TSTP Solution File: SWV273-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV273-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 10:48:43 EDT 2024
% Result : Unsatisfiable 4.62s 1.14s
% Output : Refutation 4.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3773
% Syntax : Number of formulae : 6358 (2466 unt; 0 def)
% Number of atoms : 12937 (2305 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 11160 (4581 ~;4617 |; 0 &)
% (1962 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 2032 (2030 usr;1963 prp; 0-3 aty)
% Number of functors : 206 ( 206 usr; 48 con; 0-5 aty)
% Number of variables : 7420 (7420 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f21379,plain,
$false,
inference(avatar_sat_refutation,[],[f3256,f3261,f3266,f3271,f3276,f3281,f3286,f3291,f3296,f3301,f3306,f3311,f3316,f3321,f3326,f3331,f3336,f3341,f3346,f3351,f3356,f3361,f3366,f3371,f3376,f3381,f3386,f3391,f3396,f3401,f3406,f3411,f3416,f3421,f3426,f3431,f3436,f3441,f3446,f3451,f3456,f3461,f3466,f3471,f3476,f3481,f3486,f3491,f3496,f3501,f3506,f3511,f3516,f3521,f3526,f3531,f3536,f3541,f3546,f3551,f3556,f3561,f3566,f3571,f3576,f3581,f3586,f3591,f3596,f3601,f3606,f3611,f3616,f3621,f3626,f3631,f3636,f3641,f3646,f3651,f3656,f3661,f3666,f3671,f3676,f3681,f3686,f3691,f3696,f3701,f3706,f3711,f3716,f3720,f3725,f3730,f3734,f3738,f3743,f3748,f3752,f3756,f3761,f3766,f3771,f3776,f3781,f3786,f3790,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3830,f3834,f3838,f3842,f3846,f3850,f3854,f3858,f3862,f3866,f3870,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4626,f4630,f4634,f4638,f4642,f4646,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4794,f4798,f4802,f4806,f4810,f4814,f4818,f4822,f4826,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4914,f4918,f4922,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5054,f5058,f5062,f5066,f5070,f5074,f5078,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5118,f5122,f5126,f5130,f5134,f5138,f5142,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5186,f5190,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5246,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5294,f5298,f5302,f5306,f5310,f5314,f5318,f5322,f5326,f5330,f5334,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5490,f5494,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5582,f5586,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f5622,f5626,f5630,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5718,f5722,f5726,f5730,f5734,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5778,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5890,f5894,f5898,f5902,f5906,f5910,f5915,f5920,f5925,f5929,f5933,f5937,f5942,f5946,f5951,f5955,f5959,f5963,f5968,f5973,f5978,f5983,f5988,f5992,f5997,f6764,f6768,f6772,f6776,f6780,f6785,f6789,f6793,f6797,f6801,f6805,f6809,f6814,f6819,f6824,f6828,f6832,f6836,f6841,f6845,f6849,f6853,f6857,f6861,f6865,f6869,f6873,f6878,f6883,f6888,f6893,f6898,f6903,f6908,f6913,f6918,f6923,f6928,f6933,f6938,f6943,f6948,f6953,f6957,f6961,f6965,f6969,f6973,f6978,f6983,f6988,f6992,f6996,f7000,f7004,f7008,f7012,f7017,f7022,f7026,f7031,f7036,f7040,f7044,f7048,f7052,f7056,f7060,f7064,f7068,f7073,f7078,f7082,f7087,f7091,f7096,f7107,f7112,f7119,f7123,f7127,f7131,f7135,f7139,f7143,f7147,f7151,f7155,f7159,f7164,f7168,f7172,f7176,f7180,f7184,f7188,f7192,f7196,f7200,f7204,f7208,f7212,f7216,f7220,f7224,f7228,f7232,f7236,f7240,f7244,f7248,f7252,f7256,f7260,f7264,f7268,f7272,f7276,f7280,f7284,f7288,f7292,f7296,f7300,f7304,f7308,f7313,f7317,f7321,f7325,f7329,f7333,f7337,f7341,f7345,f7349,f7353,f7357,f7361,f7365,f7369,f7373,f7377,f7381,f7385,f7389,f7393,f7397,f7401,f7405,f7409,f7413,f7417,f7421,f7425,f7429,f7433,f7437,f7442,f7446,f7451,f7455,f7460,f7464,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7509,f7513,f7517,f7521,f7525,f7529,f7533,f7537,f7541,f7545,f7549,f7553,f7557,f7561,f7565,f7569,f7573,f7577,f7581,f7585,f7589,f7593,f7597,f7601,f7605,f7609,f7613,f7617,f7621,f7625,f7629,f7633,f7637,f7641,f7645,f7649,f7653,f7657,f7661,f7665,f7669,f7673,f7677,f7681,f7685,f7689,f7693,f7697,f7701,f7705,f7709,f7714,f7719,f7723,f7727,f7731,f7759,f7793,f7804,f7812,f7820,f7824,f7828,f7832,f7836,f7840,f7845,f7849,f7853,f7857,f7861,f7865,f7869,f7873,f7878,f7882,f7886,f7891,f7895,f7899,f7903,f7907,f7911,f7915,f7919,f7923,f7927,f7931,f7936,f7940,f7944,f7948,f7952,f7956,f7960,f7964,f7968,f7972,f7976,f7985,f7989,f7993,f7997,f8001,f8005,f8009,f8013,f8017,f8021,f8025,f8029,f8033,f8037,f8041,f8045,f8049,f8053,f8057,f8061,f8065,f8069,f8073,f8077,f8081,f8085,f8089,f8093,f8097,f8101,f8105,f8109,f8113,f8117,f8121,f8125,f8129,f8134,f8138,f8142,f8146,f8151,f8155,f8159,f8163,f8167,f8171,f8175,f8179,f8183,f8187,f8191,f8196,f8200,f8210,f8333,f8337,f8341,f8346,f8350,f8354,f8358,f8362,f8366,f8370,f8374,f8378,f8382,f8387,f8391,f8395,f8399,f8403,f8407,f8411,f8415,f8419,f8423,f8427,f8431,f8435,f8439,f8443,f8447,f8451,f8455,f8459,f8463,f8467,f8472,f8476,f8480,f8484,f8488,f8492,f8496,f8500,f8504,f8508,f8512,f8516,f8520,f8524,f8528,f8532,f8536,f8540,f8544,f8548,f8552,f8557,f8561,f8565,f8569,f8573,f8577,f8581,f8585,f8589,f8593,f8597,f8601,f8605,f8609,f8613,f8617,f8621,f8625,f8629,f8633,f8637,f8641,f8645,f8649,f8653,f8657,f8661,f8665,f8669,f8673,f8677,f8681,f8685,f8689,f8693,f8697,f8773,f8801,f8820,f8867,f8892,f8925,f8929,f8933,f8938,f8942,f8946,f8950,f8954,f8958,f8962,f8966,f8970,f8974,f8978,f8982,f8986,f8990,f8994,f8998,f9002,f9006,f9010,f9014,f9018,f9022,f9026,f9030,f9034,f9038,f9042,f9046,f9050,f9054,f9059,f9063,f9068,f9072,f9076,f9080,f9084,f9088,f9092,f9096,f9100,f9104,f9108,f9112,f9116,f9120,f9124,f9128,f9132,f9136,f9140,f9144,f9148,f9152,f9156,f9160,f9164,f9168,f9172,f9176,f9180,f9184,f9188,f9192,f9196,f9200,f9204,f9208,f9212,f9216,f9220,f9224,f9228,f9233,f9237,f9242,f9246,f9253,f9257,f9261,f9265,f9269,f9273,f9280,f9337,f9387,f9419,f9461,f9478,f9489,f9504,f9508,f9512,f9516,f9520,f9524,f9528,f9532,f9537,f9541,f9545,f9549,f9553,f9557,f9561,f9565,f9569,f9573,f9577,f9581,f9585,f9589,f9593,f9597,f9601,f9605,f9609,f9613,f9617,f9621,f9625,f9629,f9633,f9637,f9641,f9645,f9649,f9653,f9657,f9661,f9665,f9669,f9673,f9677,f9681,f9685,f9689,f9693,f9697,f9701,f9705,f9709,f9713,f9717,f9721,f9725,f9729,f9733,f9737,f9741,f9745,f9749,f9753,f9757,f9761,f9765,f9769,f9773,f9777,f9781,f9785,f9789,f9793,f9797,f9802,f9810,f9814,f9818,f9822,f9826,f9830,f9834,f9838,f9872,f9881,f9931,f10157,f10255,f10259,f10263,f10267,f10271,f10275,f10279,f10283,f10287,f10291,f10295,f10299,f10303,f10307,f10311,f10315,f10319,f10323,f10327,f10331,f10335,f10339,f10343,f10347,f10351,f10355,f10359,f10363,f10367,f10371,f10376,f10381,f10385,f10389,f10393,f10397,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10433,f10437,f10441,f10445,f10449,f10453,f10457,f10461,f10465,f10469,f10473,f10477,f10481,f10485,f10490,f10494,f10498,f10502,f10506,f10510,f10514,f10518,f10522,f10526,f10530,f10534,f10538,f10542,f10546,f10550,f10554,f10558,f10562,f10566,f10570,f10574,f10578,f10582,f10586,f10590,f10594,f10598,f10602,f10606,f10610,f10617,f10621,f10625,f10629,f10633,f10637,f10641,f10645,f10649,f10653,f10657,f10661,f10665,f10669,f10673,f10677,f10681,f10685,f10689,f10693,f10701,f10705,f10709,f10713,f10717,f10721,f10725,f10729,f10733,f10737,f10742,f10746,f10750,f10754,f10758,f10762,f10766,f10770,f10774,f10778,f10785,f10789,f10793,f10828,f10964,f11029,f11251,f11801,f11805,f11809,f11813,f11817,f11821,f11825,f11829,f11833,f11837,f11841,f11847,f11851,f11855,f11859,f11863,f11867,f11871,f11875,f11879,f11883,f11891,f11895,f11899,f11903,f11907,f11911,f11915,f11919,f11923,f11927,f11936,f11940,f11944,f11948,f11952,f11956,f11960,f11964,f11968,f11972,f11977,f11981,f11985,f11989,f11993,f11997,f12001,f12005,f12009,f12013,f12017,f12026,f12030,f12034,f12038,f12042,f12046,f12050,f12054,f12058,f12062,f12067,f12071,f12075,f12079,f12083,f12087,f12091,f12095,f12099,f12103,f12118,f12122,f12126,f12130,f12134,f12138,f12142,f12146,f12150,f12154,f12164,f12168,f12172,f12176,f12180,f12184,f12188,f12192,f12196,f12200,f12209,f12213,f12217,f12221,f12225,f12229,f12233,f12237,f12241,f12245,f12254,f12258,f12265,f12269,f12273,f12277,f12282,f12290,f12294,f12299,f12330,f12334,f12338,f12342,f12346,f12350,f12354,f12564,f13096,f13293,f13407,f13530,f13615,f13619,f13623,f13627,f13631,f13635,f13639,f13643,f13647,f13651,f13655,f13659,f13663,f13667,f13671,f13675,f13679,f13683,f13687,f13691,f13695,f13699,f13703,f13707,f13711,f13715,f13719,f13723,f13727,f13731,f13735,f13739,f13743,f13747,f13751,f13755,f13759,f13763,f13767,f13771,f13775,f13779,f13784,f13788,f13792,f13796,f13800,f13804,f13808,f13812,f13816,f13820,f13824,f13828,f13832,f13836,f13840,f13844,f13848,f13852,f13856,f13860,f13864,f13868,f13892,f13896,f13900,f13904,f13908,f13912,f13916,f13920,f13924,f13928,f13952,f13956,f13961,f13970,f13974,f13978,f13982,f14297,f14562,f14705,f14980,f14984,f14988,f14992,f14996,f15000,f15004,f15008,f15012,f15016,f15020,f15024,f15028,f15032,f15036,f15040,f15044,f15048,f15052,f15056,f15060,f15064,f15068,f15072,f15076,f15080,f15084,f15088,f15092,f15096,f15100,f15104,f15108,f15112,f15116,f15120,f15124,f15128,f15132,f15136,f15140,f15144,f15148,f15152,f15156,f15160,f15164,f15168,f15172,f15176,f15180,f15184,f15188,f15192,f15196,f15200,f15204,f15208,f15212,f15216,f15220,f15225,f15229,f15253,f15258,f15276,f15281,f15301,f15305,f15309,f15313,f15317,f15321,f15325,f15329,f15333,f15337,f15341,f15345,f15352,f15482,f15855,f16011,f16387,f16391,f16395,f16399,f16403,f16407,f16411,f16415,f16419,f16423,f16427,f16431,f16435,f16439,f16443,f16462,f16466,f16470,f16474,f16478,f16482,f16486,f16491,f16495,f16499,f16504,f16508,f16512,f16516,f16520,f16524,f16528,f16532,f16536,f16540,f16544,f16548,f16552,f16556,f16560,f16564,f16568,f16572,f16576,f16580,f16584,f16588,f16593,f16597,f16601,f16605,f16609,f16613,f16617,f16621,f16625,f16629,f16633,f16637,f16641,f16645,f16649,f16654,f16682,f16687,f16745,f16750,f16754,f16849,f16854,f16953,f16958,f16988,f16993,f17010,f17014,f17019,f17027,f17032,f17040,f17046,f17052,f17056,f17061,f17065,f17071,f17077,f17081,f17085,f17089,f17093,f17099,f17132,f17136,f17150,f17290,f17416,f17676,f17986,f18246,f18327,f18331,f18335,f18339,f18343,f18347,f18351,f18355,f18359,f18363,f18367,f18371,f18375,f18379,f18383,f18387,f18391,f18395,f18399,f18403,f18407,f18411,f18415,f18419,f18423,f18427,f18431,f18435,f18439,f18443,f18447,f18451,f18455,f18459,f18463,f18467,f18471,f18475,f18479,f18483,f18487,f18491,f18495,f18499,f18503,f18507,f18511,f18515,f18519,f18523,f18527,f18531,f18535,f18539,f18543,f18547,f18551,f18557,f18583,f18589,f18593,f18678,f18683,f18708,f18712,f18716,f18721,f18729,f18733,f18738,f18743,f18748,f18753,f18757,f18761,f18765,f18770,f18792,f18796,f18800,f18804,f18809,f18814,f18819,f18824,f18830,f18835,f18841,f18846,f18859,f18863,f18868,f18884,f18888,f18892,f18896,f18900,f18945,f19076,f19916,f19920,f19924,f19928,f19932,f19936,f19940,f19946,f19952,f19961,f19965,f19969,f19973,f19977,f19981,f19985,f19989,f19993,f19997,f20002,f20006,f20010,f20014,f20018,f20022,f20026,f20030,f20034,f20038,f20042,f20046,f20050,f20054,f20058,f20062,f20066,f20070,f20074,f20078,f20082,f20094,f20413,f20417,f20422,f21002,f21183,f21201,f21205,f21209,f21213,f21217,f21222,f21226,f21230,f21237,f21241,f21245,f21249,f21253,f21257,f21261,f21265,f21269,f21273,f21278,f21282,f21286,f21344,f21376,f21378]) ).
fof(f21378,plain,
( ~ spl0_816
| spl0_1958 ),
inference(avatar_contradiction_clause,[],[f21377]) ).
fof(f21377,plain,
( $false
| ~ spl0_816
| spl0_1958 ),
inference(resolution,[],[f21277,f7436]) ).
fof(f7436,plain,
( ! [X88] : c_lessequals(X88,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7435]) ).
fof(f7435,plain,
( spl0_816
<=> ! [X88] : c_lessequals(X88,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f21277,plain,
( ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| spl0_1958 ),
inference(avatar_component_clause,[],[f21275]) ).
fof(f21275,plain,
( spl0_1958
<=> c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f21376,plain,
( spl0_1962
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1947 ),
inference(avatar_split_clause,[],[f21231,f21228,f16956,f7266,f7246,f21374]) ).
fof(f21374,plain,
( spl0_1962
<=> ! [X3,X23,X25,X1] :
( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
| c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f7246,plain,
( spl0_769
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f7266,plain,
( spl0_774
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f16956,plain,
( spl0_1764
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f21228,plain,
( spl0_1947
<=> ! [X3,X23,X25,X1] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f21231,plain,
( ! [X3,X1,X25,X23] :
( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
| c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1947 ),
inference(forward_demodulation,[],[f21229,f16982]) ).
fof(f16982,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764 ),
inference(forward_demodulation,[],[f16959,f7267]) ).
fof(f7267,plain,
( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f7266]) ).
fof(f16959,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_769
| ~ spl0_1764 ),
inference(superposition,[],[f16957,f7247]) ).
fof(f7247,plain,
( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f7246]) ).
fof(f16957,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
| ~ spl0_1764 ),
inference(avatar_component_clause,[],[f16956]) ).
fof(f21229,plain,
( ! [X3,X1,X25,X23] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 )
| ~ spl0_1947 ),
inference(avatar_component_clause,[],[f21228]) ).
fof(f21344,plain,
( spl0_1961
| ~ spl0_1740
| ~ spl0_1944 ),
inference(avatar_split_clause,[],[f21218,f21215,f16590,f21342]) ).
fof(f21342,plain,
( spl0_1961
<=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f16590,plain,
( spl0_1740
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f21215,plain,
( spl0_1944
<=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f21218,plain,
( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1740
| ~ spl0_1944 ),
inference(forward_demodulation,[],[f21216,f16592]) ).
fof(f16592,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_1740 ),
inference(avatar_component_clause,[],[f16590]) ).
fof(f21216,plain,
( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1944 ),
inference(avatar_component_clause,[],[f21215]) ).
fof(f21286,plain,
spl0_1960,
inference(avatar_split_clause,[],[f3161,f21284]) ).
fof(f21284,plain,
( spl0_1960
<=> ! [X83] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f3161,plain,
! [X83] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2981,f2831]) ).
fof(f2831,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2016,f2544]) ).
fof(f2544,axiom,
! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f2016,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2981,plain,
! [X83] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1872,f2544]) ).
fof(f1872,axiom,
! [X83] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f21282,plain,
spl0_1959,
inference(avatar_split_clause,[],[f2987,f21280]) ).
fof(f21280,plain,
( spl0_1959
<=> ! [X5,X1,X28] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f2987,plain,
! [X28,X1,X5] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
inference(definition_unfolding,[],[f119,f2716]) ).
fof(f2716,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f119,axiom,
! [X28,X1,X5] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f21278,plain,
( ~ spl0_1958
| ~ spl0_1385
| spl0_1939 ),
inference(avatar_split_clause,[],[f21233,f20999,f10752,f21275]) ).
fof(f10752,plain,
( spl0_1385
<=> ! [X20,X88] :
( ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f20999,plain,
( spl0_1939
<=> c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f21233,plain,
( ~ c_lessequals(v_H,c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| ~ spl0_1385
| spl0_1939 ),
inference(resolution,[],[f21001,f10753]) ).
fof(f10753,plain,
( ! [X88,X20] :
( c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg)) )
| ~ spl0_1385 ),
inference(avatar_component_clause,[],[f10752]) ).
fof(f21001,plain,
( ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| spl0_1939 ),
inference(avatar_component_clause,[],[f20999]) ).
