]) ).
fof(f2828,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f1019,f1023]) ).
fof(f1019,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(f9447,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1689,f9445]) ).
fof(f9445,plain,
( spl0_1171
<=> ! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1689,axiom,
! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| c_lessequals(X12,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f9443,plain,
spl0_1170,
inference(avatar_split_clause,[],[f1567,f9441]) ).
fof(f1567,axiom,
! [X3,X0,X26] : c_emptyset != c_insert(X3,X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
fof(f9439,plain,
spl0_1169,
inference(avatar_split_clause,[],[f1533,f9437]) ).
fof(f9437,plain,
( spl0_1169
<=> ! [X0,X10] : c_union(X10,c_emptyset,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f1533,axiom,
! [X10,X0] : c_union(X10,c_emptyset,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f9435,plain,
spl0_1168,
inference(avatar_split_clause,[],[f1532,f9433]) ).
fof(f1532,axiom,
! [X10,X0] : c_union(c_emptyset,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f9431,plain,
( spl0_1167
| ~ spl0_1
| ~ spl0_647 ),
inference(avatar_split_clause,[],[f7890,f5937,f3226,f9428]) ).
fof(f5937,plain,
( spl0_647
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f7890,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(t_b)
| ~ spl0_1
| ~ spl0_647 ),
inference(resolution,[],[f5938,f3228]) ).
fof(f5938,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) )
| ~ spl0_647 ),
inference(avatar_component_clause,[],[f5937]) ).
fof(f9426,plain,
spl0_1166,
inference(avatar_split_clause,[],[f1528,f9424]) ).
fof(f9424,plain,
( spl0_1166
<=> ! [X0,X10] : c_union(X10,X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f1528,axiom,
! [X10,X0] : c_union(X10,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f9422,plain,
spl0_1165,
inference(avatar_split_clause,[],[f1527,f9420]) ).
fof(f9420,plain,
( spl0_1165
<=> ! [X0,X26] : c_UNIV = c_union(X26,c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f1527,axiom,
! [X0,X26] : c_UNIV = c_union(X26,c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f9418,plain,
spl0_1164,
inference(avatar_split_clause,[],[f1526,f9416]) ).
fof(f9416,plain,
( spl0_1164
<=> ! [X0,X30] : c_UNIV = c_union(c_UNIV,X30,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f1526,axiom,
! [X0,X30] : c_UNIV = c_union(c_UNIV,X30,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f9414,plain,
spl0_1163,
inference(avatar_split_clause,[],[f1474,f9412]) ).
fof(f9412,plain,
( spl0_1163
<=> ! [X0] : c_UNIV = c_uminus(c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f1474,axiom,
! [X0] : c_UNIV = c_uminus(c_emptyset,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f9410,plain,
spl0_1162,
inference(avatar_split_clause,[],[f1470,f9408]) ).
fof(f9408,plain,
( spl0_1162
<=> ! [X0] : c_emptyset = c_uminus(c_UNIV,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f1470,axiom,
! [X0] : c_emptyset = c_uminus(c_UNIV,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f9406,plain,
spl0_1161,
inference(avatar_split_clause,[],[f1405,f9404]) ).
fof(f9404,plain,
( spl0_1161
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f1405,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_lessequals(c_0,c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f9402,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1393,f9400]) ).
fof(f9400,plain,
( spl0_1160
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f1393,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| c_less(c_0,c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f9398,plain,
spl0_1159,
inference(avatar_split_clause,[],[f1388,f9396]) ).
fof(f9396,plain,
( spl0_1159
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f1388,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_less(c_1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f9394,plain,
spl0_1158,
inference(avatar_split_clause,[],[f1387,f9392]) ).
fof(f9392,plain,
( spl0_1158
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_1,c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f1387,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__semidom(X0)
| ~ c_lessequals(c_1,c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f9390,plain,
spl0_1157,
inference(avatar_split_clause,[],[f1275,f9388]) ).
fof(f9388,plain,
( spl0_1157
<=> ! [X0] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f1275,axiom,
! [X0] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f9386,plain,
( spl0_1156
| ~ spl0_1
| ~ spl0_646 ),
inference(avatar_split_clause,[],[f7888,f5933,f3226,f9383]) ).
fof(f9383,plain,
( spl0_1156
<=> class_Ring__and__Field_Oidom(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f5933,plain,
( spl0_646
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f7888,plain,
( class_Ring__and__Field_Oidom(t_b)
| ~ spl0_1
| ~ spl0_646 ),
inference(resolution,[],[f5934,f3228]) ).
fof(f5934,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) )
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f5933]) ).
fof(f9381,plain,
spl0_1155,
inference(avatar_split_clause,[],[f1274,f9379]) ).
fof(f9379,plain,
( spl0_1155
<=> ! [X0,X16] : c_emptyset = c_Relation_ORange(c_emptyset,X16,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f1274,axiom,
! [X0,X16] : c_emptyset = c_Relation_ORange(c_emptyset,X16,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f9377,plain,
spl0_1154,
inference(avatar_split_clause,[],[f1272,f9375]) ).
fof(f9375,plain,
( spl0_1154
<=> ! [X0] : c_UNIV = c_Relation_ORange(c_Relation_OId,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f1272,axiom,
! [X0] : c_UNIV = c_Relation_ORange(c_Relation_OId,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f9373,plain,
spl0_1153,
inference(avatar_split_clause,[],[f1264,f9371]) ).
fof(f9371,plain,
( spl0_1153
<=> ! [X16,X0] : c_emptyset = c_Relation_ODomain(c_emptyset,X0,X16) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f1264,axiom,
! [X0,X16] : c_emptyset = c_Relation_ODomain(c_emptyset,X0,X16),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f9369,plain,
spl0_1152,
inference(avatar_split_clause,[],[f1262,f9367]) ).
fof(f9367,plain,
( spl0_1152
<=> ! [X0] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f1262,axiom,
! [X0] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f9365,plain,
spl0_1151,
inference(avatar_split_clause,[],[f1238,f9363]) ).
fof(f9363,plain,
( spl0_1151
<=> ! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f1238,axiom,
! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f9361,plain,
spl0_1150,
inference(avatar_split_clause,[],[f1163,f9359]) ).
fof(f9359,plain,
( spl0_1150
<=> ! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X12,X12,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f1163,axiom,
! [X0,X12] :
( ~ class_Orderings_Oorder(X0)
| ~ c_less(X12,X12,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f9357,plain,
spl0_1149,
inference(avatar_split_clause,[],[f1050,f9354]) ).
fof(f9352,plain,
spl0_1148,
inference(avatar_split_clause,[],[f996,f9350]) ).
fof(f9350,plain,
( spl0_1148
<=> ! [X10] : c_minus(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f996,axiom,
! [X10] : c_minus(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f9348,plain,
spl0_1147,
inference(avatar_split_clause,[],[f994,f9346]) ).
fof(f994,axiom,
! [X10] : c_plus(c_0,X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f9344,plain,
spl0_1146,
inference(avatar_split_clause,[],[f992,f9342]) ).
fof(f9342,plain,
( spl0_1146
<=> ! [X11] : c_0 = c_times(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f992,axiom,
! [X11] : c_0 = c_times(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f9340,plain,
( spl0_1145
| ~ spl0_1
| ~ spl0_645 ),
inference(avatar_split_clause,[],[f7886,f5929,f3226,f9337]) ).
fof(f9337,plain,
( spl0_1145
<=> class_Ring__and__Field_Oaxclass__no__zero__divisors(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f5929,plain,
( spl0_645
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f7886,plain,
( class_Ring__and__Field_Oaxclass__no__zero__divisors(t_b)
| ~ spl0_1
| ~ spl0_645 ),
inference(resolution,[],[f5930,f3228]) ).
fof(f5930,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) )
| ~ spl0_645 ),
inference(avatar_component_clause,[],[f5929]) ).
fof(f9335,plain,
spl0_1144,
inference(avatar_split_clause,[],[f950,f9333]) ).
fof(f9333,plain,
( spl0_1144
<=> ! [X24] : c_0 = c_times(X24,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f950,axiom,
! [X24] : c_0 = c_times(X24,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f9331,plain,
spl0_1143,
inference(avatar_split_clause,[],[f948,f9329]) ).
fof(f9329,plain,
( spl0_1143
<=> ! [X11] : c_0 = c_Orderings_Omin(X11,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f948,axiom,
! [X11] : c_0 = c_Orderings_Omin(X11,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f9327,plain,
spl0_1142,
inference(avatar_split_clause,[],[f947,f9325]) ).
fof(f9325,plain,
( spl0_1142
<=> ! [X11] : c_0 = c_Orderings_Omin(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f947,axiom,
! [X11] : c_0 = c_Orderings_Omin(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f9323,plain,
spl0_1141,
inference(avatar_split_clause,[],[f945,f9321]) ).
fof(f9321,plain,
( spl0_1141
<=> ! [X10] : c_Orderings_Omax(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f945,axiom,
! [X10] : c_Orderings_Omax(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f9319,plain,
spl0_1140,
inference(avatar_split_clause,[],[f944,f9317]) ).
fof(f9317,plain,
( spl0_1140
<=> ! [X10] : c_Orderings_Omax(c_0,X10,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f944,axiom,
! [X10] : c_Orderings_Omax(c_0,X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f9315,plain,
spl0_1139,
inference(avatar_split_clause,[],[f935,f9313]) ).
fof(f9313,plain,
( spl0_1139
<=> ! [X24] : c_0 = c_minus(X24,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f935,axiom,
! [X24] : c_0 = c_minus(X24,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f9311,plain,
spl0_1138,
inference(avatar_split_clause,[],[f928,f9309]) ).
fof(f928,axiom,
! [X11] : c_0 = c_minus(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f9307,plain,
spl0_1137,
inference(avatar_split_clause,[],[f920,f9305]) ).
fof(f920,axiom,
! [X10] : c_plus(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f9303,plain,
spl0_1136,
inference(avatar_split_clause,[],[f681,f9301]) ).
fof(f9301,plain,
( spl0_1136
<=> ! [X73,X0,X12] : c_List_Olist_OCons(X12,X73,X0) != X73 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f681,axiom,
! [X73,X0,X12] : c_List_Olist_OCons(X12,X73,X0) != X73,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
fof(f9299,plain,
spl0_1135,
inference(avatar_split_clause,[],[f657,f9297]) ).
fof(f9297,plain,
( spl0_1135
<=> ! [X0,X26] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X26,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f657,axiom,
! [X0,X26] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X26,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f9295,plain,
( spl0_1134
| ~ spl0_1
| ~ spl0_644 ),
inference(avatar_split_clause,[],[f7884,f5925,f3226,f9292]) ).
fof(f5925,plain,
( spl0_644
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f7884,plain,
( class_Ring__and__Field_Oordered__semidom(t_b)
| ~ spl0_1
| ~ spl0_644 ),
inference(resolution,[],[f5926,f3228]) ).
fof(f5926,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) )
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f5925]) ).
fof(f9290,plain,
spl0_1133,
inference(avatar_split_clause,[],[f656,f9288]) ).
fof(f9288,plain,
( spl0_1133
<=> ! [X0,X39] : c_List_Olist_ONil = c_List_Osublist(X39,c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f656,axiom,
! [X39,X0] : c_List_Olist_ONil = c_List_Osublist(X39,c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f9286,plain,
spl0_1132,
inference(avatar_split_clause,[],[f635,f9284]) ).
fof(f9284,plain,
( spl0_1132
<=> ! [X0,X11] : c_List_Olist_ONil = c_List_Orotate(X11,c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f635,axiom,
! [X0,X11] : c_List_Olist_ONil = c_List_Orotate(X11,c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f9282,plain,
spl0_1131,
inference(avatar_split_clause,[],[f616,f9280]) ).
fof(f616,axiom,
! [X14,X12] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X12,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f9278,plain,
spl0_1130,
inference(avatar_split_clause,[],[f613,f9276]) ).
fof(f9276,plain,
( spl0_1130
<=> ! [X12,X14] : c_List_Olist_ONil = c_List_Oremove1(X12,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f613,axiom,
! [X14,X12] : c_List_Olist_ONil = c_List_Oremove1(X12,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f9274,plain,
spl0_1129,
inference(avatar_split_clause,[],[f601,f9272]) ).
fof(f9272,plain,
( spl0_1129
<=> ! [X12,X39,X14] : ~ c_List_Onull(c_List_Olist_OCons(X12,X39,X14),X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f601,axiom,
! [X39,X14,X12] : ~ c_List_Onull(c_List_Olist_OCons(X12,X39,X14),X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f9270,plain,
spl0_1128,
inference(avatar_split_clause,[],[f522,f9268]) ).
fof(f9268,plain,
( spl0_1128
<=> ! [X56,X14] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X56,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f522,axiom,
! [X56,X14] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X56,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f9266,plain,
spl0_1127,
inference(avatar_split_clause,[],[f518,f9264]) ).
fof(f9264,plain,
( spl0_1127
<=> ! [X54,X0,X15] : c_List_Olist_ONil != c_List_Olist_OCons(X15,X54,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f518,axiom,
! [X0,X54,X15] : c_List_Olist_ONil != c_List_Olist_OCons(X15,X54,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f9262,plain,
spl0_1126,
inference(avatar_split_clause,[],[f509,f9260]) ).
fof(f9260,plain,
( spl0_1126
<=> ! [X19,X14] : c_emptyset = c_List_Olexn(X19,c_0,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f509,axiom,
! [X19,X14] : c_emptyset = c_List_Olexn(X19,c_0,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f9258,plain,
spl0_1125,
inference(avatar_split_clause,[],[f492,f9256]) ).
fof(f9256,plain,
( spl0_1125
<=> ! [X0] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f492,axiom,
! [X0] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f9254,plain,
spl0_1124,
inference(avatar_split_clause,[],[f463,f9252]) ).
fof(f9252,plain,
( spl0_1124
<=> ! [X0,X10] : c_List_Odrop(c_0,X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f463,axiom,
! [X10,X0] : c_List_Odrop(c_0,X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f9250,plain,
( spl0_1123
| ~ spl0_1
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f7882,f5921,f3226,f9247]) ).
fof(f5921,plain,
( spl0_643
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f7882,plain,
( class_OrderedGroup_Opordered__ab__group__add(t_b)
| ~ spl0_1
| ~ spl0_643 ),
inference(resolution,[],[f5922,f3228]) ).
fof(f5922,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) )
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f5921]) ).
fof(f9245,plain,
spl0_1122,
inference(avatar_split_clause,[],[f462,f9243]) ).
fof(f9243,plain,
( spl0_1122
<=> ! [X11,X14] : c_List_Olist_ONil = c_List_Odrop(X11,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f462,axiom,
! [X11,X14] : c_List_Olist_ONil = c_List_Odrop(X11,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f9241,plain,
spl0_1121,
inference(avatar_split_clause,[],[f428,f9239]) ).
fof(f9239,plain,
( spl0_1121
<=> ! [X0,X39] : c_append(X39,c_List_Olist_ONil,X0) = X39 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f428,axiom,
! [X39,X0] : c_append(X39,c_List_Olist_ONil,X0) = X39,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
fof(f9237,plain,
spl0_1120,
inference(avatar_split_clause,[],[f388,f9235]) ).
fof(f9235,plain,
( spl0_1120
<=> ! [X1] : c_0 = c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f388,axiom,
! [X1] : c_0 = c_Divides_Oop_Amod(c_0,X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f9233,plain,
spl0_1119,
inference(avatar_split_clause,[],[f385,f9231]) ).
fof(f9231,plain,
( spl0_1119
<=> ! [X3] : c_0 = c_Divides_Oop_Amod(X3,X3,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f385,axiom,
! [X3] : c_0 = c_Divides_Oop_Amod(X3,X3,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f9229,plain,
spl0_1118,
inference(avatar_split_clause,[],[f383,f9227]) ).
fof(f9227,plain,
( spl0_1118
<=> ! [X3] : c_0 = c_Divides_Oop_Amod(X3,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f383,axiom,
! [X3] : c_0 = c_Divides_Oop_Amod(X3,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f9225,plain,
spl0_1117,
inference(avatar_split_clause,[],[f368,f9223]) ).
fof(f9223,plain,
( spl0_1117
<=> ! [X1] : c_0 = c_div(c_0,X1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f368,axiom,
! [X1] : c_0 = c_div(c_0,X1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f9221,plain,
spl0_1116,
inference(avatar_split_clause,[],[f360,f9219]) ).
fof(f9219,plain,
( spl0_1116
<=> ! [X10] : c_div(X10,c_1,tc_IntDef_Oint) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f360,axiom,
! [X10] : c_div(X10,c_1,tc_IntDef_Oint) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f9217,plain,
spl0_1115,
inference(avatar_split_clause,[],[f358,f9215]) ).
fof(f9215,plain,
( spl0_1115
<=> ! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f358,axiom,
! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f9213,plain,
spl0_1114,
inference(avatar_split_clause,[],[f326,f9211]) ).
fof(f9211,plain,
( spl0_1114
<=> ! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_IntDef_Oint) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f326,axiom,
! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_IntDef_Oint) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f9209,plain,
spl0_1113,
inference(avatar_split_clause,[],[f258,f9207]) ).
fof(f9207,plain,
( spl0_1113
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_1,c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f258,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_1,c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f9202,plain,
spl0_1112,
inference(avatar_split_clause,[],[f257,f9200]) ).
fof(f9200,plain,
( spl0_1112
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_0,c_IntDef_ONats,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f257,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| c_in(c_0,c_IntDef_ONats,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f9198,plain,
spl0_1111,
inference(avatar_split_clause,[],[f252,f9196]) ).
fof(f9196,plain,
( spl0_1111
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_1,c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f252,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_1,c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f9194,plain,
spl0_1110,
inference(avatar_split_clause,[],[f251,f9192]) ).
fof(f9192,plain,
( spl0_1110
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_0,c_IntDef_OInts,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f251,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X0)
| c_in(c_0,c_IntDef_OInts,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f9190,plain,
spl0_1109,
inference(avatar_split_clause,[],[f244,f9187]) ).
fof(f9187,plain,
( spl0_1109
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f244,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(f9185,plain,
spl0_1108,
inference(avatar_split_clause,[],[f141,f9183]) ).
fof(f9183,plain,
( spl0_1108
<=> ! [X0,X19] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X19,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f141,axiom,
! [X0,X19] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X19,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
fof(f9181,plain,
spl0_1107,
inference(avatar_split_clause,[],[f135,f9179]) ).
fof(f9179,plain,
( spl0_1107
<=> ! [X11] : c_0 = c_Divides_Oop_Amod(X11,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f135,axiom,
! [X11] : c_0 = c_Divides_Oop_Amod(X11,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f9177,plain,
spl0_1106,
inference(avatar_split_clause,[],[f124,f9175]) ).
fof(f9175,plain,
( spl0_1106
<=> ! [X24] : c_0 = c_Divides_Oop_Amod(c_0,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f124,axiom,
! [X24] : c_0 = c_Divides_Oop_Amod(c_0,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f9173,plain,
spl0_1105,
inference(avatar_split_clause,[],[f107,f9171]) ).
fof(f9171,plain,
( spl0_1105
<=> ! [X24] : c_0 = c_div(c_0,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f107,axiom,
! [X24] : c_0 = c_div(c_0,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f9169,plain,
spl0_1104,
inference(avatar_split_clause,[],[f106,f9167]) ).
fof(f9167,plain,
( spl0_1104
<=> ! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_nat) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f106,axiom,
! [X10] : c_Divides_Oop_Amod(X10,c_0,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f9165,plain,
spl0_1103,
inference(avatar_split_clause,[],[f105,f9163]) ).
fof(f9163,plain,
( spl0_1103
<=> ! [X3] : c_0 = c_div(X3,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f105,axiom,
! [X3] : c_0 = c_div(X3,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f9161,plain,
( spl0_1102
| ~ spl0_1
| ~ spl0_642 ),
inference(avatar_split_clause,[],[f7875,f5917,f3226,f9158]) ).
fof(f5917,plain,
( spl0_642
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f7875,plain,
( class_OrderedGroup_Olordered__ab__group(t_b)
| ~ spl0_1
| ~ spl0_642 ),
inference(resolution,[],[f5918,f3228]) ).
fof(f5918,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) )
| ~ spl0_642 ),
inference(avatar_component_clause,[],[f5917]) ).
fof(f9156,plain,
spl0_1101,
inference(avatar_split_clause,[],[f77,f9154]) ).
fof(f9154,plain,
( spl0_1101
<=> ! [X0,X10] : c_Datatype_Ounit_Ounit__rec(X10,c_Product__Type_OUnity,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f77,axiom,
! [X10,X0] : c_Datatype_Ounit_Ounit__rec(X10,c_Product__Type_OUnity,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f9152,plain,
spl0_1100,
inference(avatar_split_clause,[],[f76,f9150]) ).
fof(f9150,plain,
( spl0_1100
<=> ! [X0,X10] : c_Datatype_Ounit_Ounit__case(X10,c_Product__Type_OUnity,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f76,axiom,
! [X10,X0] : c_Datatype_Ounit_Ounit__case(X10,c_Product__Type_OUnity,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f9148,plain,
spl0_1099,
inference(avatar_split_clause,[],[f70,f9146]) ).
fof(f9146,plain,
( spl0_1099
<=> ! [X0] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f70,axiom,
! [X0] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f9144,plain,
spl0_1098,
inference(avatar_split_clause,[],[f42,f9142]) ).
fof(f42,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_9) ).
fof(f9140,plain,
spl0_1097,
inference(avatar_split_clause,[],[f41,f9138]) ).
fof(f41,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_8) ).
fof(f9136,plain,
spl0_1096,
inference(avatar_split_clause,[],[f40,f9134]) ).
fof(f40,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_7) ).
fof(f9132,plain,
spl0_1095,
inference(avatar_split_clause,[],[f39,f9130]) ).
fof(f9130,plain,
( spl0_1095
<=> ! [X8,X7] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f39,axiom,
! [X8,X7] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_6) ).
fof(f9128,plain,
spl0_1094,
inference(avatar_split_clause,[],[f38,f9126]) ).
fof(f9126,plain,
( spl0_1094
<=> ! [X8,X7] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f38,axiom,
! [X8,X7] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_5) ).
fof(f9124,plain,
spl0_1093,
inference(avatar_split_clause,[],[f37,f9122]) ).
fof(f9122,plain,
( spl0_1093
<=> ! [X8,X7] :
( ~ class_HOL_Ominus(X8)
| class_HOL_Ominus(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f37,axiom,
! [X8,X7] :
( ~ class_HOL_Ominus(X8)
| class_HOL_Ominus(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_4) ).
fof(f9120,plain,
spl0_1092,
inference(avatar_split_clause,[],[f36,f9118]) ).
fof(f9118,plain,
( spl0_1092
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f36,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_31) ).
fof(f9116,plain,
( spl0_1091
| ~ spl0_1
| ~ spl0_641 ),
inference(avatar_split_clause,[],[f7873,f5913,f3226,f9113]) ).
fof(f9113,plain,
( spl0_1091
<=> class_OrderedGroup_Olordered__ab__group__join(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f5913,plain,
( spl0_641
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f7873,plain,
( class_OrderedGroup_Olordered__ab__group__join(t_b)
| ~ spl0_1
| ~ spl0_641 ),
inference(resolution,[],[f5914,f3228]) ).
fof(f5914,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) )
| ~ spl0_641 ),
inference(avatar_component_clause,[],[f5913]) ).
fof(f9111,plain,
spl0_1090,
inference(avatar_split_clause,[],[f35,f9109]) ).
fof(f9109,plain,
( spl0_1090
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f35,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_30) ).
fof(f9107,plain,
spl0_1089,
inference(avatar_split_clause,[],[f34,f9105]) ).
fof(f9105,plain,
( spl0_1089
<=> ! [X8,X7] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f34,axiom,
! [X8,X7] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_3) ).
fof(f9103,plain,
spl0_1088,
inference(avatar_split_clause,[],[f33,f9101]) ).
fof(f9101,plain,
( spl0_1088
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring__1(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f33,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_29) ).
fof(f9099,plain,
spl0_1087,
inference(avatar_split_clause,[],[f32,f9097]) ).
fof(f9097,plain,
( spl0_1087
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f32,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_28) ).
fof(f9095,plain,
spl0_1086,
inference(avatar_split_clause,[],[f31,f9093]) ).
fof(f31,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_27) ).
fof(f9091,plain,
spl0_1085,
inference(avatar_split_clause,[],[f30,f9089]) ).
fof(f30,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_26) ).
fof(f9087,plain,
spl0_1084,
inference(avatar_split_clause,[],[f29,f9085]) ).
fof(f29,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oaxclass__0__neq__1(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_25) ).
fof(f9083,plain,
spl0_1083,
inference(avatar_split_clause,[],[f28,f9081]) ).
fof(f9081,plain,
( spl0_1083
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f28,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__ring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_24) ).
fof(f9079,plain,
spl0_1082,
inference(avatar_split_clause,[],[f27,f9077]) ).
fof(f9077,plain,
( spl0_1082
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f27,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_23) ).
fof(f9075,plain,
spl0_1081,
inference(avatar_split_clause,[],[f26,f9073]) ).
fof(f26,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Oring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_22) ).
fof(f9071,plain,
( spl0_1080
| ~ spl0_1
| ~ spl0_640 ),
inference(avatar_split_clause,[],[f7871,f5909,f3226,f9068]) ).
fof(f9068,plain,
( spl0_1080
<=> class_OrderedGroup_Olordered__ab__group__meet(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f5909,plain,
( spl0_640
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f7871,plain,
( class_OrderedGroup_Olordered__ab__group__meet(t_b)
| ~ spl0_1
| ~ spl0_640 ),
inference(resolution,[],[f5910,f3228]) ).
fof(f5910,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) )
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f5909]) ).
fof(f9066,plain,
spl0_1079,
inference(avatar_split_clause,[],[f25,f9064]) ).
fof(f25,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0__cancel(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_21) ).
fof(f9062,plain,
spl0_1078,
inference(avatar_split_clause,[],[f24,f9060]) ).
fof(f9060,plain,
( spl0_1078
<=> ! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f24,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring__0(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_20) ).
fof(f9058,plain,
spl0_1077,
inference(avatar_split_clause,[],[f23,f9056]) ).
fof(f9056,plain,
( spl0_1077
<=> ! [X8,X7] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f23,axiom,
! [X8,X7] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_2) ).
fof(f9054,plain,
spl0_1076,
inference(avatar_split_clause,[],[f22,f9052]) ).
fof(f22,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring__0(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_19) ).
fof(f9050,plain,
spl0_1075,
inference(avatar_split_clause,[],[f21,f9048]) ).
fof(f21,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Ocomm__semiring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_18) ).
fof(f9046,plain,
spl0_1074,
inference(avatar_split_clause,[],[f20,f9044]) ).
fof(f20,axiom,
! [X8,X7] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X8)
| class_Ring__and__Field_Osemiring(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_17) ).
fof(f9042,plain,
spl0_1073,
inference(avatar_split_clause,[],[f19,f9040]) ).
fof(f9040,plain,
( spl0_1073
<=> ! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_fun(X7,X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f19,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_16) ).
fof(f9038,plain,
spl0_1072,
inference(avatar_split_clause,[],[f18,f9036]) ).
fof(f18,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_15) ).
fof(f9034,plain,
spl0_1071,
inference(avatar_split_clause,[],[f17,f9032]) ).
fof(f17,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_14) ).
fof(f9030,plain,
spl0_1070,
inference(avatar_split_clause,[],[f16,f9028]) ).
fof(f16,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_13) ).
fof(f9026,plain,
( spl0_1069
| ~ spl0_1
| ~ spl0_639 ),
inference(avatar_split_clause,[],[f7869,f5905,f3226,f9023]) ).
fof(f5905,plain,
( spl0_639
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f7869,plain,
( class_OrderedGroup_Olordered__ab__group__abs(t_b)
| ~ spl0_1
| ~ spl0_639 ),
inference(resolution,[],[f5906,f3228]) ).
fof(f5906,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) )
| ~ spl0_639 ),
inference(avatar_component_clause,[],[f5905]) ).