fof(f21273,plain,
spl0_1957,
inference(avatar_split_clause,[],[f2985,f21271]) ).
fof(f21271,plain,
( spl0_1957
<=> ! [X25,X1,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f2985,plain,
! [X1,X25,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X23,X1),X1),c_List_Oset(X25,X1),X1,X1) ),
inference(definition_unfolding,[],[f1557,f2373]) ).
fof(f2373,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f1557,axiom,
! [X1,X25,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f21269,plain,
spl0_1956,
inference(avatar_split_clause,[],[f2936,f21267]) ).
fof(f21267,plain,
( spl0_1956
<=> ! [X11,X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f2936,plain,
! [X48,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1),X48,X1) ),
inference(definition_unfolding,[],[f2165,f2129]) ).
fof(f2129,axiom,
! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f2165,axiom,
! [X48,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1),X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f21265,plain,
spl0_1955,
inference(avatar_split_clause,[],[f2909,f21263]) ).
fof(f21263,plain,
( spl0_1955
<=> ! [X41,X0,X23,X25] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f2909,plain,
! [X41,X0,X25,X23] : c_append(c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41),X25,X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,X25,X41),X41),
inference(definition_unfolding,[],[f1587,f1585,f1585]) ).
fof(f1585,axiom,
! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f1587,axiom,
! [X41,X0,X25,X23] : c_List_Oitrev(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Oitrev(X23,c_List_Olist_OCons(X0,X25,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f21261,plain,
spl0_1954,
inference(avatar_split_clause,[],[f2795,f21259]) ).
fof(f21259,plain,
( spl0_1954
<=> ! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f2795,axiom,
! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Key_0) ).
fof(f21257,plain,
spl0_1953,
inference(avatar_split_clause,[],[f2786,f21255]) ).
fof(f21255,plain,
( spl0_1953
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f2786,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_ODecrypt__dest_0) ).
fof(f21253,plain,
spl0_1952,
inference(avatar_split_clause,[],[f2122,f21251]) ).
fof(f21251,plain,
( spl0_1952
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f2122,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f21249,plain,
spl0_1951,
inference(avatar_split_clause,[],[f1864,f21247]) ).
fof(f21247,plain,
( spl0_1951
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f1864,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f21245,plain,
spl0_1950,
inference(avatar_split_clause,[],[f1800,f21243]) ).
fof(f21243,plain,
( spl0_1950
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f1800,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f21241,plain,
spl0_1949,
inference(avatar_split_clause,[],[f1796,f21239]) ).
fof(f21239,plain,
( spl0_1949
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f1796,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f21237,plain,
spl0_1948,
inference(avatar_split_clause,[],[f1795,f21235]) ).
fof(f21235,plain,
( spl0_1948
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f1795,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f21230,plain,
spl0_1947,
inference(avatar_split_clause,[],[f1726,f21228]) ).
fof(f1726,axiom,
! [X3,X1,X25,X23] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f21226,plain,
spl0_1946,
inference(avatar_split_clause,[],[f1714,f21224]) ).
fof(f21224,plain,
( spl0_1946
<=> ! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f1714,axiom,
! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f21222,plain,
spl0_1945,
inference(avatar_split_clause,[],[f1617,f21220]) ).
fof(f21220,plain,
( spl0_1945
<=> ! [X61,X5,X1,X24] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f1617,axiom,
! [X1,X24,X5,X61] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f21217,plain,
spl0_1944,
inference(avatar_split_clause,[],[f1453,f21215]) ).
fof(f1453,axiom,
! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f21213,plain,
spl0_1943,
inference(avatar_split_clause,[],[f1219,f21211]) ).
fof(f21211,plain,
( spl0_1943
<=> ! [X4,X27,X18] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f1219,axiom,
! [X18,X27,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f21209,plain,
spl0_1942,
inference(avatar_split_clause,[],[f1218,f21207]) ).
fof(f21207,plain,
( spl0_1942
<=> ! [X4,X27,X18] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f1218,axiom,
! [X18,X27,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f21205,plain,
spl0_1941,
inference(avatar_split_clause,[],[f57,f21203]) ).
fof(f21203,plain,
( spl0_1941
<=> ! [X5,X1,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f57,axiom,
! [X1,X5,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f21201,plain,
spl0_1940,
inference(avatar_split_clause,[],[f56,f21199]) ).
fof(f21199,plain,
( spl0_1940
<=> ! [X5,X1,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f56,axiom,
! [X1,X5,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f21183,plain,
( ~ spl0_1556
| spl0_1938 ),
inference(avatar_contradiction_clause,[],[f21182]) ).
fof(f21182,plain,
( $false
| ~ spl0_1556
| spl0_1938 ),
inference(resolution,[],[f20997,f13738]) ).
fof(f13738,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f13737]) ).
fof(f13737,plain,
( spl0_1556
<=> ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f20997,plain,
( ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| spl0_1938 ),
inference(avatar_component_clause,[],[f20995]) ).
fof(f20995,plain,
( spl0_1938
<=> c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f21002,plain,
( ~ spl0_1938
| ~ spl0_1939
| spl0_93
| ~ spl0_1920 ),
inference(avatar_split_clause,[],[f20865,f20028,f3713,f20999,f20995]) ).
fof(f3713,plain,
( spl0_93
<=> c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f20028,plain,
( spl0_1920
<=> ! [X13,X12,X32,X1] :
( ~ c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f20865,plain,
( ~ c_lessequals(c_Message_Oparts(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| spl0_93
| ~ spl0_1920 ),
inference(resolution,[],[f20029,f3715]) ).
fof(f3715,plain,
( ~ c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| spl0_93 ),
inference(avatar_component_clause,[],[f3713]) ).
fof(f20029,plain,
( ! [X1,X12,X32,X13] :
( c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(X13,X32,tc_set(X1)) )
| ~ spl0_1920 ),
inference(avatar_component_clause,[],[f20028]) ).
fof(f20422,plain,
( ~ spl0_1937
| ~ spl0_640
| ~ spl0_1678 ),
inference(avatar_split_clause,[],[f20086,f15307,f5912,f20419]) ).
fof(f20419,plain,
( spl0_1937
<=> c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f5912,plain,
( spl0_640
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f15307,plain,
( spl0_1678
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f20086,plain,
( ~ c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1678 ),
inference(superposition,[],[f15308,f5914]) ).
fof(f5914,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f5912]) ).
fof(f15308,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1678 ),
inference(avatar_component_clause,[],[f15307]) ).
fof(f20417,plain,
( spl0_1936
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1901 ),
inference(avatar_split_clause,[],[f19948,f19944,f16956,f7266,f7246,f20415]) ).
fof(f20415,plain,
( spl0_1936
<=> ! [X3,X0,X23,X25,X1] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f19944,plain,
( spl0_1901
<=> ! [X23,X0,X3,X25,X1] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f19948,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X0 = X3 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1901 ),
inference(forward_demodulation,[],[f19947,f16982]) ).
fof(f19947,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
| X0 = X3 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1901 ),
inference(forward_demodulation,[],[f19945,f16982]) ).
fof(f19945,plain,
( ! [X3,X0,X1,X25,X23] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
| ~ spl0_1901 ),
inference(avatar_component_clause,[],[f19944]) ).
fof(f20413,plain,
( spl0_1935
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1900 ),
inference(avatar_split_clause,[],[f19942,f19938,f16956,f7266,f7246,f20411]) ).
fof(f20411,plain,
( spl0_1935
<=> ! [X3,X0,X23,X25,X1] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X23 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f19938,plain,
( spl0_1900
<=> ! [X3,X0,X23,X25,X1] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f19942,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X23 = X25 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1900 ),
inference(forward_demodulation,[],[f19941,f16982]) ).
fof(f19941,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
| X23 = X25 )
| ~ spl0_769
| ~ spl0_774
| ~ spl0_1764
| ~ spl0_1900 ),
inference(forward_demodulation,[],[f19939,f16982]) ).
fof(f19939,plain,
( ! [X3,X0,X1,X25,X23] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
| ~ spl0_1900 ),
inference(avatar_component_clause,[],[f19938]) ).
fof(f20094,plain,
( spl0_1934
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1933 ),
inference(avatar_split_clause,[],[f20084,f20080,f10764,f10443,f6847,f5912,f20092]) ).
fof(f20092,plain,
( spl0_1934
<=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f6847,plain,
( spl0_679
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f10443,plain,
( spl0_1310
<=> ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f10764,plain,
( spl0_1388
<=> ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f20080,plain,
( spl0_1933
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f20084,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_1,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1933 ),
inference(forward_demodulation,[],[f20083,f11723]) ).
fof(f11723,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388 ),
inference(forward_demodulation,[],[f11722,f6848]) ).
fof(f6848,plain,
( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
| ~ spl0_679 ),
inference(avatar_component_clause,[],[f6847]) ).
fof(f11722,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_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388 ),
inference(forward_demodulation,[],[f11684,f11065]) ).
fof(f11065,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_640
| ~ spl0_1310 ),
inference(superposition,[],[f10444,f5914]) ).
fof(f10444,plain,
( ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_1310 ),
inference(avatar_component_clause,[],[f10443]) ).
fof(f11684,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_679
| ~ spl0_1388 ),
inference(superposition,[],[f6848,f10765]) ).
fof(f10765,plain,
( ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat))
| ~ spl0_1388 ),
inference(avatar_component_clause,[],[f10764]) ).
fof(f20083,plain,
( ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(c_1,X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1933 ),
inference(forward_demodulation,[],[f20081,f11723]) ).
fof(f20081,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1933 ),
inference(avatar_component_clause,[],[f20080]) ).
fof(f20082,plain,
spl0_1933,
inference(avatar_split_clause,[],[f3085,f20080]) ).
fof(f3085,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3084,f2156]) ).
fof(f2156,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
fof(f3084,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3083,f2154]) ).
fof(f2154,axiom,
! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3083,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2899,f2156]) ).
fof(f2899,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1882,f2544,f2544]) ).
fof(f1882,axiom,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
fof(f20078,plain,
spl0_1932,
inference(avatar_split_clause,[],[f3011,f20076]) ).
fof(f20076,plain,
( spl0_1932
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f3011,plain,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2608,f2373]) ).
fof(f2608,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f20074,plain,
spl0_1931,
inference(avatar_split_clause,[],[f3006,f20072]) ).
fof(f20072,plain,
( spl0_1931
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f3006,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2142,f2129]) ).
fof(f2142,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f20070,plain,
spl0_1930,
inference(avatar_split_clause,[],[f3005,f20068]) ).
fof(f20068,plain,
( spl0_1930
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f3005,plain,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f2141,f2129]) ).
fof(f2141,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f20066,plain,
spl0_1929,
inference(avatar_split_clause,[],[f2960,f20064]) ).
fof(f20064,plain,
( spl0_1929
<=> ! [X43,X23,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f2960,plain,
! [X21,X1,X23,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(X23,X43,X1) = c_List_Onth(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),X43,X1) ),
inference(definition_unfolding,[],[f1703,f1766]) ).
fof(f1766,axiom,
! [X21,X1,X26] : c_List_Osublist(X26,c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Otake(X21,X26,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f1703,axiom,
! [X21,X1,X23,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Otake(X21,X23,X1),X43,X1) = c_List_Onth(X23,X43,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f20062,plain,
spl0_1928,
inference(avatar_split_clause,[],[f2933,f20060]) ).
fof(f20060,plain,
( spl0_1928
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f2933,plain,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
inference(definition_unfolding,[],[f2120,f2129]) ).
fof(f2120,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1) = c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f20058,plain,
spl0_1927,
inference(avatar_split_clause,[],[f2807,f20056]) ).
fof(f20056,plain,
( spl0_1927
<=> ! [X86,X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f2807,axiom,
! [X91,X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Crypt_0) ).
fof(f20054,plain,
spl0_1926,
inference(avatar_split_clause,[],[f2802,f20052]) ).
fof(f20052,plain,
( spl0_1926
<=> ! [X20,X88,X4] :
( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
| c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f2802,axiom,
! [X88,X4,X20] :
( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
| c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oin__parts__UnE_0) ).
fof(f20050,plain,
spl0_1925,
inference(avatar_split_clause,[],[f2782,f20048]) ).
fof(f20048,plain,
( spl0_1925
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f2782,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_1) ).
fof(f20046,plain,
spl0_1924,
inference(avatar_split_clause,[],[f2781,f20044]) ).
fof(f20044,plain,
( spl0_1924
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f2781,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__synth_0) ).
fof(f20042,plain,
spl0_1923,
inference(avatar_split_clause,[],[f2774,f20040]) ).
fof(f20040,plain,
( spl0_1923
<=> ! [X86,X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f2774,axiom,
! [X91,X88,X86] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth__eq_0) ).
fof(f20038,plain,
spl0_1922,
inference(avatar_split_clause,[],[f2773,f20036]) ).
fof(f20036,plain,
( spl0_1922
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f2773,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_1) ).
fof(f20034,plain,
spl0_1921,
inference(avatar_split_clause,[],[f2674,f20032]) ).
fof(f20032,plain,
( spl0_1921
<=> ! [X13,X0,X12,X1] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f2674,axiom,
! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f20030,plain,
spl0_1920,
inference(avatar_split_clause,[],[f2647,f20028]) ).
fof(f2647,axiom,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f20026,plain,
spl0_1919,
inference(avatar_split_clause,[],[f2597,f20024]) ).
fof(f20024,plain,
( spl0_1919
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f2597,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f20022,plain,
spl0_1918,
inference(avatar_split_clause,[],[f2337,f20020]) ).
fof(f20020,plain,
( spl0_1918
<=> ! [X0,X11] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f2337,axiom,
! [X0,X11] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f20018,plain,
spl0_1917,
inference(avatar_split_clause,[],[f2329,f20016]) ).
fof(f20016,plain,
( spl0_1917
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f2329,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f20014,plain,
spl0_1916,
inference(avatar_split_clause,[],[f2326,f20012]) ).
fof(f20012,plain,
( spl0_1916
<=> ! [X21,X1,X0] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f2326,axiom,
! [X21,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f20010,plain,
spl0_1915,
inference(avatar_split_clause,[],[f2323,f20008]) ).
fof(f20008,plain,
( spl0_1915
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f2323,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f20006,plain,
spl0_1914,
inference(avatar_split_clause,[],[f2077,f20004]) ).
fof(f20004,plain,
( spl0_1914
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f2077,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f20002,plain,
( ~ spl0_1913
| ~ spl0_640
| ~ spl0_1670 ),
inference(avatar_split_clause,[],[f19953,f15223,f5912,f19999]) ).
fof(f19999,plain,
( spl0_1913
<=> c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f15223,plain,
( spl0_1670
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f19953,plain,
( ~ c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1670 ),
inference(superposition,[],[f15224,f5914]) ).
fof(f15224,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1670 ),
inference(avatar_component_clause,[],[f15223]) ).
fof(f19997,plain,
spl0_1912,
inference(avatar_split_clause,[],[f2074,f19995]) ).
fof(f19995,plain,
( spl0_1912
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f2074,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f19993,plain,
spl0_1911,
inference(avatar_split_clause,[],[f2069,f19991]) ).
fof(f19991,plain,
( spl0_1911
<=> ! [X16,X21,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f2069,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f19989,plain,
spl0_1910,
inference(avatar_split_clause,[],[f2066,f19987]) ).
fof(f19987,plain,
( spl0_1910
<=> ! [X16,X21,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f2066,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f19985,plain,
spl0_1909,
inference(avatar_split_clause,[],[f1929,f19983]) ).
fof(f19983,plain,
( spl0_1909
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
| c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f1929,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
| c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f19981,plain,
spl0_1908,
inference(avatar_split_clause,[],[f1830,f19979]) ).
fof(f19979,plain,
( spl0_1908
<=> ! [X0,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f1830,axiom,
! [X3,X0] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f19977,plain,
spl0_1907,
inference(avatar_split_clause,[],[f1829,f19975]) ).
fof(f19975,plain,
( spl0_1907
<=> ! [X0,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f1829,axiom,
! [X3,X0] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f19973,plain,
spl0_1906,
inference(avatar_split_clause,[],[f1721,f19971]) ).
fof(f19971,plain,
( spl0_1906
<=> ! [X41,X0,X23,X3] :
( X0 = X3
| c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f1721,axiom,
! [X3,X41,X0,X23] :
( X0 = X3
| c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f19969,plain,
spl0_1905,
inference(avatar_split_clause,[],[f1704,f19967]) ).
fof(f19967,plain,
( spl0_1905
<=> ! [X16,X59,X43] :
( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
| c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f1704,axiom,
! [X59,X16,X43] :
( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
| c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f19965,plain,
spl0_1904,
inference(avatar_split_clause,[],[f1697,f19963]) ).
fof(f19963,plain,
( spl0_1904
<=> ! [X21,X23,X25,X1] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f1697,axiom,
! [X21,X1,X25,X23] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f19961,plain,
spl0_1903,
inference(avatar_split_clause,[],[f1630,f19959]) ).
fof(f19959,plain,
( spl0_1903
<=> ! [X41,X60,X18,X65] :
( c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f1630,axiom,
! [X65,X41,X18,X60] :
( c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f19952,plain,
spl0_1902,
inference(avatar_split_clause,[],[f1599,f19950]) ).
fof(f19950,plain,
( spl0_1902
<=> ! [X25,X1,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f1599,axiom,
! [X1,X25,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f19946,plain,
spl0_1901,
inference(avatar_split_clause,[],[f1517,f19944]) ).
fof(f1517,axiom,
! [X3,X0,X1,X25,X23] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f19940,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1516,f19938]) ).
fof(f1516,axiom,
! [X3,X0,X1,X25,X23] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f19936,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1481,f19934]) ).
fof(f19934,plain,
( spl0_1899
<=> ! [X0,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f1481,axiom,
! [X3,X0] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f19932,plain,
spl0_1898,
inference(avatar_split_clause,[],[f1480,f19930]) ).
fof(f19930,plain,
( spl0_1898
<=> ! [X0,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f1480,axiom,
! [X3,X0] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f19928,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1473,f19926]) ).
fof(f19926,plain,
( spl0_1897
<=> ! [X18,X27] :
( c_0 = X18
| c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f1473,axiom,
! [X18,X27] :
( c_0 = X18
| c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f19924,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1472,f19922]) ).
fof(f19922,plain,
( spl0_1896
<=> ! [X18,X27] :
( c_0 = X18
| c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f1472,axiom,
! [X18,X27] :
( c_0 = X18
| c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f19920,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1292,f19918]) ).
fof(f19918,plain,
( spl0_1895
<=> ! [X2,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f1292,axiom,
! [X2,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f19916,plain,
spl0_1894,
inference(avatar_split_clause,[],[f1288,f19914]) ).
fof(f19914,plain,
( spl0_1894
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f1288,axiom,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f19076,plain,
( spl0_1893
| ~ spl0_641
| ~ spl0_1626 ),
inference(avatar_split_clause,[],[f18873,f15046,f5917,f19073]) ).
fof(f19073,plain,
( spl0_1893
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f5917,plain,
( spl0_641
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f15046,plain,
( spl0_1626
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f18873,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1626 ),
inference(superposition,[],[f15047,f5919]) ).
fof(f5919,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_641 ),
inference(avatar_component_clause,[],[f5917]) ).
fof(f15047,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1626 ),
inference(avatar_component_clause,[],[f15046]) ).
fof(f18945,plain,
( spl0_1892
| ~ spl0_640
| ~ spl0_1626 ),
inference(avatar_split_clause,[],[f18872,f15046,f5912,f18942]) ).
fof(f18942,plain,
( spl0_1892
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f18872,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_1626 ),
inference(superposition,[],[f15047,f5914]) ).
fof(f18900,plain,
spl0_1891,
inference(avatar_split_clause,[],[f3246,f18898]) ).
fof(f18898,plain,
( spl0_1891
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f3246,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3036,f2114]) ).
fof(f2114,axiom,
! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f3036,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1313,f2129]) ).
fof(f1313,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f18896,plain,
spl0_1890,
inference(avatar_split_clause,[],[f3244,f18894]) ).
fof(f18894,plain,
( spl0_1890
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f3244,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3034,f2114]) ).
fof(f3034,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1325,f2129]) ).
fof(f1325,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f18892,plain,
spl0_1889,
inference(avatar_split_clause,[],[f3236,f18890]) ).
fof(f18890,plain,
( spl0_1889
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f3236,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3028,f2114]) ).
fof(f3028,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1312,f2129]) ).
fof(f1312,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f18888,plain,
spl0_1888,
inference(avatar_split_clause,[],[f3234,f18886]) ).
fof(f18886,plain,
( spl0_1888
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f3234,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3026,f2114]) ).
fof(f3026,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X0)),X1),X1) ),
inference(definition_unfolding,[],[f1324,f2129]) ).
fof(f1324,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f18884,plain,
spl0_1887,
inference(avatar_split_clause,[],[f3202,f18882]) ).
fof(f18882,plain,
( spl0_1887
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f3202,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3002,f2156]) ).
fof(f3002,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1336,f2129]) ).
fof(f1336,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f18868,plain,
( spl0_1886
| ~ spl0_1567
| ~ spl0_1885 ),
inference(avatar_split_clause,[],[f18864,f18861,f13781,f18866]) ).
fof(f18866,plain,
( spl0_1886
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f13781,plain,
( spl0_1567
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f18861,plain,
( spl0_1885
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f18864,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1567
| ~ spl0_1885 ),
inference(forward_demodulation,[],[f18862,f13783]) ).
fof(f13783,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1567 ),
inference(avatar_component_clause,[],[f13781]) ).
fof(f18862,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1885 ),
inference(avatar_component_clause,[],[f18861]) ).
fof(f18863,plain,
spl0_1885,
inference(avatar_split_clause,[],[f3201,f18861]) ).
fof(f3201,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3001,f2156]) ).
fof(f3001,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1340,f2129]) ).
fof(f1340,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f18859,plain,
spl0_1884,
inference(avatar_split_clause,[],[f3196,f18857]) ).
fof(f18857,plain,
( spl0_1884
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f3196,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f2998,f2156]) ).
fof(f2998,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1335,f2129]) ).
fof(f1335,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f18846,plain,
( spl0_1883
| ~ spl0_1567
| ~ spl0_1882 ),
inference(avatar_split_clause,[],[f18842,f18839,f13781,f18844]) ).
fof(f18844,plain,
( spl0_1883
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f18839,plain,
( spl0_1882
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f18842,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1567
| ~ spl0_1882 ),
inference(forward_demodulation,[],[f18840,f13783]) ).
fof(f18840,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1882 ),
inference(avatar_component_clause,[],[f18839]) ).
fof(f18841,plain,
spl0_1882,
inference(avatar_split_clause,[],[f3195,f18839]) ).
fof(f3195,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2997,f2156]) ).
fof(f2997,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
inference(definition_unfolding,[],[f1339,f2129]) ).
fof(f1339,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f18835,plain,
( spl0_1881
| ~ spl0_52
| ~ spl0_1392
| ~ spl0_1880 ),
inference(avatar_split_clause,[],[f18831,f18828,f10783,f3508,f18833]) ).
fof(f18833,plain,
( spl0_1881
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f3508,plain,
( spl0_52
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f10783,plain,
( spl0_1392
<=> ! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f18828,plain,
( spl0_1880
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f18831,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1392
| ~ spl0_1880 ),
inference(forward_demodulation,[],[f18829,f11790]) ).
fof(f11790,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_52
| ~ spl0_1392 ),
inference(resolution,[],[f10784,f3510]) ).
fof(f3510,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f3508]) ).
fof(f10784,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1) )
| ~ spl0_1392 ),
inference(avatar_component_clause,[],[f10783]) ).
fof(f18829,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1880 ),
inference(avatar_component_clause,[],[f18828]) ).
fof(f18830,plain,
spl0_1880,
inference(avatar_split_clause,[],[f3164,f18828]) ).
fof(f3164,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3163,f2156]) ).
fof(f3163,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3162,f2154]) ).
fof(f3162,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2273,f2156]) ).
fof(f2273,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
fof(f18824,plain,
( spl0_1879
| ~ spl0_646
| ~ spl0_776
| ~ spl0_1541 ),
inference(avatar_split_clause,[],[f14201,f13677,f7274,f5939,f18821]) ).
fof(f18821,plain,
( spl0_1879
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f5939,plain,
( spl0_646
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f7274,plain,
( spl0_776
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f13677,plain,
( spl0_1541
<=> ! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f14201,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_646
| ~ spl0_776
| ~ spl0_1541 ),
inference(forward_demodulation,[],[f14183,f7275]) ).
fof(f7275,plain,
( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
| ~ spl0_776 ),
inference(avatar_component_clause,[],[f7274]) ).
fof(f14183,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_646
| ~ spl0_1541 ),
inference(resolution,[],[f13678,f5941]) ).
fof(f5941,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_646 ),
inference(avatar_component_clause,[],[f5939]) ).
fof(f13678,plain,
( ! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) )
| ~ spl0_1541 ),
inference(avatar_component_clause,[],[f13677]) ).
fof(f18819,plain,
( spl0_1878
| ~ spl0_52
| ~ spl0_1392
| ~ spl0_1877 ),
inference(avatar_split_clause,[],[f18815,f18812,f10783,f3508,f18817]) ).
fof(f18817,plain,
( spl0_1878
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f18812,plain,
( spl0_1877
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f18815,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_52
| ~ spl0_1392
| ~ spl0_1877 ),
inference(forward_demodulation,[],[f18813,f11790]) ).
fof(f18813,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1877 ),
inference(avatar_component_clause,[],[f18812]) ).
fof(f18814,plain,
spl0_1877,
inference(avatar_split_clause,[],[f3160,f18812]) ).
fof(f3160,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3159,f2156]) ).
fof(f3159,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3158,f2154]) ).
fof(f3158,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2272,f2156]) ).
fof(f2272,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
fof(f18809,plain,
( spl0_1876
| ~ spl0_1567
| ~ spl0_1875 ),
inference(avatar_split_clause,[],[f18805,f18802,f13781,f18807]) ).
fof(f18807,plain,
( spl0_1876
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f18802,plain,
( spl0_1875
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f18805,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1567
| ~ spl0_1875 ),
inference(forward_demodulation,[],[f18803,f13783]) ).
fof(f18803,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1875 ),
inference(avatar_component_clause,[],[f18802]) ).
fof(f18804,plain,
spl0_1875,
inference(avatar_split_clause,[],[f3129,f18802]) ).
fof(f3129,plain,
! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2935,f2156]) ).
fof(f2935,plain,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
inference(definition_unfolding,[],[f1332,f2129]) ).
fof(f1332,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f18800,plain,
spl0_1874,
inference(avatar_split_clause,[],[f3128,f18798]) ).
fof(f18798,plain,
( spl0_1874
<=> ! [X11,X1] :
( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f3128,plain,
! [X11,X1] :
( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2934,f2156]) ).
fof(f2934,plain,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X11)),X1) ),
inference(definition_unfolding,[],[f1331,f2129]) ).
fof(f1331,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X11)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f18796,plain,
spl0_1873,
inference(avatar_split_clause,[],[f3098,f18794]) ).
fof(f18794,plain,
( spl0_1873
<=> ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f3098,plain,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat),
inference(forward_demodulation,[],[f2917,f2831]) ).
fof(f2917,plain,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2765,f2544]) ).
fof(f2765,axiom,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__6_0) ).
fof(f18792,plain,
spl0_1872,
inference(avatar_split_clause,[],[f3089,f18790]) ).
fof(f18790,plain,
( spl0_1872
<=> ! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f3089,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3088,f2156]) ).
fof(f3088,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3087,f2154]) ).
fof(f3087,plain,
! [X21] : c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f3086,f2156]) ).
fof(f3086,plain,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2905,f3085]) ).
fof(f2905,plain,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1881,f2544,f2544]) ).
fof(f1881,axiom,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Suc(c_Suc(X21)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f18770,plain,
( spl0_1871
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1870 ),
inference(avatar_split_clause,[],[f18766,f18763,f10764,f10443,f6847,f5912,f18768]) ).
fof(f18768,plain,
( spl0_1871
<=> ! [X47] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f18763,plain,
( spl0_1870
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f18766,plain,
( ! [X47] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1870 ),
inference(forward_demodulation,[],[f18764,f11723]) ).
fof(f18764,plain,
( ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1870 ),
inference(avatar_component_clause,[],[f18763]) ).
fof(f18765,plain,
spl0_1870,
inference(avatar_split_clause,[],[f2980,f18763]) ).
fof(f2980,plain,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1823,f2544]) ).
fof(f1823,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f18761,plain,
spl0_1869,
inference(avatar_split_clause,[],[f2910,f18759]) ).
fof(f18759,plain,
( spl0_1869
<=> ! [X43,X0,X16,X1] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f2910,plain,
! [X0,X1,X16,X43] : c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) = c_List_Osublist(c_List_Oreplicate(X16,X0,X1),c_SetInterval_OlessThan(X43,tc_nat),X1),
inference(definition_unfolding,[],[f1775,f1766]) ).
fof(f1775,axiom,
! [X0,X1,X16,X43] : c_List_Otake(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f18757,plain,
spl0_1868,
inference(avatar_split_clause,[],[f2908,f18755]) ).
fof(f18755,plain,
( spl0_1868
<=> ! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f2908,plain,
! [X21,X1,X23] : c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) = c_Nat_Osize(c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1),tc_List_Olist(X1)),
inference(definition_unfolding,[],[f1611,f1766]) ).
fof(f1611,axiom,
! [X21,X1,X23] : c_Nat_Osize(c_List_Otake(X21,X23,X1),tc_List_Olist(X1)) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f18753,plain,
spl0_1867,
inference(avatar_split_clause,[],[f2904,f18751]) ).
fof(f18751,plain,
( spl0_1867
<=> ! [X13,X18,X1] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f2904,plain,
! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_Relation_OImage(c_Relation_Odiag(X18,X1),c_Inter(X13,X1),X1,X1),
inference(definition_unfolding,[],[f2623,f2373]) ).
fof(f2623,axiom,
! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_inter(X18,c_Inter(X13,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f18748,plain,
( spl0_1866
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1865 ),
inference(avatar_split_clause,[],[f18744,f18741,f10764,f10443,f6847,f5912,f18746]) ).
fof(f18746,plain,
( spl0_1866
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f18741,plain,
( spl0_1865
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f18744,plain,
( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1865 ),
inference(forward_demodulation,[],[f18742,f11723]) ).
fof(f18742,plain,
( ! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2)
| ~ spl0_1865 ),
inference(avatar_component_clause,[],[f18741]) ).
fof(f18743,plain,
spl0_1865,
inference(avatar_split_clause,[],[f2903,f18741]) ).
fof(f2903,plain,
! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1207,f2544]) ).
fof(f1207,axiom,
! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f18738,plain,
( spl0_1864
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1863 ),
inference(avatar_split_clause,[],[f18734,f18731,f10764,f10443,f6847,f5912,f18736]) ).
fof(f18736,plain,
( spl0_1864
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f18731,plain,
( spl0_1863
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f18734,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1863 ),
inference(forward_demodulation,[],[f18732,f11723]) ).
fof(f18732,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2)
| ~ spl0_1863 ),
inference(avatar_component_clause,[],[f18731]) ).
fof(f18733,plain,
spl0_1863,
inference(avatar_split_clause,[],[f2902,f18731]) ).
fof(f2902,plain,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1206,f2544]) ).
fof(f1206,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f18729,plain,
( spl0_1861
| spl0_1862
| ~ spl0_663
| ~ spl0_1534 ),
inference(avatar_split_clause,[],[f14101,f13649,f6778,f18727,f18724]) ).
fof(f18724,plain,
( spl0_1861
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f18727,plain,
( spl0_1862
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f6778,plain,
( spl0_663
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f13649,plain,
( spl0_1534
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f14101,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_663
| ~ spl0_1534 ),
inference(resolution,[],[f13650,f6779]) ).
fof(f6779,plain,
( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
| ~ spl0_663 ),
inference(avatar_component_clause,[],[f6778]) ).
fof(f13650,plain,
( ! [X48,X11,X1] :
( ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1534 ),
inference(avatar_component_clause,[],[f13649]) ).
fof(f18721,plain,
( spl0_1860
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1859 ),
inference(avatar_split_clause,[],[f18717,f18714,f10764,f10443,f6847,f5912,f18719]) ).
fof(f18719,plain,
( spl0_1860
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f18714,plain,
( spl0_1859
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f18717,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X16,tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1859 ),
inference(forward_demodulation,[],[f18715,f11723]) ).
fof(f18715,plain,
( ! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2)
| ~ spl0_1859 ),
inference(avatar_component_clause,[],[f18714]) ).
fof(f18716,plain,
spl0_1859,
inference(avatar_split_clause,[],[f2901,f18714]) ).
fof(f2901,plain,
! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1203,f2544]) ).
fof(f1203,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f18712,plain,
spl0_1858,
inference(avatar_split_clause,[],[f2889,f18710]) ).
fof(f18710,plain,
( spl0_1858
<=> ! [X18,X5,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f2889,plain,
! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),tc_prod(X1,X1)),
inference(definition_unfolding,[],[f120,f2716]) ).
fof(f120,axiom,
! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f18708,plain,
spl0_1857,
inference(avatar_split_clause,[],[f2881,f18706]) ).
fof(f18706,plain,
( spl0_1857
<=> ! [X5,X1] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f2881,plain,
! [X1,X5] : c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2708,f2716]) ).
fof(f2708,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f18683,plain,
( spl0_1856
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1855 ),
inference(avatar_split_clause,[],[f18679,f18676,f10764,f10443,f6847,f5912,f18681]) ).
fof(f18681,plain,
( spl0_1856
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f18676,plain,
( spl0_1855
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f18679,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1855 ),
inference(forward_demodulation,[],[f18677,f11723]) ).
fof(f18677,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1855 ),
inference(avatar_component_clause,[],[f18676]) ).
fof(f18678,plain,
spl0_1855,
inference(avatar_split_clause,[],[f2879,f18676]) ).
fof(f2879,plain,
! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2027,f2544,f2544]) ).
fof(f2027,axiom,
! [X21,X15] : c_plus(X15,c_Suc(X21),tc_nat) = c_Suc(c_plus(X15,X21,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f18593,plain,
( spl0_1854
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1852 ),
inference(avatar_split_clause,[],[f18585,f18581,f10764,f10443,f6847,f5912,f18591]) ).
fof(f18591,plain,
( spl0_1854
<=> ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f18581,plain,
( spl0_1852
<=> ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f18585,plain,
( ! [X21,X15] : c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat) = c_plus(c_1,c_plus(X15,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1852 ),
inference(forward_demodulation,[],[f18584,f11723]) ).
fof(f18584,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1852 ),
inference(forward_demodulation,[],[f18582,f11723]) ).
fof(f18582,plain,
( ! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1852 ),
inference(avatar_component_clause,[],[f18581]) ).
fof(f18589,plain,
( spl0_1853
| ~ spl0_833
| ~ spl0_1516 ),
inference(avatar_split_clause,[],[f13597,f12344,f7515,f18587]) ).
fof(f18587,plain,
( spl0_1853
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f7515,plain,
( spl0_833
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f12344,plain,
( spl0_1516
<=> ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f13597,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_833
| ~ spl0_1516 ),
inference(superposition,[],[f7516,f12345]) ).
fof(f12345,plain,
( ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3
| ~ spl0_1516 ),
inference(avatar_component_clause,[],[f12344]) ).
fof(f7516,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f7515]) ).
fof(f18583,plain,
spl0_1852,
inference(avatar_split_clause,[],[f2878,f18581]) ).
fof(f2878,plain,
! [X21,X15] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X15,X21,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
inference(definition_unfolding,[],[f2101,f2544,f2544]) ).
fof(f2101,axiom,
! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f18557,plain,
( spl0_1851
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1850 ),
inference(avatar_split_clause,[],[f18553,f18549,f10764,f10443,f6847,f5912,f18555]) ).
fof(f18555,plain,
( spl0_1851
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f18549,plain,
( spl0_1850
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f18553,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_plus(c_1,X15,tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1850 ),
inference(forward_demodulation,[],[f18552,f11723]) ).
fof(f18552,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1850 ),
inference(forward_demodulation,[],[f18550,f11723]) ).
fof(f18550,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1850 ),
inference(avatar_component_clause,[],[f18549]) ).
fof(f18551,plain,
spl0_1850,
inference(avatar_split_clause,[],[f2877,f18549]) ).
fof(f2877,plain,
! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2035,f2544,f2544]) ).
fof(f2035,axiom,
! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Suc(X15),c_Suc(X21),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f18547,plain,
spl0_1849,
inference(avatar_split_clause,[],[f2819,f18545]) ).
fof(f18545,plain,
( spl0_1849
<=> ! [X87,X86,X88] :
( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f2819,axiom,
! [X88,X86,X87] :
( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OMPair_0) ).
fof(f18543,plain,
spl0_1848,
inference(avatar_split_clause,[],[f2816,f18541]) ).
fof(f18541,plain,
( spl0_1848
<=> ! [X86,X91,X88] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f2816,axiom,
! [X91,X88,X86] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OCrypt_0) ).
fof(f18539,plain,
spl0_1847,
inference(avatar_split_clause,[],[f2696,f18537]) ).
fof(f18537,plain,
( spl0_1847
<=> ! [X12,X27,X1,X18] :
( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f2696,axiom,
! [X1,X18,X27,X12] :
( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_1) ).
fof(f18535,plain,
spl0_1846,
inference(avatar_split_clause,[],[f2694,f18533]) ).
fof(f18533,plain,
( spl0_1846
<=> ! [X12,X0,X1] :
( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
| c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f2694,axiom,
! [X0,X1,X12] :
( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
| c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_2) ).
fof(f18531,plain,
spl0_1845,
inference(avatar_split_clause,[],[f2690,f18529]) ).
fof(f18529,plain,
( spl0_1845
<=> ! [X13,X0,X12,X1] :
( ~ c_in(X0,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f2690,axiom,
! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f18527,plain,
spl0_1844,
inference(avatar_split_clause,[],[f2573,f18525]) ).
fof(f18525,plain,
( spl0_1844
<=> ! [X16,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f2573,axiom,
! [X1,X16] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f18523,plain,
( spl0_1843
| ~ spl0_816
| ~ spl0_1498 ),
inference(avatar_split_clause,[],[f13509,f12235,f7435,f18521]) ).