fof(f9021,plain,
spl0_1068,
inference(avatar_split_clause,[],[f15,f9019]) ).
fof(f15,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Oab__group__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_12) ).
fof(f9017,plain,
spl0_1067,
inference(avatar_split_clause,[],[f14,f9015]) ).
fof(f14,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__ab__semigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_11) ).
fof(f9013,plain,
spl0_1066,
inference(avatar_split_clause,[],[f13,f9011]) ).
fof(f13,axiom,
! [X8,X7] :
( ~ class_OrderedGroup_Oab__group__add(X8)
| class_OrderedGroup_Ocancel__semigroup__add(tc_fun(X7,X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_10) ).
fof(f9009,plain,
( spl0_1065
| ~ spl0_1
| ~ spl0_638 ),
inference(avatar_split_clause,[],[f7867,f5901,f3226,f9006]) ).
fof(f9006,plain,
( spl0_1065
<=> class_HOL_Ominus(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f5901,plain,
( spl0_638
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f7867,plain,
( class_HOL_Ominus(t_b)
| ~ spl0_1
| ~ spl0_638 ),
inference(resolution,[],[f5902,f3228]) ).
fof(f5902,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) )
| ~ spl0_638 ),
inference(avatar_component_clause,[],[f5901]) ).
fof(f9003,plain,
( spl0_1064
| ~ spl0_1
| ~ spl0_637 ),
inference(avatar_split_clause,[],[f7865,f5897,f3226,f9000]) ).
fof(f9000,plain,
( spl0_1064
<=> class_Ring__and__Field_Opordered__ring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f5897,plain,
( spl0_637
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f7865,plain,
( class_Ring__and__Field_Opordered__ring(t_b)
| ~ spl0_1
| ~ spl0_637 ),
inference(resolution,[],[f5898,f3228]) ).
fof(f5898,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) )
| ~ spl0_637 ),
inference(avatar_component_clause,[],[f5897]) ).
fof(f8998,plain,
( spl0_1063
| ~ spl0_1
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f7863,f5893,f3226,f8995]) ).
fof(f8995,plain,
( spl0_1063
<=> class_Ring__and__Field_Olordered__ring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f5893,plain,
( spl0_636
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f7863,plain,
( class_Ring__and__Field_Olordered__ring(t_b)
| ~ spl0_1
| ~ spl0_636 ),
inference(resolution,[],[f5894,f3228]) ).
fof(f5894,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) )
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f5893]) ).
fof(f8992,plain,
( spl0_1062
| ~ spl0_1
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f7861,f5889,f3226,f8989]) ).
fof(f8989,plain,
( spl0_1062
<=> class_Ring__and__Field_Oordered__ring__strict(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f5889,plain,
( spl0_635
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f7861,plain,
( class_Ring__and__Field_Oordered__ring__strict(t_b)
| ~ spl0_1
| ~ spl0_635 ),
inference(resolution,[],[f5890,f3228]) ).
fof(f5890,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) )
| ~ spl0_635 ),
inference(avatar_component_clause,[],[f5889]) ).
fof(f8987,plain,
( spl0_1061
| ~ spl0_1
| ~ spl0_634 ),
inference(avatar_split_clause,[],[f7859,f5885,f3226,f8984]) ).
fof(f8984,plain,
( spl0_1061
<=> class_Ring__and__Field_Oaxclass__abs__if(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f5885,plain,
( spl0_634
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f7859,plain,
( class_Ring__and__Field_Oaxclass__abs__if(t_b)
| ~ spl0_1
| ~ spl0_634 ),
inference(resolution,[],[f5886,f3228]) ).
fof(f5886,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) )
| ~ spl0_634 ),
inference(avatar_component_clause,[],[f5885]) ).
fof(f8982,plain,
( spl0_1060
| ~ spl0_1
| ~ spl0_633 ),
inference(avatar_split_clause,[],[f7857,f5881,f3226,f8979]) ).
fof(f5881,plain,
( spl0_633
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f7857,plain,
( class_Orderings_Oord(t_b)
| ~ spl0_1
| ~ spl0_633 ),
inference(resolution,[],[f5882,f3228]) ).
fof(f5882,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) )
| ~ spl0_633 ),
inference(avatar_component_clause,[],[f5881]) ).
fof(f8963,plain,
( spl0_1059
| ~ spl0_1
| ~ spl0_632 ),
inference(avatar_split_clause,[],[f7850,f5877,f3226,f8960]) ).
fof(f5877,plain,
( spl0_632
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f7850,plain,
( class_Orderings_Oorder(t_b)
| ~ spl0_1
| ~ spl0_632 ),
inference(resolution,[],[f5878,f3228]) ).
fof(f5878,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) )
| ~ spl0_632 ),
inference(avatar_component_clause,[],[f5877]) ).
fof(f8946,plain,
spl0_1058,
inference(avatar_split_clause,[],[f3043,f8943]) ).
fof(f8943,plain,
( spl0_1058
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f3043,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f285,f268]) ).
fof(f268,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f285,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(f8941,plain,
spl0_1057,
inference(avatar_split_clause,[],[f3038,f8939]) ).
fof(f8939,plain,
( spl0_1057
<=> ! [X10] : c_Binomial_Obinomial(X10,c_1) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f3038,plain,
! [X10] : c_Binomial_Obinomial(X10,c_1) = X10,
inference(forward_demodulation,[],[f2830,f2814]) ).
fof(f2830,plain,
! [X10] : c_Binomial_Obinomial(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X10,
inference(definition_unfolding,[],[f55,f1438]) ).
fof(f55,axiom,
! [X10] : c_Binomial_Obinomial(X10,c_Suc(c_0)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f8937,plain,
spl0_1056,
inference(avatar_split_clause,[],[f2813,f8934]) ).
fof(f8932,plain,
spl0_1055,
inference(avatar_split_clause,[],[f1871,f8930]) ).
fof(f8930,plain,
( spl0_1055
<=> ! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f1871,axiom,
! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f8928,plain,
spl0_1054,
inference(avatar_split_clause,[],[f1749,f8926]) ).
fof(f8926,plain,
( spl0_1054
<=> ! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f1749,axiom,
! [X8] :
( ~ class_Finite__Set_Ofinite(X8)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f8924,plain,
( spl0_1053
| ~ spl0_1
| ~ spl0_631 ),
inference(avatar_split_clause,[],[f7848,f5873,f3226,f8921]) ).
fof(f8921,plain,
( spl0_1053
<=> class_OrderedGroup_Opordered__ab__semigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f5873,plain,
( spl0_631
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f7848,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(t_b)
| ~ spl0_1
| ~ spl0_631 ),
inference(resolution,[],[f5874,f3228]) ).
fof(f5874,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) )
| ~ spl0_631 ),
inference(avatar_component_clause,[],[f5873]) ).
fof(f8919,plain,
spl0_1052,
inference(avatar_split_clause,[],[f1733,f8917]) ).
fof(f8917,plain,
( spl0_1052
<=> ! [X0,X26] : c_lessequals(X26,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f1733,axiom,
! [X0,X26] : c_lessequals(X26,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f8915,plain,
spl0_1051,
inference(avatar_split_clause,[],[f1722,f8913]) ).
fof(f8913,plain,
( spl0_1051
<=> ! [X0,X26] : c_lessequals(c_emptyset,X26,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f1722,axiom,
! [X0,X26] : c_lessequals(c_emptyset,X26,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f8911,plain,
spl0_1050,
inference(avatar_split_clause,[],[f1665,f8909]) ).
fof(f8909,plain,
( spl0_1050
<=> ! [X0,X39] : c_List_Odistinct(c_List_Oremdups(X39,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f1665,axiom,
! [X39,X0] : c_List_Odistinct(c_List_Oremdups(X39,X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f8907,plain,
spl0_1049,
inference(avatar_split_clause,[],[f1649,f8905]) ).
fof(f8905,plain,
( spl0_1049
<=> ! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f1649,axiom,
! [X0] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f8903,plain,
spl0_1048,
inference(avatar_split_clause,[],[f1608,f8901]) ).
fof(f8901,plain,
( spl0_1048
<=> ! [X0] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f1608,axiom,
! [X0] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f8899,plain,
spl0_1047,
inference(avatar_split_clause,[],[f1592,f8897]) ).
fof(f8897,plain,
( spl0_1047
<=> ! [X0,X26] : c_lessequals(X26,c_UNIV,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f1592,axiom,
! [X0,X26] : c_lessequals(X26,c_UNIV,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f8895,plain,
spl0_1046,
inference(avatar_split_clause,[],[f1585,f8893]) ).
fof(f8893,plain,
( spl0_1046
<=> ! [X0,X26] : ~ c_less(X26,c_emptyset,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f1585,axiom,
! [X0,X26] : ~ c_less(X26,c_emptyset,tc_set(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f8891,plain,
spl0_1045,
inference(avatar_split_clause,[],[f1545,f8889]) ).
fof(f8889,plain,
( spl0_1045
<=> ! [X0] : c_emptyset = c_Union(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f1545,axiom,
! [X0] : c_emptyset = c_Union(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f8887,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1543,f8885]) ).
fof(f8885,plain,
( spl0_1044
<=> ! [X0] : c_UNIV = c_Union(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f1543,axiom,
! [X0] : c_UNIV = c_Union(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f8883,plain,
spl0_1043,
inference(avatar_split_clause,[],[f1519,f8881]) ).
fof(f8881,plain,
( spl0_1043
<=> ! [X0] : c_UNIV = c_Pow(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f1519,axiom,
! [X0] : c_UNIV = c_Pow(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f8879,plain,
( spl0_1042
| ~ spl0_1
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f7846,f5869,f3226,f8876]) ).
fof(f8876,plain,
( spl0_1042
<=> class_Ring__and__Field_Opordered__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f5869,plain,
( spl0_630
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f7846,plain,
( class_Ring__and__Field_Opordered__semiring(t_b)
| ~ spl0_1
| ~ spl0_630 ),
inference(resolution,[],[f5870,f3228]) ).
fof(f5870,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) )
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f5869]) ).
fof(f8874,plain,
spl0_1041,
inference(avatar_split_clause,[],[f1513,f8872]) ).
fof(f8872,plain,
( spl0_1041
<=> ! [X0] : c_UNIV = c_Inter(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f1513,axiom,
! [X0] : c_UNIV = c_Inter(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f8870,plain,
spl0_1040,
inference(avatar_split_clause,[],[f1506,f8868]) ).
fof(f8868,plain,
( spl0_1040
<=> ! [X0] : c_emptyset = c_Inter(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f1506,axiom,
! [X0] : c_emptyset = c_Inter(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f8866,plain,
spl0_1039,
inference(avatar_split_clause,[],[f1461,f8863]) ).
fof(f8863,plain,
( spl0_1039
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f1461,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f8861,plain,
spl0_1038,
inference(avatar_split_clause,[],[f1422,f8858]) ).
fof(f8858,plain,
( spl0_1038
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f1422,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f8856,plain,
spl0_1037,
inference(avatar_split_clause,[],[f1280,f8854]) ).
fof(f8854,plain,
( spl0_1037
<=> ! [X0] : c_emptyset = c_Relation_Odiag(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f8852,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1058,f8849]) ).
fof(f8849,plain,
( spl0_1036
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1058,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(f8847,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1057,f8844]) ).
fof(f8844,plain,
( spl0_1035
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f1057,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(f8842,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1046,f8840]) ).
fof(f8840,plain,
( spl0_1034
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1046,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f8838,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1045,f8836]) ).
fof(f8836,plain,
( spl0_1033
<=> ! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f1045,axiom,
! [X0] :
( ~ class_Ring__and__Field_Oordered__idom(X0)
| ~ c_IntDef_Oneg(c_0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f8834,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1029,f8832]) ).
fof(f8832,plain,
( spl0_1032
<=> ! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_IntDef_Oiszero(c_1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1029,axiom,
! [X0] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X0)
| ~ c_IntDef_Oiszero(c_1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f8830,plain,
( spl0_1031
| ~ spl0_1
| ~ spl0_629 ),
inference(avatar_split_clause,[],[f7844,f5865,f3226,f8827]) ).
fof(f8827,plain,
( spl0_1031
<=> class_Ring__and__Field_Opordered__comm__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f5865,plain,
( spl0_629
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f7844,plain,
( class_Ring__and__Field_Opordered__comm__semiring(t_b)
| ~ spl0_1
| ~ spl0_629 ),
inference(resolution,[],[f5866,f3228]) ).
fof(f5866,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) )
| ~ spl0_629 ),
inference(avatar_component_clause,[],[f5865]) ).
fof(f8825,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1024,f8823]) ).
fof(f8823,plain,
( spl0_1030
<=> ! [X33] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X33) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1024,axiom,
! [X33] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X33),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f8821,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1009,f8819]) ).
fof(f8819,plain,
( spl0_1029
<=> ! [X10] : c_Numeral_Obin__add(X10,c_Numeral_OPls) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f8817,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1008,f8815]) ).
fof(f8813,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1000,f8810]) ).
fof(f8810,plain,
( spl0_1027
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1000,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(f8808,plain,
spl0_1026,
inference(avatar_split_clause,[],[f999,f8805]) ).
fof(f999,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(f8803,plain,
spl0_1025,
inference(avatar_split_clause,[],[f760,f8800]) ).
fof(f760,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(f8798,plain,
spl0_1024,
inference(avatar_split_clause,[],[f679,f8796]) ).
fof(f8796,plain,
( spl0_1024
<=> ! [X23] : c_List_Olist_ONil = c_List_Oupt(X23,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f679,axiom,
! [X23] : c_List_Olist_ONil = c_List_Oupt(X23,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f8794,plain,
spl0_1023,
inference(avatar_split_clause,[],[f672,f8792]) ).
fof(f8792,plain,
( spl0_1023
<=> ! [X14] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f672,axiom,
! [X14] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f8790,plain,
spl0_1022,
inference(avatar_split_clause,[],[f645,f8788]) ).
fof(f8788,plain,
( spl0_1022
<=> ! [X0] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f645,axiom,
! [X0] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
fof(f8786,plain,
spl0_1021,
inference(avatar_split_clause,[],[f630,f8784]) ).
fof(f8784,plain,
( spl0_1021
<=> ! [X0] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f630,axiom,
! [X0] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f8782,plain,
( spl0_1020
| ~ spl0_1
| ~ spl0_628 ),
inference(avatar_split_clause,[],[f7842,f5861,f3226,f8779]) ).
fof(f8779,plain,
( spl0_1020
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f5861,plain,
( spl0_628
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f7842,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_b)
| ~ spl0_1
| ~ spl0_628 ),
inference(resolution,[],[f5862,f3228]) ).
fof(f5862,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) )
| ~ spl0_628 ),
inference(avatar_component_clause,[],[f5861]) ).
fof(f8777,plain,
spl0_1019,
inference(avatar_split_clause,[],[f610,f8775]) ).
fof(f8775,plain,
( spl0_1019
<=> ! [X0] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f610,axiom,
! [X0] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
fof(f8773,plain,
spl0_1018,
inference(avatar_split_clause,[],[f582,f8770]) ).
fof(f8770,plain,
( spl0_1018
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f582,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(f8768,plain,
spl0_1017,
inference(avatar_split_clause,[],[f581,f8765]) ).
fof(f8765,plain,
( spl0_1017
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f581,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(f8763,plain,
spl0_1016,
inference(avatar_split_clause,[],[f580,f8760]) ).
fof(f8760,plain,
( spl0_1016
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f580,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(f8758,plain,
spl0_1015,
inference(avatar_split_clause,[],[f579,f8755]) ).
fof(f8755,plain,
( spl0_1015
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f579,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(f8753,plain,
spl0_1014,
inference(avatar_split_clause,[],[f578,f8750]) ).
fof(f8750,plain,
( spl0_1014
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f578,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(f8748,plain,
spl0_1013,
inference(avatar_split_clause,[],[f577,f8745]) ).
fof(f8745,plain,
( spl0_1013
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f577,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(f8743,plain,
spl0_1012,
inference(avatar_split_clause,[],[f576,f8740]) ).
fof(f8740,plain,
( spl0_1012
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f576,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(f8738,plain,
spl0_1011,
inference(avatar_split_clause,[],[f575,f8735]) ).
fof(f8735,plain,
( spl0_1011
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f575,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(f8733,plain,
spl0_1010,
inference(avatar_split_clause,[],[f574,f8730]) ).
fof(f8730,plain,
( spl0_1010
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f574,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(f8728,plain,
( spl0_1009
| ~ spl0_1
| ~ spl0_627 ),
inference(avatar_split_clause,[],[f7840,f5857,f3226,f8725]) ).
fof(f5857,plain,
( spl0_627
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f7840,plain,
( class_OrderedGroup_Oab__group__add(t_b)
| ~ spl0_1
| ~ spl0_627 ),
inference(resolution,[],[f5858,f3228]) ).
fof(f5858,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) )
| ~ spl0_627 ),
inference(avatar_component_clause,[],[f5857]) ).
fof(f8723,plain,
spl0_1008,
inference(avatar_split_clause,[],[f573,f8720]) ).
fof(f8720,plain,
( spl0_1008
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f573,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(f8718,plain,
spl0_1007,
inference(avatar_split_clause,[],[f572,f8715]) ).
fof(f8715,plain,
( spl0_1007
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f572,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(f8713,plain,
spl0_1006,
inference(avatar_split_clause,[],[f571,f8710]) ).
fof(f8710,plain,
( spl0_1006
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f571,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(f8708,plain,
spl0_1005,
inference(avatar_split_clause,[],[f570,f8705]) ).
fof(f8705,plain,
( spl0_1005
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f570,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(f8703,plain,
spl0_1004,
inference(avatar_split_clause,[],[f569,f8700]) ).
fof(f8700,plain,
( spl0_1004
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f569,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(f8698,plain,
spl0_1003,
inference(avatar_split_clause,[],[f568,f8695]) ).
fof(f8695,plain,
( spl0_1003
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f568,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(f8693,plain,
spl0_1002,
inference(avatar_split_clause,[],[f567,f8690]) ).
fof(f8690,plain,
( spl0_1002
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f567,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(f8688,plain,
spl0_1001,
inference(avatar_split_clause,[],[f532,f8686]) ).
fof(f8686,plain,
( spl0_1001
<=> ! [X0] : c_UNIV = c_List_Olists(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f532,axiom,
! [X0] : c_UNIV = c_List_Olists(c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f8684,plain,
spl0_1000,
inference(avatar_split_clause,[],[f461,f8682]) ).
fof(f8682,plain,
( spl0_1000
<=> ! [X50,X23] : c_List_Odistinct(c_List_Oupt(X23,X50),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f461,axiom,
! [X50,X23] : c_List_Odistinct(c_List_Oupt(X23,X50),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f8680,plain,
spl0_999,
inference(avatar_split_clause,[],[f437,f8678]) ).
fof(f8678,plain,
( spl0_999
<=> ! [X14] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f437,axiom,
! [X14] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f8676,plain,
( spl0_998
| ~ spl0_1
| ~ spl0_626 ),
inference(avatar_split_clause,[],[f7838,f5853,f3226,f8673]) ).
fof(f8673,plain,
( spl0_998
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f5853,plain,
( spl0_626
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f7838,plain,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(t_b)
| ~ spl0_1
| ~ spl0_626 ),
inference(resolution,[],[f5854,f3228]) ).
fof(f5854,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) )
| ~ spl0_626 ),
inference(avatar_component_clause,[],[f5853]) ).
fof(f8671,plain,
spl0_997,
inference(avatar_split_clause,[],[f430,f8669]) ).
fof(f8669,plain,
( spl0_997
<=> ! [X14] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f430,axiom,
! [X14] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f8667,plain,
spl0_996,
inference(avatar_split_clause,[],[f408,f8665]) ).
fof(f8665,plain,
( spl0_996
<=> ! [X0] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f8663,plain,
spl0_995,
inference(avatar_split_clause,[],[f318,f8661]) ).
fof(f318,axiom,
! [X11] : c_lessequals(c_0,c_IntDef_Oint(X11),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f8659,plain,
spl0_994,
inference(avatar_split_clause,[],[f278,f8657]) ).
fof(f278,axiom,
! [X10] : c_IntDef_Onat(c_IntDef_Oint(X10)) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f8655,plain,
spl0_993,
inference(avatar_split_clause,[],[f272,f8653]) ).
fof(f272,axiom,
! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f8651,plain,
~ spl0_992,
inference(avatar_split_clause,[],[f203,f8648]) ).
fof(f203,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(f8646,plain,
spl0_991,
inference(avatar_split_clause,[],[f190,f8644]) ).
fof(f8644,plain,
( spl0_991
<=> ! [X0,X10] : c_Fun_Oid(X10,X0) = X10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f190,axiom,
! [X10,X0] : c_Fun_Oid(X10,X0) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f8642,plain,
spl0_990,
inference(avatar_split_clause,[],[f189,f8640]) ).
fof(f189,axiom,
! [X10] : c_NatArith_Oof__nat(X10,tc_nat) = X10,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f8638,plain,
spl0_989,
inference(avatar_split_clause,[],[f172,f8636]) ).
fof(f8636,plain,
( spl0_989
<=> ! [X0] : c_0 = c_Finite__Set_Ocard(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f172,axiom,
! [X0] : c_0 = c_Finite__Set_Ocard(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f8634,plain,
spl0_988,
inference(avatar_split_clause,[],[f149,f8631]) ).
fof(f8631,plain,
( spl0_988
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f149,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(f8629,plain,
( spl0_987
| ~ spl0_1
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7836,f5849,f3226,f8626]) ).
fof(f8626,plain,
( spl0_987
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f5849,plain,
( spl0_625
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f7836,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_b)
| ~ spl0_1
| ~ spl0_625 ),
inference(resolution,[],[f5850,f3228]) ).
fof(f5850,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) )
| ~ spl0_625 ),
inference(avatar_component_clause,[],[f5849]) ).
fof(f8624,plain,
spl0_986,
inference(avatar_split_clause,[],[f148,f8621]) ).
fof(f8621,plain,
( spl0_986
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f148,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(f8619,plain,
spl0_985,
inference(avatar_split_clause,[],[f78,f8616]) ).
fof(f8616,plain,
( spl0_985
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f78,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(f8614,plain,
spl0_984,
inference(avatar_split_clause,[],[f68,f8612]) ).
fof(f8612,plain,
( spl0_984
<=> ! [X0,X15] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X15,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f68,axiom,
! [X0,X15] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X15,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2_0) ).
fof(f8610,plain,
spl0_983,
inference(avatar_split_clause,[],[f66,f8608]) ).
fof(f8608,plain,
( spl0_983
<=> ! [X0] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f66,axiom,
! [X0] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f8606,plain,
spl0_982,
inference(avatar_split_clause,[],[f59,f8604]) ).
fof(f8604,plain,
( spl0_982
<=> ! [X11] : c_1 = c_Binomial_Obinomial(X11,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f59,axiom,
! [X11] : c_1 = c_Binomial_Obinomial(X11,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f8602,plain,
spl0_981,
inference(avatar_split_clause,[],[f58,f8600]) ).
fof(f8600,plain,
( spl0_981
<=> ! [X11] : c_Binomial_Obinomial(X11,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f58,axiom,
! [X11] : c_Binomial_Obinomial(X11,c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f8598,plain,
spl0_980,
inference(avatar_split_clause,[],[f53,f8596]) ).
fof(f53,axiom,
! [X8] :
( ~ class_OrderedGroup_Osemigroup__add(X8)
| class_OrderedGroup_Osemigroup__add(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_9) ).
fof(f8594,plain,
spl0_979,
inference(avatar_split_clause,[],[f52,f8592]) ).
fof(f8592,plain,
( spl0_979
<=> ! [X8] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f52,axiom,
! [X8] :
( ~ class_HOL_Oone(X8)
| class_HOL_Oone(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_8) ).
fof(f8590,plain,
spl0_978,
inference(avatar_split_clause,[],[f51,f8588]) ).
fof(f8588,plain,
( spl0_978
<=> ! [X8] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f51,axiom,
! [X8] :
( ~ class_HOL_Ozero(X8)
| class_HOL_Ozero(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_7) ).
fof(f8586,plain,
spl0_977,
inference(avatar_split_clause,[],[f50,f8584]) ).
fof(f8584,plain,
( spl0_977
<=> ! [X8] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f50,axiom,
! [X8] :
( ~ class_HOL_Otimes(X8)
| class_HOL_Otimes(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_6) ).
fof(f8582,plain,
( spl0_976
| ~ spl0_1
| ~ spl0_624 ),
inference(avatar_split_clause,[],[f7834,f5845,f3226,f8579]) ).
fof(f8579,plain,
( spl0_976
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f5845,plain,
( spl0_624
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f7834,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_b)
| ~ spl0_1
| ~ spl0_624 ),
inference(resolution,[],[f5846,f3228]) ).
fof(f5846,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) )
| ~ spl0_624 ),
inference(avatar_component_clause,[],[f5845]) ).
fof(f8577,plain,
spl0_975,
inference(avatar_split_clause,[],[f49,f8575]) ).
fof(f8575,plain,
( spl0_975
<=> ! [X8] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f49,axiom,
! [X8] :
( ~ class_HOL_Oplus(X8)
| class_HOL_Oplus(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_5) ).
fof(f8573,plain,
spl0_974,
inference(avatar_split_clause,[],[f48,f8571]) ).
fof(f8571,plain,
( spl0_974
<=> ! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_set(X8)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f48,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Ocomm__monoid__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_15) ).
fof(f8569,plain,
spl0_973,
inference(avatar_split_clause,[],[f47,f8567]) ).
fof(f47,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Omonoid__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_14) ).
fof(f8565,plain,
spl0_972,
inference(avatar_split_clause,[],[f46,f8563]) ).
fof(f46,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X8)
| class_OrderedGroup_Oab__semigroup__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_13) ).
fof(f8561,plain,
spl0_971,
inference(avatar_split_clause,[],[f45,f8559]) ).
fof(f45,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Ocomm__monoid__add(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_12) ).
fof(f8557,plain,
spl0_970,
inference(avatar_split_clause,[],[f44,f8555]) ).
fof(f44,axiom,
! [X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X8)
| class_OrderedGroup_Oab__semigroup__add(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_11) ).
fof(f8553,plain,
spl0_969,
inference(avatar_split_clause,[],[f43,f8551]) ).
fof(f43,axiom,
! [X8] :
( ~ class_OrderedGroup_Osemigroup__mult(X8)
| class_OrderedGroup_Osemigroup__mult(tc_set(X8)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_10) ).
fof(f8549,plain,
( spl0_968
| ~ spl0_1
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f7832,f5841,f3226,f8546]) ).
fof(f5841,plain,
( spl0_623
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f7832,plain,
( class_LOrder_Omeet__semilorder(t_b)
| ~ spl0_1
| ~ spl0_623 ),
inference(resolution,[],[f5842,f3228]) ).
fof(f5842,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) )
| ~ spl0_623 ),
inference(avatar_component_clause,[],[f5841]) ).
fof(f8500,plain,
( spl0_967
| ~ spl0_1
| ~ spl0_622 ),
inference(avatar_split_clause,[],[f7825,f5837,f3226,f8497]) ).
fof(f5837,plain,
( spl0_622
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f7825,plain,
( class_LOrder_Ojoin__semilorder(t_b)
| ~ spl0_1
| ~ spl0_622 ),
inference(resolution,[],[f5838,f3228]) ).
fof(f5838,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) )
| ~ spl0_622 ),
inference(avatar_component_clause,[],[f5837]) ).
fof(f8475,plain,
( spl0_966
| ~ spl0_1
| ~ spl0_621 ),
inference(avatar_split_clause,[],[f7823,f5833,f3226,f8472]) ).
fof(f8472,plain,
( spl0_966
<=> class_LOrder_Olorder(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f5833,plain,
( spl0_621
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f7823,plain,
( class_LOrder_Olorder(t_b)
| ~ spl0_1
| ~ spl0_621 ),
inference(resolution,[],[f5834,f3228]) ).
fof(f5834,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) )
| ~ spl0_621 ),
inference(avatar_component_clause,[],[f5833]) ).