fof(f18521,plain,
( spl0_1843
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(c_Message_Osynth(X0)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f12235,plain,
( spl0_1498
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f13509,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(c_Message_Osynth(X0)),tc_set(tc_Message_Omsg))
| ~ spl0_816
| ~ spl0_1498 ),
inference(resolution,[],[f12236,f7436]) ).
fof(f12236,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1498 ),
inference(avatar_component_clause,[],[f12235]) ).
fof(f18519,plain,
spl0_1842,
inference(avatar_split_clause,[],[f2565,f18517]) ).
fof(f18517,plain,
( spl0_1842
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X59,X43,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f2565,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X59,X43,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f18515,plain,
spl0_1841,
inference(avatar_split_clause,[],[f2556,f18513]) ).
fof(f18513,plain,
( spl0_1841
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f2556,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f18511,plain,
spl0_1840,
inference(avatar_split_clause,[],[f2553,f18509]) ).
fof(f18509,plain,
( spl0_1840
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X14,X1)
| ~ c_less(X26,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f2553,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X14,X1)
| ~ c_less(X26,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f18507,plain,
spl0_1839,
inference(avatar_split_clause,[],[f2526,f18505]) ).
fof(f18505,plain,
( spl0_1839
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f2526,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f18503,plain,
spl0_1838,
inference(avatar_split_clause,[],[f2521,f18501]) ).
fof(f18501,plain,
( spl0_1838
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_lessequals(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f2521,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_lessequals(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f18499,plain,
spl0_1837,
inference(avatar_split_clause,[],[f2324,f18497]) ).
fof(f18497,plain,
( spl0_1837
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X0,c_0,X1)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f2324,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X0,c_0,X1)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f18495,plain,
spl0_1836,
inference(avatar_split_clause,[],[f2307,f18493]) ).
fof(f18493,plain,
( spl0_1836
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f2307,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f18491,plain,
spl0_1835,
inference(avatar_split_clause,[],[f2305,f18489]) ).
fof(f18489,plain,
( spl0_1835
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f2305,axiom,
! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f18487,plain,
spl0_1834,
inference(avatar_split_clause,[],[f2266,f18485]) ).
fof(f18485,plain,
( spl0_1834
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X48,X2)
| ~ c_lessequals(X3,X48,X2)
| c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f2266,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X48,X2)
| ~ c_lessequals(X3,X48,X2)
| c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f18483,plain,
spl0_1833,
inference(avatar_split_clause,[],[f2261,f18481]) ).
fof(f18481,plain,
( spl0_1833
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X48,X2)
| c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f2261,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X48,X2)
| c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f18479,plain,
( spl0_1832
| ~ spl0_1176
| ~ spl0_1463 ),
inference(avatar_split_clause,[],[f13143,f12073,f9506,f18477]) ).
fof(f18477,plain,
( spl0_1832
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f9506,plain,
( spl0_1176
<=> ! [X2,X27,X1,X18] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f12073,plain,
( spl0_1463
<=> ! [X2,X1,X3] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f13143,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1176
| ~ spl0_1463 ),
inference(superposition,[],[f9507,f12074]) ).
fof(f12074,plain,
( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
| ~ spl0_1463 ),
inference(avatar_component_clause,[],[f12073]) ).
fof(f9507,plain,
( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
| ~ spl0_1176 ),
inference(avatar_component_clause,[],[f9506]) ).
fof(f18475,plain,
spl0_1831,
inference(avatar_split_clause,[],[f2258,f18473]) ).
fof(f18473,plain,
( spl0_1831
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X48,X0,X1)
| ~ c_less(X48,X3,X1)
| c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f2258,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X48,X0,X1)
| ~ c_less(X48,X3,X1)
| c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f18471,plain,
spl0_1830,
inference(avatar_split_clause,[],[f2255,f18469]) ).
fof(f18469,plain,
( spl0_1830
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X0,X48,X1)
| ~ c_less(X3,X48,X1)
| c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f2255,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X0,X48,X1)
| ~ c_less(X3,X48,X1)
| c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f18467,plain,
spl0_1829,
inference(avatar_split_clause,[],[f2237,f18465]) ).
fof(f18465,plain,
( spl0_1829
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f2237,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f18463,plain,
spl0_1828,
inference(avatar_split_clause,[],[f2228,f18461]) ).
fof(f18461,plain,
( spl0_1828
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f2228,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f18459,plain,
spl0_1827,
inference(avatar_split_clause,[],[f2214,f18457]) ).
fof(f18457,plain,
( spl0_1827
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f2214,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f18455,plain,
spl0_1826,
inference(avatar_split_clause,[],[f1843,f18453]) ).
fof(f18453,plain,
( spl0_1826
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f1843,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f18451,plain,
spl0_1825,
inference(avatar_split_clause,[],[f1836,f18449]) ).
fof(f18449,plain,
( spl0_1825
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f1836,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f18447,plain,
spl0_1824,
inference(avatar_split_clause,[],[f1824,f18445]) ).
fof(f18445,plain,
( spl0_1824
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f1824,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f18443,plain,
spl0_1823,
inference(avatar_split_clause,[],[f1821,f18441]) ).
fof(f18441,plain,
( spl0_1823
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f1821,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f18439,plain,
spl0_1822,
inference(avatar_split_clause,[],[f1809,f18437]) ).
fof(f18437,plain,
( spl0_1822
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f1809,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f18435,plain,
( spl0_1821
| ~ spl0_783
| ~ spl0_807
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10236,f9820,f7399,f7302,f18433]) ).
fof(f18433,plain,
( spl0_1821
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f7302,plain,
( spl0_783
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f7399,plain,
( spl0_807
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f9820,plain,
( spl0_1253
<=> ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f10236,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_807
| ~ spl0_1253 ),
inference(forward_demodulation,[],[f10225,f7303]) ).
fof(f7303,plain,
( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
| ~ spl0_783 ),
inference(avatar_component_clause,[],[f7302]) ).
fof(f10225,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X0)),tc_Message_Omsg)
| ~ spl0_807
| ~ spl0_1253 ),
inference(superposition,[],[f9821,f7400]) ).
fof(f7400,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
| ~ spl0_807 ),
inference(avatar_component_clause,[],[f7399]) ).
fof(f9821,plain,
( ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_1253 ),
inference(avatar_component_clause,[],[f9820]) ).
fof(f18431,plain,
spl0_1820,
inference(avatar_split_clause,[],[f1781,f18429]) ).
fof(f18429,plain,
( spl0_1820
<=> ! [X21,X1,X0] :
( c_0 = X21
| c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f1781,axiom,
! [X21,X0,X1] :
( c_0 = X21
| c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f18427,plain,
spl0_1819,
inference(avatar_split_clause,[],[f1699,f18425]) ).
fof(f18425,plain,
( spl0_1819
<=> ! [X43,X23,X3,X1] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f1699,axiom,
! [X3,X1,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f18423,plain,
spl0_1818,
inference(avatar_split_clause,[],[f1633,f18421]) ).
fof(f18421,plain,
( spl0_1818
<=> ! [X1,X43,X3] :
( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f1633,axiom,
! [X3,X1,X43] :
( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f18419,plain,
spl0_1817,
inference(avatar_split_clause,[],[f1592,f18417]) ).
fof(f18417,plain,
( spl0_1817
<=> ! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f1592,axiom,
! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f18415,plain,
spl0_1816,
inference(avatar_split_clause,[],[f1525,f18413]) ).
fof(f18413,plain,
( spl0_1816
<=> ! [X12,X1,X23,X25] :
( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f1525,axiom,
! [X1,X25,X12,X23] :
( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f18411,plain,
spl0_1815,
inference(avatar_split_clause,[],[f1524,f18409]) ).
fof(f18409,plain,
( spl0_1815
<=> ! [X23,X12,X25,X1] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f1524,axiom,
! [X1,X12,X23,X25] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f18407,plain,
spl0_1814,
inference(avatar_split_clause,[],[f1417,f18405]) ).
fof(f18405,plain,
( spl0_1814
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f1417,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f18403,plain,
spl0_1813,
inference(avatar_split_clause,[],[f1403,f18401]) ).
fof(f18401,plain,
( spl0_1813
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f1403,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f18399,plain,
spl0_1812,
inference(avatar_split_clause,[],[f1402,f18397]) ).
fof(f18397,plain,
( spl0_1812
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f1402,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f18395,plain,
spl0_1811,
inference(avatar_split_clause,[],[f1366,f18393]) ).
fof(f18393,plain,
( spl0_1811
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f1366,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f18391,plain,
( spl0_1810
| ~ spl0_783
| ~ spl0_808
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10235,f9820,f7403,f7302,f18389]) ).
fof(f18389,plain,
( spl0_1810
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f7403,plain,
( spl0_808
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f10235,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_808
| ~ spl0_1253 ),
inference(forward_demodulation,[],[f10224,f7303]) ).
fof(f10224,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X0)),tc_Message_Omsg)
| ~ spl0_808
| ~ spl0_1253 ),
inference(superposition,[],[f9821,f7404]) ).
fof(f7404,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
| ~ spl0_808 ),
inference(avatar_component_clause,[],[f7403]) ).
fof(f18387,plain,
spl0_1809,
inference(avatar_split_clause,[],[f1365,f18385]) ).
fof(f18385,plain,
( spl0_1809
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f1365,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f18383,plain,
spl0_1808,
inference(avatar_split_clause,[],[f1362,f18381]) ).
fof(f18381,plain,
( spl0_1808
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f1362,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f18379,plain,
spl0_1807,
inference(avatar_split_clause,[],[f1360,f18377]) ).
fof(f18377,plain,
( spl0_1807
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f1360,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f18375,plain,
spl0_1806,
inference(avatar_split_clause,[],[f1359,f18373]) ).
fof(f18373,plain,
( spl0_1806
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f1359,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f18371,plain,
spl0_1805,
inference(avatar_split_clause,[],[f1306,f18369]) ).
fof(f18369,plain,
( spl0_1805
<=> ! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
| c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f1306,axiom,
! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
| c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f18367,plain,
spl0_1804,
inference(avatar_split_clause,[],[f1290,f18365]) ).
fof(f18365,plain,
( spl0_1804
<=> ! [X2,X5,X1] :
( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f1290,axiom,
! [X2,X1,X5] :
( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f18363,plain,
spl0_1803,
inference(avatar_split_clause,[],[f1289,f18361]) ).
fof(f18361,plain,
( spl0_1803
<=> ! [X2,X5,X1] :
( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f1289,axiom,
! [X2,X1,X5] :
( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f18359,plain,
spl0_1802,
inference(avatar_split_clause,[],[f114,f18357]) ).
fof(f18357,plain,
( spl0_1802
<=> ! [X13,X12,X27,X2,X1] :
( ~ c_in(X27,X13,X1)
| c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f114,axiom,
! [X2,X1,X27,X12,X13] :
( ~ c_in(X27,X13,X1)
| c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f18355,plain,
spl0_1801,
inference(avatar_split_clause,[],[f113,f18353]) ).
fof(f18353,plain,
( spl0_1801
<=> ! [X18,X13,X12,X2,X1] :
( ~ c_in(X18,X12,X1)
| c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f113,axiom,
! [X2,X18,X1,X12,X13] :
( ~ c_in(X18,X12,X1)
| c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f18351,plain,
spl0_1800,
inference(avatar_split_clause,[],[f76,f18349]) ).
fof(f18349,plain,
( spl0_1800
<=> ! [X5,X18,X27,X2,X1] :
( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f76,axiom,
! [X2,X1,X18,X27,X5] :
( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f18347,plain,
( spl0_1799
| ~ spl0_783
| ~ spl0_809
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10234,f9820,f7407,f7302,f18345]) ).
fof(f18345,plain,
( spl0_1799
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f7407,plain,
( spl0_809
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f10234,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_809
| ~ spl0_1253 ),
inference(forward_demodulation,[],[f10223,f7303]) ).
fof(f10223,plain,
( ! [X0] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X0)),tc_Message_Omsg)
| ~ spl0_809
| ~ spl0_1253 ),
inference(superposition,[],[f9821,f7408]) ).
fof(f7408,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f7407]) ).
fof(f18343,plain,
spl0_1798,
inference(avatar_split_clause,[],[f72,f18341]) ).
fof(f18341,plain,
( spl0_1798
<=> ! [X12,X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f72,axiom,
! [X2,X1,X27,X5,X12] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f18339,plain,
spl0_1797,
inference(avatar_split_clause,[],[f71,f18337]) ).
fof(f18337,plain,
( spl0_1797
<=> ! [X1,X28] :
( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f71,axiom,
! [X28,X1] :
( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f18335,plain,
spl0_1796,
inference(avatar_split_clause,[],[f70,f18333]) ).
fof(f18333,plain,
( spl0_1796
<=> ! [X18,X5,X27,X2,X1] :
( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f70,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f18331,plain,
spl0_1795,
inference(avatar_split_clause,[],[f58,f18329]) ).
fof(f18329,plain,
( spl0_1795
<=> ! [X12,X0,X1,X26] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f58,axiom,
! [X0,X1,X26,X12] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f18327,plain,
spl0_1794,
inference(avatar_split_clause,[],[f46,f18325]) ).
fof(f18325,plain,
( spl0_1794
<=> ! [X24,X23,X12,X1] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f46,axiom,
! [X1,X24,X12,X23] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f18246,plain,
( spl0_1793
| ~ spl0_783
| ~ spl0_806
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10232,f9820,f7395,f7302,f18244]) ).
fof(f18244,plain,
( spl0_1793
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f7395,plain,
( spl0_806
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f10232,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_783
| ~ spl0_806
| ~ spl0_1253 ),
inference(forward_demodulation,[],[f10221,f7303]) ).
fof(f10221,plain,
( ! [X0] : c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) = c_plus(c_0,c_1,tc_nat)
| ~ spl0_806
| ~ spl0_1253 ),
inference(superposition,[],[f9821,f7396]) ).
fof(f7396,plain,
( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
| ~ spl0_806 ),
inference(avatar_component_clause,[],[f7395]) ).
fof(f17986,plain,
( spl0_1792
| ~ spl0_857
| ~ spl0_1253 ),
inference(avatar_split_clause,[],[f10230,f9820,f7611,f17984]) ).
fof(f17984,plain,
( spl0_1792
<=> ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f7611,plain,
( spl0_857
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f10230,plain,
( ! [X0] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X0),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_857
| ~ spl0_1253 ),
inference(superposition,[],[f7612,f9821]) ).
fof(f7612,plain,
( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
| ~ spl0_857 ),
inference(avatar_component_clause,[],[f7611]) ).
fof(f17676,plain,
( spl0_1791
| ~ spl0_641
| ~ spl0_1128
| ~ spl0_1252 ),
inference(avatar_split_clause,[],[f10220,f9816,f9110,f5917,f17674]) ).
fof(f17674,plain,
( spl0_1791
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f9110,plain,
( spl0_1128
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f9816,plain,
( spl0_1252
<=> ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f10220,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1128
| ~ spl0_1252 ),
inference(forward_demodulation,[],[f10217,f9111]) ).
fof(f9111,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1128 ),
inference(avatar_component_clause,[],[f9110]) ).
fof(f10217,plain,
( ! [X0] : c_less(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1252 ),
inference(superposition,[],[f9817,f5919]) ).
fof(f9817,plain,
( ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1252 ),
inference(avatar_component_clause,[],[f9816]) ).
fof(f17416,plain,
( spl0_1789
| ~ spl0_1790
| ~ spl0_112
| ~ spl0_1222 ),
inference(avatar_split_clause,[],[f10043,f9691,f3800,f17413,f17410]) ).
fof(f17410,plain,
( spl0_1789
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f17413,plain,
( spl0_1790
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f3800,plain,
( spl0_112
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f9691,plain,
( spl0_1222
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f10043,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_112
| ~ spl0_1222 ),
inference(resolution,[],[f9692,f3801]) ).
fof(f3801,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3800]) ).
fof(f9692,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X3,X1) = X3 )
| ~ spl0_1222 ),
inference(avatar_component_clause,[],[f9691]) ).
fof(f17290,plain,
( spl0_1788
| ~ spl0_709
| ~ spl0_732
| ~ spl0_883
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f10024,f9671,f7716,f7084,f6985,f17287]) ).
fof(f17287,plain,
( spl0_1788
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f6985,plain,
( spl0_709
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f7084,plain,
( spl0_732
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f7716,plain,
( spl0_883
<=> 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_883])]) ).
fof(f9671,plain,
( spl0_1217
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f10024,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_709
| ~ spl0_732
| ~ spl0_883
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f10023,f6987]) ).
fof(f6987,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_709 ),
inference(avatar_component_clause,[],[f6985]) ).
fof(f10023,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_732
| ~ spl0_883
| ~ spl0_1217 ),
inference(forward_demodulation,[],[f10019,f7718]) ).
fof(f7718,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_883 ),
inference(avatar_component_clause,[],[f7716]) ).
fof(f10019,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),c_Numeral_OPls)
| ~ spl0_732
| ~ spl0_1217 ),
inference(superposition,[],[f9672,f7086]) ).
fof(f7086,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_732 ),
inference(avatar_component_clause,[],[f7084]) ).
fof(f9672,plain,
( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0)
| ~ spl0_1217 ),
inference(avatar_component_clause,[],[f9671]) ).
fof(f17150,plain,
( spl0_1785
| spl0_1787 ),
inference(avatar_split_clause,[],[f3251,f17148,f17127]) ).
fof(f17127,plain,
( spl0_1785
<=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f17148,plain,
( spl0_1787
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f3251,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1) ),
inference(inner_rewriting,[],[f2334]) ).
fof(f2334,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f17136,plain,
( ~ spl0_707
| ~ spl0_1785 ),
inference(avatar_contradiction_clause,[],[f17135]) ).
fof(f17135,plain,
( $false
| ~ spl0_707
| ~ spl0_1785 ),
inference(trivial_inequality_removal,[],[f17133]) ).
fof(f17133,plain,
( c_0 != c_0
| ~ spl0_707
| ~ spl0_1785 ),
inference(superposition,[],[f17128,f6977]) ).
fof(f6977,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f6975]) ).
fof(f6975,plain,
( spl0_707
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f17128,plain,
( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_1785 ),
inference(avatar_component_clause,[],[f17127]) ).
fof(f17132,plain,
( spl0_1785
| spl0_1786 ),
inference(avatar_split_clause,[],[f3250,f17130,f17127]) ).
fof(f17130,plain,
( spl0_1786
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f3250,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1) ),
inference(inner_rewriting,[],[f2317]) ).
fof(f2317,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f17099,plain,
( spl0_1784
| ~ spl0_640
| ~ spl0_679
| ~ spl0_774
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1673
| ~ spl0_1783 ),
inference(avatar_split_clause,[],[f17095,f17091,f15256,f10764,f10443,f7266,f6847,f5912,f17097]) ).
fof(f17097,plain,
( spl0_1784
<=> ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f15256,plain,
( spl0_1673
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f17091,plain,
( spl0_1783
<=> ! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f17095,plain,
( ! [X3] :
( c_plus(c_1,c_minus(X3,c_1,tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_774
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1673
| ~ spl0_1783 ),
inference(forward_demodulation,[],[f17094,f15259]) ).