fof(f8450,plain,
( spl0_965
| ~ spl0_1
| ~ spl0_620 ),
inference(avatar_split_clause,[],[f7821,f5829,f3226,f8447]) ).
fof(f5829,plain,
( spl0_620
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f7821,plain,
( class_Orderings_Olinorder(t_b)
| ~ spl0_1
| ~ spl0_620 ),
inference(resolution,[],[f5830,f3228]) ).
fof(f5830,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) )
| ~ spl0_620 ),
inference(avatar_component_clause,[],[f5829]) ).
fof(f8425,plain,
( spl0_964
| ~ spl0_1
| ~ spl0_619 ),
inference(avatar_split_clause,[],[f7819,f5825,f3226,f8422]) ).
fof(f8422,plain,
( spl0_964
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f5825,plain,
( spl0_619
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f7819,plain,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_b)
| ~ spl0_1
| ~ spl0_619 ),
inference(resolution,[],[f5826,f3228]) ).
fof(f5826,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) )
| ~ spl0_619 ),
inference(avatar_component_clause,[],[f5825]) ).
fof(f8401,plain,
( spl0_963
| ~ spl0_1
| ~ spl0_618 ),
inference(avatar_split_clause,[],[f7817,f5821,f3226,f8398]) ).
fof(f8398,plain,
( spl0_963
<=> class_Ring__and__Field_Oordered__semiring__strict(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f5821,plain,
( spl0_618
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f7817,plain,
( class_Ring__and__Field_Oordered__semiring__strict(t_b)
| ~ spl0_1
| ~ spl0_618 ),
inference(resolution,[],[f5822,f3228]) ).
fof(f5822,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) )
| ~ spl0_618 ),
inference(avatar_component_clause,[],[f5821]) ).
fof(f8386,plain,
( spl0_962
| ~ spl0_1
| ~ spl0_617 ),
inference(avatar_split_clause,[],[f7815,f5817,f3226,f8383]) ).
fof(f8383,plain,
( spl0_962
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f5817,plain,
( spl0_617
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f7815,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(t_b)
| ~ spl0_1
| ~ spl0_617 ),
inference(resolution,[],[f5818,f3228]) ).
fof(f5818,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) )
| ~ spl0_617 ),
inference(avatar_component_clause,[],[f5817]) ).
fof(f8371,plain,
( spl0_961
| ~ spl0_1
| ~ spl0_616 ),
inference(avatar_split_clause,[],[f7813,f5813,f3226,f8368]) ).
fof(f8368,plain,
( spl0_961
<=> class_Ring__and__Field_Oring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f5813,plain,
( spl0_616
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f7813,plain,
( class_Ring__and__Field_Oring(t_b)
| ~ spl0_1
| ~ spl0_616 ),
inference(resolution,[],[f5814,f3228]) ).
fof(f5814,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) )
| ~ spl0_616 ),
inference(avatar_component_clause,[],[f5813]) ).
fof(f8356,plain,
( spl0_960
| ~ spl0_1
| ~ spl0_615 ),
inference(avatar_split_clause,[],[f7811,f5809,f3226,f8353]) ).
fof(f8353,plain,
( spl0_960
<=> class_HOL_Oplus(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f5809,plain,
( spl0_615
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f7811,plain,
( class_HOL_Oplus(t_b)
| ~ spl0_1
| ~ spl0_615 ),
inference(resolution,[],[f5810,f3228]) ).
fof(f5810,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) )
| ~ spl0_615 ),
inference(avatar_component_clause,[],[f5809]) ).
fof(f8334,plain,
( spl0_959
| ~ spl0_1
| ~ spl0_614 ),
inference(avatar_split_clause,[],[f7809,f5805,f3226,f8331]) ).
fof(f8331,plain,
( spl0_959
<=> class_OrderedGroup_Osemigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f5805,plain,
( spl0_614
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f7809,plain,
( class_OrderedGroup_Osemigroup__add(t_b)
| ~ spl0_1
| ~ spl0_614 ),
inference(resolution,[],[f5806,f3228]) ).
fof(f5806,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) )
| ~ spl0_614 ),
inference(avatar_component_clause,[],[f5805]) ).
fof(f8314,plain,
( spl0_958
| ~ spl0_1
| ~ spl0_613 ),
inference(avatar_split_clause,[],[f7807,f5801,f3226,f8311]) ).
fof(f8311,plain,
( spl0_958
<=> class_OrderedGroup_Ocancel__semigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f5801,plain,
( spl0_613
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f7807,plain,
( class_OrderedGroup_Ocancel__semigroup__add(t_b)
| ~ spl0_1
| ~ spl0_613 ),
inference(resolution,[],[f5802,f3228]) ).
fof(f5802,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) )
| ~ spl0_613 ),
inference(avatar_component_clause,[],[f5801]) ).
fof(f8268,plain,
( spl0_957
| ~ spl0_1
| ~ spl0_612 ),
inference(avatar_split_clause,[],[f7800,f5797,f3226,f8265]) ).
fof(f8265,plain,
( spl0_957
<=> class_OrderedGroup_Oab__semigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f5797,plain,
( spl0_612
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f7800,plain,
( class_OrderedGroup_Oab__semigroup__add(t_b)
| ~ spl0_1
| ~ spl0_612 ),
inference(resolution,[],[f5798,f3228]) ).
fof(f5798,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) )
| ~ spl0_612 ),
inference(avatar_component_clause,[],[f5797]) ).
fof(f8243,plain,
( spl0_956
| ~ spl0_1
| ~ spl0_611 ),
inference(avatar_split_clause,[],[f7798,f5793,f3226,f8240]) ).
fof(f8240,plain,
( spl0_956
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f5793,plain,
( spl0_611
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f7798,plain,
( class_OrderedGroup_Ocancel__ab__semigroup__add(t_b)
| ~ spl0_1
| ~ spl0_611 ),
inference(resolution,[],[f5794,f3228]) ).
fof(f5794,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) )
| ~ spl0_611 ),
inference(avatar_component_clause,[],[f5793]) ).
fof(f8218,plain,
( spl0_955
| ~ spl0_1
| ~ spl0_610 ),
inference(avatar_split_clause,[],[f7796,f5789,f3226,f8215]) ).
fof(f8215,plain,
( spl0_955
<=> class_HOL_Ozero(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f5789,plain,
( spl0_610
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f7796,plain,
( class_HOL_Ozero(t_b)
| ~ spl0_1
| ~ spl0_610 ),
inference(resolution,[],[f5790,f3228]) ).
fof(f5790,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) )
| ~ spl0_610 ),
inference(avatar_component_clause,[],[f5789]) ).
fof(f8193,plain,
( spl0_954
| ~ spl0_1
| ~ spl0_609 ),
inference(avatar_split_clause,[],[f7794,f5785,f3226,f8190]) ).
fof(f5785,plain,
( spl0_609
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f7794,plain,
( class_OrderedGroup_Ocomm__monoid__add(t_b)
| ~ spl0_1
| ~ spl0_609 ),
inference(resolution,[],[f5786,f3228]) ).
fof(f5786,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) )
| ~ spl0_609 ),
inference(avatar_component_clause,[],[f5785]) ).
fof(f8168,plain,
( spl0_953
| ~ spl0_1
| ~ spl0_608 ),
inference(avatar_split_clause,[],[f7792,f5781,f3226,f8165]) ).
fof(f8165,plain,
( spl0_953
<=> class_HOL_Otimes(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f5781,plain,
( spl0_608
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f7792,plain,
( class_HOL_Otimes(t_b)
| ~ spl0_1
| ~ spl0_608 ),
inference(resolution,[],[f5782,f3228]) ).
fof(f5782,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) )
| ~ spl0_608 ),
inference(avatar_component_clause,[],[f5781]) ).
fof(f8143,plain,
( spl0_952
| ~ spl0_1
| ~ spl0_607 ),
inference(avatar_split_clause,[],[f7790,f5777,f3226,f8140]) ).
fof(f8140,plain,
( spl0_952
<=> class_OrderedGroup_Osemigroup__mult(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f5777,plain,
( spl0_607
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f7790,plain,
( class_OrderedGroup_Osemigroup__mult(t_b)
| ~ spl0_1
| ~ spl0_607 ),
inference(resolution,[],[f5778,f3228]) ).
fof(f5778,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) )
| ~ spl0_607 ),
inference(avatar_component_clause,[],[f5777]) ).
fof(f8118,plain,
( spl0_951
| ~ spl0_1
| ~ spl0_606 ),
inference(avatar_split_clause,[],[f7788,f5773,f3226,f8115]) ).
fof(f8115,plain,
( spl0_951
<=> class_Ring__and__Field_Osemiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f5773,plain,
( spl0_606
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f7788,plain,
( class_Ring__and__Field_Osemiring(t_b)
| ~ spl0_1
| ~ spl0_606 ),
inference(resolution,[],[f5774,f3228]) ).
fof(f5774,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) )
| ~ spl0_606 ),
inference(avatar_component_clause,[],[f5773]) ).
fof(f8093,plain,
( spl0_950
| ~ spl0_1
| ~ spl0_605 ),
inference(avatar_split_clause,[],[f7786,f5769,f3226,f8090]) ).
fof(f8090,plain,
( spl0_950
<=> class_Ring__and__Field_Oring__1(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f5769,plain,
( spl0_605
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f7786,plain,
( class_Ring__and__Field_Oring__1(t_b)
| ~ spl0_1
| ~ spl0_605 ),
inference(resolution,[],[f5770,f3228]) ).
fof(f5770,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) )
| ~ spl0_605 ),
inference(avatar_component_clause,[],[f5769]) ).
fof(f8068,plain,
( spl0_949
| ~ spl0_1
| ~ spl0_604 ),
inference(avatar_split_clause,[],[f7784,f5765,f3226,f8065]) ).
fof(f8065,plain,
( spl0_949
<=> class_Ring__and__Field_Osemiring__0(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f5765,plain,
( spl0_604
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f7784,plain,
( class_Ring__and__Field_Osemiring__0(t_b)
| ~ spl0_1
| ~ spl0_604 ),
inference(resolution,[],[f5766,f3228]) ).
fof(f5766,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) )
| ~ spl0_604 ),
inference(avatar_component_clause,[],[f5765]) ).
fof(f8043,plain,
( spl0_948
| ~ spl0_1
| ~ spl0_603 ),
inference(avatar_split_clause,[],[f7782,f5761,f3226,f8040]) ).
fof(f8040,plain,
( spl0_948
<=> class_Ring__and__Field_Osemiring__0__cancel(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f5761,plain,
( spl0_603
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f7782,plain,
( class_Ring__and__Field_Osemiring__0__cancel(t_b)
| ~ spl0_1
| ~ spl0_603 ),
inference(resolution,[],[f5762,f3228]) ).
fof(f5762,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) )
| ~ spl0_603 ),
inference(avatar_component_clause,[],[f5761]) ).
fof(f7969,plain,
( spl0_947
| ~ spl0_1
| ~ spl0_602 ),
inference(avatar_split_clause,[],[f7775,f5757,f3226,f7966]) ).
fof(f7966,plain,
( spl0_947
<=> class_OrderedGroup_Oab__semigroup__mult(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f5757,plain,
( spl0_602
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f7775,plain,
( class_OrderedGroup_Oab__semigroup__mult(t_b)
| ~ spl0_1
| ~ spl0_602 ),
inference(resolution,[],[f5758,f3228]) ).
fof(f5758,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) )
| ~ spl0_602 ),
inference(avatar_component_clause,[],[f5757]) ).
fof(f7949,plain,
( spl0_946
| ~ spl0_1
| ~ spl0_601 ),
inference(avatar_split_clause,[],[f7773,f5753,f3226,f7946]) ).
fof(f7946,plain,
( spl0_946
<=> class_Ring__and__Field_Ocomm__semiring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f5753,plain,
( spl0_601
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f7773,plain,
( class_Ring__and__Field_Ocomm__semiring(t_b)
| ~ spl0_1
| ~ spl0_601 ),
inference(resolution,[],[f5754,f3228]) ).
fof(f5754,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) )
| ~ spl0_601 ),
inference(avatar_component_clause,[],[f5753]) ).
fof(f7934,plain,
( spl0_945
| ~ spl0_1
| ~ spl0_600 ),
inference(avatar_split_clause,[],[f7771,f5749,f3226,f7931]) ).
fof(f7931,plain,
( spl0_945
<=> class_Ring__and__Field_Ocomm__semiring__0(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f5749,plain,
( spl0_600
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f7771,plain,
( class_Ring__and__Field_Ocomm__semiring__0(t_b)
| ~ spl0_1
| ~ spl0_600 ),
inference(resolution,[],[f5750,f3228]) ).
fof(f5750,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) )
| ~ spl0_600 ),
inference(avatar_component_clause,[],[f5749]) ).
fof(f7919,plain,
( spl0_944
| ~ spl0_1
| ~ spl0_599 ),
inference(avatar_split_clause,[],[f7769,f5745,f3226,f7916]) ).
fof(f7916,plain,
( spl0_944
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f5745,plain,
( spl0_599
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f7769,plain,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(t_b)
| ~ spl0_1
| ~ spl0_599 ),
inference(resolution,[],[f5746,f3228]) ).
fof(f5746,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) )
| ~ spl0_599 ),
inference(avatar_component_clause,[],[f5745]) ).
fof(f7904,plain,
( spl0_943
| ~ spl0_1
| ~ spl0_598 ),
inference(avatar_split_clause,[],[f7767,f5741,f3226,f7901]) ).
fof(f7901,plain,
( spl0_943
<=> class_HOL_Oone(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f5741,plain,
( spl0_598
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f7767,plain,
( class_HOL_Oone(t_b)
| ~ spl0_1
| ~ spl0_598 ),
inference(resolution,[],[f5742,f3228]) ).
fof(f5742,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) )
| ~ spl0_598 ),
inference(avatar_component_clause,[],[f5741]) ).
fof(f7881,plain,
( spl0_942
| ~ spl0_1
| ~ spl0_597 ),
inference(avatar_split_clause,[],[f7765,f5737,f3226,f7878]) ).
fof(f5737,plain,
( spl0_597
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f7765,plain,
( class_OrderedGroup_Omonoid__mult(t_b)
| ~ spl0_1
| ~ spl0_597 ),
inference(resolution,[],[f5738,f3228]) ).
fof(f5738,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) )
| ~ spl0_597 ),
inference(avatar_component_clause,[],[f5737]) ).
fof(f7856,plain,
( spl0_941
| ~ spl0_1
| ~ spl0_596 ),
inference(avatar_split_clause,[],[f7763,f5733,f3226,f7853]) ).
fof(f7853,plain,
( spl0_941
<=> class_Ring__and__Field_Oaxclass__0__neq__1(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f5733,plain,
( spl0_596
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f7763,plain,
( class_Ring__and__Field_Oaxclass__0__neq__1(t_b)
| ~ spl0_1
| ~ spl0_596 ),
inference(resolution,[],[f5734,f3228]) ).
fof(f5734,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) )
| ~ spl0_596 ),
inference(avatar_component_clause,[],[f5733]) ).
fof(f7831,plain,
( spl0_940
| ~ spl0_1
| ~ spl0_595 ),
inference(avatar_split_clause,[],[f7761,f5729,f3226,f7828]) ).
fof(f7828,plain,
( spl0_940
<=> class_Ring__and__Field_Osemiring__1(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f5729,plain,
( spl0_595
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f7761,plain,
( class_Ring__and__Field_Osemiring__1(t_b)
| ~ spl0_1
| ~ spl0_595 ),
inference(resolution,[],[f5730,f3228]) ).
fof(f5730,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) )
| ~ spl0_595 ),
inference(avatar_component_clause,[],[f5729]) ).
fof(f7806,plain,
( spl0_939
| ~ spl0_1
| ~ spl0_594 ),
inference(avatar_split_clause,[],[f7759,f5725,f3226,f7803]) ).
fof(f7803,plain,
( spl0_939
<=> class_Ring__and__Field_Ocomm__ring(t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f5725,plain,
( spl0_594
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f7759,plain,
( class_Ring__and__Field_Ocomm__ring(t_b)
| ~ spl0_1
| ~ spl0_594 ),
inference(resolution,[],[f5726,f3228]) ).
fof(f5726,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) )
| ~ spl0_594 ),
inference(avatar_component_clause,[],[f5725]) ).
fof(f7781,plain,
( spl0_938
| ~ spl0_1
| ~ spl0_593 ),
inference(avatar_split_clause,[],[f7757,f5721,f3226,f7778]) ).
fof(f5721,plain,
( spl0_593
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f7757,plain,
( class_Ring__and__Field_Ocomm__ring__1(t_b)
| ~ spl0_1
| ~ spl0_593 ),
inference(resolution,[],[f5722,f3228]) ).
fof(f5722,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) )
| ~ spl0_593 ),
inference(avatar_component_clause,[],[f5721]) ).
fof(f7122,plain,
( ~ spl0_937
| ~ spl0_132
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f7096,f3883,f3873,f7119]) ).
fof(f7119,plain,
( spl0_937
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f3883,plain,
( spl0_134
<=> ! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f7096,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_132
| ~ spl0_134 ),
inference(superposition,[],[f3884,f3875]) ).
fof(f3884,plain,
( ! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint)
| ~ spl0_134 ),
inference(avatar_component_clause,[],[f3883]) ).
fof(f7101,plain,
( ~ spl0_936
| ~ spl0_131
| ~ spl0_134 ),
inference(avatar_split_clause,[],[f7095,f3883,f3868,f7098]) ).
fof(f7098,plain,
( spl0_936
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f7095,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_131
| ~ spl0_134 ),
inference(superposition,[],[f3884,f3870]) ).
fof(f7094,plain,
spl0_935,
inference(avatar_split_clause,[],[f3053,f7091]) ).
fof(f7091,plain,
( spl0_935
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f3053,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f380,f358]) ).
fof(f380,axiom,
! [X12] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,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(f7089,plain,
spl0_934,
inference(avatar_split_clause,[],[f3034,f7087]) ).
fof(f7087,plain,
( spl0_934
<=> ! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f3034,plain,
! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat),
inference(forward_demodulation,[],[f2818,f2814]) ).
fof(f2818,plain,
! [X9] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X9,tc_nat),
inference(definition_unfolding,[],[f1645,f1438]) ).
fof(f1645,axiom,
! [X9] : c_Divides_Oop_Advd(c_Suc(c_0),X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f7085,plain,
spl0_933,
inference(avatar_split_clause,[],[f3032,f7082]) ).
fof(f7082,plain,
( spl0_933
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f3032,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f271,f268]) ).
fof(f271,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(f7080,plain,
spl0_932,
inference(avatar_split_clause,[],[f3031,f7077]) ).
fof(f7077,plain,
( spl0_932
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f3031,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2816,f2814]) ).
fof(f2816,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f238,f1438]) ).
fof(f238,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f7075,plain,
spl0_931,
inference(avatar_split_clause,[],[f2780,f7073]) ).
fof(f7073,plain,
( spl0_931
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f2780,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f7071,plain,
spl0_930,
inference(avatar_split_clause,[],[f2779,f7069]) ).
fof(f7069,plain,
( spl0_930
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f2779,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f7067,plain,
spl0_929,
inference(avatar_split_clause,[],[f2778,f7065]) ).
fof(f7065,plain,
( spl0_929
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f2778,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f7063,plain,
spl0_928,
inference(avatar_split_clause,[],[f2777,f7061]) ).
fof(f7061,plain,
( spl0_928
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f2777,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f7059,plain,
spl0_927,
inference(avatar_split_clause,[],[f2776,f7057]) ).
fof(f7057,plain,
( spl0_927
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f2776,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f7055,plain,
spl0_926,
inference(avatar_split_clause,[],[f2775,f7053]) ).
fof(f7053,plain,
( spl0_926
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f2775,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f7051,plain,
spl0_925,
inference(avatar_split_clause,[],[f2774,f7049]) ).
fof(f7049,plain,
( spl0_925
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2774,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f7047,plain,
spl0_924,
inference(avatar_split_clause,[],[f2773,f7045]) ).
fof(f7045,plain,
( spl0_924
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2773,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
fof(f7043,plain,
spl0_923,
inference(avatar_split_clause,[],[f2772,f7041]) ).
fof(f7041,plain,
( spl0_923
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f2772,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
fof(f7039,plain,
spl0_922,
inference(avatar_split_clause,[],[f2771,f7037]) ).
fof(f7037,plain,
( spl0_922
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f2771,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
fof(f7035,plain,
spl0_921,
inference(avatar_split_clause,[],[f2770,f7033]) ).
fof(f7033,plain,
( spl0_921
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f2770,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
fof(f7031,plain,
spl0_920,
inference(avatar_split_clause,[],[f2769,f7029]) ).
fof(f7029,plain,
( spl0_920
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f2769,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f7027,plain,
spl0_919,
inference(avatar_split_clause,[],[f2768,f7025]) ).
fof(f7025,plain,
( spl0_919
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2768,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f7023,plain,
spl0_918,
inference(avatar_split_clause,[],[f2767,f7021]) ).
fof(f7021,plain,
( spl0_918
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f2767,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f7019,plain,
spl0_917,
inference(avatar_split_clause,[],[f2766,f7017]) ).
fof(f7017,plain,
( spl0_917
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f2766,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f7015,plain,
spl0_916,
inference(avatar_split_clause,[],[f2765,f7013]) ).
fof(f7013,plain,
( spl0_916
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2765,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f7011,plain,
spl0_915,
inference(avatar_split_clause,[],[f2764,f7009]) ).
fof(f7009,plain,
( spl0_915
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f2764,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f7007,plain,
spl0_914,
inference(avatar_split_clause,[],[f2763,f7005]) ).
fof(f7005,plain,
( spl0_914
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f2763,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
fof(f7003,plain,
spl0_913,
inference(avatar_split_clause,[],[f2762,f7001]) ).
fof(f7001,plain,
( spl0_913
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f2762,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
fof(f6999,plain,
spl0_912,
inference(avatar_split_clause,[],[f2761,f6997]) ).
fof(f6997,plain,
( spl0_912
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f2761,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f6995,plain,
spl0_911,
inference(avatar_split_clause,[],[f2760,f6993]) ).
fof(f6993,plain,
( spl0_911
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f2760,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f6991,plain,
spl0_910,
inference(avatar_split_clause,[],[f2759,f6989]) ).
fof(f6989,plain,
( spl0_910
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f2759,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f6987,plain,
spl0_909,
inference(avatar_split_clause,[],[f2758,f6985]) ).
fof(f6985,plain,
( spl0_909
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f2758,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
fof(f6983,plain,
spl0_908,
inference(avatar_split_clause,[],[f2757,f6981]) ).
fof(f6981,plain,
( spl0_908
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f2757,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
fof(f6979,plain,
spl0_907,
inference(avatar_split_clause,[],[f2756,f6977]) ).
fof(f6977,plain,
( spl0_907
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f2756,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f6975,plain,
spl0_906,
inference(avatar_split_clause,[],[f2755,f6973]) ).
fof(f6973,plain,
( spl0_906
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f2755,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
fof(f6971,plain,
spl0_905,
inference(avatar_split_clause,[],[f2754,f6969]) ).
fof(f6969,plain,
( spl0_905
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2754,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
fof(f6967,plain,
spl0_904,
inference(avatar_split_clause,[],[f2753,f6965]) ).
fof(f6965,plain,
( spl0_904
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2753,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f6963,plain,
spl0_903,
inference(avatar_split_clause,[],[f2752,f6961]) ).
fof(f6961,plain,
( spl0_903
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f2752,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f6959,plain,
spl0_902,
inference(avatar_split_clause,[],[f2751,f6957]) ).
fof(f6957,plain,
( spl0_902
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2751,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f6955,plain,
spl0_901,
inference(avatar_split_clause,[],[f2750,f6953]) ).
fof(f2750,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f6951,plain,
spl0_900,
inference(avatar_split_clause,[],[f2749,f6949]) ).
fof(f6949,plain,
( spl0_900
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2749,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
fof(f6947,plain,
spl0_899,
inference(avatar_split_clause,[],[f2748,f6945]) ).
fof(f6945,plain,
( spl0_899
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2748,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
fof(f6943,plain,
spl0_898,
inference(avatar_split_clause,[],[f2747,f6941]) ).
fof(f6941,plain,
( spl0_898
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2747,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f6939,plain,
spl0_897,
inference(avatar_split_clause,[],[f2746,f6937]) ).
fof(f2746,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f6935,plain,
spl0_896,
inference(avatar_split_clause,[],[f2745,f6933]) ).
fof(f6933,plain,
( spl0_896
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2745,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
fof(f6931,plain,
spl0_895,
inference(avatar_split_clause,[],[f2744,f6929]) ).
fof(f6929,plain,
( spl0_895
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2744,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
fof(f6927,plain,
spl0_894,
inference(avatar_split_clause,[],[f2743,f6925]) ).
fof(f6925,plain,
( spl0_894
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2743,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
fof(f6923,plain,
spl0_893,
inference(avatar_split_clause,[],[f2742,f6921]) ).
fof(f6921,plain,
( spl0_893
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2742,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
fof(f6919,plain,
spl0_892,
inference(avatar_split_clause,[],[f2741,f6917]) ).
fof(f6917,plain,
( spl0_892
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2741,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f6915,plain,
spl0_891,
inference(avatar_split_clause,[],[f2740,f6913]) ).
fof(f6913,plain,
( spl0_891
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2740,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
fof(f6911,plain,
spl0_890,
inference(avatar_split_clause,[],[f2739,f6909]) ).
fof(f6909,plain,
( spl0_890
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2739,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
fof(f6907,plain,
spl0_889,
inference(avatar_split_clause,[],[f2738,f6905]) ).
fof(f2738,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f6903,plain,
spl0_888,
inference(avatar_split_clause,[],[f2737,f6901]) ).
fof(f6901,plain,
( spl0_888
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f2737,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f6899,plain,
spl0_887,
inference(avatar_split_clause,[],[f2736,f6897]) ).
fof(f6897,plain,
( spl0_887
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f2736,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f6895,plain,
spl0_886,
inference(avatar_split_clause,[],[f2735,f6893]) ).
fof(f2735,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
fof(f6891,plain,
spl0_885,
inference(avatar_split_clause,[],[f2734,f6889]) ).
fof(f2734,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f6887,plain,
spl0_884,
inference(avatar_split_clause,[],[f2733,f6885]) ).
fof(f6885,plain,
( spl0_884
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2733,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
fof(f6883,plain,
spl0_883,
inference(avatar_split_clause,[],[f2732,f6881]) ).
fof(f6881,plain,
( spl0_883
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2732,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
fof(f6879,plain,
spl0_882,
inference(avatar_split_clause,[],[f2731,f6877]) ).
fof(f6877,plain,
( spl0_882
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2731,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
fof(f6875,plain,
spl0_881,
inference(avatar_split_clause,[],[f2730,f6873]) ).
fof(f6873,plain,
( spl0_881
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2730,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
fof(f6871,plain,
spl0_880,
inference(avatar_split_clause,[],[f2729,f6869]) ).
fof(f6869,plain,
( spl0_880
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2729,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
fof(f6867,plain,
spl0_879,
inference(avatar_split_clause,[],[f2728,f6865]) ).
fof(f6865,plain,
( spl0_879
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2728,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f6863,plain,
spl0_878,
inference(avatar_split_clause,[],[f2727,f6861]) ).
fof(f2727,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
fof(f6859,plain,
spl0_877,
inference(avatar_split_clause,[],[f2726,f6857]) ).
fof(f2726,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
fof(f6855,plain,
spl0_876,
inference(avatar_split_clause,[],[f2725,f6853]) ).
fof(f2725,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
fof(f6851,plain,
spl0_875,
inference(avatar_split_clause,[],[f2724,f6849]) ).
fof(f2724,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
fof(f6847,plain,
spl0_874,
inference(avatar_split_clause,[],[f2723,f6845]) ).
fof(f2723,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
fof(f6843,plain,
spl0_873,
inference(avatar_split_clause,[],[f2722,f6841]) ).
fof(f6841,plain,
( spl0_873
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2722,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).