fof(f15259,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_774
| ~ spl0_1673 ),
inference(superposition,[],[f15257,f7267]) ).
fof(f15257,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
| ~ spl0_1673 ),
inference(avatar_component_clause,[],[f15256]) ).
fof(f17094,plain,
( ! [X3] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1783 ),
inference(forward_demodulation,[],[f17092,f11723]) ).
fof(f17092,plain,
( ! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) )
| ~ spl0_1783 ),
inference(avatar_component_clause,[],[f17091]) ).
fof(f17093,plain,
spl0_1783,
inference(avatar_split_clause,[],[f3139,f17091]) ).
fof(f3139,plain,
! [X3] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X3,tc_nat),tc_nat),tc_nat),tc_nat) = X3
| ~ c_less(c_0,X3,tc_nat) ),
inference(forward_demodulation,[],[f2952,f2884]) ).
fof(f2884,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2547,f2544]) ).
fof(f2547,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f2952,plain,
! [X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X3 ),
inference(definition_unfolding,[],[f2024,f2544,f2544]) ).
fof(f2024,axiom,
! [X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_Suc(c_minus(X3,c_Suc(c_0),tc_nat)) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f17089,plain,
spl0_1782,
inference(avatar_split_clause,[],[f2983,f17087]) ).
fof(f17087,plain,
( spl0_1782
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f2983,plain,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2609,f2373]) ).
fof(f2609,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f17085,plain,
spl0_1781,
inference(avatar_split_clause,[],[f2982,f17083]) ).
fof(f17083,plain,
( spl0_1781
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f2982,plain,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),tc_set(X1)) ),
inference(definition_unfolding,[],[f2610,f2373]) ).
fof(f2610,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f17081,plain,
spl0_1780,
inference(avatar_split_clause,[],[f2978,f17079]) ).
fof(f17079,plain,
( spl0_1780
<=> ! [X20,X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f2978,plain,
! [X1,X19,X20] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f30,f2373]) ).
fof(f30,axiom,
! [X1,X19,X20] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f17077,plain,
spl0_1779,
inference(avatar_split_clause,[],[f2977,f17075]) ).
fof(f17075,plain,
( spl0_1779
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f2977,plain,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Relation_OImage(c_Relation_Odiag(X19,X1),X20,X1,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
inference(definition_unfolding,[],[f31,f2373]) ).
fof(f31,axiom,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f17071,plain,
spl0_1778,
inference(avatar_split_clause,[],[f2971,f17069]) ).
fof(f17069,plain,
( spl0_1778
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f2971,plain,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2021,f2544,f2544]) ).
fof(f2021,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f17065,plain,
spl0_1777,
inference(avatar_split_clause,[],[f2967,f17063]) ).
fof(f17063,plain,
( spl0_1777
<=> ! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f2967,plain,
! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2019,f2544,f2544]) ).
fof(f2019,axiom,
! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f17061,plain,
( spl0_1776
| ~ spl0_646
| ~ spl0_1197 ),
inference(avatar_split_clause,[],[f9934,f9591,f5939,f17058]) ).
fof(f17058,plain,
( spl0_1776
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f9591,plain,
( spl0_1197
<=> ! [X59,X3] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f9934,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_646
| ~ spl0_1197 ),
inference(resolution,[],[f9592,f5941]) ).
fof(f9592,plain,
( ! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f9591]) ).
fof(f17056,plain,
spl0_1775,
inference(avatar_split_clause,[],[f2963,f17054]) ).
fof(f17054,plain,
( spl0_1775
<=> ! [X18,X13,X12,X1] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f2963,plain,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X18,X12,X1),X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2680,f2373]) ).
fof(f2680,axiom,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
fof(f17052,plain,
spl0_1774,
inference(avatar_split_clause,[],[f2961,f17050]) ).
fof(f17050,plain,
( spl0_1774
<=> ! [X13,X12,X27,X1] :
( ~ c_in(X27,X12,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f2961,plain,
! [X1,X27,X12,X13] :
( ~ c_in(X27,X12,X1)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X12,X1),c_insert(X27,X13,X1),X1,X1) ),
inference(definition_unfolding,[],[f2664,f2373]) ).
fof(f2664,axiom,
! [X1,X27,X12,X13] :
( ~ c_in(X27,X12,X1)
| c_emptyset != c_inter(X12,c_insert(X27,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
fof(f17046,plain,
spl0_1773,
inference(avatar_split_clause,[],[f2959,f17044]) ).
fof(f17044,plain,
( spl0_1773
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f2959,plain,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2022,f2544,f2544]) ).
fof(f2022,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f17040,plain,
spl0_1772,
inference(avatar_split_clause,[],[f2954,f17038]) ).
fof(f17038,plain,
( spl0_1772
<=> ! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f2954,plain,
! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2020,f2544,f2544]) ).
fof(f2020,axiom,
! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f17032,plain,
( spl0_1771
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1770 ),
inference(avatar_split_clause,[],[f17028,f17025,f10764,f10443,f6847,f5912,f17030]) ).
fof(f17030,plain,
( spl0_1771
<=> ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f17025,plain,
( spl0_1770
<=> ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f17028,plain,
( ! [X41,X15] :
( c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_plus(c_1,X15,tc_nat),X41)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1770 ),
inference(forward_demodulation,[],[f17026,f11723]) ).
fof(f17026,plain,
( ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) )
| ~ spl0_1770 ),
inference(avatar_component_clause,[],[f17025]) ).
fof(f17027,plain,
spl0_1770,
inference(avatar_split_clause,[],[f2939,f17025]) ).
fof(f2939,plain,
! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X41) ),
inference(definition_unfolding,[],[f1802,f2544]) ).
fof(f1802,axiom,
! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_NatArith_Oof__nat(c_Suc(X15),X41) = c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f17019,plain,
( spl0_1769
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1768 ),
inference(avatar_split_clause,[],[f17015,f17012,f10764,f10443,f6847,f5912,f17017]) ).
fof(f17017,plain,
( spl0_1769
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f17012,plain,
( spl0_1768
<=> ! [X0,X23,X21,X1] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f17015,plain,
( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_plus(c_1,X21,tc_nat),X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1768 ),
inference(forward_demodulation,[],[f17013,f11723]) ).
fof(f17013,plain,
( ! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1)
| ~ spl0_1768 ),
inference(avatar_component_clause,[],[f17012]) ).
fof(f17014,plain,
spl0_1768,
inference(avatar_split_clause,[],[f2898,f17012]) ).
fof(f2898,plain,
! [X21,X0,X1,X23] : c_List_Onth(X23,X21,X1) = c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1),
inference(definition_unfolding,[],[f1693,f2544]) ).
fof(f1693,axiom,
! [X21,X0,X1,X23] : c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Suc(X21),X1) = c_List_Onth(X23,X21,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f17010,plain,
( spl0_1767
| ~ spl0_784
| ~ spl0_1129 ),
inference(avatar_split_clause,[],[f9424,f9114,f7306,f17008]) ).
fof(f17008,plain,
( spl0_1767
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f7306,plain,
( spl0_784
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f9114,plain,
( spl0_1129
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f9424,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_784
| ~ spl0_1129 ),
inference(superposition,[],[f9115,f7307]) ).
fof(f7307,plain,
( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
| ~ spl0_784 ),
inference(avatar_component_clause,[],[f7306]) ).
fof(f9115,plain,
( ! [X21,X15] :
( c_0 != c_minus(X15,X21,tc_nat)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f9114]) ).
fof(f16993,plain,
( spl0_1766
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1765 ),
inference(avatar_split_clause,[],[f16989,f16986,f10764,f10443,f6847,f5912,f16991]) ).
fof(f16991,plain,
( spl0_1766
<=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f16986,plain,
( spl0_1765
<=> ! [X0,X21,X23,X1] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f16989,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_plus(c_1,X21,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1765 ),
inference(forward_demodulation,[],[f16987,f11723]) ).
fof(f16987,plain,
( ! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1)
| ~ spl0_1765 ),
inference(avatar_component_clause,[],[f16986]) ).
fof(f16988,plain,
spl0_1765,
inference(avatar_split_clause,[],[f2897,f16986]) ).
fof(f2897,plain,
! [X21,X0,X1,X23] : c_List_Odrop(X21,X23,X1) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),c_List_Olist_OCons(X0,X23,X1),X1),
inference(definition_unfolding,[],[f1572,f2544]) ).
fof(f1572,axiom,
! [X21,X0,X1,X23] : c_List_Odrop(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(X21,X23,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f16958,plain,
( spl0_1764
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1763 ),
inference(avatar_split_clause,[],[f16954,f16951,f10764,f10443,f6847,f5912,f16956]) ).
fof(f16951,plain,
( spl0_1763
<=> ! [X41,X0,X21] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f16954,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_plus(c_1,X21,tc_nat),X0,X41)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1763 ),
inference(forward_demodulation,[],[f16952,f11723]) ).
fof(f16952,plain,
( ! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41)
| ~ spl0_1763 ),
inference(avatar_component_clause,[],[f16951]) ).
fof(f16953,plain,
spl0_1763,
inference(avatar_split_clause,[],[f2895,f16951]) ).
fof(f2895,plain,
! [X21,X41,X0] : c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X0,X41),
inference(definition_unfolding,[],[f1723,f2544]) ).
fof(f1723,axiom,
! [X21,X41,X0] : c_List_Oreplicate(c_Suc(X21),X0,X41) = c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f16854,plain,
( spl0_1762
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1761 ),
inference(avatar_split_clause,[],[f16850,f16847,f10764,f10443,f6847,f5912,f16852]) ).
fof(f16852,plain,
( spl0_1762
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f16847,plain,
( spl0_1761
<=> ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f16850,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_plus(c_1,X15,tc_nat),X21,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1761 ),
inference(forward_demodulation,[],[f16848,f11723]) ).
fof(f16848,plain,
( ! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat)
| ~ spl0_1761 ),
inference(avatar_component_clause,[],[f16847]) ).
fof(f16849,plain,
spl0_1761,
inference(avatar_split_clause,[],[f2894,f16847]) ).
fof(f2894,plain,
! [X21,X15] : c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),X21,tc_nat),
inference(definition_unfolding,[],[f2099,f2544]) ).
fof(f2099,axiom,
! [X21,X15] : c_times(c_Suc(X15),X21,tc_nat) = c_plus(X21,c_times(X15,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f16754,plain,
( spl0_1760
| ~ spl0_879
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f8869,f8587,f7699,f16752]) ).
fof(f16752,plain,
( spl0_1760
<=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f7699,plain,
( spl0_879
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f8587,plain,
( spl0_1049
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f8869,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_879
| ~ spl0_1049 ),
inference(superposition,[],[f7700,f8588]) ).
fof(f8588,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1049 ),
inference(avatar_component_clause,[],[f8587]) ).
fof(f7700,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_879 ),
inference(avatar_component_clause,[],[f7699]) ).
fof(f16750,plain,
( spl0_1759
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1758 ),
inference(avatar_split_clause,[],[f16746,f16743,f10764,f10443,f6847,f5912,f16748]) ).
fof(f16748,plain,
( spl0_1759
<=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f16743,plain,
( spl0_1758
<=> ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f16746,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1758 ),
inference(forward_demodulation,[],[f16744,f11723]) ).
fof(f16744,plain,
( ! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1758 ),
inference(avatar_component_clause,[],[f16743]) ).
fof(f16745,plain,
spl0_1758,
inference(avatar_split_clause,[],[f2893,f16743]) ).
fof(f2893,plain,
! [X21,X15] : c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) = c_times(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2057,f2544]) ).
fof(f2057,axiom,
! [X21,X15] : c_times(X15,c_Suc(X21),tc_nat) = c_plus(X15,c_times(X15,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f16687,plain,
( spl0_1757
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1756 ),
inference(avatar_split_clause,[],[f16683,f16680,f10764,f10443,f6847,f5912,f16685]) ).
fof(f16685,plain,
( spl0_1757
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f16680,plain,
( spl0_1756
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f16683,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1756 ),
inference(forward_demodulation,[],[f16681,f11723]) ).
fof(f16681,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat)
| ~ spl0_1756 ),
inference(avatar_component_clause,[],[f16680]) ).
fof(f16682,plain,
spl0_1756,
inference(avatar_split_clause,[],[f2892,f16680]) ).
fof(f2892,plain,
! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2345,f2544]) ).
fof(f2345,axiom,
! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_nat) = c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f16654,plain,
( spl0_1755
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1754 ),
inference(avatar_split_clause,[],[f16650,f16647,f10764,f10443,f6847,f5912,f16652]) ).
fof(f16652,plain,
( spl0_1755
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f16647,plain,
( spl0_1754
<=> ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f16650,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_plus(c_1,X21,tc_nat),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1754 ),
inference(forward_demodulation,[],[f16648,f11723]) ).
fof(f16648,plain,
( ! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1754 ),
inference(avatar_component_clause,[],[f16647]) ).
fof(f16649,plain,
spl0_1754,
inference(avatar_split_clause,[],[f2891,f16647]) ).
fof(f2891,plain,
! [X21,X28] : c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X28,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1465,f2544]) ).
fof(f1465,axiom,
! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_IntDef_Oint) = c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f16645,plain,
spl0_1753,
inference(avatar_split_clause,[],[f2890,f16643]) ).
fof(f16643,plain,
( spl0_1753
<=> ! [X13,X12,X1] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f2890,plain,
! [X1,X12,X13] : c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
inference(definition_unfolding,[],[f2586,f2373]) ).
fof(f2586,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f16641,plain,
spl0_1752,
inference(avatar_split_clause,[],[f2776,f16639]) ).
fof(f16639,plain,
( spl0_1752
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f2776,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OHash__synth_0) ).
fof(f16637,plain,
( spl0_1751
| ~ spl0_9
| ~ spl0_1038 ),
inference(avatar_split_clause,[],[f8856,f8542,f3293,f16635]) ).
fof(f16635,plain,
( spl0_1751
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f3293,plain,
( spl0_9
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f8542,plain,
( spl0_1038
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f8856,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_9
| ~ spl0_1038 ),
inference(resolution,[],[f8543,f3295]) ).
fof(f3295,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f3293]) ).
fof(f8543,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 )
| ~ spl0_1038 ),
inference(avatar_component_clause,[],[f8542]) ).
fof(f16633,plain,
spl0_1750,
inference(avatar_split_clause,[],[f2675,f16631]) ).
fof(f16631,plain,
( spl0_1750
<=> ! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f2675,axiom,
! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f16629,plain,
spl0_1749,
inference(avatar_split_clause,[],[f2650,f16627]) ).
fof(f16627,plain,
( spl0_1749
<=> ! [X13,X12,X1] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f2650,axiom,
! [X1,X12,X13] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f16625,plain,
spl0_1748,
inference(avatar_split_clause,[],[f2596,f16623]) ).
fof(f16623,plain,
( spl0_1748
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f2596,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f16621,plain,
spl0_1747,
inference(avatar_split_clause,[],[f2585,f16619]) ).
fof(f16619,plain,
( spl0_1747
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f2585,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f16617,plain,
spl0_1746,
inference(avatar_split_clause,[],[f2584,f16615]) ).
fof(f16615,plain,
( spl0_1746
<=> ! [X13,X12,X1] :
( c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f2584,axiom,
! [X1,X12,X13] :
( c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f16613,plain,
spl0_1745,
inference(avatar_split_clause,[],[f2574,f16611]) ).
fof(f16611,plain,
( spl0_1745
<=> ! [X13,X12,X1] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f2574,axiom,
! [X1,X12,X13] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f16609,plain,
spl0_1744,
inference(avatar_split_clause,[],[f2360,f16607]) ).
fof(f16607,plain,
( spl0_1744
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f2360,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f16605,plain,
spl0_1743,
inference(avatar_split_clause,[],[f2359,f16603]) ).
fof(f16603,plain,
( spl0_1743
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f2359,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f16601,plain,
spl0_1742,
inference(avatar_split_clause,[],[f2194,f16599]) ).
fof(f16599,plain,
( spl0_1742
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f2194,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f16597,plain,
spl0_1741,
inference(avatar_split_clause,[],[f2193,f16595]) ).
fof(f16595,plain,
( spl0_1741
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f2193,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f16593,plain,
( spl0_1740
| ~ spl0_52
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f8848,f8526,f3508,f16590]) ).
fof(f8526,plain,
( spl0_1034
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f8848,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034 ),
inference(resolution,[],[f8527,f3510]) ).
fof(f8527,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f8526]) ).
fof(f16588,plain,
spl0_1739,
inference(avatar_split_clause,[],[f2192,f16586]) ).
fof(f16586,plain,
( spl0_1739
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f2192,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f16584,plain,
spl0_1738,
inference(avatar_split_clause,[],[f2191,f16582]) ).
fof(f16582,plain,
( spl0_1738
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f2191,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f16580,plain,
spl0_1737,
inference(avatar_split_clause,[],[f2189,f16578]) ).
fof(f16578,plain,
( spl0_1737
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f2189,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f16576,plain,
spl0_1736,
inference(avatar_split_clause,[],[f2188,f16574]) ).
fof(f16574,plain,
( spl0_1736
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f2188,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f16572,plain,
spl0_1735,
inference(avatar_split_clause,[],[f2187,f16570]) ).
fof(f16570,plain,
( spl0_1735
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f2187,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f16568,plain,
spl0_1734,
inference(avatar_split_clause,[],[f2186,f16566]) ).
fof(f16566,plain,
( spl0_1734
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f2186,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f16564,plain,
spl0_1733,
inference(avatar_split_clause,[],[f2146,f16562]) ).
fof(f16562,plain,
( spl0_1733
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f2146,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f16560,plain,
spl0_1732,
inference(avatar_split_clause,[],[f2145,f16558]) ).
fof(f16558,plain,
( spl0_1732
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f2145,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f16556,plain,
spl0_1731,
inference(avatar_split_clause,[],[f2138,f16554]) ).
fof(f16554,plain,
( spl0_1731
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f2138,axiom,
! [X0,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f16552,plain,
spl0_1730,
inference(avatar_split_clause,[],[f2137,f16550]) ).
fof(f16550,plain,
( spl0_1730
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f2137,axiom,
! [X0,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f16548,plain,
( spl0_1729
| ~ spl0_879
| ~ spl0_1023 ),
inference(avatar_split_clause,[],[f8814,f8482,f7699,f16546]) ).
fof(f16546,plain,
( spl0_1729
<=> ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f8482,plain,
( spl0_1023
<=> ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f8814,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_879
| ~ spl0_1023 ),
inference(superposition,[],[f7700,f8483]) ).
fof(f8483,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1023 ),
inference(avatar_component_clause,[],[f8482]) ).
fof(f16544,plain,
spl0_1728,
inference(avatar_split_clause,[],[f2119,f16542]) ).
fof(f16542,plain,
( spl0_1728
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f2119,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f16540,plain,
spl0_1727,
inference(avatar_split_clause,[],[f2116,f16538]) ).
fof(f16538,plain,
( spl0_1727
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f2116,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f16536,plain,
spl0_1726,
inference(avatar_split_clause,[],[f1971,f16534]) ).
fof(f16534,plain,
( spl0_1726
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(c_1,X2),X18,X2)
| c_less(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f1971,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(c_1,X2),X18,X2)
| c_less(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f16532,plain,
spl0_1725,
inference(avatar_split_clause,[],[f1970,f16530]) ).
fof(f16530,plain,
( spl0_1725
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(X18,X2),c_1,X2)
| c_less(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f1970,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(X18,X2),c_1,X2)
| c_less(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f16528,plain,
spl0_1724,
inference(avatar_split_clause,[],[f1967,f16526]) ).
fof(f16526,plain,
( spl0_1724
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f1967,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f16524,plain,
spl0_1723,
inference(avatar_split_clause,[],[f1966,f16522]) ).
fof(f16522,plain,
( spl0_1723
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f1966,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f16520,plain,
spl0_1722,
inference(avatar_split_clause,[],[f1960,f16518]) ).
fof(f16518,plain,
( spl0_1722
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f1960,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f16516,plain,
spl0_1721,
inference(avatar_split_clause,[],[f1959,f16514]) ).
fof(f16514,plain,
( spl0_1721
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f1959,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f16512,plain,
spl0_1720,
inference(avatar_split_clause,[],[f1944,f16510]) ).
fof(f16510,plain,
( spl0_1720
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f1944,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f16508,plain,
spl0_1719,
inference(avatar_split_clause,[],[f1943,f16506]) ).
fof(f16506,plain,
( spl0_1719
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f1943,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f16504,plain,
( spl0_1718
| ~ spl0_968
| ~ spl0_969 ),
inference(avatar_split_clause,[],[f8313,f8136,f8131,f16501]) ).
fof(f16501,plain,
( spl0_1718
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f8131,plain,
( spl0_968
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f8136,plain,
( spl0_969
<=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f8313,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_968
| ~ spl0_969 ),
inference(superposition,[],[f8137,f8133]) ).
fof(f8133,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8131]) ).
fof(f8137,plain,
( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
| ~ spl0_969 ),
inference(avatar_component_clause,[],[f8136]) ).
fof(f16499,plain,
spl0_1717,
inference(avatar_split_clause,[],[f1869,f16497]) ).
fof(f16497,plain,
( spl0_1717
<=> ! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f1869,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f16495,plain,
spl0_1716,
inference(avatar_split_clause,[],[f1780,f16493]) ).
fof(f16493,plain,
( spl0_1716
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f1780,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f16491,plain,
spl0_1715,
inference(avatar_split_clause,[],[f1764,f16489]) ).
fof(f16489,plain,
( spl0_1715
<=> ! [X0,X12,X1] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f1764,axiom,
! [X0,X1,X12] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f16486,plain,
spl0_1714,
inference(avatar_split_clause,[],[f1727,f16484]) ).
fof(f16484,plain,
( spl0_1714
<=> ! [X25,X1,X3] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f1727,axiom,
! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f16482,plain,
spl0_1713,
inference(avatar_split_clause,[],[f1724,f16480]) ).
fof(f16480,plain,
( spl0_1713
<=> ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f1724,axiom,
! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f16478,plain,
spl0_1712,
inference(avatar_split_clause,[],[f1713,f16476]) ).
fof(f16476,plain,
( spl0_1712
<=> ! [X41,X0,X23] :
( ~ c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f1713,axiom,
! [X41,X0,X23] :
( ~ c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f16474,plain,
spl0_1711,
inference(avatar_split_clause,[],[f1701,f16472]) ).
fof(f16472,plain,
( spl0_1711
<=> ! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f1701,axiom,
! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f16470,plain,
spl0_1710,
inference(avatar_split_clause,[],[f1700,f16468]) ).
fof(f16468,plain,
( spl0_1710
<=> ! [X59,X0,X23,X43,X1] :
( X43 = X59
| c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f1700,axiom,
! [X59,X0,X1,X23,X43] :
( X43 = X59
| c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f16466,plain,
spl0_1709,
inference(avatar_split_clause,[],[f1618,f16464]) ).
fof(f16464,plain,
( spl0_1709
<=> ! [X5,X1,X0] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f1618,axiom,
! [X0,X1,X5] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f16462,plain,
spl0_1708,
inference(avatar_split_clause,[],[f1605,f16460]) ).
fof(f16460,plain,
( spl0_1708
<=> ! [X1,X23] :
( c_List_Oremdups(X23,X1) = X23
| c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f1605,axiom,
! [X1,X23] :
( c_List_Oremdups(X23,X1) = X23
| c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f16443,plain,
spl0_1707,
inference(avatar_split_clause,[],[f1545,f16441]) ).
fof(f16441,plain,
( spl0_1707
<=> ! [X25,X1,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f1545,axiom,
! [X1,X25,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f16439,plain,
spl0_1706,
inference(avatar_split_clause,[],[f1538,f16437]) ).
fof(f16437,plain,
( spl0_1706
<=> ! [X41,X0,X23] :
( c_List_Olist_ONil = X23
| c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f1538,axiom,
! [X41,X0,X23] :
( c_List_Olist_ONil = X23
| c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f16435,plain,
spl0_1705,
inference(avatar_split_clause,[],[f1519,f16433]) ).
fof(f16433,plain,
( spl0_1705
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f1519,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f16431,plain,
spl0_1704,
inference(avatar_split_clause,[],[f1515,f16429]) ).
fof(f16429,plain,
( spl0_1704
<=> ! [X25,X5,X1] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f1515,axiom,
! [X1,X5,X25] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f16427,plain,
spl0_1703,
inference(avatar_split_clause,[],[f1507,f16425]) ).
fof(f16425,plain,
( spl0_1703
<=> ! [X50,X1,X24] :
( c_List_Olist_ONil = X24
| c_List_Olist_ONil != c_List_Oconcat(X50,X1)
| ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f1507,axiom,
! [X50,X1,X24] :
( c_List_Olist_ONil = X24
| c_List_Olist_ONil != c_List_Oconcat(X50,X1)
| ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
fof(f16423,plain,
spl0_1702,
inference(avatar_split_clause,[],[f1506,f16421]) ).
fof(f16421,plain,
( spl0_1702
<=> ! [X5,X1,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f1506,axiom,
! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f16419,plain,
spl0_1701,
inference(avatar_split_clause,[],[f1311,f16417]) ).
fof(f16417,plain,
( spl0_1701
<=> ! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f1311,axiom,
! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f16415,plain,
spl0_1700,
inference(avatar_split_clause,[],[f1303,f16413]) ).
fof(f16413,plain,
( spl0_1700
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f1303,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f16411,plain,
spl0_1699,
inference(avatar_split_clause,[],[f1302,f16409]) ).
fof(f16409,plain,
( spl0_1699
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f1302,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f16407,plain,
spl0_1698,
inference(avatar_split_clause,[],[f1301,f16405]) ).
fof(f16405,plain,
( spl0_1698
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f1301,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f16403,plain,
( spl0_1697
| ~ spl0_799
| ~ spl0_1665 ),
inference(avatar_split_clause,[],[f16070,f15202,f7367,f16401]) ).
fof(f16401,plain,
( spl0_1697
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f7367,plain,
( spl0_799
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f15202,plain,
( spl0_1665
<=> ! [X18,X13,X12,X1] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f16070,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_799
| ~ spl0_1665 ),
inference(forward_demodulation,[],[f16042,f7368]) ).
fof(f7368,plain,
( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7367]) ).
fof(f16042,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_799
| ~ spl0_1665 ),
inference(superposition,[],[f15203,f7368]) ).
fof(f15203,plain,
( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
| ~ spl0_1665 ),
inference(avatar_component_clause,[],[f15202]) ).
fof(f16399,plain,
spl0_1696,
inference(avatar_split_clause,[],[f1272,f16397]) ).
fof(f16397,plain,
( spl0_1696
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f1272,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f16395,plain,
spl0_1695,
inference(avatar_split_clause,[],[f1257,f16393]) ).
fof(f16393,plain,
( spl0_1695
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f1257,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f16391,plain,
spl0_1694,
inference(avatar_split_clause,[],[f81,f16389]) ).
fof(f16389,plain,
( spl0_1694
<=> ! [X12,X1,X18] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f81,axiom,
! [X18,X1,X12] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f16387,plain,
spl0_1693,
inference(avatar_split_clause,[],[f47,f16385]) ).
fof(f16385,plain,
( spl0_1693
<=> ! [X12,X1,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f47,axiom,
! [X1,X12,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f16011,plain,
( spl0_1692
| ~ spl0_663
| ~ spl0_1657 ),
inference(avatar_split_clause,[],[f15952,f15170,f6778,f16009]) ).
fof(f16009,plain,
( spl0_1692
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f15170,plain,
( spl0_1657
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f15952,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_663
| ~ spl0_1657 ),
inference(resolution,[],[f15171,f6779]) ).
fof(f15171,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| c_lessequals(X3,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1657 ),
inference(avatar_component_clause,[],[f15170]) ).
fof(f15855,plain,
( spl0_1691
| ~ spl0_745
| ~ spl0_1629 ),
inference(avatar_split_clause,[],[f15706,f15058,f7149,f15853]) ).
fof(f15853,plain,
( spl0_1691
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f7149,plain,
( spl0_745
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f15058,plain,
( spl0_1629
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f15706,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_745
| ~ spl0_1629 ),
inference(trivial_inequality_removal,[],[f15696]) ).
fof(f15696,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_745
| ~ spl0_1629 ),
inference(superposition,[],[f15059,f7150]) ).
fof(f7150,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
| ~ spl0_745 ),
inference(avatar_component_clause,[],[f7149]) ).
fof(f15059,plain,
( ! [X21,X3,X1] :
( c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Orotate(X21,X3,X1) = X3 )
| ~ spl0_1629 ),
inference(avatar_component_clause,[],[f15058]) ).
fof(f15482,plain,
( spl0_1689
| ~ spl0_1690
| ~ spl0_854
| ~ spl0_948 ),
inference(avatar_split_clause,[],[f8277,f8051,f7599,f15479,f15476]) ).
fof(f15476,plain,
( spl0_1689
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f15479,plain,
( spl0_1690
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f7599,plain,
( spl0_854
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f8051,plain,
( spl0_948
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f8277,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_854
| ~ spl0_948 ),
inference(resolution,[],[f8052,f7600]) ).
fof(f7600,plain,
( ! [X43] :
( ~ c_lessequals(X43,c_0,tc_nat)
| c_0 = X43 )
| ~ spl0_854 ),
inference(avatar_component_clause,[],[f7599]) ).
fof(f8052,plain,
( ! [X18,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_948 ),
inference(avatar_component_clause,[],[f8051]) ).
fof(f15352,plain,
( spl0_1688
| ~ spl0_640
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8224,f7913,f5912,f15350]) ).
fof(f15350,plain,
( spl0_1688
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f7913,plain,
( spl0_914
<=> ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f8224,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_914 ),
inference(superposition,[],[f7914,f5914]) ).
fof(f7914,plain,
( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f7913]) ).
fof(f15345,plain,
spl0_1687,
inference(avatar_split_clause,[],[f3249,f15343]) ).
fof(f15343,plain,
( spl0_1687
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f3249,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3248,f2115]) ).
fof(f2115,axiom,
! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3248,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3038,f2830]) ).
fof(f2830,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f2126,f2129]) ).
fof(f2126,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f3038,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1317,f2129]) ).
fof(f1317,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f15341,plain,
spl0_1686,
inference(avatar_split_clause,[],[f3242,f15339]) ).
fof(f15339,plain,
( spl0_1686
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f3242,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3241,f2115]) ).
fof(f3241,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3032,f2830]) ).
fof(f3032,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1321,f2129]) ).
fof(f1321,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f15337,plain,
spl0_1685,
inference(avatar_split_clause,[],[f3239,f15335]) ).
fof(f15335,plain,
( spl0_1685
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f3239,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3238,f2115]) ).
fof(f3238,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3030,f2830]) ).
fof(f3030,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1316,f2129]) ).
fof(f1316,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f15333,plain,
spl0_1684,
inference(avatar_split_clause,[],[f3232,f15331]) ).
fof(f15331,plain,
( spl0_1684
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f3232,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3231,f2115]) ).
fof(f3231,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f3024,f2830]) ).
fof(f3024,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1320,f2129]) ).
fof(f1320,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f15329,plain,
spl0_1683,
inference(avatar_split_clause,[],[f3213,f15327]) ).
fof(f15327,plain,
( spl0_1683
<=> ! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f3213,plain,
! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f3010,f2831]) ).
fof(f3010,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2097,f2544]) ).
fof(f2097,axiom,
! [X21,X15] :
( ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f15325,plain,
spl0_1682,
inference(avatar_split_clause,[],[f3127,f15323]) ).
fof(f15323,plain,
( spl0_1682
<=> ! [X1,X47] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f3127,plain,
! [X47,X1] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1330,f2156]) ).
fof(f1330,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f15321,plain,
spl0_1681,
inference(avatar_split_clause,[],[f3126,f15319]) ).
fof(f15319,plain,
( spl0_1681
<=> ! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f3126,plain,
! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1329,f2156]) ).
fof(f1329,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X11),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f15317,plain,
spl0_1680,
inference(avatar_split_clause,[],[f3099,f15315]) ).
fof(f15315,plain,
( spl0_1680
<=> ! [X5,X1] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f3099,plain,
! [X1,X5] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
inference(forward_demodulation,[],[f1636,f1639]) ).
fof(f1639,axiom,
! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f1636,axiom,
! [X1,X5] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)),tc_List_Olist(X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f15313,plain,
spl0_1679,
inference(avatar_split_clause,[],[f3095,f15311]) ).
fof(f15311,plain,
( spl0_1679
<=> ! [X18,X64,X1] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f3095,plain,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat),
inference(forward_demodulation,[],[f2914,f2831]) ).
fof(f2914,plain,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1627,f2544]) ).
fof(f1627,axiom,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f15309,plain,
( spl0_1678
| ~ spl0_641
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8223,f7913,f5917,f15307]) ).
fof(f8223,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_914 ),
inference(superposition,[],[f7914,f5919]) ).
fof(f15305,plain,
spl0_1677,
inference(avatar_split_clause,[],[f3091,f15303]) ).
fof(f15303,plain,
( spl0_1677
<=> ! [X18,X13,X32,X1] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f3091,plain,
! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1),
inference(forward_demodulation,[],[f2643,f2644]) ).
fof(f2644,axiom,
! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f2643,axiom,
! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_insert(X18,c_union(X13,X32,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f15301,plain,
spl0_1676,
inference(avatar_split_clause,[],[f2992,f15299]) ).
fof(f15299,plain,
( spl0_1676
<=> ! [X21,X1,X3] :
( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f2992,plain,
! [X21,X3,X1] :
( c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
inference(definition_unfolding,[],[f1770,f1766]) ).
fof(f1770,axiom,
! [X21,X3,X1] :
( c_List_Otake(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f15281,plain,
( spl0_1675
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1674 ),
inference(avatar_split_clause,[],[f15277,f15274,f10764,f10443,f6847,f5912,f15279]) ).
fof(f15279,plain,
( spl0_1675
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f15274,plain,
( spl0_1674
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f15277,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_plus(c_1,X14,tc_nat),X26,tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1674 ),
inference(forward_demodulation,[],[f15275,f11723]) ).
fof(f15275,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat)
| ~ spl0_1674 ),
inference(avatar_component_clause,[],[f15274]) ).
fof(f15276,plain,
spl0_1674,
inference(avatar_split_clause,[],[f2885,f15274]) ).
fof(f2885,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),X26,tc_nat),
inference(definition_unfolding,[],[f2540,f2544]) ).
fof(f2540,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Suc(X14),X26,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f15258,plain,
( spl0_1673
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1672 ),
inference(avatar_split_clause,[],[f15254,f15251,f10764,f10443,f6847,f5912,f15256]) ).
fof(f15251,plain,
( spl0_1672
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f15254,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_plus(c_1,X26,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1672 ),
inference(forward_demodulation,[],[f15252,f11723]) ).
fof(f15252,plain,
( ! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat)
| ~ spl0_1672 ),
inference(avatar_component_clause,[],[f15251]) ).
fof(f15253,plain,
spl0_1672,
inference(avatar_split_clause,[],[f2884,f15251]) ).
fof(f15229,plain,
( spl0_1671
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1669 ),
inference(avatar_split_clause,[],[f15221,f15218,f10764,f10443,f6847,f5912,f15227]) ).
fof(f15227,plain,
( spl0_1671
<=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f15218,plain,
( spl0_1669
<=> ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f15221,plain,
( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_plus(c_1,X21,tc_nat),X23,X1)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1669 ),
inference(forward_demodulation,[],[f15219,f11723]) ).
fof(f15219,plain,
( ! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1)
| ~ spl0_1669 ),
inference(avatar_component_clause,[],[f15218]) ).
fof(f15225,plain,
( spl0_1670
| ~ spl0_640
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8222,f7913,f5912,f15223]) ).
fof(f8222,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_914 ),
inference(superposition,[],[f7914,f5914]) ).
fof(f15220,plain,
spl0_1669,
inference(avatar_split_clause,[],[f2883,f15218]) ).
fof(f2883,plain,
! [X21,X1,X23] : c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X23,X1),
inference(definition_unfolding,[],[f1738,f2544]) ).
fof(f1738,axiom,
! [X21,X1,X23] : c_List_Orotate(c_Suc(X21),X23,X1) = c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f15216,plain,
spl0_1668,
inference(avatar_split_clause,[],[f2722,f15214]) ).
fof(f15214,plain,
( spl0_1668
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f2722,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f15212,plain,
spl0_1667,
inference(avatar_split_clause,[],[f2719,f15210]) ).
fof(f15210,plain,
( spl0_1667
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f2719,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f15208,plain,
spl0_1666,
inference(avatar_split_clause,[],[f2657,f15206]) ).
fof(f15206,plain,
( spl0_1666
<=> ! [X24,X12,X32,X1] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f2657,axiom,
! [X1,X24,X12,X32] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f15204,plain,
spl0_1665,
inference(avatar_split_clause,[],[f2644,f15202]) ).
fof(f15200,plain,
spl0_1664,
inference(avatar_split_clause,[],[f2640,f15198]) ).
fof(f15198,plain,
( spl0_1664
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f2640,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f15196,plain,
spl0_1663,
inference(avatar_split_clause,[],[f2620,f15194]) ).
fof(f15194,plain,
( spl0_1663
<=> ! [X24,X12,X32,X1] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f2620,axiom,
! [X1,X24,X12,X32] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f15192,plain,
spl0_1662,
inference(avatar_split_clause,[],[f2593,f15190]) ).
fof(f15190,plain,
( spl0_1662
<=> ! [X13,X12,X1] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f2593,axiom,
! [X1,X12,X13] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f15188,plain,
spl0_1661,
inference(avatar_split_clause,[],[f2572,f15186]) ).
fof(f15186,plain,
( spl0_1661
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f2572,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f15184,plain,
spl0_1660,
inference(avatar_split_clause,[],[f2571,f15182]) ).
fof(f15182,plain,
( spl0_1660
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f2571,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f15180,plain,
( spl0_1659
| ~ spl0_640
| ~ spl0_911 ),
inference(avatar_split_clause,[],[f8212,f7901,f5912,f15178]) ).
fof(f15178,plain,
( spl0_1659
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f7901,plain,
( spl0_911
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f8212,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_640
| ~ spl0_911 ),
inference(superposition,[],[f7902,f5914]) ).