fof(f6839,plain,
spl0_872,
inference(avatar_split_clause,[],[f2721,f6837]) ).
fof(f6837,plain,
( spl0_872
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2721,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).
fof(f6835,plain,
spl0_871,
inference(avatar_split_clause,[],[f2720,f6833]) ).
fof(f6833,plain,
( spl0_871
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2720,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f6831,plain,
spl0_870,
inference(avatar_split_clause,[],[f2719,f6829]) ).
fof(f6829,plain,
( spl0_870
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2719,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f6827,plain,
spl0_869,
inference(avatar_split_clause,[],[f2718,f6825]) ).
fof(f6825,plain,
( spl0_869
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2718,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f6823,plain,
spl0_868,
inference(avatar_split_clause,[],[f2717,f6821]) ).
fof(f6821,plain,
( spl0_868
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2717,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f6819,plain,
spl0_867,
inference(avatar_split_clause,[],[f2716,f6817]) ).
fof(f6817,plain,
( spl0_867
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2716,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f6815,plain,
spl0_866,
inference(avatar_split_clause,[],[f2715,f6813]) ).
fof(f6813,plain,
( spl0_866
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2715,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).
fof(f6811,plain,
spl0_865,
inference(avatar_split_clause,[],[f2714,f6809]) ).
fof(f6809,plain,
( spl0_865
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2714,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f6807,plain,
spl0_864,
inference(avatar_split_clause,[],[f2713,f6805]) ).
fof(f6805,plain,
( spl0_864
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2713,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f6803,plain,
spl0_863,
inference(avatar_split_clause,[],[f2712,f6801]) ).
fof(f6801,plain,
( spl0_863
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2712,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f6799,plain,
spl0_862,
inference(avatar_split_clause,[],[f2711,f6797]) ).
fof(f6797,plain,
( spl0_862
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2711,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f6795,plain,
spl0_861,
inference(avatar_split_clause,[],[f2710,f6793]) ).
fof(f6793,plain,
( spl0_861
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2710,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f6791,plain,
spl0_860,
inference(avatar_split_clause,[],[f2709,f6789]) ).
fof(f6789,plain,
( spl0_860
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2709,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).
fof(f6787,plain,
spl0_859,
inference(avatar_split_clause,[],[f2708,f6785]) ).
fof(f6785,plain,
( spl0_859
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2708,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).
fof(f6783,plain,
spl0_858,
inference(avatar_split_clause,[],[f2707,f6781]) ).
fof(f6781,plain,
( spl0_858
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f2707,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).
fof(f6779,plain,
spl0_857,
inference(avatar_split_clause,[],[f2706,f6777]) ).
fof(f6777,plain,
( spl0_857
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2706,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).
fof(f6775,plain,
spl0_856,
inference(avatar_split_clause,[],[f2705,f6773]) ).
fof(f6773,plain,
( spl0_856
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2705,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f6771,plain,
spl0_855,
inference(avatar_split_clause,[],[f2704,f6769]) ).
fof(f6769,plain,
( spl0_855
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2704,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f6767,plain,
spl0_854,
inference(avatar_split_clause,[],[f2703,f6765]) ).
fof(f6765,plain,
( spl0_854
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2703,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f6763,plain,
spl0_853,
inference(avatar_split_clause,[],[f2702,f6761]) ).
fof(f6761,plain,
( spl0_853
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2702,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).
fof(f6759,plain,
spl0_852,
inference(avatar_split_clause,[],[f2701,f6757]) ).
fof(f6757,plain,
( spl0_852
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f2701,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f6755,plain,
spl0_851,
inference(avatar_split_clause,[],[f2700,f6753]) ).
fof(f2700,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
fof(f6751,plain,
spl0_850,
inference(avatar_split_clause,[],[f2699,f6749]) ).
fof(f2699,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f6747,plain,
spl0_849,
inference(avatar_split_clause,[],[f2698,f6745]) ).
fof(f6745,plain,
( spl0_849
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f2698,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).
fof(f6743,plain,
spl0_848,
inference(avatar_split_clause,[],[f2697,f6741]) ).
fof(f6741,plain,
( spl0_848
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f2697,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).
fof(f6739,plain,
spl0_847,
inference(avatar_split_clause,[],[f2696,f6737]) ).
fof(f6737,plain,
( spl0_847
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f2696,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).
fof(f6735,plain,
spl0_846,
inference(avatar_split_clause,[],[f2695,f6733]) ).
fof(f6733,plain,
( spl0_846
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f2695,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).
fof(f6731,plain,
spl0_845,
inference(avatar_split_clause,[],[f2694,f6729]) ).
fof(f6729,plain,
( spl0_845
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f2694,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f6727,plain,
spl0_844,
inference(avatar_split_clause,[],[f2693,f6725]) ).
fof(f6725,plain,
( spl0_844
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f2693,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f6723,plain,
spl0_843,
inference(avatar_split_clause,[],[f2692,f6721]) ).
fof(f6721,plain,
( spl0_843
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f2692,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f6719,plain,
spl0_842,
inference(avatar_split_clause,[],[f2691,f6717]) ).
fof(f6717,plain,
( spl0_842
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f2691,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f6715,plain,
spl0_841,
inference(avatar_split_clause,[],[f2690,f6713]) ).
fof(f6713,plain,
( spl0_841
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f2690,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).
fof(f6711,plain,
spl0_840,
inference(avatar_split_clause,[],[f2689,f6709]) ).
fof(f6709,plain,
( spl0_840
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f2689,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f6707,plain,
spl0_839,
inference(avatar_split_clause,[],[f2688,f6705]) ).
fof(f6705,plain,
( spl0_839
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f2688,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f6703,plain,
spl0_838,
inference(avatar_split_clause,[],[f2687,f6701]) ).
fof(f6701,plain,
( spl0_838
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f2687,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
fof(f6699,plain,
spl0_837,
inference(avatar_split_clause,[],[f2686,f6697]) ).
fof(f6697,plain,
( spl0_837
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f2686,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
fof(f6695,plain,
spl0_836,
inference(avatar_split_clause,[],[f2685,f6693]) ).
fof(f6693,plain,
( spl0_836
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2685,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
fof(f6691,plain,
spl0_835,
inference(avatar_split_clause,[],[f2684,f6689]) ).
fof(f6689,plain,
( spl0_835
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f2684,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
fof(f6687,plain,
spl0_834,
inference(avatar_split_clause,[],[f2683,f6685]) ).
fof(f6685,plain,
( spl0_834
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2683,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f6683,plain,
spl0_833,
inference(avatar_split_clause,[],[f2682,f6681]) ).
fof(f6681,plain,
( spl0_833
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f2682,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
fof(f6679,plain,
spl0_832,
inference(avatar_split_clause,[],[f2681,f6677]) ).
fof(f6677,plain,
( spl0_832
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2681,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
fof(f6675,plain,
spl0_831,
inference(avatar_split_clause,[],[f2680,f6673]) ).
fof(f6673,plain,
( spl0_831
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2680,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f6671,plain,
spl0_830,
inference(avatar_split_clause,[],[f2679,f6669]) ).
fof(f6669,plain,
( spl0_830
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2679,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f6667,plain,
spl0_829,
inference(avatar_split_clause,[],[f2678,f6665]) ).
fof(f6665,plain,
( spl0_829
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2678,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f6663,plain,
spl0_828,
inference(avatar_split_clause,[],[f2677,f6661]) ).
fof(f6661,plain,
( spl0_828
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2677,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f6659,plain,
spl0_827,
inference(avatar_split_clause,[],[f2676,f6657]) ).
fof(f6657,plain,
( spl0_827
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2676,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).
fof(f6655,plain,
spl0_826,
inference(avatar_split_clause,[],[f2675,f6653]) ).
fof(f6653,plain,
( spl0_826
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2675,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).
fof(f6651,plain,
spl0_825,
inference(avatar_split_clause,[],[f2674,f6649]) ).
fof(f6649,plain,
( spl0_825
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2674,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f6647,plain,
spl0_824,
inference(avatar_split_clause,[],[f2673,f6645]) ).
fof(f6645,plain,
( spl0_824
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2673,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f6643,plain,
spl0_823,
inference(avatar_split_clause,[],[f2672,f6641]) ).
fof(f6641,plain,
( spl0_823
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2672,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f6639,plain,
spl0_822,
inference(avatar_split_clause,[],[f2671,f6637]) ).
fof(f6637,plain,
( spl0_822
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2671,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f6635,plain,
spl0_821,
inference(avatar_split_clause,[],[f2670,f6633]) ).
fof(f6633,plain,
( spl0_821
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2670,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f6631,plain,
spl0_820,
inference(avatar_split_clause,[],[f2669,f6629]) ).
fof(f6629,plain,
( spl0_820
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2669,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f6627,plain,
spl0_819,
inference(avatar_split_clause,[],[f2668,f6625]) ).
fof(f6625,plain,
( spl0_819
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2668,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f6623,plain,
spl0_818,
inference(avatar_split_clause,[],[f2667,f6621]) ).
fof(f6621,plain,
( spl0_818
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2667,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f6619,plain,
spl0_817,
inference(avatar_split_clause,[],[f2666,f6617]) ).
fof(f6617,plain,
( spl0_817
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2666,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).
fof(f6615,plain,
spl0_816,
inference(avatar_split_clause,[],[f2665,f6613]) ).
fof(f6613,plain,
( spl0_816
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f2665,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f6611,plain,
spl0_815,
inference(avatar_split_clause,[],[f2664,f6609]) ).
fof(f6609,plain,
( spl0_815
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2664,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f6607,plain,
spl0_814,
inference(avatar_split_clause,[],[f2663,f6605]) ).
fof(f6605,plain,
( spl0_814
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2663,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f6603,plain,
spl0_813,
inference(avatar_split_clause,[],[f2662,f6601]) ).
fof(f6601,plain,
( spl0_813
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2662,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f6599,plain,
spl0_812,
inference(avatar_split_clause,[],[f2661,f6597]) ).
fof(f6597,plain,
( spl0_812
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2661,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f6595,plain,
spl0_811,
inference(avatar_split_clause,[],[f2660,f6593]) ).
fof(f6593,plain,
( spl0_811
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f2660,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).
fof(f6591,plain,
spl0_810,
inference(avatar_split_clause,[],[f2659,f6589]) ).
fof(f6589,plain,
( spl0_810
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f2659,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).
fof(f6587,plain,
spl0_809,
inference(avatar_split_clause,[],[f2658,f6585]) ).
fof(f6585,plain,
( spl0_809
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f2658,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).
fof(f6583,plain,
spl0_808,
inference(avatar_split_clause,[],[f2657,f6581]) ).
fof(f6581,plain,
( spl0_808
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2657,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).
fof(f6579,plain,
spl0_807,
inference(avatar_split_clause,[],[f2656,f6577]) ).
fof(f6577,plain,
( spl0_807
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2656,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f6575,plain,
spl0_806,
inference(avatar_split_clause,[],[f2655,f6573]) ).
fof(f6573,plain,
( spl0_806
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2655,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f6571,plain,
spl0_805,
inference(avatar_split_clause,[],[f2654,f6569]) ).
fof(f6569,plain,
( spl0_805
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2654,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f6567,plain,
spl0_804,
inference(avatar_split_clause,[],[f2653,f6565]) ).
fof(f6565,plain,
( spl0_804
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2653,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
fof(f6563,plain,
spl0_803,
inference(avatar_split_clause,[],[f2652,f6561]) ).
fof(f6561,plain,
( spl0_803
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2652,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
fof(f6559,plain,
spl0_802,
inference(avatar_split_clause,[],[f2651,f6557]) ).
fof(f6557,plain,
( spl0_802
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2651,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f6555,plain,
spl0_801,
inference(avatar_split_clause,[],[f2650,f6553]) ).
fof(f6553,plain,
( spl0_801
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2650,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
fof(f6551,plain,
spl0_800,
inference(avatar_split_clause,[],[f2649,f6549]) ).
fof(f6549,plain,
( spl0_800
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2649,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
fof(f6547,plain,
spl0_799,
inference(avatar_split_clause,[],[f2648,f6545]) ).
fof(f6545,plain,
( spl0_799
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f2648,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f6543,plain,
spl0_798,
inference(avatar_split_clause,[],[f2647,f6541]) ).
fof(f6541,plain,
( spl0_798
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2647,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f6539,plain,
spl0_797,
inference(avatar_split_clause,[],[f2646,f6537]) ).
fof(f6537,plain,
( spl0_797
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2646,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
fof(f6535,plain,
spl0_796,
inference(avatar_split_clause,[],[f2645,f6533]) ).
fof(f6533,plain,
( spl0_796
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2645,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f6531,plain,
spl0_795,
inference(avatar_split_clause,[],[f2644,f6529]) ).
fof(f6529,plain,
( spl0_795
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2644,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f6527,plain,
spl0_794,
inference(avatar_split_clause,[],[f2643,f6525]) ).
fof(f6525,plain,
( spl0_794
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2643,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f6523,plain,
spl0_793,
inference(avatar_split_clause,[],[f2642,f6521]) ).
fof(f6521,plain,
( spl0_793
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2642,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f6519,plain,
spl0_792,
inference(avatar_split_clause,[],[f2641,f6517]) ).
fof(f6517,plain,
( spl0_792
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2641,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
fof(f6515,plain,
spl0_791,
inference(avatar_split_clause,[],[f2640,f6513]) ).
fof(f6513,plain,
( spl0_791
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2640,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
fof(f6511,plain,
spl0_790,
inference(avatar_split_clause,[],[f2639,f6509]) ).
fof(f6509,plain,
( spl0_790
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2639,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f6507,plain,
spl0_789,
inference(avatar_split_clause,[],[f2638,f6505]) ).
fof(f6505,plain,
( spl0_789
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2638,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f6503,plain,
spl0_788,
inference(avatar_split_clause,[],[f2612,f6501]) ).
fof(f6501,plain,
( spl0_788
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2612,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
fof(f6499,plain,
spl0_787,
inference(avatar_split_clause,[],[f2611,f6497]) ).
fof(f6497,plain,
( spl0_787
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f2611,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
fof(f6495,plain,
spl0_786,
inference(avatar_split_clause,[],[f2610,f6493]) ).
fof(f6493,plain,
( spl0_786
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f2610,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f6491,plain,
spl0_785,
inference(avatar_split_clause,[],[f2609,f6489]) ).
fof(f6489,plain,
( spl0_785
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f2609,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
fof(f6487,plain,
spl0_784,
inference(avatar_split_clause,[],[f2608,f6485]) ).
fof(f6485,plain,
( spl0_784
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f2608,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f6483,plain,
spl0_783,
inference(avatar_split_clause,[],[f2607,f6481]) ).
fof(f6481,plain,
( spl0_783
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f2607,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
fof(f6479,plain,
spl0_782,
inference(avatar_split_clause,[],[f2606,f6477]) ).
fof(f6477,plain,
( spl0_782
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f2606,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
fof(f6475,plain,
spl0_781,
inference(avatar_split_clause,[],[f2605,f6473]) ).
fof(f6473,plain,
( spl0_781
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f2605,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f6471,plain,
spl0_780,
inference(avatar_split_clause,[],[f2604,f6469]) ).
fof(f6469,plain,
( spl0_780
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f2604,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f6467,plain,
spl0_779,
inference(avatar_split_clause,[],[f2603,f6465]) ).
fof(f6465,plain,
( spl0_779
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f2603,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f6463,plain,
spl0_778,
inference(avatar_split_clause,[],[f2602,f6461]) ).
fof(f6461,plain,
( spl0_778
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2602,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f6459,plain,
spl0_777,
inference(avatar_split_clause,[],[f2601,f6457]) ).
fof(f6457,plain,
( spl0_777
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2601,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f6455,plain,
spl0_776,
inference(avatar_split_clause,[],[f2600,f6453]) ).
fof(f6453,plain,
( spl0_776
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f2600,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f6451,plain,
spl0_775,
inference(avatar_split_clause,[],[f2599,f6449]) ).
fof(f6449,plain,
( spl0_775
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f2599,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
fof(f6447,plain,
spl0_774,
inference(avatar_split_clause,[],[f2598,f6445]) ).
fof(f6445,plain,
( spl0_774
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f2598,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f6443,plain,
spl0_773,
inference(avatar_split_clause,[],[f2597,f6441]) ).
fof(f6441,plain,
( spl0_773
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f2597,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f6439,plain,
spl0_772,
inference(avatar_split_clause,[],[f2596,f6437]) ).
fof(f6437,plain,
( spl0_772
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f2596,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
fof(f6435,plain,
spl0_771,
inference(avatar_split_clause,[],[f2595,f6433]) ).
fof(f6433,plain,
( spl0_771
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f2595,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f6431,plain,
spl0_770,
inference(avatar_split_clause,[],[f2594,f6429]) ).
fof(f6429,plain,
( spl0_770
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f2594,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
fof(f6427,plain,
spl0_769,
inference(avatar_split_clause,[],[f2593,f6425]) ).
fof(f6425,plain,
( spl0_769
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f2593,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
fof(f6423,plain,
spl0_768,
inference(avatar_split_clause,[],[f2592,f6421]) ).
fof(f6421,plain,
( spl0_768
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f2592,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f6419,plain,
spl0_767,
inference(avatar_split_clause,[],[f2591,f6417]) ).
fof(f6417,plain,
( spl0_767
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f2591,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f6415,plain,
spl0_766,
inference(avatar_split_clause,[],[f2590,f6413]) ).
fof(f6413,plain,
( spl0_766
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f2590,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
fof(f6411,plain,
spl0_765,
inference(avatar_split_clause,[],[f2589,f6409]) ).
fof(f6409,plain,
( spl0_765
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f2589,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f6407,plain,
spl0_764,
inference(avatar_split_clause,[],[f2588,f6405]) ).
fof(f6405,plain,
( spl0_764
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f2588,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f6403,plain,
spl0_763,
inference(avatar_split_clause,[],[f2587,f6401]) ).
fof(f6401,plain,
( spl0_763
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f2587,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f6399,plain,
spl0_762,
inference(avatar_split_clause,[],[f2586,f6397]) ).
fof(f6397,plain,
( spl0_762
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f2586,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f6395,plain,
spl0_761,
inference(avatar_split_clause,[],[f2585,f6393]) ).
fof(f6393,plain,
( spl0_761
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f2585,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f6391,plain,
spl0_760,
inference(avatar_split_clause,[],[f2584,f6389]) ).
fof(f6389,plain,
( spl0_760
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f2584,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f6387,plain,
spl0_759,
inference(avatar_split_clause,[],[f2583,f6385]) ).
fof(f6385,plain,
( spl0_759
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f2583,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f6383,plain,
spl0_758,
inference(avatar_split_clause,[],[f2582,f6381]) ).
fof(f6381,plain,
( spl0_758
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f2582,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f6379,plain,
spl0_757,
inference(avatar_split_clause,[],[f2581,f6377]) ).
fof(f6377,plain,
( spl0_757
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f2581,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
fof(f6375,plain,
spl0_756,
inference(avatar_split_clause,[],[f2580,f6373]) ).
fof(f6373,plain,
( spl0_756
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f2580,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
fof(f6371,plain,
spl0_755,
inference(avatar_split_clause,[],[f2579,f6369]) ).
fof(f6369,plain,
( spl0_755
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f2579,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
fof(f6367,plain,
spl0_754,
inference(avatar_split_clause,[],[f2578,f6365]) ).
fof(f6365,plain,
( spl0_754
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f2578,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f6363,plain,
spl0_753,
inference(avatar_split_clause,[],[f2577,f6361]) ).
fof(f6361,plain,
( spl0_753
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f2577,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f6359,plain,
spl0_752,
inference(avatar_split_clause,[],[f2576,f6357]) ).
fof(f6357,plain,
( spl0_752
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f2576,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f6355,plain,
spl0_751,
inference(avatar_split_clause,[],[f2575,f6353]) ).
fof(f6353,plain,
( spl0_751
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f2575,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f6351,plain,
spl0_750,
inference(avatar_split_clause,[],[f2574,f6349]) ).
fof(f6349,plain,
( spl0_750
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f2574,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
fof(f6347,plain,
spl0_749,
inference(avatar_split_clause,[],[f2573,f6345]) ).
fof(f6345,plain,
( spl0_749
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f2573,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
fof(f6343,plain,
spl0_748,
inference(avatar_split_clause,[],[f2572,f6341]) ).
fof(f6341,plain,
( spl0_748
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f2572,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
fof(f6339,plain,
spl0_747,
inference(avatar_split_clause,[],[f2571,f6337]) ).
fof(f6337,plain,
( spl0_747
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2571,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
fof(f6335,plain,
spl0_746,
inference(avatar_split_clause,[],[f2570,f6333]) ).
fof(f6333,plain,
( spl0_746
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f2570,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f6331,plain,
spl0_745,
inference(avatar_split_clause,[],[f2569,f6329]) ).
fof(f6329,plain,
( spl0_745
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f2569,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
fof(f6327,plain,
spl0_744,
inference(avatar_split_clause,[],[f2568,f6325]) ).
fof(f6325,plain,
( spl0_744
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f2568,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f6323,plain,
spl0_743,
inference(avatar_split_clause,[],[f2567,f6321]) ).
fof(f6321,plain,
( spl0_743
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f2567,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f6319,plain,
spl0_742,
inference(avatar_split_clause,[],[f2566,f6317]) ).
fof(f6317,plain,
( spl0_742
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2566,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f6315,plain,
spl0_741,
inference(avatar_split_clause,[],[f2565,f6313]) ).
fof(f6313,plain,
( spl0_741
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2565,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f6311,plain,
spl0_740,
inference(avatar_split_clause,[],[f2564,f6309]) ).
fof(f6309,plain,
( spl0_740
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2564,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
fof(f6307,plain,
spl0_739,
inference(avatar_split_clause,[],[f2563,f6305]) ).
fof(f6305,plain,
( spl0_739
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f2563,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f6303,plain,
spl0_738,
inference(avatar_split_clause,[],[f2562,f6301]) ).
fof(f6301,plain,
( spl0_738
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2562,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f6299,plain,
spl0_737,
inference(avatar_split_clause,[],[f2561,f6297]) ).
fof(f6297,plain,
( spl0_737
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2561,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f6295,plain,
spl0_736,
inference(avatar_split_clause,[],[f2560,f6293]) ).
fof(f6293,plain,
( spl0_736
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f2560,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f6291,plain,
spl0_735,
inference(avatar_split_clause,[],[f2559,f6289]) ).
fof(f6289,plain,
( spl0_735
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2559,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f6287,plain,
spl0_734,
inference(avatar_split_clause,[],[f2558,f6285]) ).
fof(f6285,plain,
( spl0_734
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2558,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f6283,plain,
spl0_733,
inference(avatar_split_clause,[],[f2557,f6281]) ).
fof(f6281,plain,
( spl0_733
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2557,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f6279,plain,
spl0_732,
inference(avatar_split_clause,[],[f2556,f6277]) ).
fof(f6277,plain,
( spl0_732
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2556,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f6275,plain,
spl0_731,
inference(avatar_split_clause,[],[f2555,f6273]) ).
fof(f6273,plain,
( spl0_731
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2555,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f6271,plain,
spl0_730,
inference(avatar_split_clause,[],[f2554,f6269]) ).
fof(f6269,plain,
( spl0_730
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2554,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f6267,plain,
spl0_729,
inference(avatar_split_clause,[],[f2553,f6265]) ).
fof(f6265,plain,
( spl0_729
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2553,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f6263,plain,
spl0_728,
inference(avatar_split_clause,[],[f2552,f6261]) ).
fof(f6261,plain,
( spl0_728
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2552,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f6259,plain,
spl0_727,
inference(avatar_split_clause,[],[f2551,f6257]) ).
fof(f6257,plain,
( spl0_727
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f2551,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f6255,plain,
spl0_726,
inference(avatar_split_clause,[],[f2550,f6253]) ).
fof(f6253,plain,
( spl0_726
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2550,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f6251,plain,
spl0_725,
inference(avatar_split_clause,[],[f2549,f6249]) ).
fof(f6249,plain,
( spl0_725
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2549,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f6247,plain,
spl0_724,
inference(avatar_split_clause,[],[f2548,f6245]) ).
fof(f6245,plain,
( spl0_724
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2548,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f6243,plain,
spl0_723,
inference(avatar_split_clause,[],[f2547,f6241]) ).
fof(f6241,plain,
( spl0_723
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2547,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f6239,plain,
spl0_722,
inference(avatar_split_clause,[],[f2546,f6237]) ).
fof(f6237,plain,
( spl0_722
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2546,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f6235,plain,
spl0_721,
inference(avatar_split_clause,[],[f2545,f6233]) ).
fof(f6233,plain,
( spl0_721
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2545,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f6231,plain,
spl0_720,
inference(avatar_split_clause,[],[f2544,f6229]) ).
fof(f6229,plain,
( spl0_720
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2544,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f6227,plain,
spl0_719,
inference(avatar_split_clause,[],[f2543,f6225]) ).
fof(f6225,plain,
( spl0_719
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2543,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f6223,plain,
spl0_718,
inference(avatar_split_clause,[],[f2542,f6221]) ).
fof(f6221,plain,
( spl0_718
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f2542,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f6219,plain,
spl0_717,
inference(avatar_split_clause,[],[f2541,f6217]) ).
fof(f6217,plain,
( spl0_717
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f2541,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f6215,plain,
spl0_716,
inference(avatar_split_clause,[],[f2540,f6213]) ).
fof(f6213,plain,
( spl0_716
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2540,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f6211,plain,
spl0_715,
inference(avatar_split_clause,[],[f2539,f6209]) ).
fof(f6209,plain,
( spl0_715
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f2539,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f6207,plain,
spl0_714,
inference(avatar_split_clause,[],[f2538,f6205]) ).
fof(f6205,plain,
( spl0_714
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f2538,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f6203,plain,
spl0_713,
inference(avatar_split_clause,[],[f2537,f6201]) ).
fof(f6201,plain,
( spl0_713
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f2537,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f6199,plain,
spl0_712,
inference(avatar_split_clause,[],[f2536,f6197]) ).
fof(f6197,plain,
( spl0_712
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f2536,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f6195,plain,
spl0_711,
inference(avatar_split_clause,[],[f2535,f6193]) ).
fof(f6193,plain,
( spl0_711
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f2535,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f6191,plain,
spl0_710,
inference(avatar_split_clause,[],[f2534,f6189]) ).
fof(f6189,plain,
( spl0_710
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f2534,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f6187,plain,
spl0_709,
inference(avatar_split_clause,[],[f2533,f6185]) ).
fof(f6185,plain,
( spl0_709
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f2533,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f6183,plain,
spl0_708,
inference(avatar_split_clause,[],[f2532,f6181]) ).
fof(f6181,plain,
( spl0_708
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f2532,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f6179,plain,
spl0_707,
inference(avatar_split_clause,[],[f2531,f6177]) ).
fof(f6177,plain,
( spl0_707
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f2531,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f6175,plain,
spl0_706,
inference(avatar_split_clause,[],[f2530,f6173]) ).
fof(f6173,plain,
( spl0_706
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f2530,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f6171,plain,
spl0_705,
inference(avatar_split_clause,[],[f2529,f6169]) ).
fof(f6169,plain,
( spl0_705
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f2529,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f6167,plain,
spl0_704,
inference(avatar_split_clause,[],[f2528,f6165]) ).
fof(f6165,plain,
( spl0_704
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f2528,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
fof(f6163,plain,
spl0_703,
inference(avatar_split_clause,[],[f2527,f6161]) ).
fof(f6161,plain,
( spl0_703
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f2527,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
fof(f6159,plain,
spl0_702,
inference(avatar_split_clause,[],[f2526,f6157]) ).
fof(f6157,plain,
( spl0_702
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f2526,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f6155,plain,
spl0_701,
inference(avatar_split_clause,[],[f2525,f6153]) ).
fof(f6153,plain,
( spl0_701
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f2525,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
fof(f6151,plain,
spl0_700,
inference(avatar_split_clause,[],[f2524,f6149]) ).
fof(f6149,plain,
( spl0_700
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f2524,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f6147,plain,
spl0_699,
inference(avatar_split_clause,[],[f2523,f6145]) ).
fof(f6145,plain,
( spl0_699
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f2523,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f6143,plain,
spl0_698,
inference(avatar_split_clause,[],[f2522,f6141]) ).
fof(f6141,plain,
( spl0_698
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f2522,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
fof(f6139,plain,
spl0_697,
inference(avatar_split_clause,[],[f2521,f6137]) ).
fof(f6137,plain,
( spl0_697
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f2521,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f6135,plain,
spl0_696,
inference(avatar_split_clause,[],[f2520,f6133]) ).
fof(f6133,plain,
( spl0_696
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f2520,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
fof(f6131,plain,
spl0_695,
inference(avatar_split_clause,[],[f2519,f6129]) ).
fof(f6129,plain,
( spl0_695
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2519,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
fof(f6127,plain,
spl0_694,
inference(avatar_split_clause,[],[f2518,f6125]) ).
fof(f6125,plain,
( spl0_694
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2518,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f6123,plain,
spl0_693,
inference(avatar_split_clause,[],[f2517,f6121]) ).
fof(f6121,plain,
( spl0_693
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f2517,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f6119,plain,
spl0_692,
inference(avatar_split_clause,[],[f2516,f6117]) ).
fof(f6117,plain,
( spl0_692
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f2516,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f6115,plain,
spl0_691,
inference(avatar_split_clause,[],[f2515,f6113]) ).
fof(f6113,plain,
( spl0_691
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f2515,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
fof(f6111,plain,
spl0_690,
inference(avatar_split_clause,[],[f2514,f6109]) ).
fof(f6109,plain,
( spl0_690
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f2514,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f6107,plain,
spl0_689,
inference(avatar_split_clause,[],[f2513,f6105]) ).
fof(f6105,plain,
( spl0_689
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f2513,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f6103,plain,
spl0_688,
inference(avatar_split_clause,[],[f2512,f6101]) ).
fof(f6101,plain,
( spl0_688
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f2512,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f6099,plain,
spl0_687,
inference(avatar_split_clause,[],[f2511,f6097]) ).
fof(f6097,plain,
( spl0_687
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f2511,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
fof(f6095,plain,
spl0_686,
inference(avatar_split_clause,[],[f2510,f6093]) ).
fof(f6093,plain,
( spl0_686
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f2510,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
fof(f6091,plain,
spl0_685,
inference(avatar_split_clause,[],[f2509,f6089]) ).
fof(f6089,plain,
( spl0_685
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f2509,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f6087,plain,
spl0_684,
inference(avatar_split_clause,[],[f2508,f6085]) ).
fof(f6085,plain,
( spl0_684
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f2508,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f6083,plain,
spl0_683,
inference(avatar_split_clause,[],[f2507,f6081]) ).
fof(f6081,plain,
( spl0_683
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f2507,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f6079,plain,
spl0_682,
inference(avatar_split_clause,[],[f2506,f6077]) ).
fof(f6077,plain,
( spl0_682
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f2506,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f6075,plain,
spl0_681,
inference(avatar_split_clause,[],[f2505,f6073]) ).
fof(f6073,plain,
( spl0_681
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f2505,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
fof(f6071,plain,
spl0_680,
inference(avatar_split_clause,[],[f2504,f6069]) ).
fof(f6069,plain,
( spl0_680
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f2504,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f6067,plain,
spl0_679,
inference(avatar_split_clause,[],[f2503,f6065]) ).
fof(f6065,plain,
( spl0_679
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f2503,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f6063,plain,
spl0_678,
inference(avatar_split_clause,[],[f2502,f6061]) ).
fof(f6061,plain,
( spl0_678
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f2502,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f6059,plain,
spl0_677,
inference(avatar_split_clause,[],[f2501,f6057]) ).
fof(f6057,plain,
( spl0_677
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f2501,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f6055,plain,
spl0_676,
inference(avatar_split_clause,[],[f2500,f6053]) ).
fof(f6053,plain,
( spl0_676
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f2500,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f6051,plain,
spl0_675,
inference(avatar_split_clause,[],[f2499,f6049]) ).
fof(f6049,plain,
( spl0_675
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f2499,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f6047,plain,
spl0_674,
inference(avatar_split_clause,[],[f2498,f6045]) ).
fof(f6045,plain,
( spl0_674
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f2498,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f6043,plain,
spl0_673,
inference(avatar_split_clause,[],[f2497,f6041]) ).
fof(f6041,plain,
( spl0_673
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2497,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f6039,plain,
spl0_672,
inference(avatar_split_clause,[],[f2496,f6037]) ).
fof(f6037,plain,
( spl0_672
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f2496,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f6035,plain,
spl0_671,
inference(avatar_split_clause,[],[f2495,f6033]) ).
fof(f6033,plain,
( spl0_671
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2495,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f6031,plain,
spl0_670,
inference(avatar_split_clause,[],[f2494,f6029]) ).
fof(f6029,plain,
( spl0_670
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f2494,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f6027,plain,
spl0_669,
inference(avatar_split_clause,[],[f2493,f6025]) ).
fof(f6025,plain,
( spl0_669
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f2493,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f6023,plain,
spl0_668,
inference(avatar_split_clause,[],[f2492,f6021]) ).
fof(f6021,plain,
( spl0_668
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f2492,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f6019,plain,
spl0_667,
inference(avatar_split_clause,[],[f2491,f6017]) ).
fof(f6017,plain,
( spl0_667
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f2491,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f6015,plain,
spl0_666,
inference(avatar_split_clause,[],[f2490,f6013]) ).
fof(f6013,plain,
( spl0_666
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f2490,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f6011,plain,
spl0_665,
inference(avatar_split_clause,[],[f2489,f6009]) ).
fof(f6009,plain,
( spl0_665
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f2489,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f6007,plain,
spl0_664,
inference(avatar_split_clause,[],[f2488,f6005]) ).
fof(f6005,plain,
( spl0_664
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f2488,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f6003,plain,
spl0_663,
inference(avatar_split_clause,[],[f2487,f6001]) ).
fof(f6001,plain,
( spl0_663
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f2487,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
fof(f5999,plain,
spl0_662,
inference(avatar_split_clause,[],[f2486,f5997]) ).
fof(f5997,plain,
( spl0_662
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2486,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5995,plain,
spl0_661,
inference(avatar_split_clause,[],[f2485,f5993]) ).
fof(f5993,plain,
( spl0_661
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f2485,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5991,plain,
spl0_660,
inference(avatar_split_clause,[],[f2484,f5989]) ).
fof(f5989,plain,
( spl0_660
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f2484,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5987,plain,
spl0_659,
inference(avatar_split_clause,[],[f2483,f5985]) ).
fof(f5985,plain,
( spl0_659
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2483,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5983,plain,
spl0_658,
inference(avatar_split_clause,[],[f2482,f5981]) ).
fof(f5981,plain,
( spl0_658
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f2482,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5979,plain,
spl0_657,
inference(avatar_split_clause,[],[f2481,f5977]) ).
fof(f5977,plain,
( spl0_657
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2481,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
fof(f5975,plain,
spl0_656,
inference(avatar_split_clause,[],[f2480,f5973]) ).
fof(f5973,plain,
( spl0_656
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2480,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
fof(f5971,plain,
spl0_655,
inference(avatar_split_clause,[],[f2479,f5969]) ).
fof(f5969,plain,
( spl0_655
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2479,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
fof(f5967,plain,
spl0_654,
inference(avatar_split_clause,[],[f2478,f5965]) ).
fof(f5965,plain,
( spl0_654
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2478,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
fof(f5963,plain,
spl0_653,
inference(avatar_split_clause,[],[f2477,f5961]) ).
fof(f5961,plain,
( spl0_653
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2477,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5959,plain,
spl0_652,
inference(avatar_split_clause,[],[f2476,f5957]) ).
fof(f5957,plain,
( spl0_652
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2476,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5955,plain,
spl0_651,
inference(avatar_split_clause,[],[f2475,f5953]) ).
fof(f5953,plain,
( spl0_651
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2475,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5951,plain,
spl0_650,
inference(avatar_split_clause,[],[f2474,f5949]) ).
fof(f2474,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5947,plain,
spl0_649,
inference(avatar_split_clause,[],[f2473,f5945]) ).
fof(f2473,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5943,plain,
spl0_648,
inference(avatar_split_clause,[],[f2472,f5941]) ).
fof(f2472,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5939,plain,
spl0_647,
inference(avatar_split_clause,[],[f2471,f5937]) ).
fof(f2471,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5935,plain,
spl0_646,
inference(avatar_split_clause,[],[f2470,f5933]) ).
fof(f2470,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5931,plain,
spl0_645,
inference(avatar_split_clause,[],[f2469,f5929]) ).
fof(f2469,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
fof(f5927,plain,
spl0_644,
inference(avatar_split_clause,[],[f2468,f5925]) ).
fof(f2468,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5923,plain,
spl0_643,
inference(avatar_split_clause,[],[f2467,f5921]) ).
fof(f2467,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5919,plain,
spl0_642,
inference(avatar_split_clause,[],[f2466,f5917]) ).
fof(f2466,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5915,plain,
spl0_641,
inference(avatar_split_clause,[],[f2465,f5913]) ).
fof(f2465,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5911,plain,
spl0_640,
inference(avatar_split_clause,[],[f2464,f5909]) ).
fof(f2464,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5907,plain,
spl0_639,
inference(avatar_split_clause,[],[f2463,f5905]) ).
fof(f2463,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5903,plain,
spl0_638,
inference(avatar_split_clause,[],[f2462,f5901]) ).
fof(f2462,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
fof(f5899,plain,
spl0_637,
inference(avatar_split_clause,[],[f2461,f5897]) ).
fof(f2461,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5895,plain,
spl0_636,
inference(avatar_split_clause,[],[f2460,f5893]) ).
fof(f2460,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5891,plain,
spl0_635,
inference(avatar_split_clause,[],[f2459,f5889]) ).
fof(f2459,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5887,plain,
spl0_634,
inference(avatar_split_clause,[],[f2458,f5885]) ).
fof(f2458,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5883,plain,
spl0_633,
inference(avatar_split_clause,[],[f2457,f5881]) ).
fof(f2457,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5879,plain,
spl0_632,
inference(avatar_split_clause,[],[f2456,f5877]) ).
fof(f2456,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5875,plain,
spl0_631,
inference(avatar_split_clause,[],[f2455,f5873]) ).
fof(f2455,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5871,plain,
spl0_630,
inference(avatar_split_clause,[],[f2454,f5869]) ).
fof(f2454,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5867,plain,
spl0_629,
inference(avatar_split_clause,[],[f2453,f5865]) ).
fof(f2453,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5863,plain,
spl0_628,
inference(avatar_split_clause,[],[f2452,f5861]) ).
fof(f2452,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5859,plain,
spl0_627,
inference(avatar_split_clause,[],[f2451,f5857]) ).
fof(f2451,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5855,plain,
spl0_626,
inference(avatar_split_clause,[],[f2450,f5853]) ).
fof(f2450,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5851,plain,
spl0_625,
inference(avatar_split_clause,[],[f2449,f5849]) ).
fof(f2449,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5847,plain,
spl0_624,
inference(avatar_split_clause,[],[f2448,f5845]) ).
fof(f2448,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5843,plain,
spl0_623,
inference(avatar_split_clause,[],[f2447,f5841]) ).
fof(f2447,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5839,plain,
spl0_622,
inference(avatar_split_clause,[],[f2446,f5837]) ).
fof(f2446,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5835,plain,
spl0_621,
inference(avatar_split_clause,[],[f2445,f5833]) ).
fof(f2445,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5831,plain,
spl0_620,
inference(avatar_split_clause,[],[f2444,f5829]) ).
fof(f2444,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5827,plain,
spl0_619,
inference(avatar_split_clause,[],[f2443,f5825]) ).
fof(f2443,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5823,plain,
spl0_618,
inference(avatar_split_clause,[],[f2442,f5821]) ).
fof(f2442,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5819,plain,
spl0_617,
inference(avatar_split_clause,[],[f2441,f5817]) ).
fof(f2441,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5815,plain,
spl0_616,
inference(avatar_split_clause,[],[f2440,f5813]) ).
fof(f2440,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5811,plain,
spl0_615,
inference(avatar_split_clause,[],[f2439,f5809]) ).
fof(f2439,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).
fof(f5807,plain,
spl0_614,
inference(avatar_split_clause,[],[f2438,f5805]) ).
fof(f2438,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).
fof(f5803,plain,
spl0_613,
inference(avatar_split_clause,[],[f2437,f5801]) ).
fof(f2437,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5799,plain,
spl0_612,
inference(avatar_split_clause,[],[f2436,f5797]) ).
fof(f2436,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).
fof(f5795,plain,
spl0_611,
inference(avatar_split_clause,[],[f2435,f5793]) ).
fof(f2435,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5791,plain,
spl0_610,
inference(avatar_split_clause,[],[f2434,f5789]) ).
fof(f2434,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).
fof(f5787,plain,
spl0_609,
inference(avatar_split_clause,[],[f2433,f5785]) ).
fof(f2433,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5783,plain,
spl0_608,
inference(avatar_split_clause,[],[f2432,f5781]) ).
fof(f2432,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
fof(f5779,plain,
spl0_607,
inference(avatar_split_clause,[],[f2431,f5777]) ).
fof(f2431,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f5775,plain,
spl0_606,
inference(avatar_split_clause,[],[f2430,f5773]) ).
fof(f2430,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5771,plain,
spl0_605,
inference(avatar_split_clause,[],[f2429,f5769]) ).
fof(f2429,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5767,plain,
spl0_604,
inference(avatar_split_clause,[],[f2428,f5765]) ).
fof(f2428,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5763,plain,
spl0_603,
inference(avatar_split_clause,[],[f2427,f5761]) ).
fof(f2427,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5759,plain,
spl0_602,
inference(avatar_split_clause,[],[f2426,f5757]) ).
fof(f2426,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f5755,plain,
spl0_601,
inference(avatar_split_clause,[],[f2425,f5753]) ).
fof(f2425,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5751,plain,
spl0_600,
inference(avatar_split_clause,[],[f2424,f5749]) ).
fof(f2424,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f5747,plain,
spl0_599,
inference(avatar_split_clause,[],[f2423,f5745]) ).
fof(f2423,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f5743,plain,
spl0_598,
inference(avatar_split_clause,[],[f2422,f5741]) ).
fof(f2422,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f5739,plain,
spl0_597,
inference(avatar_split_clause,[],[f2421,f5737]) ).
fof(f2421,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f5735,plain,
spl0_596,
inference(avatar_split_clause,[],[f2420,f5733]) ).
fof(f2420,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f5731,plain,
spl0_595,
inference(avatar_split_clause,[],[f2419,f5729]) ).
fof(f2419,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f5727,plain,
spl0_594,
inference(avatar_split_clause,[],[f2418,f5725]) ).
fof(f2418,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f5723,plain,
spl0_593,
inference(avatar_split_clause,[],[f2417,f5721]) ).
fof(f2417,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f5719,plain,
spl0_592,
inference(avatar_split_clause,[],[f2355,f5717]) ).
fof(f5717,plain,
( spl0_592
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2355,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
fof(f5715,plain,
spl0_591,
inference(avatar_split_clause,[],[f2354,f5713]) ).
fof(f5713,plain,
( spl0_591
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2354,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
fof(f5711,plain,
spl0_590,
inference(avatar_split_clause,[],[f2353,f5709]) ).
fof(f5709,plain,
( spl0_590
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2353,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f5707,plain,
spl0_589,
inference(avatar_split_clause,[],[f2352,f5705]) ).
fof(f5705,plain,
( spl0_589
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2352,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
fof(f5703,plain,
spl0_588,
inference(avatar_split_clause,[],[f2351,f5701]) ).
fof(f5701,plain,
( spl0_588
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2351,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
fof(f5699,plain,
spl0_587,
inference(avatar_split_clause,[],[f2350,f5697]) ).
fof(f5697,plain,
( spl0_587
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2350,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f5695,plain,
spl0_586,
inference(avatar_split_clause,[],[f2349,f5693]) ).
fof(f5693,plain,
( spl0_586
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2349,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f5691,plain,
spl0_585,
inference(avatar_split_clause,[],[f2348,f5689]) ).
fof(f5689,plain,
( spl0_585
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2348,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f5687,plain,
spl0_584,
inference(avatar_split_clause,[],[f2347,f5685]) ).
fof(f5685,plain,
( spl0_584
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2347,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f5683,plain,
spl0_583,
inference(avatar_split_clause,[],[f2346,f5681]) ).
fof(f5681,plain,
( spl0_583
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2346,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f5679,plain,
spl0_582,
inference(avatar_split_clause,[],[f2345,f5677]) ).
fof(f5677,plain,
( spl0_582
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2345,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f5675,plain,
spl0_581,
inference(avatar_split_clause,[],[f2344,f5673]) ).
fof(f5673,plain,
( spl0_581
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2344,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f5671,plain,
spl0_580,
inference(avatar_split_clause,[],[f2343,f5669]) ).
fof(f5669,plain,
( spl0_580
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2343,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f5667,plain,
spl0_579,
inference(avatar_split_clause,[],[f2342,f5665]) ).
fof(f5665,plain,
( spl0_579
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2342,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f5663,plain,
spl0_578,
inference(avatar_split_clause,[],[f2341,f5661]) ).
fof(f5661,plain,
( spl0_578
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2341,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f5659,plain,
spl0_577,
inference(avatar_split_clause,[],[f2340,f5657]) ).
fof(f5657,plain,
( spl0_577
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2340,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f5655,plain,
spl0_576,
inference(avatar_split_clause,[],[f2339,f5653]) ).
fof(f5653,plain,
( spl0_576
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2339,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f5651,plain,
spl0_575,
inference(avatar_split_clause,[],[f2338,f5649]) ).
fof(f5649,plain,
( spl0_575
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2338,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
fof(f5647,plain,
spl0_574,
inference(avatar_split_clause,[],[f2337,f5645]) ).
fof(f5645,plain,
( spl0_574
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2337,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f5643,plain,
spl0_573,
inference(avatar_split_clause,[],[f2336,f5641]) ).
fof(f5641,plain,
( spl0_573
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2336,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f5639,plain,
spl0_572,
inference(avatar_split_clause,[],[f2335,f5637]) ).
fof(f5637,plain,
( spl0_572
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2335,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f5635,plain,
spl0_571,
inference(avatar_split_clause,[],[f2334,f5633]) ).
fof(f5633,plain,
( spl0_571
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2334,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f5631,plain,
spl0_570,
inference(avatar_split_clause,[],[f2333,f5629]) ).
fof(f5629,plain,
( spl0_570
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2333,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f5627,plain,
spl0_569,
inference(avatar_split_clause,[],[f2332,f5625]) ).
fof(f5625,plain,
( spl0_569
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2332,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f5623,plain,
spl0_568,
inference(avatar_split_clause,[],[f2331,f5621]) ).
fof(f5621,plain,
( spl0_568
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2331,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f5619,plain,
spl0_567,
inference(avatar_split_clause,[],[f2330,f5617]) ).
fof(f5617,plain,
( spl0_567
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2330,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f5615,plain,
spl0_566,
inference(avatar_split_clause,[],[f2329,f5613]) ).
fof(f5613,plain,
( spl0_566
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2329,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
fof(f5611,plain,
spl0_565,
inference(avatar_split_clause,[],[f2328,f5609]) ).
fof(f5609,plain,
( spl0_565
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2328,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
fof(f5607,plain,
spl0_564,
inference(avatar_split_clause,[],[f2327,f5605]) ).
fof(f5605,plain,
( spl0_564
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2327,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f5603,plain,
spl0_563,
inference(avatar_split_clause,[],[f2326,f5601]) ).
fof(f5601,plain,
( spl0_563
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2326,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f5599,plain,
spl0_562,
inference(avatar_split_clause,[],[f2325,f5597]) ).
fof(f5597,plain,
( spl0_562
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2325,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f5595,plain,
spl0_561,
inference(avatar_split_clause,[],[f2324,f5593]) ).
fof(f5593,plain,
( spl0_561
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2324,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f5591,plain,
spl0_560,
inference(avatar_split_clause,[],[f2323,f5589]) ).
fof(f5589,plain,
( spl0_560
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2323,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f5587,plain,
spl0_559,
inference(avatar_split_clause,[],[f2322,f5585]) ).
fof(f5585,plain,
( spl0_559
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2322,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f5583,plain,
spl0_558,
inference(avatar_split_clause,[],[f2321,f5581]) ).
fof(f5581,plain,
( spl0_558
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2321,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f5579,plain,
spl0_557,
inference(avatar_split_clause,[],[f2320,f5577]) ).
fof(f5577,plain,
( spl0_557
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2320,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).
fof(f5575,plain,
spl0_556,
inference(avatar_split_clause,[],[f2319,f5573]) ).
fof(f5573,plain,
( spl0_556
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2319,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f5571,plain,
spl0_555,
inference(avatar_split_clause,[],[f2318,f5569]) ).
fof(f5569,plain,
( spl0_555
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2318,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f5567,plain,
spl0_554,
inference(avatar_split_clause,[],[f2317,f5565]) ).
fof(f5565,plain,
( spl0_554
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2317,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f5563,plain,
spl0_553,
inference(avatar_split_clause,[],[f2316,f5561]) ).
fof(f5561,plain,
( spl0_553
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2316,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f5559,plain,
spl0_552,
inference(avatar_split_clause,[],[f2315,f5557]) ).
fof(f5557,plain,
( spl0_552
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2315,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f5555,plain,
spl0_551,
inference(avatar_split_clause,[],[f2314,f5553]) ).
fof(f5553,plain,
( spl0_551
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2314,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f5551,plain,
spl0_550,
inference(avatar_split_clause,[],[f2313,f5549]) ).
fof(f5549,plain,
( spl0_550
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2313,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f5547,plain,
spl0_549,
inference(avatar_split_clause,[],[f2312,f5545]) ).
fof(f5545,plain,
( spl0_549
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2312,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f5543,plain,
spl0_548,
inference(avatar_split_clause,[],[f2311,f5541]) ).
fof(f5541,plain,
( spl0_548
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2311,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).
fof(f5539,plain,
spl0_547,
inference(avatar_split_clause,[],[f2310,f5537]) ).
fof(f5537,plain,
( spl0_547
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2310,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).
fof(f5535,plain,
spl0_546,
inference(avatar_split_clause,[],[f2309,f5533]) ).
fof(f5533,plain,
( spl0_546
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2309,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f5531,plain,
spl0_545,
inference(avatar_split_clause,[],[f2308,f5529]) ).
fof(f5529,plain,
( spl0_545
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2308,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).
fof(f5527,plain,
spl0_544,
inference(avatar_split_clause,[],[f2307,f5525]) ).
fof(f5525,plain,
( spl0_544
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2307,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f5523,plain,
spl0_543,
inference(avatar_split_clause,[],[f2306,f5521]) ).
fof(f5521,plain,
( spl0_543
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2306,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f5519,plain,
spl0_542,
inference(avatar_split_clause,[],[f2305,f5517]) ).
fof(f5517,plain,
( spl0_542
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2305,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).
fof(f5515,plain,
spl0_541,
inference(avatar_split_clause,[],[f2304,f5513]) ).
fof(f5513,plain,
( spl0_541
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2304,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f5511,plain,
spl0_540,
inference(avatar_split_clause,[],[f2303,f5509]) ).
fof(f5509,plain,
( spl0_540
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2303,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).
fof(f5507,plain,
spl0_539,
inference(avatar_split_clause,[],[f2302,f5505]) ).
fof(f5505,plain,
( spl0_539
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2302,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).
fof(f5503,plain,
spl0_538,
inference(avatar_split_clause,[],[f2301,f5501]) ).
fof(f5501,plain,
( spl0_538
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2301,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f5499,plain,
spl0_537,
inference(avatar_split_clause,[],[f2300,f5497]) ).
fof(f5497,plain,
( spl0_537
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2300,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f5495,plain,
spl0_536,
inference(avatar_split_clause,[],[f2299,f5493]) ).
fof(f5493,plain,
( spl0_536
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2299,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f5491,plain,
spl0_535,
inference(avatar_split_clause,[],[f2298,f5489]) ).
fof(f5489,plain,
( spl0_535
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2298,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f5487,plain,
spl0_534,
inference(avatar_split_clause,[],[f2297,f5485]) ).
fof(f5485,plain,
( spl0_534
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2297,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f5483,plain,
spl0_533,
inference(avatar_split_clause,[],[f2296,f5481]) ).
fof(f5481,plain,
( spl0_533
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2296,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f5479,plain,
spl0_532,
inference(avatar_split_clause,[],[f2295,f5477]) ).
fof(f5477,plain,
( spl0_532
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2295,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f5475,plain,
spl0_531,
inference(avatar_split_clause,[],[f2294,f5473]) ).
fof(f5473,plain,
( spl0_531
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2294,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f5471,plain,
spl0_530,
inference(avatar_split_clause,[],[f2293,f5469]) ).
fof(f5469,plain,
( spl0_530
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2293,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f5467,plain,
spl0_529,
inference(avatar_split_clause,[],[f2292,f5465]) ).
fof(f5465,plain,
( spl0_529
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2292,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f5463,plain,
spl0_528,
inference(avatar_split_clause,[],[f2291,f5461]) ).
fof(f5461,plain,
( spl0_528
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2291,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f5459,plain,
spl0_527,
inference(avatar_split_clause,[],[f2290,f5457]) ).
fof(f5457,plain,
( spl0_527
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2290,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).
fof(f5455,plain,
spl0_526,
inference(avatar_split_clause,[],[f2289,f5453]) ).
fof(f5453,plain,
( spl0_526
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2289,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f5451,plain,
spl0_525,
inference(avatar_split_clause,[],[f2288,f5449]) ).
fof(f5449,plain,
( spl0_525
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2288,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).
fof(f5447,plain,
spl0_524,
inference(avatar_split_clause,[],[f2287,f5445]) ).
fof(f5445,plain,
( spl0_524
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2287,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f5443,plain,
spl0_523,
inference(avatar_split_clause,[],[f2286,f5441]) ).
fof(f5441,plain,
( spl0_523
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2286,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).
fof(f5439,plain,
spl0_522,
inference(avatar_split_clause,[],[f2285,f5437]) ).
fof(f5437,plain,
( spl0_522
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2285,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).
fof(f5435,plain,
spl0_521,
inference(avatar_split_clause,[],[f2284,f5433]) ).
fof(f5433,plain,
( spl0_521
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2284,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f5431,plain,
spl0_520,
inference(avatar_split_clause,[],[f2283,f5429]) ).
fof(f5429,plain,
( spl0_520
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2283,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).
fof(f5427,plain,
spl0_519,
inference(avatar_split_clause,[],[f2282,f5425]) ).
fof(f5425,plain,
( spl0_519
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2282,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f5423,plain,
spl0_518,
inference(avatar_split_clause,[],[f2281,f5421]) ).
fof(f5421,plain,
( spl0_518
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2281,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).
fof(f5419,plain,
spl0_517,
inference(avatar_split_clause,[],[f2280,f5417]) ).
fof(f5417,plain,
( spl0_517
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2280,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f5415,plain,
spl0_516,
inference(avatar_split_clause,[],[f2279,f5413]) ).
fof(f5413,plain,
( spl0_516
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2279,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).
fof(f5411,plain,
spl0_515,
inference(avatar_split_clause,[],[f2278,f5409]) ).
fof(f5409,plain,
( spl0_515
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2278,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).
fof(f5407,plain,
spl0_514,
inference(avatar_split_clause,[],[f2277,f5405]) ).
fof(f5405,plain,
( spl0_514
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2277,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f5403,plain,
spl0_513,
inference(avatar_split_clause,[],[f2276,f5401]) ).
fof(f5401,plain,
( spl0_513
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2276,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f5399,plain,
spl0_512,
inference(avatar_split_clause,[],[f2275,f5397]) ).