fof(f7902,plain,
( ! [X21,X15] :
( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
| X15 = X21 )
| ~ spl0_911 ),
inference(avatar_component_clause,[],[f7901]) ).
fof(f15176,plain,
spl0_1658,
inference(avatar_split_clause,[],[f2561,f15174]) ).
fof(f15174,plain,
( spl0_1658
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f2561,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f15172,plain,
spl0_1657,
inference(avatar_split_clause,[],[f2560,f15170]) ).
fof(f2560,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f15168,plain,
spl0_1656,
inference(avatar_split_clause,[],[f2548,f15166]) ).
fof(f15166,plain,
( spl0_1656
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f2548,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f15164,plain,
spl0_1655,
inference(avatar_split_clause,[],[f2541,f15162]) ).
fof(f15162,plain,
( spl0_1655
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f2541,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f15160,plain,
spl0_1654,
inference(avatar_split_clause,[],[f2539,f15158]) ).
fof(f15158,plain,
( spl0_1654
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f2539,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f15156,plain,
spl0_1653,
inference(avatar_split_clause,[],[f2538,f15154]) ).
fof(f15154,plain,
( spl0_1653
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f2538,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f15152,plain,
spl0_1652,
inference(avatar_split_clause,[],[f2533,f15150]) ).
fof(f15150,plain,
( spl0_1652
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f2533,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f15148,plain,
spl0_1651,
inference(avatar_split_clause,[],[f2532,f15146]) ).
fof(f15146,plain,
( spl0_1651
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f2532,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f15144,plain,
spl0_1650,
inference(avatar_split_clause,[],[f2490,f15142]) ).
fof(f15142,plain,
( spl0_1650
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f2490,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f15140,plain,
spl0_1649,
inference(avatar_split_clause,[],[f2489,f15138]) ).
fof(f15138,plain,
( spl0_1649
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f2489,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f15136,plain,
( spl0_1648
| ~ spl0_641
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f8204,f7818,f5917,f15134]) ).
fof(f15134,plain,
( spl0_1648
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f7818,plain,
( spl0_891
<=> ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f8204,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_891 ),
inference(superposition,[],[f7819,f5919]) ).
fof(f7819,plain,
( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_891 ),
inference(avatar_component_clause,[],[f7818]) ).
fof(f15132,plain,
spl0_1647,
inference(avatar_split_clause,[],[f2467,f15130]) ).
fof(f15130,plain,
( spl0_1647
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f2467,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f15128,plain,
spl0_1646,
inference(avatar_split_clause,[],[f2312,f15126]) ).
fof(f15126,plain,
( spl0_1646
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f2312,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f15124,plain,
spl0_1645,
inference(avatar_split_clause,[],[f2306,f15122]) ).
fof(f15122,plain,
( spl0_1645
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f2306,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f15120,plain,
spl0_1644,
inference(avatar_split_clause,[],[f2304,f15118]) ).
fof(f15118,plain,
( spl0_1644
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f2304,axiom,
! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f15116,plain,
spl0_1643,
inference(avatar_split_clause,[],[f2209,f15114]) ).
fof(f15114,plain,
( spl0_1643
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f2209,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f15112,plain,
spl0_1642,
inference(avatar_split_clause,[],[f2208,f15110]) ).
fof(f15110,plain,
( spl0_1642
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f2208,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f15108,plain,
spl0_1641,
inference(avatar_split_clause,[],[f2080,f15106]) ).
fof(f15106,plain,
( spl0_1641
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f2080,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f15104,plain,
spl0_1640,
inference(avatar_split_clause,[],[f2060,f15102]) ).
fof(f15102,plain,
( spl0_1640
<=> ! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f2060,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f15100,plain,
spl0_1639,
inference(avatar_split_clause,[],[f2058,f15098]) ).
fof(f15098,plain,
( spl0_1639
<=> ! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f2058,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f15096,plain,
spl0_1638,
inference(avatar_split_clause,[],[f2037,f15094]) ).
fof(f15094,plain,
( spl0_1638
<=> ! [X16,X59,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f2037,axiom,
! [X59,X16,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f15092,plain,
( spl0_1637
| ~ spl0_640
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f8203,f7818,f5912,f15090]) ).
fof(f15090,plain,
( spl0_1637
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f8203,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_891 ),
inference(superposition,[],[f7819,f5914]) ).
fof(f15088,plain,
spl0_1636,
inference(avatar_split_clause,[],[f2028,f15086]) ).
fof(f15086,plain,
( spl0_1636
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f2028,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f15084,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1863,f15082]) ).
fof(f15082,plain,
( spl0_1635
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f1863,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f15080,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1860,f15078]) ).
fof(f15078,plain,
( spl0_1634
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f1860,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f15076,plain,
spl0_1633,
inference(avatar_split_clause,[],[f1847,f15074]) ).
fof(f15074,plain,
( spl0_1633
<=> ! [X47] :
( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f1847,axiom,
! [X47] :
( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f15072,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1827,f15070]) ).
fof(f15070,plain,
( spl0_1632
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f1827,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f15068,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1801,f15066]) ).
fof(f15066,plain,
( spl0_1631
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f1801,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f15064,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1749,f15062]) ).
fof(f15062,plain,
( spl0_1630
<=> ! [X25,X1,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f1749,axiom,
! [X1,X25,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f15060,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1739,f15058]) ).
fof(f1739,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f15056,plain,
spl0_1628,
inference(avatar_split_clause,[],[f1725,f15054]) ).
fof(f15054,plain,
( spl0_1628
<=> ! [X25,X1,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f1725,axiom,
! [X1,X25,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f15052,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1708,f15050]) ).
fof(f15050,plain,
( spl0_1627
<=> ! [X41,X0,X23,X25] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f1708,axiom,
! [X41,X0,X25,X23] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f15048,plain,
( spl0_1626
| ~ spl0_640
| ~ spl0_891 ),
inference(avatar_split_clause,[],[f8201,f7818,f5912,f15046]) ).
fof(f8201,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_891 ),
inference(superposition,[],[f7819,f5914]) ).
fof(f15044,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1696,f15042]) ).
fof(f15042,plain,
( spl0_1625
<=> ! [X3,X23,X25,X1] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f1696,axiom,
! [X3,X1,X25,X23] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f15040,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1691,f15038]) ).
fof(f15038,plain,
( spl0_1624
<=> ! [X58,X0,X23,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f1691,axiom,
! [X58,X0,X1,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f15036,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1690,f15034]) ).
fof(f15034,plain,
( spl0_1623
<=> ! [X3,X0,X23,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f1690,axiom,
! [X3,X0,X1,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f15032,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1601,f15030]) ).
fof(f15030,plain,
( spl0_1622
<=> ! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f1601,axiom,
! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f15028,plain,
spl0_1621,
inference(avatar_split_clause,[],[f1577,f15026]) ).
fof(f15026,plain,
( spl0_1621
<=> ! [X43,X0,X16,X1] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f1577,axiom,
! [X0,X1,X16,X43] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f15024,plain,
spl0_1620,
inference(avatar_split_clause,[],[f1574,f15022]) ).
fof(f15022,plain,
( spl0_1620
<=> ! [X15,X23,X21,X1] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f1574,axiom,
! [X21,X1,X15,X23] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f15020,plain,
spl0_1619,
inference(avatar_split_clause,[],[f1554,f15018]) ).
fof(f15018,plain,
( spl0_1619
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(X23,X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f1554,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(X23,X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f15016,plain,
spl0_1618,
inference(avatar_split_clause,[],[f1547,f15014]) ).
fof(f15014,plain,
( spl0_1618
<=> ! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f1547,axiom,
! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f15012,plain,
spl0_1617,
inference(avatar_split_clause,[],[f1518,f15010]) ).
fof(f15010,plain,
( spl0_1617
<=> ! [X51,X23,X25,X1] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f1518,axiom,
! [X51,X1,X25,X23] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f15008,plain,
spl0_1616,
inference(avatar_split_clause,[],[f1508,f15006]) ).
fof(f15006,plain,
( spl0_1616
<=> ! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f1508,axiom,
! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f15004,plain,
spl0_1615,
inference(avatar_split_clause,[],[f1495,f15002]) ).
fof(f15002,plain,
( spl0_1615
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f1495,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f15000,plain,
spl0_1614,
inference(avatar_split_clause,[],[f1239,f14998]) ).
fof(f14998,plain,
( spl0_1614
<=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f1239,axiom,
! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f14996,plain,
spl0_1613,
inference(avatar_split_clause,[],[f1237,f14994]) ).
fof(f14994,plain,
( spl0_1613
<=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f1237,axiom,
! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f14992,plain,
spl0_1612,
inference(avatar_split_clause,[],[f1217,f14990]) ).
fof(f14990,plain,
( spl0_1612
<=> ! [X21,X15] :
( ~ c_less(c_1,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f1217,axiom,
! [X21,X15] :
( ~ c_less(c_1,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f14988,plain,
spl0_1611,
inference(avatar_split_clause,[],[f127,f14986]) ).
fof(f14986,plain,
( spl0_1611
<=> ! [X35,X36,X2,X1] :
( ~ c_Wellfounded__Recursion_Owf(X35,X2)
| ~ c_Wellfounded__Recursion_Owf(X36,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f127,axiom,
! [X2,X36,X1,X35] :
( ~ c_Wellfounded__Recursion_Owf(X35,X2)
| ~ c_Wellfounded__Recursion_Owf(X36,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f14984,plain,
spl0_1610,
inference(avatar_split_clause,[],[f125,f14982]) ).
fof(f14982,plain,
( spl0_1610
<=> ! [X34,X33,X2,X1] :
( ~ c_Relation_Otrans(X33,X2)
| ~ c_Relation_Otrans(X34,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f125,axiom,
! [X2,X1,X34,X33] :
( ~ c_Relation_Otrans(X33,X2)
| ~ c_Relation_Otrans(X34,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f14980,plain,
spl0_1609,
inference(avatar_split_clause,[],[f80,f14978]) ).
fof(f14978,plain,
( spl0_1609
<=> ! [X12,X1,X4] :
( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
| ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f80,axiom,
! [X1,X4,X12] :
( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
| ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f14705,plain,
( ~ spl0_39
| ~ spl0_1608
| ~ spl0_1317
| spl0_1440 ),
inference(avatar_split_clause,[],[f12991,f11974,f10471,f14702,f3443]) ).
fof(f3443,plain,
( spl0_39
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f14702,plain,
( spl0_1608
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f10471,plain,
( spl0_1317
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f11974,plain,
( spl0_1440
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f12991,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1317
| spl0_1440 ),
inference(resolution,[],[f11976,f10472]) ).
fof(f10472,plain,
( ! [X18,X1] :
( c_lessequals(c_0,c_uminus(X18,X1),X1)
| ~ c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
| ~ spl0_1317 ),
inference(avatar_component_clause,[],[f10471]) ).
fof(f11976,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1440 ),
inference(avatar_component_clause,[],[f11974]) ).
fof(f14562,plain,
( spl0_1607
| ~ spl0_884
| ~ spl0_1321 ),
inference(avatar_split_clause,[],[f12201,f10487,f7721,f14559]) ).
fof(f14559,plain,
( spl0_1607
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f7721,plain,
( spl0_884
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f10487,plain,
( spl0_1321
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f12201,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_884
| ~ spl0_1321 ),
inference(superposition,[],[f10489,f7722]) ).
fof(f7722,plain,
( ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f7721]) ).
fof(f10489,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1321 ),
inference(avatar_component_clause,[],[f10487]) ).
fof(f14297,plain,
( ~ spl0_1606
| spl0_100
| ~ spl0_819
| ~ spl0_1127
| ~ spl0_1260 ),
inference(avatar_split_clause,[],[f12113,f9928,f9106,f7448,f3745,f14294]) ).
fof(f14294,plain,
( spl0_1606
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f3745,plain,
( spl0_100
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f7448,plain,
( spl0_819
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f9106,plain,
( spl0_1127
<=> ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f9928,plain,
( spl0_1260
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f12113,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_819
| ~ spl0_1127
| ~ spl0_1260 ),
inference(forward_demodulation,[],[f12107,f7450]) ).
fof(f7450,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7448]) ).
fof(f12107,plain,
( ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_1127
| ~ spl0_1260 ),
inference(superposition,[],[f9107,f9930]) ).
fof(f9930,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1260 ),
inference(avatar_component_clause,[],[f9928]) ).
fof(f9107,plain,
( ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) )
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f9106]) ).
fof(f13982,plain,
spl0_1605,
inference(avatar_split_clause,[],[f3205,f13980]) ).
fof(f13980,plain,
( spl0_1605
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f3205,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3004,f2114]) ).
fof(f3004,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1334,f2129]) ).
fof(f1334,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f13978,plain,
spl0_1604,
inference(avatar_split_clause,[],[f3200,f13976]) ).
fof(f13976,plain,
( spl0_1604
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f3200,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f3000,f2114]) ).
fof(f3000,plain,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X1),X1) ),
inference(definition_unfolding,[],[f1333,f2129]) ).
fof(f1333,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f13974,plain,
spl0_1603,
inference(avatar_split_clause,[],[f3090,f13972]) ).
fof(f13972,plain,
( spl0_1603
<=> ! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f3090,plain,
! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2907,f2831]) ).
fof(f2907,plain,
! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1870,f2544]) ).
fof(f1870,axiom,
! [X83] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f13970,plain,
spl0_1602,
inference(avatar_split_clause,[],[f3009,f13968]) ).
fof(f13968,plain,
( spl0_1602
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f3009,plain,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Osublist(X23,c_SetInterval_OlessThan(X21,tc_nat),X1) ),
inference(definition_unfolding,[],[f1772,f1766]) ).
fof(f1772,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Otake(X21,X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f13961,plain,
( spl0_1601
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1600 ),
inference(avatar_split_clause,[],[f13957,f13954,f10764,f10443,f6847,f5912,f13959]) ).
fof(f13959,plain,
( spl0_1601
<=> ! [X47] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f13954,plain,
( spl0_1600
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f13957,plain,
( ! [X47] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1600 ),
inference(forward_demodulation,[],[f13955,f11723]) ).
fof(f13955,plain,
( ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1600 ),
inference(avatar_component_clause,[],[f13954]) ).
fof(f13956,plain,
spl0_1600,
inference(avatar_split_clause,[],[f2975,f13954]) ).
fof(f2975,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X47,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1822,f2544]) ).
fof(f1822,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f13952,plain,
spl0_1599,
inference(avatar_split_clause,[],[f2973,f13950]) ).
fof(f13950,plain,
( spl0_1599
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f2973,plain,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2606,f2373]) ).
fof(f2606,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f13928,plain,
spl0_1598,
inference(avatar_split_clause,[],[f2972,f13926]) ).
fof(f13926,plain,
( spl0_1598
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f2972,plain,
! [X1,X4,X12,X13] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),X1) ),
inference(definition_unfolding,[],[f2607,f2373]) ).
fof(f2607,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f13924,plain,
spl0_1597,
inference(avatar_split_clause,[],[f2942,f13922]) ).
fof(f13922,plain,
( spl0_1597
<=> ! [X21,X15] :
( X15 = X21
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f2942,plain,
! [X21,X15] :
( X15 = X21
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2017,f2544,f2544]) ).
fof(f2017,axiom,
! [X21,X15] :
( X15 = X21
| c_Suc(X21) != c_Suc(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f13920,plain,
spl0_1596,
inference(avatar_split_clause,[],[f2888,f13918]) ).
fof(f13918,plain,
( spl0_1596
<=> ! [X21,X1,X3] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f2888,plain,
! [X21,X3,X1] : c_append(c_List_Osublist(X3,c_SetInterval_OlessThan(X21,tc_nat),X1),c_List_Odrop(X21,X3,X1),X1) = X3,
inference(definition_unfolding,[],[f1535,f1766]) ).
fof(f1535,axiom,
! [X21,X3,X1] : c_append(c_List_Otake(X21,X3,X1),c_List_Odrop(X21,X3,X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f13916,plain,
spl0_1595,
inference(avatar_split_clause,[],[f2745,f13914]) ).
fof(f13914,plain,
( spl0_1595
<=> ! [X86,X91,X88] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f2745,axiom,
! [X91,X88,X86] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Crypt_0) ).
fof(f13912,plain,
spl0_1594,
inference(avatar_split_clause,[],[f2727,f13910]) ).
fof(f13910,plain,
( spl0_1594
<=> ! [X0,X3] :
( ~ c_less(X0,X3,tc_nat)
| c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f2727,axiom,
! [X3,X0] :
( ~ c_less(X0,X3,tc_nat)
| c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f13908,plain,
spl0_1593,
inference(avatar_split_clause,[],[f2726,f13906]) ).
fof(f13906,plain,
( spl0_1593
<=> ! [X0,X3] :
( c_less(X0,X3,tc_nat)
| ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f2726,axiom,
! [X3,X0] :
( c_less(X0,X3,tc_nat)
| ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f13904,plain,
spl0_1592,
inference(avatar_split_clause,[],[f2683,f13902]) ).
fof(f13902,plain,
( spl0_1592
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_in(X18,X12,X1)
| ~ c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f2683,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_in(X18,X12,X1)
| ~ c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f13900,plain,
spl0_1591,
inference(avatar_split_clause,[],[f2658,f13898]) ).
fof(f13898,plain,
( spl0_1591
<=> ! [X13,X18,X1] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f2658,axiom,
! [X18,X1,X13] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f13896,plain,
spl0_1590,
inference(avatar_split_clause,[],[f2655,f13894]) ).
fof(f13894,plain,
( spl0_1590
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f2655,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f13892,plain,
spl0_1589,
inference(avatar_split_clause,[],[f2621,f13890]) ).
fof(f13890,plain,
( spl0_1589
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f2621,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f13868,plain,
spl0_1588,
inference(avatar_split_clause,[],[f2488,f13866]) ).
fof(f13866,plain,
( spl0_1588
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_times(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f2488,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_times(X18,X27,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f13864,plain,
spl0_1587,
inference(avatar_split_clause,[],[f2475,f13862]) ).
fof(f13862,plain,
( spl0_1587
<=> ! [X18,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X18,X4,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f2475,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X18,X4,X1) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right2_0) ).
fof(f13860,plain,
spl0_1586,
inference(avatar_split_clause,[],[f2471,f13858]) ).
fof(f13858,plain,
( spl0_1586
<=> ! [X18,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X4,X18,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f2471,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X4,X18,X1) != X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f13856,plain,
spl0_1585,
inference(avatar_split_clause,[],[f2363,f13854]) ).
fof(f13854,plain,
( spl0_1585
<=> ! [X2,X42,X18,X84,X27,X1] :
( X27 = X84
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f2363,axiom,
! [X2,X18,X1,X27,X84,X42] :
( X27 = X84
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f13852,plain,
spl0_1584,
inference(avatar_split_clause,[],[f2362,f13850]) ).
fof(f13850,plain,
( spl0_1584
<=> ! [X18,X42,X84,X27,X2,X1] :
( X18 = X42
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f2362,axiom,
! [X2,X18,X1,X27,X84,X42] :
( X18 = X42
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f13848,plain,
spl0_1583,
inference(avatar_split_clause,[],[f2349,f13846]) ).