fof(f5397,plain,
( spl0_512
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2275,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f5395,plain,
spl0_511,
inference(avatar_split_clause,[],[f2274,f5393]) ).
fof(f5393,plain,
( spl0_511
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2274,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f5391,plain,
spl0_510,
inference(avatar_split_clause,[],[f2273,f5389]) ).
fof(f5389,plain,
( spl0_510
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2273,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).
fof(f5387,plain,
spl0_509,
inference(avatar_split_clause,[],[f2272,f5385]) ).
fof(f5385,plain,
( spl0_509
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2272,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f5383,plain,
spl0_508,
inference(avatar_split_clause,[],[f2271,f5381]) ).
fof(f5381,plain,
( spl0_508
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2271,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f5379,plain,
spl0_507,
inference(avatar_split_clause,[],[f2270,f5377]) ).
fof(f5377,plain,
( spl0_507
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2270,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f5375,plain,
spl0_506,
inference(avatar_split_clause,[],[f2269,f5373]) ).
fof(f5373,plain,
( spl0_506
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2269,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f5371,plain,
spl0_505,
inference(avatar_split_clause,[],[f2268,f5369]) ).
fof(f5369,plain,
( spl0_505
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2268,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f5367,plain,
spl0_504,
inference(avatar_split_clause,[],[f2267,f5365]) ).
fof(f5365,plain,
( spl0_504
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2267,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f5363,plain,
spl0_503,
inference(avatar_split_clause,[],[f2266,f5361]) ).
fof(f5361,plain,
( spl0_503
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2266,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f5359,plain,
spl0_502,
inference(avatar_split_clause,[],[f2265,f5357]) ).
fof(f5357,plain,
( spl0_502
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2265,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f5355,plain,
spl0_501,
inference(avatar_split_clause,[],[f2264,f5353]) ).
fof(f5353,plain,
( spl0_501
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2264,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f5351,plain,
spl0_500,
inference(avatar_split_clause,[],[f2228,f5349]) ).
fof(f5349,plain,
( spl0_500
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2228,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f5347,plain,
spl0_499,
inference(avatar_split_clause,[],[f2227,f5345]) ).
fof(f5345,plain,
( spl0_499
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2227,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f5343,plain,
spl0_498,
inference(avatar_split_clause,[],[f2226,f5341]) ).
fof(f5341,plain,
( spl0_498
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2226,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f5339,plain,
spl0_497,
inference(avatar_split_clause,[],[f2225,f5337]) ).
fof(f5337,plain,
( spl0_497
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2225,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f5335,plain,
spl0_496,
inference(avatar_split_clause,[],[f2224,f5333]) ).
fof(f5333,plain,
( spl0_496
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2224,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f5331,plain,
spl0_495,
inference(avatar_split_clause,[],[f2223,f5329]) ).
fof(f5329,plain,
( spl0_495
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2223,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
fof(f5327,plain,
spl0_494,
inference(avatar_split_clause,[],[f2222,f5325]) ).
fof(f5325,plain,
( spl0_494
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2222,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f5323,plain,
spl0_493,
inference(avatar_split_clause,[],[f2221,f5321]) ).
fof(f5321,plain,
( spl0_493
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2221,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f5319,plain,
spl0_492,
inference(avatar_split_clause,[],[f2220,f5317]) ).
fof(f5317,plain,
( spl0_492
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2220,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f5315,plain,
spl0_491,
inference(avatar_split_clause,[],[f2219,f5313]) ).
fof(f5313,plain,
( spl0_491
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2219,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f5311,plain,
spl0_490,
inference(avatar_split_clause,[],[f2218,f5309]) ).
fof(f5309,plain,
( spl0_490
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2218,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f5307,plain,
spl0_489,
inference(avatar_split_clause,[],[f2217,f5305]) ).
fof(f5305,plain,
( spl0_489
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2217,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f5303,plain,
spl0_488,
inference(avatar_split_clause,[],[f2216,f5301]) ).
fof(f5301,plain,
( spl0_488
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2216,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f5299,plain,
spl0_487,
inference(avatar_split_clause,[],[f2215,f5297]) ).
fof(f5297,plain,
( spl0_487
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2215,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
fof(f5295,plain,
spl0_486,
inference(avatar_split_clause,[],[f2214,f5293]) ).
fof(f5293,plain,
( spl0_486
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2214,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
fof(f5291,plain,
spl0_485,
inference(avatar_split_clause,[],[f2213,f5289]) ).
fof(f5289,plain,
( spl0_485
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2213,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f5287,plain,
spl0_484,
inference(avatar_split_clause,[],[f2212,f5285]) ).
fof(f5285,plain,
( spl0_484
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2212,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f5283,plain,
spl0_483,
inference(avatar_split_clause,[],[f2211,f5281]) ).
fof(f5281,plain,
( spl0_483
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2211,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
fof(f5279,plain,
spl0_482,
inference(avatar_split_clause,[],[f2210,f5277]) ).
fof(f5277,plain,
( spl0_482
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2210,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
fof(f5275,plain,
spl0_481,
inference(avatar_split_clause,[],[f2209,f5273]) ).
fof(f5273,plain,
( spl0_481
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2209,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
fof(f5271,plain,
spl0_480,
inference(avatar_split_clause,[],[f2208,f5269]) ).
fof(f5269,plain,
( spl0_480
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2208,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
fof(f5267,plain,
spl0_479,
inference(avatar_split_clause,[],[f2207,f5265]) ).
fof(f5265,plain,
( spl0_479
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2207,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f5263,plain,
spl0_478,
inference(avatar_split_clause,[],[f2206,f5261]) ).
fof(f5261,plain,
( spl0_478
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2206,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f5259,plain,
spl0_477,
inference(avatar_split_clause,[],[f2205,f5257]) ).
fof(f5257,plain,
( spl0_477
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2205,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
fof(f5255,plain,
spl0_476,
inference(avatar_split_clause,[],[f2204,f5253]) ).
fof(f5253,plain,
( spl0_476
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2204,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
fof(f5251,plain,
spl0_475,
inference(avatar_split_clause,[],[f2203,f5249]) ).
fof(f5249,plain,
( spl0_475
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2203,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f5247,plain,
spl0_474,
inference(avatar_split_clause,[],[f2202,f5245]) ).
fof(f5245,plain,
( spl0_474
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2202,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f5243,plain,
spl0_473,
inference(avatar_split_clause,[],[f2201,f5241]) ).
fof(f5241,plain,
( spl0_473
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2201,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
fof(f5239,plain,
spl0_472,
inference(avatar_split_clause,[],[f2200,f5237]) ).
fof(f5237,plain,
( spl0_472
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2200,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f5235,plain,
spl0_471,
inference(avatar_split_clause,[],[f2199,f5233]) ).
fof(f5233,plain,
( spl0_471
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2199,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f5231,plain,
spl0_470,
inference(avatar_split_clause,[],[f2198,f5229]) ).
fof(f5229,plain,
( spl0_470
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2198,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f5227,plain,
spl0_469,
inference(avatar_split_clause,[],[f2197,f5225]) ).
fof(f5225,plain,
( spl0_469
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2197,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f5223,plain,
spl0_468,
inference(avatar_split_clause,[],[f2196,f5221]) ).
fof(f5221,plain,
( spl0_468
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2196,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f5219,plain,
spl0_467,
inference(avatar_split_clause,[],[f2195,f5217]) ).
fof(f2195,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f5215,plain,
spl0_466,
inference(avatar_split_clause,[],[f2194,f5213]) ).
fof(f5213,plain,
( spl0_466
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2194,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
fof(f5211,plain,
spl0_465,
inference(avatar_split_clause,[],[f2193,f5209]) ).
fof(f5209,plain,
( spl0_465
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2193,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
fof(f5207,plain,
spl0_464,
inference(avatar_split_clause,[],[f2192,f5205]) ).
fof(f5205,plain,
( spl0_464
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2192,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
fof(f5203,plain,
spl0_463,
inference(avatar_split_clause,[],[f2191,f5201]) ).
fof(f5201,plain,
( spl0_463
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2191,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f5199,plain,
spl0_462,
inference(avatar_split_clause,[],[f2190,f5197]) ).
fof(f5197,plain,
( spl0_462
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2190,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
fof(f5195,plain,
spl0_461,
inference(avatar_split_clause,[],[f2189,f5193]) ).
fof(f5193,plain,
( spl0_461
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2189,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f5191,plain,
spl0_460,
inference(avatar_split_clause,[],[f2188,f5189]) ).
fof(f5189,plain,
( spl0_460
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2188,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
fof(f5187,plain,
spl0_459,
inference(avatar_split_clause,[],[f2187,f5185]) ).
fof(f5185,plain,
( spl0_459
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2187,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
fof(f5183,plain,
spl0_458,
inference(avatar_split_clause,[],[f2186,f5181]) ).
fof(f5181,plain,
( spl0_458
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2186,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f5179,plain,
spl0_457,
inference(avatar_split_clause,[],[f2185,f5177]) ).
fof(f5177,plain,
( spl0_457
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2185,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
fof(f5175,plain,
spl0_456,
inference(avatar_split_clause,[],[f2184,f5173]) ).
fof(f5173,plain,
( spl0_456
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2184,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
fof(f5171,plain,
spl0_455,
inference(avatar_split_clause,[],[f2183,f5169]) ).
fof(f5169,plain,
( spl0_455
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2183,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f5167,plain,
spl0_454,
inference(avatar_split_clause,[],[f2182,f5165]) ).
fof(f5165,plain,
( spl0_454
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2182,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f5163,plain,
spl0_453,
inference(avatar_split_clause,[],[f2181,f5161]) ).
fof(f5161,plain,
( spl0_453
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2181,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
fof(f5159,plain,
spl0_452,
inference(avatar_split_clause,[],[f2180,f5157]) ).
fof(f5157,plain,
( spl0_452
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2180,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f5155,plain,
spl0_451,
inference(avatar_split_clause,[],[f2179,f5153]) ).
fof(f5153,plain,
( spl0_451
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2179,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f5151,plain,
spl0_450,
inference(avatar_split_clause,[],[f2178,f5149]) ).
fof(f5149,plain,
( spl0_450
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2178,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f5147,plain,
spl0_449,
inference(avatar_split_clause,[],[f2177,f5145]) ).
fof(f5145,plain,
( spl0_449
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2177,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
fof(f5143,plain,
spl0_448,
inference(avatar_split_clause,[],[f2176,f5141]) ).
fof(f5141,plain,
( spl0_448
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2176,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
fof(f5139,plain,
spl0_447,
inference(avatar_split_clause,[],[f2175,f5137]) ).
fof(f5137,plain,
( spl0_447
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2175,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f5135,plain,
spl0_446,
inference(avatar_split_clause,[],[f2174,f5133]) ).
fof(f5133,plain,
( spl0_446
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2174,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f5131,plain,
spl0_445,
inference(avatar_split_clause,[],[f2173,f5129]) ).
fof(f5129,plain,
( spl0_445
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2173,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
fof(f5127,plain,
spl0_444,
inference(avatar_split_clause,[],[f2172,f5125]) ).
fof(f5125,plain,
( spl0_444
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2172,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f5123,plain,
spl0_443,
inference(avatar_split_clause,[],[f2171,f5121]) ).
fof(f5121,plain,
( spl0_443
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2171,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
fof(f5119,plain,
spl0_442,
inference(avatar_split_clause,[],[f2170,f5117]) ).
fof(f5117,plain,
( spl0_442
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2170,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
fof(f5115,plain,
spl0_441,
inference(avatar_split_clause,[],[f2169,f5113]) ).
fof(f5113,plain,
( spl0_441
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2169,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
fof(f5111,plain,
spl0_440,
inference(avatar_split_clause,[],[f2168,f5109]) ).
fof(f5109,plain,
( spl0_440
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2168,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
fof(f5107,plain,
spl0_439,
inference(avatar_split_clause,[],[f2167,f5105]) ).
fof(f5105,plain,
( spl0_439
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2167,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
fof(f5103,plain,
spl0_438,
inference(avatar_split_clause,[],[f2166,f5101]) ).
fof(f5101,plain,
( spl0_438
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2166,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f5099,plain,
spl0_437,
inference(avatar_split_clause,[],[f2165,f5097]) ).
fof(f5097,plain,
( spl0_437
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2165,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f5095,plain,
spl0_436,
inference(avatar_split_clause,[],[f2164,f5093]) ).
fof(f5093,plain,
( spl0_436
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2164,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
fof(f5091,plain,
spl0_435,
inference(avatar_split_clause,[],[f2163,f5089]) ).
fof(f5089,plain,
( spl0_435
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2163,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f5087,plain,
spl0_434,
inference(avatar_split_clause,[],[f2162,f5085]) ).
fof(f5085,plain,
( spl0_434
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2162,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f5083,plain,
spl0_433,
inference(avatar_split_clause,[],[f2161,f5081]) ).
fof(f5081,plain,
( spl0_433
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2161,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
fof(f5079,plain,
spl0_432,
inference(avatar_split_clause,[],[f2160,f5077]) ).
fof(f5077,plain,
( spl0_432
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2160,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
fof(f5075,plain,
spl0_431,
inference(avatar_split_clause,[],[f2159,f5073]) ).
fof(f2159,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
fof(f5071,plain,
spl0_430,
inference(avatar_split_clause,[],[f2158,f5069]) ).
fof(f5069,plain,
( spl0_430
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2158,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
fof(f5067,plain,
spl0_429,
inference(avatar_split_clause,[],[f2157,f5065]) ).
fof(f5065,plain,
( spl0_429
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2157,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
fof(f5063,plain,
spl0_428,
inference(avatar_split_clause,[],[f2156,f5061]) ).
fof(f5061,plain,
( spl0_428
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2156,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
fof(f5059,plain,
spl0_427,
inference(avatar_split_clause,[],[f2155,f5057]) ).
fof(f5057,plain,
( spl0_427
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2155,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f5055,plain,
spl0_426,
inference(avatar_split_clause,[],[f2154,f5053]) ).
fof(f5053,plain,
( spl0_426
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2154,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f5051,plain,
spl0_425,
inference(avatar_split_clause,[],[f2153,f5049]) ).
fof(f5049,plain,
( spl0_425
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2153,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
fof(f5047,plain,
spl0_424,
inference(avatar_split_clause,[],[f2152,f5045]) ).
fof(f5045,plain,
( spl0_424
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2152,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f5043,plain,
spl0_423,
inference(avatar_split_clause,[],[f2151,f5041]) ).
fof(f5041,plain,
( spl0_423
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2151,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f5039,plain,
spl0_422,
inference(avatar_split_clause,[],[f2150,f5037]) ).
fof(f5037,plain,
( spl0_422
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2150,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f5035,plain,
spl0_421,
inference(avatar_split_clause,[],[f2149,f5033]) ).
fof(f5033,plain,
( spl0_421
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2149,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
fof(f5031,plain,
spl0_420,
inference(avatar_split_clause,[],[f2148,f5029]) ).
fof(f5029,plain,
( spl0_420
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2148,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f5027,plain,
spl0_419,
inference(avatar_split_clause,[],[f2147,f5025]) ).
fof(f5025,plain,
( spl0_419
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2147,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f5023,plain,
spl0_418,
inference(avatar_split_clause,[],[f2146,f5021]) ).
fof(f5021,plain,
( spl0_418
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2146,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f5019,plain,
spl0_417,
inference(avatar_split_clause,[],[f2145,f5017]) ).
fof(f5017,plain,
( spl0_417
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2145,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f5015,plain,
spl0_416,
inference(avatar_split_clause,[],[f2144,f5013]) ).
fof(f5013,plain,
( spl0_416
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2144,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f5011,plain,
spl0_415,
inference(avatar_split_clause,[],[f2143,f5009]) ).
fof(f5009,plain,
( spl0_415
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2143,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f5007,plain,
spl0_414,
inference(avatar_split_clause,[],[f2142,f5005]) ).
fof(f5005,plain,
( spl0_414
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2142,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f5003,plain,
spl0_413,
inference(avatar_split_clause,[],[f2141,f5001]) ).
fof(f5001,plain,
( spl0_413
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2141,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4999,plain,
spl0_412,
inference(avatar_split_clause,[],[f2140,f4997]) ).
fof(f4997,plain,
( spl0_412
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2140,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4995,plain,
spl0_411,
inference(avatar_split_clause,[],[f2139,f4993]) ).
fof(f4993,plain,
( spl0_411
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2139,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4991,plain,
spl0_410,
inference(avatar_split_clause,[],[f2138,f4989]) ).
fof(f4989,plain,
( spl0_410
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2138,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
fof(f4987,plain,
spl0_409,
inference(avatar_split_clause,[],[f2137,f4985]) ).
fof(f4985,plain,
( spl0_409
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2137,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
fof(f4983,plain,
spl0_408,
inference(avatar_split_clause,[],[f2136,f4981]) ).
fof(f4981,plain,
( spl0_408
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2136,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4979,plain,
spl0_407,
inference(avatar_split_clause,[],[f2135,f4977]) ).
fof(f4977,plain,
( spl0_407
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2135,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
fof(f4975,plain,
spl0_406,
inference(avatar_split_clause,[],[f2134,f4973]) ).
fof(f4973,plain,
( spl0_406
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2134,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4971,plain,
spl0_405,
inference(avatar_split_clause,[],[f2133,f4969]) ).
fof(f4969,plain,
( spl0_405
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2133,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
fof(f4967,plain,
spl0_404,
inference(avatar_split_clause,[],[f2132,f4965]) ).
fof(f4965,plain,
( spl0_404
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2132,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4963,plain,
spl0_403,
inference(avatar_split_clause,[],[f2131,f4961]) ).
fof(f4961,plain,
( spl0_403
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2131,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
fof(f4959,plain,
spl0_402,
inference(avatar_split_clause,[],[f2130,f4957]) ).
fof(f4957,plain,
( spl0_402
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2130,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
fof(f4955,plain,
spl0_401,
inference(avatar_split_clause,[],[f2129,f4953]) ).
fof(f4953,plain,
( spl0_401
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2129,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4951,plain,
spl0_400,
inference(avatar_split_clause,[],[f2128,f4949]) ).
fof(f4949,plain,
( spl0_400
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2128,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4947,plain,
spl0_399,
inference(avatar_split_clause,[],[f2127,f4945]) ).
fof(f4945,plain,
( spl0_399
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2127,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4943,plain,
spl0_398,
inference(avatar_split_clause,[],[f2126,f4941]) ).
fof(f4941,plain,
( spl0_398
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2126,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).
fof(f4939,plain,
spl0_397,
inference(avatar_split_clause,[],[f2125,f4937]) ).
fof(f4937,plain,
( spl0_397
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2125,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).
fof(f4935,plain,
spl0_396,
inference(avatar_split_clause,[],[f2124,f4933]) ).
fof(f4933,plain,
( spl0_396
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2124,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4931,plain,
spl0_395,
inference(avatar_split_clause,[],[f2123,f4929]) ).
fof(f4929,plain,
( spl0_395
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2123,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).
fof(f4927,plain,
spl0_394,
inference(avatar_split_clause,[],[f2122,f4925]) ).
fof(f4925,plain,
( spl0_394
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2122,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).
fof(f4923,plain,
spl0_393,
inference(avatar_split_clause,[],[f2121,f4921]) ).
fof(f4921,plain,
( spl0_393
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2121,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4919,plain,
spl0_392,
inference(avatar_split_clause,[],[f2120,f4917]) ).
fof(f4917,plain,
( spl0_392
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2120,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4915,plain,
spl0_391,
inference(avatar_split_clause,[],[f2119,f4913]) ).
fof(f4913,plain,
( spl0_391
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2119,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).
fof(f4911,plain,
spl0_390,
inference(avatar_split_clause,[],[f2118,f4909]) ).
fof(f4909,plain,
( spl0_390
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2118,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4907,plain,
spl0_389,
inference(avatar_split_clause,[],[f2117,f4905]) ).
fof(f4905,plain,
( spl0_389
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2117,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4903,plain,
spl0_388,
inference(avatar_split_clause,[],[f2116,f4901]) ).
fof(f4901,plain,
( spl0_388
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2116,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4899,plain,
spl0_387,
inference(avatar_split_clause,[],[f2115,f4897]) ).
fof(f4897,plain,
( spl0_387
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2115,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4895,plain,
spl0_386,
inference(avatar_split_clause,[],[f2114,f4893]) ).
fof(f4893,plain,
( spl0_386
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2114,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4891,plain,
spl0_385,
inference(avatar_split_clause,[],[f2113,f4889]) ).
fof(f4889,plain,
( spl0_385
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2113,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).
fof(f4887,plain,
spl0_384,
inference(avatar_split_clause,[],[f2112,f4885]) ).
fof(f4885,plain,
( spl0_384
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2112,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4883,plain,
spl0_383,
inference(avatar_split_clause,[],[f2111,f4881]) ).
fof(f4881,plain,
( spl0_383
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2111,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).
fof(f4879,plain,
spl0_382,
inference(avatar_split_clause,[],[f2110,f4877]) ).
fof(f4877,plain,
( spl0_382
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2110,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).
fof(f4875,plain,
spl0_381,
inference(avatar_split_clause,[],[f2109,f4873]) ).
fof(f4873,plain,
( spl0_381
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2109,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4871,plain,
spl0_380,
inference(avatar_split_clause,[],[f2108,f4869]) ).
fof(f4869,plain,
( spl0_380
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2108,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4867,plain,
spl0_379,
inference(avatar_split_clause,[],[f2107,f4865]) ).
fof(f4865,plain,
( spl0_379
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2107,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
fof(f4863,plain,
spl0_378,
inference(avatar_split_clause,[],[f2106,f4861]) ).
fof(f4861,plain,
( spl0_378
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2106,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
fof(f4859,plain,
spl0_377,
inference(avatar_split_clause,[],[f2105,f4857]) ).
fof(f4857,plain,
( spl0_377
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2105,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
fof(f4855,plain,
spl0_376,
inference(avatar_split_clause,[],[f2104,f4853]) ).
fof(f4853,plain,
( spl0_376
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2104,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4851,plain,
spl0_375,
inference(avatar_split_clause,[],[f2103,f4849]) ).
fof(f4849,plain,
( spl0_375
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2103,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
fof(f4847,plain,
spl0_374,
inference(avatar_split_clause,[],[f2102,f4845]) ).
fof(f2102,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4843,plain,
spl0_373,
inference(avatar_split_clause,[],[f2101,f4841]) ).
fof(f4841,plain,
( spl0_373
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2101,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
fof(f4839,plain,
spl0_372,
inference(avatar_split_clause,[],[f2100,f4837]) ).
fof(f4837,plain,
( spl0_372
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2100,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
fof(f4835,plain,
spl0_371,
inference(avatar_split_clause,[],[f2099,f4833]) ).
fof(f4833,plain,
( spl0_371
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2099,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).
fof(f4831,plain,
spl0_370,
inference(avatar_split_clause,[],[f2098,f4829]) ).
fof(f4829,plain,
( spl0_370
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2098,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
fof(f4827,plain,
spl0_369,
inference(avatar_split_clause,[],[f2097,f4825]) ).
fof(f4825,plain,
( spl0_369
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2097,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).
fof(f4823,plain,
spl0_368,
inference(avatar_split_clause,[],[f2096,f4821]) ).
fof(f4821,plain,
( spl0_368
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2096,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).
fof(f4819,plain,
spl0_367,
inference(avatar_split_clause,[],[f2095,f4817]) ).
fof(f4817,plain,
( spl0_367
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2095,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).
fof(f4815,plain,
spl0_366,
inference(avatar_split_clause,[],[f2094,f4813]) ).
fof(f4813,plain,
( spl0_366
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2094,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4811,plain,
spl0_365,
inference(avatar_split_clause,[],[f2093,f4809]) ).
fof(f4809,plain,
( spl0_365
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2093,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4807,plain,
spl0_364,
inference(avatar_split_clause,[],[f2092,f4805]) ).
fof(f4805,plain,
( spl0_364
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2092,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4803,plain,
spl0_363,
inference(avatar_split_clause,[],[f2091,f4801]) ).
fof(f4801,plain,
( spl0_363
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2091,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4799,plain,
spl0_362,
inference(avatar_split_clause,[],[f2090,f4797]) ).
fof(f4797,plain,
( spl0_362
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2090,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4795,plain,
spl0_361,
inference(avatar_split_clause,[],[f2089,f4793]) ).
fof(f4793,plain,
( spl0_361
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2089,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4791,plain,
spl0_360,
inference(avatar_split_clause,[],[f2088,f4789]) ).
fof(f4789,plain,
( spl0_360
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2088,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4787,plain,
spl0_359,
inference(avatar_split_clause,[],[f2087,f4785]) ).
fof(f4785,plain,
( spl0_359
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2087,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4783,plain,
spl0_358,
inference(avatar_split_clause,[],[f2086,f4781]) ).
fof(f4781,plain,
( spl0_358
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2086,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4779,plain,
spl0_357,
inference(avatar_split_clause,[],[f2085,f4777]) ).
fof(f4777,plain,
( spl0_357
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2085,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4775,plain,
spl0_356,
inference(avatar_split_clause,[],[f2084,f4773]) ).
fof(f4773,plain,
( spl0_356
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2084,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4771,plain,
spl0_355,
inference(avatar_split_clause,[],[f2083,f4769]) ).
fof(f4769,plain,
( spl0_355
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2083,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4767,plain,
spl0_354,
inference(avatar_split_clause,[],[f2082,f4765]) ).
fof(f4765,plain,
( spl0_354
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2082,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4763,plain,
spl0_353,
inference(avatar_split_clause,[],[f2081,f4761]) ).
fof(f4761,plain,
( spl0_353
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2081,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4759,plain,
spl0_352,
inference(avatar_split_clause,[],[f2080,f4757]) ).
fof(f4757,plain,
( spl0_352
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2080,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4755,plain,
spl0_351,
inference(avatar_split_clause,[],[f2079,f4753]) ).
fof(f4753,plain,
( spl0_351
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2079,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4751,plain,
spl0_350,
inference(avatar_split_clause,[],[f2078,f4749]) ).
fof(f4749,plain,
( spl0_350
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2078,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4747,plain,
spl0_349,
inference(avatar_split_clause,[],[f2077,f4745]) ).
fof(f4745,plain,
( spl0_349
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2077,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).
fof(f4743,plain,
spl0_348,
inference(avatar_split_clause,[],[f2075,f4741]) ).
fof(f4741,plain,
( spl0_348
<=> ! [X87] :
( ~ class_Orderings_Oorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2075,axiom,
! [X87] :
( ~ class_Orderings_Oorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4739,plain,
spl0_347,
inference(avatar_split_clause,[],[f2074,f4737]) ).
fof(f4737,plain,
( spl0_347
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2074,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4735,plain,
spl0_346,
inference(avatar_split_clause,[],[f2073,f4733]) ).
fof(f4733,plain,
( spl0_346
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2073,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4731,plain,
spl0_345,
inference(avatar_split_clause,[],[f2072,f4729]) ).
fof(f4729,plain,
( spl0_345
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2072,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4727,plain,
spl0_344,
inference(avatar_split_clause,[],[f2071,f4725]) ).
fof(f4725,plain,
( spl0_344
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2071,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4723,plain,
spl0_343,
inference(avatar_split_clause,[],[f2070,f4721]) ).
fof(f4721,plain,
( spl0_343
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2070,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4719,plain,
spl0_342,
inference(avatar_split_clause,[],[f2069,f4717]) ).
fof(f2069,axiom,
! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
fof(f4715,plain,
spl0_341,
inference(avatar_split_clause,[],[f2068,f4713]) ).
fof(f2068,axiom,
! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
fof(f4711,plain,
spl0_340,
inference(avatar_split_clause,[],[f2067,f4709]) ).
fof(f4709,plain,
( spl0_340
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2067,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4707,plain,
spl0_339,
inference(avatar_split_clause,[],[f2066,f4705]) ).
fof(f4705,plain,
( spl0_339
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2066,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4703,plain,
spl0_338,
inference(avatar_split_clause,[],[f2065,f4701]) ).
fof(f4701,plain,
( spl0_338
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2065,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
fof(f4699,plain,
spl0_337,
inference(avatar_split_clause,[],[f2064,f4697]) ).
fof(f4697,plain,
( spl0_337
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2064,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
fof(f4695,plain,
spl0_336,
inference(avatar_split_clause,[],[f2063,f4693]) ).
fof(f4693,plain,
( spl0_336
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2063,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
fof(f4691,plain,
spl0_335,
inference(avatar_split_clause,[],[f2062,f4689]) ).
fof(f4689,plain,
( spl0_335
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2062,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4687,plain,
spl0_334,
inference(avatar_split_clause,[],[f2061,f4685]) ).
fof(f4685,plain,
( spl0_334
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2061,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4683,plain,
spl0_333,
inference(avatar_split_clause,[],[f2060,f4681]) ).
fof(f4681,plain,
( spl0_333
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2060,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4679,plain,
spl0_332,
inference(avatar_split_clause,[],[f2059,f4677]) ).
fof(f4677,plain,
( spl0_332
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2059,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
fof(f4675,plain,
spl0_331,
inference(avatar_split_clause,[],[f2058,f4673]) ).
fof(f4673,plain,
( spl0_331
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2058,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
fof(f4671,plain,
spl0_330,
inference(avatar_split_clause,[],[f2057,f4669]) ).
fof(f4669,plain,
( spl0_330
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2057,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4667,plain,
spl0_329,
inference(avatar_split_clause,[],[f2056,f4665]) ).
fof(f4665,plain,
( spl0_329
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2056,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
fof(f4663,plain,
spl0_328,
inference(avatar_split_clause,[],[f2055,f4661]) ).
fof(f4661,plain,
( spl0_328
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2055,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4659,plain,
spl0_327,
inference(avatar_split_clause,[],[f2054,f4657]) ).
fof(f4657,plain,
( spl0_327
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2054,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4655,plain,
spl0_326,
inference(avatar_split_clause,[],[f2053,f4653]) ).
fof(f4653,plain,
( spl0_326
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2053,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4651,plain,
spl0_325,
inference(avatar_split_clause,[],[f2052,f4649]) ).
fof(f4649,plain,
( spl0_325
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2052,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4647,plain,
spl0_324,
inference(avatar_split_clause,[],[f2051,f4645]) ).
fof(f4645,plain,
( spl0_324
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2051,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4643,plain,
spl0_323,
inference(avatar_split_clause,[],[f2050,f4641]) ).
fof(f4641,plain,
( spl0_323
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2050,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
fof(f4639,plain,
spl0_322,
inference(avatar_split_clause,[],[f2049,f4637]) ).
fof(f4637,plain,
( spl0_322
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2049,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
fof(f4635,plain,
spl0_321,
inference(avatar_split_clause,[],[f2048,f4633]) ).
fof(f4633,plain,
( spl0_321
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2048,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
fof(f4631,plain,
spl0_320,
inference(avatar_split_clause,[],[f2047,f4629]) ).
fof(f4629,plain,
( spl0_320
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2047,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4627,plain,
spl0_319,
inference(avatar_split_clause,[],[f2046,f4625]) ).
fof(f4625,plain,
( spl0_319
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2046,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4623,plain,
spl0_318,
inference(avatar_split_clause,[],[f2045,f4621]) ).
fof(f4621,plain,
( spl0_318
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2045,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4619,plain,
spl0_317,
inference(avatar_split_clause,[],[f2044,f4617]) ).
fof(f4617,plain,
( spl0_317
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2044,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
fof(f4615,plain,
spl0_316,
inference(avatar_split_clause,[],[f2043,f4613]) ).
fof(f4613,plain,
( spl0_316
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2043,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
fof(f4611,plain,
spl0_315,
inference(avatar_split_clause,[],[f2042,f4609]) ).
fof(f4609,plain,
( spl0_315
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2042,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4607,plain,
spl0_314,
inference(avatar_split_clause,[],[f2041,f4605]) ).
fof(f4605,plain,
( spl0_314
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2041,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
fof(f4603,plain,
spl0_313,
inference(avatar_split_clause,[],[f2040,f4601]) ).
fof(f4601,plain,
( spl0_313
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2040,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4599,plain,
spl0_312,
inference(avatar_split_clause,[],[f2039,f4597]) ).
fof(f4597,plain,
( spl0_312
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2039,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
fof(f4595,plain,
spl0_311,
inference(avatar_split_clause,[],[f2038,f4593]) ).
fof(f4593,plain,
( spl0_311
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2038,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4591,plain,
spl0_310,
inference(avatar_split_clause,[],[f2037,f4589]) ).
fof(f4589,plain,
( spl0_310
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2037,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4587,plain,
spl0_309,
inference(avatar_split_clause,[],[f2036,f4585]) ).
fof(f4585,plain,
( spl0_309
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2036,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4583,plain,
spl0_308,
inference(avatar_split_clause,[],[f2035,f4581]) ).
fof(f4581,plain,
( spl0_308
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2035,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4579,plain,
spl0_307,
inference(avatar_split_clause,[],[f2034,f4577]) ).
fof(f4577,plain,
( spl0_307
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2034,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4575,plain,
spl0_306,
inference(avatar_split_clause,[],[f2033,f4573]) ).
fof(f4573,plain,
( spl0_306
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2033,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
fof(f4571,plain,
spl0_305,
inference(avatar_split_clause,[],[f2032,f4569]) ).
fof(f4569,plain,
( spl0_305
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2032,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4567,plain,
spl0_304,
inference(avatar_split_clause,[],[f2031,f4565]) ).
fof(f4565,plain,
( spl0_304
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2031,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4563,plain,
spl0_303,
inference(avatar_split_clause,[],[f2030,f4561]) ).
fof(f4561,plain,
( spl0_303
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2030,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
fof(f4559,plain,
spl0_302,
inference(avatar_split_clause,[],[f2029,f4557]) ).
fof(f4557,plain,
( spl0_302
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2029,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
fof(f4555,plain,
spl0_301,
inference(avatar_split_clause,[],[f2028,f4553]) ).
fof(f4553,plain,
( spl0_301
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2028,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4551,plain,
spl0_300,
inference(avatar_split_clause,[],[f2027,f4549]) ).
fof(f4549,plain,
( spl0_300
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2027,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
fof(f4547,plain,
spl0_299,
inference(avatar_split_clause,[],[f2026,f4545]) ).
fof(f4545,plain,
( spl0_299
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2026,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4543,plain,
spl0_298,
inference(avatar_split_clause,[],[f2025,f4541]) ).
fof(f4541,plain,
( spl0_298
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2025,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4539,plain,
spl0_297,
inference(avatar_split_clause,[],[f2024,f4537]) ).
fof(f4537,plain,
( spl0_297
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2024,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4535,plain,
spl0_296,
inference(avatar_split_clause,[],[f2023,f4533]) ).
fof(f4533,plain,
( spl0_296
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2023,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4531,plain,
spl0_295,
inference(avatar_split_clause,[],[f2022,f4529]) ).
fof(f4529,plain,
( spl0_295
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2022,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4527,plain,
spl0_294,
inference(avatar_split_clause,[],[f2021,f4525]) ).
fof(f4525,plain,
( spl0_294
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2021,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4523,plain,
spl0_293,
inference(avatar_split_clause,[],[f2020,f4521]) ).
fof(f4521,plain,
( spl0_293
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2020,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4519,plain,
spl0_292,
inference(avatar_split_clause,[],[f2019,f4517]) ).
fof(f4517,plain,
( spl0_292
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2019,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4515,plain,
spl0_291,
inference(avatar_split_clause,[],[f2018,f4513]) ).
fof(f4513,plain,
( spl0_291
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2018,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4511,plain,
spl0_290,
inference(avatar_split_clause,[],[f2017,f4509]) ).
fof(f4509,plain,
( spl0_290
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2017,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
fof(f4507,plain,
spl0_289,
inference(avatar_split_clause,[],[f2016,f4505]) ).
fof(f4505,plain,
( spl0_289
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2016,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
fof(f4503,plain,
spl0_288,
inference(avatar_split_clause,[],[f2015,f4501]) ).
fof(f2015,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4499,plain,
spl0_287,
inference(avatar_split_clause,[],[f2014,f4497]) ).
fof(f4497,plain,
( spl0_287
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2014,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4495,plain,
spl0_286,
inference(avatar_split_clause,[],[f2013,f4493]) ).
fof(f4493,plain,
( spl0_286
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2013,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4491,plain,
spl0_285,
inference(avatar_split_clause,[],[f2012,f4489]) ).
fof(f4489,plain,
( spl0_285
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2012,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4487,plain,
spl0_284,
inference(avatar_split_clause,[],[f2011,f4485]) ).
fof(f4485,plain,
( spl0_284
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2011,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4483,plain,
spl0_283,
inference(avatar_split_clause,[],[f2010,f4481]) ).
fof(f4481,plain,
( spl0_283
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2010,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4479,plain,
spl0_282,
inference(avatar_split_clause,[],[f2009,f4477]) ).
fof(f4477,plain,
( spl0_282
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2009,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
fof(f4475,plain,
spl0_281,
inference(avatar_split_clause,[],[f2008,f4473]) ).
fof(f4473,plain,
( spl0_281
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2008,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4471,plain,
spl0_280,
inference(avatar_split_clause,[],[f2007,f4469]) ).
fof(f4469,plain,
( spl0_280
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2007,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
fof(f4467,plain,
spl0_279,
inference(avatar_split_clause,[],[f2006,f4465]) ).
fof(f4465,plain,
( spl0_279
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2006,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4463,plain,
spl0_278,
inference(avatar_split_clause,[],[f2005,f4461]) ).
fof(f4461,plain,
( spl0_278
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2005,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4459,plain,
spl0_277,
inference(avatar_split_clause,[],[f2004,f4457]) ).
fof(f4457,plain,
( spl0_277
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2004,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4455,plain,
spl0_276,
inference(avatar_split_clause,[],[f2003,f4453]) ).
fof(f4453,plain,
( spl0_276
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2003,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4451,plain,
spl0_275,
inference(avatar_split_clause,[],[f2002,f4449]) ).
fof(f4449,plain,
( spl0_275
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2002,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
fof(f4447,plain,
spl0_274,
inference(avatar_split_clause,[],[f2001,f4445]) ).
fof(f4445,plain,
( spl0_274
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2001,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
fof(f4443,plain,
spl0_273,
inference(avatar_split_clause,[],[f2000,f4441]) ).
fof(f4441,plain,
( spl0_273
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2000,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4439,plain,
spl0_272,
inference(avatar_split_clause,[],[f1999,f4437]) ).
fof(f4437,plain,
( spl0_272
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f1999,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
fof(f4435,plain,
spl0_271,
inference(avatar_split_clause,[],[f1998,f4433]) ).
fof(f4433,plain,
( spl0_271
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1998,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4431,plain,
spl0_270,
inference(avatar_split_clause,[],[f1997,f4429]) ).
fof(f4429,plain,
( spl0_270
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1997,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4427,plain,
spl0_269,
inference(avatar_split_clause,[],[f1996,f4425]) ).
fof(f4425,plain,
( spl0_269
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1996,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4423,plain,
spl0_268,
inference(avatar_split_clause,[],[f1995,f4421]) ).
fof(f4421,plain,
( spl0_268
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1995,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4419,plain,
spl0_267,
inference(avatar_split_clause,[],[f1994,f4417]) ).
fof(f4417,plain,
( spl0_267
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1994,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4415,plain,
spl0_266,
inference(avatar_split_clause,[],[f1993,f4413]) ).
fof(f4413,plain,
( spl0_266
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1993,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4411,plain,
spl0_265,
inference(avatar_split_clause,[],[f1992,f4409]) ).
fof(f4409,plain,
( spl0_265
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1992,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4407,plain,
spl0_264,
inference(avatar_split_clause,[],[f1991,f4405]) ).
fof(f4405,plain,
( spl0_264
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1991,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4403,plain,
spl0_263,
inference(avatar_split_clause,[],[f1990,f4401]) ).
fof(f4401,plain,
( spl0_263
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1990,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
fof(f4399,plain,
spl0_262,
inference(avatar_split_clause,[],[f1989,f4397]) ).
fof(f4397,plain,
( spl0_262
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1989,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4395,plain,
spl0_261,
inference(avatar_split_clause,[],[f1988,f4393]) ).
fof(f4393,plain,
( spl0_261
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1988,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
fof(f4391,plain,
spl0_260,
inference(avatar_split_clause,[],[f1987,f4389]) ).
fof(f4389,plain,
( spl0_260
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1987,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4387,plain,
spl0_259,
inference(avatar_split_clause,[],[f1986,f4385]) ).
fof(f4385,plain,
( spl0_259
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1986,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4383,plain,
spl0_258,
inference(avatar_split_clause,[],[f1985,f4381]) ).
fof(f4381,plain,
( spl0_258
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1985,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4379,plain,
spl0_257,
inference(avatar_split_clause,[],[f1984,f4377]) ).
fof(f4377,plain,
( spl0_257
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1984,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4375,plain,
spl0_256,
inference(avatar_split_clause,[],[f1983,f4373]) ).
fof(f4373,plain,
( spl0_256
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1983,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
fof(f4371,plain,
spl0_255,
inference(avatar_split_clause,[],[f1982,f4369]) ).
fof(f4369,plain,
( spl0_255
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1982,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
fof(f4367,plain,
spl0_254,
inference(avatar_split_clause,[],[f1981,f4365]) ).
fof(f4365,plain,
( spl0_254
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1981,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4363,plain,
spl0_253,
inference(avatar_split_clause,[],[f1980,f4361]) ).
fof(f4361,plain,
( spl0_253
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1980,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
fof(f4359,plain,
spl0_252,
inference(avatar_split_clause,[],[f1979,f4357]) ).
fof(f4357,plain,
( spl0_252
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1979,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4355,plain,
spl0_251,
inference(avatar_split_clause,[],[f1978,f4353]) ).
fof(f4353,plain,
( spl0_251
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1978,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4351,plain,
spl0_250,
inference(avatar_split_clause,[],[f1977,f4349]) ).
fof(f4349,plain,
( spl0_250
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1977,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4347,plain,
spl0_249,
inference(avatar_split_clause,[],[f1976,f4345]) ).
fof(f4345,plain,
( spl0_249
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1976,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4343,plain,
spl0_248,
inference(avatar_split_clause,[],[f1975,f4341]) ).
fof(f4341,plain,
( spl0_248
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1975,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4339,plain,
spl0_247,
inference(avatar_split_clause,[],[f1974,f4337]) ).
fof(f4337,plain,
( spl0_247
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1974,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4335,plain,
spl0_246,
inference(avatar_split_clause,[],[f1973,f4333]) ).
fof(f4333,plain,
( spl0_246
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1973,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4331,plain,
spl0_245,
inference(avatar_split_clause,[],[f1972,f4329]) ).
fof(f4329,plain,
( spl0_245
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1972,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
fof(f4327,plain,
spl0_244,
inference(avatar_split_clause,[],[f1971,f4325]) ).
fof(f4325,plain,
( spl0_244
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1971,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4323,plain,
spl0_243,
inference(avatar_split_clause,[],[f1970,f4321]) ).
fof(f4321,plain,
( spl0_243
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1970,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
fof(f4319,plain,
spl0_242,
inference(avatar_split_clause,[],[f1969,f4317]) ).
fof(f4317,plain,
( spl0_242
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1969,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4315,plain,
spl0_241,
inference(avatar_split_clause,[],[f1968,f4313]) ).
fof(f4313,plain,
( spl0_241
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1968,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4311,plain,
spl0_240,
inference(avatar_split_clause,[],[f1967,f4309]) ).
fof(f4309,plain,
( spl0_240
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1967,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4307,plain,
spl0_239,
inference(avatar_split_clause,[],[f1966,f4305]) ).
fof(f4305,plain,
( spl0_239
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1966,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4303,plain,
spl0_238,
inference(avatar_split_clause,[],[f1965,f4301]) ).
fof(f4301,plain,
( spl0_238
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1965,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4299,plain,
spl0_237,
inference(avatar_split_clause,[],[f1964,f4297]) ).
fof(f4297,plain,
( spl0_237
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1964,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4295,plain,
spl0_236,
inference(avatar_split_clause,[],[f1963,f4293]) ).
fof(f4293,plain,
( spl0_236
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1963,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
fof(f4291,plain,
spl0_235,
inference(avatar_split_clause,[],[f1962,f4289]) ).
fof(f4289,plain,
( spl0_235
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1962,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
fof(f4287,plain,
spl0_234,
inference(avatar_split_clause,[],[f1961,f4285]) ).
fof(f4285,plain,
( spl0_234
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1961,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4283,plain,
spl0_233,
inference(avatar_split_clause,[],[f1960,f4281]) ).
fof(f4281,plain,
( spl0_233
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1960,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
fof(f4279,plain,
spl0_232,
inference(avatar_split_clause,[],[f1959,f4277]) ).
fof(f4277,plain,
( spl0_232
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1959,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4275,plain,
spl0_231,
inference(avatar_split_clause,[],[f1958,f4273]) ).
fof(f4273,plain,
( spl0_231
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1958,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4271,plain,
spl0_230,
inference(avatar_split_clause,[],[f1957,f4269]) ).
fof(f4269,plain,
( spl0_230
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1957,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4267,plain,
spl0_229,
inference(avatar_split_clause,[],[f1956,f4265]) ).
fof(f4265,plain,
( spl0_229
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1956,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4263,plain,
spl0_228,
inference(avatar_split_clause,[],[f1955,f4261]) ).
fof(f4261,plain,
( spl0_228
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1955,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f4259,plain,
spl0_227,
inference(avatar_split_clause,[],[f1954,f4257]) ).
fof(f4257,plain,
( spl0_227
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1954,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f4255,plain,
spl0_226,
inference(avatar_split_clause,[],[f1953,f4253]) ).
fof(f4253,plain,
( spl0_226
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1953,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f4251,plain,
spl0_225,
inference(avatar_split_clause,[],[f1952,f4249]) ).
fof(f4249,plain,
( spl0_225
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1952,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).
fof(f4247,plain,
spl0_224,
inference(avatar_split_clause,[],[f1951,f4245]) ).
fof(f4245,plain,
( spl0_224
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1951,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f4243,plain,
spl0_223,
inference(avatar_split_clause,[],[f1950,f4241]) ).
fof(f4241,plain,
( spl0_223
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1950,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
fof(f4239,plain,
spl0_222,
inference(avatar_split_clause,[],[f1949,f4237]) ).
fof(f4237,plain,
( spl0_222
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1949,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f4235,plain,
spl0_221,
inference(avatar_split_clause,[],[f1948,f4233]) ).
fof(f4233,plain,
( spl0_221
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1948,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f4231,plain,
spl0_220,
inference(avatar_split_clause,[],[f1947,f4229]) ).
fof(f4229,plain,
( spl0_220
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1947,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f4227,plain,
spl0_219,
inference(avatar_split_clause,[],[f1946,f4225]) ).
fof(f4225,plain,
( spl0_219
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1946,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).
fof(f4223,plain,
spl0_218,
inference(avatar_split_clause,[],[f1945,f4221]) ).
fof(f4221,plain,
( spl0_218
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1945,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).
fof(f4219,plain,
spl0_217,
inference(avatar_split_clause,[],[f1944,f4217]) ).
fof(f4217,plain,
( spl0_217
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1944,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f4215,plain,
spl0_216,
inference(avatar_split_clause,[],[f1943,f4213]) ).
fof(f4213,plain,
( spl0_216
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1943,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).
fof(f4211,plain,
spl0_215,
inference(avatar_split_clause,[],[f1942,f4209]) ).
fof(f4209,plain,
( spl0_215
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1942,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f4207,plain,
spl0_214,
inference(avatar_split_clause,[],[f1941,f4205]) ).
fof(f4205,plain,
( spl0_214
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1941,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f4203,plain,
spl0_213,
inference(avatar_split_clause,[],[f1940,f4201]) ).
fof(f4201,plain,
( spl0_213
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1940,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f4199,plain,
spl0_212,
inference(avatar_split_clause,[],[f1939,f4197]) ).
fof(f4197,plain,
( spl0_212
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1939,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f4195,plain,
spl0_211,
inference(avatar_split_clause,[],[f1938,f4193]) ).
fof(f4193,plain,
( spl0_211
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1938,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
fof(f4191,plain,
spl0_210,
inference(avatar_split_clause,[],[f1937,f4189]) ).
fof(f4189,plain,
( spl0_210
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1937,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
fof(f4187,plain,
spl0_209,
inference(avatar_split_clause,[],[f1936,f4185]) ).
fof(f4185,plain,
( spl0_209
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1936,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
fof(f4183,plain,
spl0_208,
inference(avatar_split_clause,[],[f1935,f4181]) ).
fof(f4181,plain,
( spl0_208
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1935,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f4179,plain,
spl0_207,
inference(avatar_split_clause,[],[f1934,f4177]) ).
fof(f4177,plain,
( spl0_207
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1934,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
fof(f4175,plain,
spl0_206,
inference(avatar_split_clause,[],[f1933,f4173]) ).
fof(f4173,plain,
( spl0_206
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1933,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
fof(f4171,plain,
spl0_205,
inference(avatar_split_clause,[],[f1932,f4169]) ).
fof(f4169,plain,
( spl0_205
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1932,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
fof(f4167,plain,
spl0_204,
inference(avatar_split_clause,[],[f1931,f4165]) ).
fof(f1931,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
fof(f4163,plain,
spl0_203,
inference(avatar_split_clause,[],[f1930,f4161]) ).
fof(f1930,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
fof(f4159,plain,
spl0_202,
inference(avatar_split_clause,[],[f1929,f4157]) ).
fof(f1929,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
fof(f4155,plain,
spl0_201,
inference(avatar_split_clause,[],[f1928,f4153]) ).
fof(f4153,plain,
( spl0_201
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1928,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f4151,plain,
spl0_200,
inference(avatar_split_clause,[],[f1927,f4149]) ).
fof(f4149,plain,
( spl0_200
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1927,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
fof(f4147,plain,
spl0_199,
inference(avatar_split_clause,[],[f1926,f4145]) ).
fof(f4145,plain,
( spl0_199
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1926,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
fof(f4143,plain,
spl0_198,
inference(avatar_split_clause,[],[f1925,f4141]) ).
fof(f1925,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
fof(f4139,plain,
spl0_197,
inference(avatar_split_clause,[],[f1924,f4137]) ).
fof(f1924,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
fof(f4135,plain,
spl0_196,
inference(avatar_split_clause,[],[f1923,f4133]) ).
fof(f1923,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
fof(f4131,plain,
spl0_195,
inference(avatar_split_clause,[],[f1922,f4129]) ).
fof(f1922,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
fof(f4127,plain,
spl0_194,
inference(avatar_split_clause,[],[f1921,f4125]) ).
fof(f1921,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
fof(f4123,plain,
spl0_193,
inference(avatar_split_clause,[],[f1920,f4121]) ).
fof(f4121,plain,
( spl0_193
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1920,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f4119,plain,
spl0_192,
inference(avatar_split_clause,[],[f1919,f4117]) ).
fof(f4117,plain,
( spl0_192
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1919,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f4115,plain,
spl0_191,
inference(avatar_split_clause,[],[f1918,f4113]) ).
fof(f4113,plain,
( spl0_191
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1918,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).
fof(f4111,plain,
spl0_190,
inference(avatar_split_clause,[],[f1917,f4109]) ).
fof(f4109,plain,
( spl0_190
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1917,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).
fof(f4107,plain,
spl0_189,
inference(avatar_split_clause,[],[f1916,f4105]) ).
fof(f4105,plain,
( spl0_189
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1916,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).
fof(f4103,plain,
spl0_188,
inference(avatar_split_clause,[],[f1915,f4101]) ).
fof(f1915,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).
fof(f4099,plain,
spl0_187,
inference(avatar_split_clause,[],[f1914,f4097]) ).
fof(f1914,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f4095,plain,
spl0_186,
inference(avatar_split_clause,[],[f1913,f4093]) ).
fof(f1913,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
fof(f4091,plain,
spl0_185,
inference(avatar_split_clause,[],[f1912,f4089]) ).
fof(f4089,plain,
( spl0_185
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1912,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f4087,plain,
spl0_184,
inference(avatar_split_clause,[],[f1911,f4085]) ).
fof(f4085,plain,
( spl0_184
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1911,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).
fof(f4083,plain,
spl0_183,
inference(avatar_split_clause,[],[f1910,f4081]) ).
fof(f4081,plain,
( spl0_183
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1910,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f4079,plain,
spl0_182,
inference(avatar_split_clause,[],[f1909,f4077]) ).
fof(f4077,plain,
( spl0_182
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1909,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f4075,plain,
spl0_181,
inference(avatar_split_clause,[],[f1908,f4073]) ).
fof(f4073,plain,
( spl0_181
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1908,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).
fof(f4071,plain,
spl0_180,
inference(avatar_split_clause,[],[f1907,f4069]) ).
fof(f4069,plain,
( spl0_180
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1907,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).
fof(f4067,plain,
spl0_179,
inference(avatar_split_clause,[],[f1906,f4065]) ).
fof(f4065,plain,
( spl0_179
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Numeral_Onumber(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1906,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Numeral_Onumber(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f4063,plain,
spl0_178,
inference(avatar_split_clause,[],[f1905,f4061]) ).
fof(f4061,plain,
( spl0_178
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1905,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).
fof(f4059,plain,
spl0_177,
inference(avatar_split_clause,[],[f1904,f4057]) ).
fof(f4057,plain,
( spl0_177
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1904,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f4055,plain,
spl0_176,
inference(avatar_split_clause,[],[f1903,f4053]) ).
fof(f4053,plain,
( spl0_176
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1903,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f4051,plain,
spl0_175,
inference(avatar_split_clause,[],[f1902,f4049]) ).
fof(f4049,plain,
( spl0_175
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1902,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f4047,plain,
spl0_174,
inference(avatar_split_clause,[],[f1901,f4045]) ).
fof(f4045,plain,
( spl0_174
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1901,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f4043,plain,
spl0_173,
inference(avatar_split_clause,[],[f1900,f4041]) ).
fof(f4041,plain,
( spl0_173
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1900,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f4039,plain,
spl0_172,
inference(avatar_split_clause,[],[f1899,f4037]) ).
fof(f4037,plain,
( spl0_172
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1899,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f4035,plain,
spl0_171,
inference(avatar_split_clause,[],[f1898,f4033]) ).
fof(f4033,plain,
( spl0_171
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1898,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f4031,plain,
spl0_170,
inference(avatar_split_clause,[],[f1897,f4029]) ).
fof(f4029,plain,
( spl0_170
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1897,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f4027,plain,
spl0_169,
inference(avatar_split_clause,[],[f1896,f4025]) ).
fof(f4025,plain,
( spl0_169
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1896,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f4023,plain,
spl0_168,
inference(avatar_split_clause,[],[f1895,f4021]) ).
fof(f4021,plain,
( spl0_168
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1895,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f4019,plain,
spl0_167,
inference(avatar_split_clause,[],[f1894,f4017]) ).
fof(f4017,plain,
( spl0_167
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1894,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).
fof(f4015,plain,
spl0_166,
inference(avatar_split_clause,[],[f1893,f4013]) ).
fof(f4013,plain,
( spl0_166
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1893,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f4011,plain,
spl0_165,
inference(avatar_split_clause,[],[f1892,f4009]) ).
fof(f4009,plain,
( spl0_165
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1892,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f4007,plain,
spl0_164,
inference(avatar_split_clause,[],[f1891,f4005]) ).
fof(f4005,plain,
( spl0_164
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1891,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f4003,plain,
spl0_163,
inference(avatar_split_clause,[],[f1890,f4001]) ).
fof(f4001,plain,
( spl0_163
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1890,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3999,plain,
spl0_162,
inference(avatar_split_clause,[],[f1889,f3997]) ).
fof(f3997,plain,
( spl0_162
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1889,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3995,plain,
spl0_161,
inference(avatar_split_clause,[],[f1888,f3993]) ).
fof(f3993,plain,
( spl0_161
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1888,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3991,plain,
spl0_160,
inference(avatar_split_clause,[],[f1887,f3989]) ).
fof(f3989,plain,
( spl0_160
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1887,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3987,plain,
spl0_159,
inference(avatar_split_clause,[],[f1886,f3985]) ).
fof(f3985,plain,
( spl0_159
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1886,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).
fof(f3983,plain,
spl0_158,
inference(avatar_split_clause,[],[f1885,f3981]) ).
fof(f3981,plain,
( spl0_158
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1885,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3979,plain,
spl0_157,
inference(avatar_split_clause,[],[f1884,f3977]) ).
fof(f3977,plain,
( spl0_157
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1884,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3975,plain,
spl0_156,
inference(avatar_split_clause,[],[f1883,f3973]) ).
fof(f3973,plain,
( spl0_156
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1883,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).
fof(f3971,plain,
spl0_155,
inference(avatar_split_clause,[],[f1882,f3969]) ).
fof(f3969,plain,
( spl0_155
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1882,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).
fof(f3967,plain,
spl0_154,
inference(avatar_split_clause,[],[f1881,f3965]) ).
fof(f3965,plain,
( spl0_154
<=> ! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1881,axiom,
! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3963,plain,
spl0_153,
inference(avatar_split_clause,[],[f1880,f3961]) ).
fof(f3961,plain,
( spl0_153
<=> ! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1880,axiom,
! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3959,plain,
spl0_152,
inference(avatar_split_clause,[],[f1879,f3957]) ).
fof(f3957,plain,
( spl0_152
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1879,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3955,plain,
spl0_151,
inference(avatar_split_clause,[],[f1878,f3953]) ).
fof(f3953,plain,
( spl0_151
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1878,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3951,plain,
spl0_150,
inference(avatar_split_clause,[],[f1877,f3949]) ).
fof(f3949,plain,
( spl0_150
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1877,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3947,plain,
spl0_149,
inference(avatar_split_clause,[],[f1876,f3945]) ).
fof(f3945,plain,
( spl0_149
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1876,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3943,plain,
spl0_148,
inference(avatar_split_clause,[],[f1875,f3941]) ).
fof(f3941,plain,
( spl0_148
<=> ! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1875,axiom,
! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3939,plain,
spl0_147,
inference(avatar_split_clause,[],[f1874,f3937]) ).
fof(f3937,plain,
( spl0_147
<=> ! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1874,axiom,
! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3935,plain,
spl0_146,
inference(avatar_split_clause,[],[f1719,f3933]) ).
fof(f1719,axiom,
! [X0,X12] : c_in(X12,c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3931,plain,
spl0_145,
inference(avatar_split_clause,[],[f1687,f3929]) ).
fof(f3929,plain,
( spl0_145
<=> ! [X11] : ~ c_less(X11,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1687,axiom,
! [X11] : ~ c_less(X11,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3927,plain,
spl0_144,
inference(avatar_split_clause,[],[f1685,f3925]) ).
fof(f3925,plain,
( spl0_144
<=> ! [X11] : c_lessequals(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1685,axiom,
! [X11] : c_lessequals(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3923,plain,
spl0_143,
inference(avatar_split_clause,[],[f1661,f3921]) ).
fof(f3921,plain,
( spl0_143
<=> ! [X24] : c_Divides_Oop_Advd(c_1,X24,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1661,axiom,
! [X24] : c_Divides_Oop_Advd(c_1,X24,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3919,plain,
spl0_142,
inference(avatar_split_clause,[],[f1660,f3917]) ).
fof(f3917,plain,
( spl0_142
<=> ! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1660,axiom,
! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3915,plain,
spl0_141,
inference(avatar_split_clause,[],[f1644,f3913]) ).
fof(f3913,plain,
( spl0_141
<=> ! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1644,axiom,
! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3911,plain,
spl0_140,
inference(avatar_split_clause,[],[f1566,f3909]) ).
fof(f3909,plain,
( spl0_140
<=> ! [X25,X0] : ~ c_in(X25,c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1566,axiom,
! [X0,X25] : ~ c_in(X25,c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3907,plain,
spl0_139,
inference(avatar_split_clause,[],[f1049,f3904]) ).
fof(f3904,plain,
( spl0_139
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1049,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(f3902,plain,
spl0_138,
inference(avatar_split_clause,[],[f985,f3900]) ).
fof(f3900,plain,
( spl0_138
<=> ! [X11] : ~ c_less(X11,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f985,axiom,
! [X11] : ~ c_less(X11,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3898,plain,
spl0_137,
inference(avatar_split_clause,[],[f943,f3895]) ).
fof(f3895,plain,
( spl0_137
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f943,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3893,plain,
spl0_136,
inference(avatar_split_clause,[],[f603,f3891]) ).
fof(f3891,plain,
( spl0_136
<=> ! [X12,X14] : ~ c_List_Oop_Amem(X12,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f603,axiom,
! [X14,X12] : ~ c_List_Oop_Amem(X12,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3889,plain,
spl0_135,
inference(avatar_split_clause,[],[f376,f3887]) ).
fof(f3887,plain,
( spl0_135
<=> ! [X24] : c_Divides_Oop_Advd(X24,X24,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f376,axiom,
! [X24] : c_Divides_Oop_Advd(X24,X24,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3885,plain,
spl0_134,
inference(avatar_split_clause,[],[f287,f3883]) ).
fof(f287,axiom,
! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3881,plain,
spl0_133,
inference(avatar_split_clause,[],[f280,f3878]) ).
fof(f3878,plain,
( spl0_133
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f280,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3876,plain,
spl0_132,
inference(avatar_split_clause,[],[f268,f3873]) ).
fof(f3871,plain,
spl0_131,
inference(avatar_split_clause,[],[f265,f3868]) ).
fof(f265,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3866,plain,
spl0_130,
inference(avatar_split_clause,[],[f123,f3864]) ).
fof(f3864,plain,
( spl0_130
<=> ! [X24] : c_Divides_Oop_Advd(X24,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f123,axiom,
! [X24] : c_Divides_Oop_Advd(X24,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3862,plain,
spl0_129,
inference(avatar_split_clause,[],[f1870,f3860]) ).
fof(f3860,plain,
( spl0_129
<=> ! [X8] : class_Orderings_Oorder(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1870,axiom,
! [X8] : class_Orderings_Oorder(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3858,plain,
spl0_128,
inference(avatar_split_clause,[],[f1869,f3856]) ).
fof(f3856,plain,
( spl0_128
<=> ! [X8] : class_Orderings_Oord(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1869,axiom,
! [X8] : class_Orderings_Oord(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3854,plain,
spl0_127,
inference(avatar_split_clause,[],[f1868,f3852]) ).
fof(f3852,plain,
( spl0_127
<=> ! [X8] : class_HOL_Ominus(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1868,axiom,
! [X8] : class_HOL_Ominus(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
fof(f3850,plain,
spl0_126,
inference(avatar_split_clause,[],[f1747,f3847]) ).
fof(f3847,plain,
( spl0_126
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1747,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(f3845,plain,
spl0_125,
inference(avatar_split_clause,[],[f1745,f3842]) ).
fof(f3842,plain,
( spl0_125
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1745,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(f3840,plain,
spl0_124,
inference(avatar_split_clause,[],[f1744,f3838]) ).
fof(f3838,plain,
( spl0_124
<=> ! [X0] : c_Wellfounded__Recursion_Owf(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1744,axiom,
! [X0] : c_Wellfounded__Recursion_Owf(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3836,plain,
~ spl0_123,
inference(avatar_split_clause,[],[f1523,f3833]) ).
fof(f3833,plain,
( spl0_123
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1523,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3831,plain,
~ spl0_122,
inference(avatar_split_clause,[],[f1204,f3828]) ).
fof(f3828,plain,
( spl0_122
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1204,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3826,plain,
spl0_121,
inference(avatar_split_clause,[],[f1197,f3823]) ).
fof(f3823,plain,
( spl0_121
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1197,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3821,plain,
spl0_120,
inference(avatar_split_clause,[],[f1184,f3818]) ).
fof(f3818,plain,
( spl0_120
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1184,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3816,plain,
~ spl0_119,
inference(avatar_split_clause,[],[f1054,f3813]) ).
fof(f3813,plain,
( spl0_119
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1054,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).
fof(f3811,plain,
spl0_118,
inference(avatar_split_clause,[],[f600,f3809]) ).
fof(f3809,plain,
( spl0_118
<=> ! [X14] : c_List_Onull(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f600,axiom,
! [X14] : c_List_Onull(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3807,plain,
spl0_117,
inference(avatar_split_clause,[],[f445,f3805]) ).
fof(f3805,plain,
( spl0_117
<=> ! [X14] : c_List_Odistinct(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f445,axiom,
! [X14] : c_List_Odistinct(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3803,plain,
~ spl0_116,
inference(avatar_split_clause,[],[f264,f3800]) ).
fof(f264,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3798,plain,
~ spl0_115,
inference(avatar_split_clause,[],[f144,f3795]) ).
fof(f3795,plain,
( spl0_115
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f144,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3793,plain,
~ spl0_114,
inference(avatar_split_clause,[],[f2808,f3790]) ).
fof(f2808,axiom,
~ c_lessequals(c_0,c_minus(v_f(v_x),v_g(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3788,plain,
spl0_113,
inference(avatar_split_clause,[],[f2806,f3785]) ).
fof(f2806,axiom,
c_lessequals(c_0,c_minus(v_f(v_x),v_k(v_x),t_b),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3783,plain,
spl0_112,
inference(avatar_split_clause,[],[f1866,f3780]) ).
fof(f3780,plain,
( spl0_112
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1866,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
fof(f3778,plain,
spl0_111,
inference(avatar_split_clause,[],[f1865,f3775]) ).
fof(f3775,plain,
( spl0_111
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1865,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3773,plain,
spl0_110,
inference(avatar_split_clause,[],[f1864,f3770]) ).
fof(f3770,plain,
( spl0_110
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1864,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3768,plain,
spl0_109,
inference(avatar_split_clause,[],[f1863,f3765]) ).
fof(f3765,plain,
( spl0_109
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1863,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3763,plain,
spl0_108,
inference(avatar_split_clause,[],[f1862,f3760]) ).
fof(f1862,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3758,plain,
spl0_107,
inference(avatar_split_clause,[],[f1860,f3755]) ).
fof(f3755,plain,
( spl0_107
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1860,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3753,plain,
spl0_106,
inference(avatar_split_clause,[],[f1859,f3750]) ).
fof(f3750,plain,
( spl0_106
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1859,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3748,plain,
spl0_105,
inference(avatar_split_clause,[],[f1857,f3745]) ).
fof(f3745,plain,
( spl0_105
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1857,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3743,plain,
spl0_104,
inference(avatar_split_clause,[],[f1856,f3740]) ).
fof(f3740,plain,
( spl0_104
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1856,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3738,plain,
spl0_103,
inference(avatar_split_clause,[],[f1855,f3735]) ).
fof(f3735,plain,
( spl0_103
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1855,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3733,plain,
spl0_102,
inference(avatar_split_clause,[],[f1854,f3730]) ).
fof(f3730,plain,
( spl0_102
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1854,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3728,plain,
spl0_101,
inference(avatar_split_clause,[],[f1853,f3725]) ).
fof(f1853,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3723,plain,
spl0_100,
inference(avatar_split_clause,[],[f1852,f3720]) ).
fof(f3720,plain,
( spl0_100
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1852,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3718,plain,
spl0_99,
inference(avatar_split_clause,[],[f1851,f3715]) ).
fof(f3715,plain,
( spl0_99
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1851,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3713,plain,
spl0_98,
inference(avatar_split_clause,[],[f1850,f3710]) ).
fof(f3710,plain,
( spl0_98
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1850,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3708,plain,
spl0_97,
inference(avatar_split_clause,[],[f1849,f3705]) ).
fof(f3705,plain,
( spl0_97
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1849,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3703,plain,
spl0_96,
inference(avatar_split_clause,[],[f1848,f3700]) ).
fof(f3700,plain,
( spl0_96
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1848,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3698,plain,
spl0_95,
inference(avatar_split_clause,[],[f1847,f3695]) ).
fof(f3695,plain,
( spl0_95
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1847,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3693,plain,
spl0_94,
inference(avatar_split_clause,[],[f1846,f3690]) ).
fof(f3690,plain,
( spl0_94
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1846,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3688,plain,
spl0_93,
inference(avatar_split_clause,[],[f1845,f3685]) ).
fof(f1845,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3683,plain,
spl0_92,
inference(avatar_split_clause,[],[f1844,f3680]) ).
fof(f3680,plain,
( spl0_92
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1844,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3678,plain,
spl0_91,
inference(avatar_split_clause,[],[f1843,f3675]) ).
fof(f3675,plain,
( spl0_91
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1843,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3673,plain,
spl0_90,
inference(avatar_split_clause,[],[f1842,f3670]) ).
fof(f3670,plain,
( spl0_90
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1842,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3668,plain,
spl0_89,
inference(avatar_split_clause,[],[f1841,f3665]) ).
fof(f3665,plain,
( spl0_89
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1841,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3663,plain,
spl0_88,
inference(avatar_split_clause,[],[f1840,f3660]) ).
fof(f3660,plain,
( spl0_88
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1840,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3658,plain,
spl0_87,
inference(avatar_split_clause,[],[f1839,f3655]) ).
fof(f3655,plain,
( spl0_87
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1839,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3653,plain,
spl0_86,
inference(avatar_split_clause,[],[f1838,f3650]) ).
fof(f3650,plain,
( spl0_86
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1838,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3648,plain,
spl0_85,
inference(avatar_split_clause,[],[f1837,f3645]) ).
fof(f3645,plain,
( spl0_85
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1837,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3643,plain,
spl0_84,
inference(avatar_split_clause,[],[f1836,f3640]) ).
fof(f3640,plain,
( spl0_84
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1836,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3638,plain,
spl0_83,
inference(avatar_split_clause,[],[f1835,f3635]) ).
fof(f1835,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3633,plain,
spl0_82,
inference(avatar_split_clause,[],[f1834,f3630]) ).
fof(f3630,plain,
( spl0_82
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1834,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3628,plain,
spl0_81,
inference(avatar_split_clause,[],[f1833,f3625]) ).
fof(f3625,plain,
( spl0_81
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1833,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3623,plain,
spl0_80,
inference(avatar_split_clause,[],[f1832,f3620]) ).
fof(f3620,plain,
( spl0_80
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1832,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3618,plain,
spl0_79,
inference(avatar_split_clause,[],[f1831,f3615]) ).
fof(f3615,plain,
( spl0_79
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1831,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3613,plain,
spl0_78,
inference(avatar_split_clause,[],[f1830,f3610]) ).
fof(f3610,plain,
( spl0_78
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1830,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3608,plain,
spl0_77,
inference(avatar_split_clause,[],[f1829,f3605]) ).
fof(f3605,plain,
( spl0_77
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1829,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3603,plain,
spl0_76,
inference(avatar_split_clause,[],[f1828,f3600]) ).
fof(f3600,plain,
( spl0_76
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1828,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
fof(f3598,plain,
spl0_75,
inference(avatar_split_clause,[],[f1827,f3595]) ).
fof(f3595,plain,
( spl0_75
<=> class_OrderedGroup_Osemigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1827,axiom,
class_OrderedGroup_Osemigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).
fof(f3593,plain,
spl0_74,
inference(avatar_split_clause,[],[f1826,f3590]) ).
fof(f3590,plain,
( spl0_74
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1826,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).
fof(f3588,plain,
spl0_73,
inference(avatar_split_clause,[],[f1825,f3585]) ).
fof(f3585,plain,
( spl0_73
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1825,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).
fof(f3583,plain,
spl0_72,
inference(avatar_split_clause,[],[f1824,f3580]) ).
fof(f3580,plain,
( spl0_72
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1824,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3578,plain,
spl0_71,
inference(avatar_split_clause,[],[f1822,f3575]) ).
fof(f3575,plain,
( spl0_71
<=> class_HOL_Otimes(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1822,axiom,
class_HOL_Otimes(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).
fof(f3573,plain,
spl0_70,
inference(avatar_split_clause,[],[f1821,f3570]) ).
fof(f3570,plain,
( spl0_70
<=> class_HOL_Oplus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1821,axiom,
class_HOL_Oplus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).
fof(f3568,plain,
spl0_69,
inference(avatar_split_clause,[],[f1820,f3565]) ).
fof(f3565,plain,
( spl0_69
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1820,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).
fof(f3563,plain,
spl0_68,
inference(avatar_split_clause,[],[f1819,f3560]) ).
fof(f3560,plain,
( spl0_68
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1819,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3558,plain,
spl0_67,
inference(avatar_split_clause,[],[f1816,f3555]) ).
fof(f3555,plain,
( spl0_67
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1816,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3553,plain,
spl0_66,
inference(avatar_split_clause,[],[f1815,f3550]) ).
fof(f3550,plain,
( spl0_66
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1815,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3548,plain,
spl0_65,
inference(avatar_split_clause,[],[f1814,f3545]) ).
fof(f3545,plain,
( spl0_65
<=> class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1814,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
fof(f3543,plain,
spl0_64,
inference(avatar_split_clause,[],[f1813,f3540]) ).
fof(f3540,plain,
( spl0_64
<=> class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1813,axiom,
class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
fof(f3538,plain,
spl0_63,
inference(avatar_split_clause,[],[f1812,f3535]) ).
fof(f3535,plain,
( spl0_63
<=> class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1812,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
fof(f3533,plain,
spl0_62,
inference(avatar_split_clause,[],[f1810,f3530]) ).
fof(f3530,plain,
( spl0_62
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1810,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3528,plain,
spl0_61,
inference(avatar_split_clause,[],[f1807,f3525]) ).
fof(f1807,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3523,plain,
spl0_60,
inference(avatar_split_clause,[],[f1806,f3520]) ).
fof(f3520,plain,
( spl0_60
<=> class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1806,axiom,
class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
fof(f3518,plain,
spl0_59,
inference(avatar_split_clause,[],[f1805,f3515]) ).
fof(f3515,plain,
( spl0_59
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1805,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3513,plain,
spl0_58,
inference(avatar_split_clause,[],[f1804,f3510]) ).
fof(f1804,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3508,plain,
spl0_57,
inference(avatar_split_clause,[],[f1803,f3505]) ).
fof(f3505,plain,
( spl0_57
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1803,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3503,plain,
spl0_56,
inference(avatar_split_clause,[],[f1802,f3500]) ).
fof(f1802,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3498,plain,
spl0_55,
inference(avatar_split_clause,[],[f1801,f3495]) ).
fof(f3495,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1801,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3493,plain,
spl0_54,
inference(avatar_split_clause,[],[f1800,f3490]) ).
fof(f3490,plain,
( spl0_54
<=> class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1800,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
fof(f3488,plain,
spl0_53,
inference(avatar_split_clause,[],[f1799,f3485]) ).
fof(f3485,plain,
( spl0_53
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1799,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3483,plain,
spl0_52,
inference(avatar_split_clause,[],[f1798,f3480]) ).
fof(f3480,plain,
( spl0_52
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1798,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3478,plain,
spl0_51,
inference(avatar_split_clause,[],[f1797,f3475]) ).
fof(f3475,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1797,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3473,plain,
spl0_50,
inference(avatar_split_clause,[],[f1796,f3470]) ).
fof(f3470,plain,
( spl0_50
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1796,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3468,plain,
spl0_49,
inference(avatar_split_clause,[],[f1795,f3465]) ).
fof(f3465,plain,
( spl0_49
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1795,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3463,plain,
spl0_48,
inference(avatar_split_clause,[],[f1794,f3460]) ).
fof(f3460,plain,
( spl0_48
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1794,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3458,plain,
spl0_47,
inference(avatar_split_clause,[],[f1793,f3455]) ).
fof(f1793,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3453,plain,
spl0_46,
inference(avatar_split_clause,[],[f1792,f3450]) ).
fof(f1792,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3448,plain,
spl0_45,
inference(avatar_split_clause,[],[f1791,f3445]) ).
fof(f3445,plain,
( spl0_45
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1791,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3443,plain,
spl0_44,
inference(avatar_split_clause,[],[f1790,f3440]) ).
fof(f3440,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1790,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3438,plain,
spl0_43,
inference(avatar_split_clause,[],[f1789,f3435]) ).
fof(f3435,plain,
( spl0_43
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1789,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3433,plain,
spl0_42,
inference(avatar_split_clause,[],[f1788,f3430]) ).
fof(f3430,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1788,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3428,plain,
spl0_41,
inference(avatar_split_clause,[],[f1787,f3425]) ).
fof(f3425,plain,
( spl0_41
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1787,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3423,plain,
spl0_40,
inference(avatar_split_clause,[],[f1786,f3420]) ).
fof(f3420,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1786,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3418,plain,
spl0_39,
inference(avatar_split_clause,[],[f1785,f3415]) ).
fof(f3415,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1785,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3413,plain,
spl0_38,
inference(avatar_split_clause,[],[f1784,f3410]) ).
fof(f3410,plain,
( spl0_38
<=> class_HOL_Ozero(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1784,axiom,
class_HOL_Ozero(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
fof(f3408,plain,
spl0_37,
inference(avatar_split_clause,[],[f1783,f3405]) ).
fof(f3405,plain,
( spl0_37
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1783,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3403,plain,
spl0_36,
inference(avatar_split_clause,[],[f1782,f3400]) ).
fof(f3400,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1782,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3398,plain,
spl0_35,
inference(avatar_split_clause,[],[f1781,f3395]) ).
fof(f3395,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1781,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3393,plain,
spl0_34,
inference(avatar_split_clause,[],[f1780,f3390]) ).
fof(f3390,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1780,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3388,plain,
spl0_33,
inference(avatar_split_clause,[],[f1779,f3385]) ).
fof(f1779,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3383,plain,
spl0_32,
inference(avatar_split_clause,[],[f1778,f3380]) ).
fof(f3380,plain,
( spl0_32
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1778,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3378,plain,
spl0_31,
inference(avatar_split_clause,[],[f1777,f3375]) ).
fof(f1777,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3373,plain,
spl0_30,
inference(avatar_split_clause,[],[f1776,f3370]) ).
fof(f1776,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3368,plain,
spl0_29,
inference(avatar_split_clause,[],[f1775,f3365]) ).
fof(f1775,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3363,plain,
spl0_28,
inference(avatar_split_clause,[],[f1774,f3360]) ).
fof(f1774,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3358,plain,
spl0_27,
inference(avatar_split_clause,[],[f1773,f3355]) ).
fof(f3355,plain,
( spl0_27
<=> class_HOL_Otimes(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1773,axiom,
class_HOL_Otimes(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
fof(f3353,plain,
spl0_26,
inference(avatar_split_clause,[],[f1772,f3350]) ).
fof(f1772,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3348,plain,
spl0_25,
inference(avatar_split_clause,[],[f1771,f3345]) ).
fof(f3345,plain,
( spl0_25
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1771,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3343,plain,
spl0_24,
inference(avatar_split_clause,[],[f1770,f3340]) ).
fof(f3340,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1770,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3338,plain,
spl0_23,
inference(avatar_split_clause,[],[f1769,f3335]) ).
fof(f3335,plain,
( spl0_23
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1769,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3333,plain,
spl0_22,
inference(avatar_split_clause,[],[f1768,f3330]) ).
fof(f3330,plain,
( spl0_22
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1768,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3328,plain,
spl0_21,
inference(avatar_split_clause,[],[f1767,f3325]) ).
fof(f3325,plain,
( spl0_21
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1767,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3323,plain,
spl0_20,
inference(avatar_split_clause,[],[f1766,f3320]) ).
fof(f1766,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3318,plain,
spl0_19,
inference(avatar_split_clause,[],[f1765,f3315]) ).
fof(f3315,plain,
( spl0_19
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1765,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3313,plain,
spl0_18,
inference(avatar_split_clause,[],[f1764,f3310]) ).
fof(f3310,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1764,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3308,plain,
spl0_17,
inference(avatar_split_clause,[],[f1763,f3305]) ).
fof(f3305,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1763,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3303,plain,
spl0_16,
inference(avatar_split_clause,[],[f1762,f3300]) ).
fof(f3300,plain,
( spl0_16
<=> class_HOL_Oplus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1762,axiom,
class_HOL_Oplus(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
fof(f3298,plain,
spl0_15,
inference(avatar_split_clause,[],[f1761,f3295]) ).
fof(f3295,plain,
( spl0_15
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1761,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3293,plain,
spl0_14,
inference(avatar_split_clause,[],[f1760,f3290]) ).
fof(f3290,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1760,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3288,plain,
spl0_13,
inference(avatar_split_clause,[],[f1759,f3285]) ).
fof(f1759,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3283,plain,
spl0_12,
inference(avatar_split_clause,[],[f1758,f3280]) ).
fof(f3280,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1758,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3278,plain,
spl0_11,
inference(avatar_split_clause,[],[f1757,f3275]) ).
fof(f3275,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1757,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3273,plain,
spl0_10,
inference(avatar_split_clause,[],[f1756,f3270]) ).
fof(f3270,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1756,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3268,plain,
spl0_9,
inference(avatar_split_clause,[],[f1755,f3265]) ).
fof(f3265,plain,
( spl0_9
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1755,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3263,plain,
spl0_8,
inference(avatar_split_clause,[],[f1754,f3260]) ).
fof(f1754,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3258,plain,
spl0_7,
inference(avatar_split_clause,[],[f1753,f3255]) ).
fof(f3255,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1753,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3253,plain,
spl0_6,
inference(avatar_split_clause,[],[f1752,f3250]) ).
fof(f3250,plain,
( spl0_6
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1752,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3248,plain,
spl0_5,
inference(avatar_split_clause,[],[f1751,f3245]) ).
fof(f3245,plain,
( spl0_5
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1751,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3243,plain,
spl0_4,
inference(avatar_split_clause,[],[f1750,f3240]) ).
fof(f3240,plain,
( spl0_4
<=> class_HOL_Ominus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1750,axiom,
class_HOL_Ominus(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
fof(f3238,plain,
spl0_3,
inference(avatar_split_clause,[],[f2807,f3235]) ).
fof(f2807,axiom,
c_lessequals(v_g(v_x),v_k(v_x),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3233,plain,
spl0_2,
inference(avatar_split_clause,[],[f2805,f3231]) ).
fof(f2805,axiom,
! [X29] : c_lessequals(c_0,v_k(X29),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3229,plain,
spl0_1,
inference(avatar_split_clause,[],[f2809,f3226]) ).
fof(f2809,axiom,
class_Ring__and__Field_Oordered__idom(t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : ANA027-1 : TPTP v8.2.0. Released v3.2.0.
% 0.00/0.10 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.30 % Computer : n014.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 300
% 0.10/0.30 % DateTime : Mon May 20 07:48:53 EDT 2024
% 0.10/0.30 % CPUTime :
% 0.10/0.30 % (9158)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.40 % (9161)WARNING: value z3 for option sas not known
% 0.15/0.40 % (9159)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.40 % (9165)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)
% 0.15/0.40 % (9160)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.40 % (9161)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)
% 0.15/0.40 % (9162)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.40 % (9164)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.41 % (9163)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)
% 1.80/0.67 TRYING [1]
% 5.08/1.11 TRYING [2]
% 7.09/1.42 TRYING [1]
% 9.25/1.70 % (9163)First to succeed.
% 9.25/1.72 TRYING [1]
% 9.91/1.80 % (9163)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9158"
% 9.91/1.80 % (9163)Refutation found. Thanks to Tanya!
% 9.91/1.80 % SZS status Unsatisfiable for theBenchmark
% 9.91/1.80 % SZS output start Proof for theBenchmark
% See solution above
% 10.08/1.87 % (9163)------------------------------
% 10.08/1.87 % (9163)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 10.08/1.87 % (9163)Termination reason: Refutation
% 10.08/1.87
% 10.08/1.87 % (9163)Memory used [KB]: 20182
% 10.08/1.87 % (9163)Time elapsed: 1.392 s
% 10.08/1.87 % (9163)Instructions burned: 2627 (million)
% 10.08/1.87 % (9158)Success in time 1.533 s
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