fof(f13846,plain,
( spl0_1583
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_0 = c_Nat_Opower(c_0,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f2349,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_0 = c_Nat_Opower(c_0,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f13844,plain,
spl0_1582,
inference(avatar_split_clause,[],[f2348,f13842]) ).
fof(f13842,plain,
( spl0_1582
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X21,tc_nat)
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f2348,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X21,tc_nat)
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f13840,plain,
spl0_1581,
inference(avatar_split_clause,[],[f2268,f13838]) ).
fof(f13838,plain,
( spl0_1581
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f2268,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f13836,plain,
spl0_1580,
inference(avatar_split_clause,[],[f2263,f13834]) ).
fof(f13834,plain,
( spl0_1580
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f2263,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f13832,plain,
spl0_1579,
inference(avatar_split_clause,[],[f2246,f13830]) ).
fof(f13830,plain,
( spl0_1579
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f2246,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f13828,plain,
( spl0_1578
| ~ spl0_709
| ~ spl0_710
| ~ spl0_712
| ~ spl0_785
| ~ spl0_1515 ),
inference(avatar_split_clause,[],[f13592,f12340,f7310,f6998,f6990,f6985,f13826]) ).
fof(f13826,plain,
( spl0_1578
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f6990,plain,
( spl0_710
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f6998,plain,
( spl0_712
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f7310,plain,
( spl0_785
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f12340,plain,
( spl0_1515
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f13592,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_709
| ~ spl0_710
| ~ spl0_712
| ~ spl0_785
| ~ spl0_1515 ),
inference(forward_demodulation,[],[f13591,f6991]) ).
fof(f6991,plain,
( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
| ~ spl0_710 ),
inference(avatar_component_clause,[],[f6990]) ).
fof(f13591,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_709
| ~ spl0_712
| ~ spl0_785
| ~ spl0_1515 ),
inference(forward_demodulation,[],[f13590,f7312]) ).
fof(f7312,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_785 ),
inference(avatar_component_clause,[],[f7310]) ).
fof(f13590,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0)
| ~ spl0_709
| ~ spl0_712
| ~ spl0_1515 ),
inference(forward_demodulation,[],[f13579,f6999]) ).
fof(f6999,plain,
( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f6998]) ).
fof(f13579,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X0) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OPls,X0),X0)
| ~ spl0_709
| ~ spl0_1515 ),
inference(superposition,[],[f12341,f6987]) ).
fof(f12341,plain,
( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11)
| ~ spl0_1515 ),
inference(avatar_component_clause,[],[f12340]) ).
fof(f13824,plain,
spl0_1577,
inference(avatar_split_clause,[],[f2242,f13822]) ).
fof(f13822,plain,
( spl0_1577
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f2242,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f13820,plain,
spl0_1576,
inference(avatar_split_clause,[],[f2236,f13818]) ).
fof(f13818,plain,
( spl0_1576
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f2236,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f13816,plain,
spl0_1575,
inference(avatar_split_clause,[],[f2235,f13814]) ).
fof(f13814,plain,
( spl0_1575
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f2235,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f13812,plain,
spl0_1574,
inference(avatar_split_clause,[],[f2232,f13810]) ).
fof(f13810,plain,
( spl0_1574
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f2232,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f13808,plain,
spl0_1573,
inference(avatar_split_clause,[],[f2231,f13806]) ).
fof(f13806,plain,
( spl0_1573
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f2231,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f13804,plain,
spl0_1572,
inference(avatar_split_clause,[],[f2195,f13802]) ).
fof(f13802,plain,
( spl0_1572
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f2195,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f13800,plain,
spl0_1571,
inference(avatar_split_clause,[],[f2190,f13798]) ).
fof(f13798,plain,
( spl0_1571
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f2190,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f13796,plain,
spl0_1570,
inference(avatar_split_clause,[],[f2111,f13794]) ).
fof(f13794,plain,
( spl0_1570
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f2111,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f13792,plain,
spl0_1569,
inference(avatar_split_clause,[],[f2085,f13790]) ).
fof(f13790,plain,
( spl0_1569
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f2085,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f13788,plain,
spl0_1568,
inference(avatar_split_clause,[],[f2084,f13786]) ).
fof(f13786,plain,
( spl0_1568
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f2084,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f13784,plain,
( spl0_1567
| ~ spl0_708
| ~ spl0_710
| ~ spl0_732
| ~ spl0_785
| ~ spl0_884
| ~ spl0_1514 ),
inference(avatar_split_clause,[],[f13573,f12336,f7721,f7310,f7084,f6990,f6980,f13781]) ).
fof(f6980,plain,
( spl0_708
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f12336,plain,
( spl0_1514
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f13573,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_708
| ~ spl0_710
| ~ spl0_732
| ~ spl0_785
| ~ spl0_884
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13572,f6982]) ).
fof(f6982,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_708 ),
inference(avatar_component_clause,[],[f6980]) ).
fof(f13572,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_710
| ~ spl0_732
| ~ spl0_785
| ~ spl0_884
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13571,f7312]) ).
fof(f13571,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_710
| ~ spl0_732
| ~ spl0_884
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13570,f6991]) ).
fof(f13570,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_732
| ~ spl0_884
| ~ spl0_1514 ),
inference(forward_demodulation,[],[f13564,f7722]) ).
fof(f13564,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_732
| ~ spl0_1514 ),
inference(superposition,[],[f12337,f7086]) ).
fof(f12337,plain,
( ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1)
| ~ spl0_1514 ),
inference(avatar_component_clause,[],[f12336]) ).
fof(f13779,plain,
spl0_1566,
inference(avatar_split_clause,[],[f2083,f13777]) ).
fof(f13777,plain,
( spl0_1566
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f2083,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f13775,plain,
spl0_1565,
inference(avatar_split_clause,[],[f2082,f13773]) ).
fof(f13773,plain,
( spl0_1565
<=> ! [X21,X16,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f2082,axiom,
! [X21,X16,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f13771,plain,
spl0_1564,
inference(avatar_split_clause,[],[f2076,f13769]) ).
fof(f13769,plain,
( spl0_1564
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f2076,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f13767,plain,
spl0_1563,
inference(avatar_split_clause,[],[f2075,f13765]) ).
fof(f13765,plain,
( spl0_1563
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f2075,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f13763,plain,
spl0_1562,
inference(avatar_split_clause,[],[f2073,f13761]) ).
fof(f13761,plain,
( spl0_1562
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f2073,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f13759,plain,
spl0_1561,
inference(avatar_split_clause,[],[f2072,f13757]) ).
fof(f13757,plain,
( spl0_1561
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f2072,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f13755,plain,
spl0_1560,
inference(avatar_split_clause,[],[f2071,f13753]) ).
fof(f13753,plain,
( spl0_1560
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f2071,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f13751,plain,
spl0_1559,
inference(avatar_split_clause,[],[f2070,f13749]) ).
fof(f13749,plain,
( spl0_1559
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f2070,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f13747,plain,
spl0_1558,
inference(avatar_split_clause,[],[f2068,f13745]) ).
fof(f13745,plain,
( spl0_1558
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f2068,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f13743,plain,
spl0_1557,
inference(avatar_split_clause,[],[f2067,f13741]) ).
fof(f13741,plain,
( spl0_1557
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f2067,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f13739,plain,
( spl0_1556
| ~ spl0_663
| ~ spl0_1496 ),
inference(avatar_split_clause,[],[f13488,f12227,f6778,f13737]) ).
fof(f12227,plain,
( spl0_1496
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f13488,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oparts(X0),tc_set(tc_Message_Omsg))
| ~ spl0_663
| ~ spl0_1496 ),
inference(resolution,[],[f12228,f6779]) ).
fof(f12228,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1496 ),
inference(avatar_component_clause,[],[f12227]) ).
fof(f13735,plain,
spl0_1555,
inference(avatar_split_clause,[],[f1927,f13733]) ).
fof(f13733,plain,
( spl0_1555
<=> ! [X2,X27] :
( ~ class_HOL_Oone(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_1 != c_uminus(X27,X2)
| c_uminus(c_1,X2) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f1927,axiom,
! [X2,X27] :
( ~ class_HOL_Oone(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_1 != c_uminus(X27,X2)
| c_uminus(c_1,X2) = X27 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f13731,plain,
spl0_1554,
inference(avatar_split_clause,[],[f1868,f13729]) ).
fof(f13729,plain,
( spl0_1554
<=> ! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f1868,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f13727,plain,
spl0_1553,
inference(avatar_split_clause,[],[f1820,f13725]) ).
fof(f13725,plain,
( spl0_1553
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X15,X21,tc_nat)
| c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1820,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X15,X21,tc_nat)
| c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f13723,plain,
spl0_1552,
inference(avatar_split_clause,[],[f1819,f13721]) ).
fof(f13721,plain,
( spl0_1552
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(X15,X21,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f1819,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(X15,X21,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f13719,plain,
spl0_1551,
inference(avatar_split_clause,[],[f1817,f13717]) ).
fof(f13717,plain,
( spl0_1551
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f1817,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f13715,plain,
spl0_1550,
inference(avatar_split_clause,[],[f1816,f13713]) ).
fof(f13713,plain,
( spl0_1550
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f1816,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f13711,plain,
spl0_1549,
inference(avatar_split_clause,[],[f1760,f13709]) ).
fof(f13709,plain,
( spl0_1549
<=> ! [X0,X1,X23] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
| c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f1760,axiom,
! [X0,X1,X23] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
| c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_0) ).
fof(f13707,plain,
spl0_1548,
inference(avatar_split_clause,[],[f1756,f13705]) ).
fof(f13705,plain,
( spl0_1548
<=> ! [X21,X1,X0] :
( c_0 = X21
| c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f1756,axiom,
! [X21,X0,X1] :
( c_0 = X21
| c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f13703,plain,
spl0_1547,
inference(avatar_split_clause,[],[f1710,f13701]) ).
fof(f13701,plain,
( spl0_1547
<=> ! [X41,X0,X3,X25] :
( X0 = X3
| c_List_Oop_Amem(X0,X25,X41)
| ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f1710,axiom,
! [X3,X41,X0,X25] :
( X0 = X3
| c_List_Oop_Amem(X0,X25,X41)
| ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f13699,plain,
spl0_1546,
inference(avatar_split_clause,[],[f1640,f13697]) ).
fof(f13697,plain,
( spl0_1546
<=> ! [X41,X12,X66] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f1640,axiom,
! [X41,X66,X12] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f13695,plain,
( spl0_1545
| ~ spl0_663
| ~ spl0_1488 ),
inference(avatar_split_clause,[],[f13377,f12190,f6778,f13693]) ).
fof(f13693,plain,
( spl0_1545
<=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f12190,plain,
( spl0_1488
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f13377,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
| ~ spl0_663
| ~ spl0_1488 ),
inference(resolution,[],[f12191,f6779]) ).
fof(f12191,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1488 ),
inference(avatar_component_clause,[],[f12190]) ).
fof(f13691,plain,
spl0_1544,
inference(avatar_split_clause,[],[f1632,f13689]) ).
fof(f13689,plain,
( spl0_1544
<=> ! [X0,X3,X43,X1] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
| c_List_Olist__update(X3,X43,X0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f1632,axiom,
! [X3,X0,X1,X43] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
| c_List_Olist__update(X3,X43,X0,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f13687,plain,
spl0_1543,
inference(avatar_split_clause,[],[f1612,f13685]) ).
fof(f13685,plain,
( spl0_1543
<=> ! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f1612,axiom,
! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f13683,plain,
spl0_1542,
inference(avatar_split_clause,[],[f1600,f13681]) ).
fof(f13681,plain,
( spl0_1542
<=> ! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f1600,axiom,
! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f13679,plain,
spl0_1541,
inference(avatar_split_clause,[],[f1596,f13677]) ).
fof(f1596,axiom,
! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f13675,plain,
spl0_1540,
inference(avatar_split_clause,[],[f1544,f13673]) ).
fof(f13673,plain,
( spl0_1540
<=> ! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f1544,axiom,
! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f13671,plain,
spl0_1539,
inference(avatar_split_clause,[],[f1456,f13669]) ).
fof(f13669,plain,
( spl0_1539
<=> ! [X5,X49] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f1456,axiom,
! [X49,X5] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f13667,plain,
spl0_1538,
inference(avatar_split_clause,[],[f1431,f13665]) ).
fof(f13665,plain,
( spl0_1538
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f1431,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f13663,plain,
spl0_1537,
inference(avatar_split_clause,[],[f1415,f13661]) ).
fof(f13661,plain,
( spl0_1537
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f1415,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f13659,plain,
spl0_1536,
inference(avatar_split_clause,[],[f1414,f13657]) ).
fof(f13657,plain,
( spl0_1536
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f1414,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f13655,plain,
spl0_1535,
inference(avatar_split_clause,[],[f1411,f13653]) ).
fof(f13653,plain,
( spl0_1535
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f1411,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f13651,plain,
spl0_1534,
inference(avatar_split_clause,[],[f1410,f13649]) ).
fof(f1410,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f13647,plain,
spl0_1533,
inference(avatar_split_clause,[],[f1281,f13645]) ).
fof(f13645,plain,
( spl0_1533
<=> ! [X13,X1,X46] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f1281,axiom,
! [X46,X1,X13] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f13643,plain,
spl0_1532,
inference(avatar_split_clause,[],[f1198,f13641]) ).
fof(f13641,plain,
( spl0_1532
<=> ! [X9,X7,X8,X10,X2,X1] :
( X7 = X8
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f1198,axiom,
! [X2,X10,X1,X8,X9,X7] :
( X7 = X8
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f13639,plain,
spl0_1531,
inference(avatar_split_clause,[],[f1197,f13637]) ).
fof(f13637,plain,
( spl0_1531
<=> ! [X7,X10,X8,X9,X2,X1] :
( X9 = X10
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f1197,axiom,
! [X2,X10,X1,X8,X9,X7] :
( X9 = X10
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f13635,plain,
spl0_1530,
inference(avatar_split_clause,[],[f99,f13633]) ).
fof(f13633,plain,
( spl0_1530
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f99,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f13631,plain,
spl0_1529,
inference(avatar_split_clause,[],[f96,f13629]) ).
fof(f13629,plain,
( spl0_1529
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f96,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f13627,plain,
spl0_1528,
inference(avatar_split_clause,[],[f59,f13625]) ).
fof(f13625,plain,
( spl0_1528
<=> ! [X0,X12,X1,X26] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f59,axiom,
! [X0,X1,X26,X12] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f13623,plain,
spl0_1527,
inference(avatar_split_clause,[],[f48,f13621]) ).
fof(f13621,plain,
( spl0_1527
<=> ! [X12,X1,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f48,axiom,
! [X1,X12,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f13619,plain,
spl0_1526,
inference(avatar_split_clause,[],[f43,f13617]) ).
fof(f13617,plain,
( spl0_1526
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f43,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f13615,plain,
spl0_1525,
inference(avatar_split_clause,[],[f27,f13613]) ).
fof(f13613,plain,
( spl0_1525
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f27,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f13530,plain,
( spl0_1524
| ~ spl0_114
| ~ spl0_1483 ),
inference(avatar_split_clause,[],[f13310,f12170,f3808,f13528]) ).
fof(f13528,plain,
( spl0_1524
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f3808,plain,
( spl0_114
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f12170,plain,
( spl0_1483
<=> ! [X18,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f13310,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_114
| ~ spl0_1483 ),
inference(resolution,[],[f12171,f3809]) ).
fof(f3809,plain,
( ! [X0,X1] : c_in(X0,c_UNIV,X1)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f3808]) ).
fof(f12171,plain,
( ! [X18,X1,X5] :
( ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1))
| ~ c_Wellfounded__Recursion_Owf(X5,X1) )
| ~ spl0_1483 ),
inference(avatar_component_clause,[],[f12170]) ).
fof(f13407,plain,
( spl0_1523
| ~ spl0_1146
| ~ spl0_1483 ),
inference(avatar_split_clause,[],[f13304,f12170,f9182,f13405]) ).
fof(f13405,plain,
( spl0_1523
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f9182,plain,
( spl0_1146
<=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f13304,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1146
| ~ spl0_1483 ),
inference(resolution,[],[f12171,f9183]) ).
fof(f9183,plain,
( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_1146 ),
inference(avatar_component_clause,[],[f9182]) ).
fof(f13293,plain,
( spl0_1522
| ~ spl0_1006
| ~ spl0_1247 ),
inference(avatar_split_clause,[],[f11932,f9791,f8413,f13291]) ).
fof(f13291,plain,
( spl0_1522
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f8413,plain,
( spl0_1006
<=> ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f9791,plain,
( spl0_1247
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f11932,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1006
| ~ spl0_1247 ),
inference(superposition,[],[f8414,f9792]) ).
fof(f9792,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1247 ),
inference(avatar_component_clause,[],[f9791]) ).
fof(f8414,plain,
( ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1006 ),
inference(avatar_component_clause,[],[f8413]) ).
fof(f13096,plain,
( spl0_1521
| ~ spl0_767
| ~ spl0_1420 ),
inference(avatar_split_clause,[],[f12571,f11889,f7238,f13094]) ).
fof(f13094,plain,
( spl0_1521
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f7238,plain,
( spl0_767
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f11889,plain,
( spl0_1420
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f12571,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_767
| ~ spl0_1420 ),
inference(superposition,[],[f7239,f11890]) ).
fof(f11890,plain,
( ! [X3,X1] :
( c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3
| c_List_Olist_ONil = X3 )
| ~ spl0_1420 ),
inference(avatar_component_clause,[],[f11889]) ).
fof(f7239,plain,
( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ spl0_767 ),
inference(avatar_component_clause,[],[f7238]) ).
fof(f12564,plain,
( ~ spl0_1519
| spl0_1520
| ~ spl0_112
| ~ spl0_1316 ),
inference(avatar_split_clause,[],[f11101,f10467,f3800,f12562,f12558]) ).
fof(f12558,plain,
( spl0_1519
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f12562,plain,
( spl0_1520
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f10467,plain,
( spl0_1316
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f11101,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_112
| ~ spl0_1316 ),
inference(resolution,[],[f10468,f3801]) ).
fof(f10468,plain,
( ! [X18,X1] :
( ~ c_lessequals(c_0,c_uminus(X18,X1),X1)
| c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
| ~ spl0_1316 ),
inference(avatar_component_clause,[],[f10467]) ).
fof(f12354,plain,
spl0_1518,
inference(avatar_split_clause,[],[f3157,f12352]) ).
fof(f12352,plain,
( spl0_1518
<=> ! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f3157,plain,
! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2976,f2831]) ).
fof(f2976,plain,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1871,f2544,f2544]) ).
fof(f1871,axiom,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f12350,plain,
spl0_1517,
inference(avatar_split_clause,[],[f3140,f12348]) ).
fof(f12348,plain,
( spl0_1517
<=> ! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f3140,plain,
! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ),
inference(forward_demodulation,[],[f2953,f2884]) ).
fof(f2953,plain,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X43,tc_nat),tc_nat),tc_nat),X21,tc_nat) ),
inference(definition_unfolding,[],[f2036,f2544]) ).
fof(f2036,axiom,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f12346,plain,
spl0_1516,
inference(avatar_split_clause,[],[f3094,f12344]) ).
fof(f3094,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f3093,f2156]) ).
fof(f3093,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f3092,f2154]) ).
fof(f3092,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f1883,f2156]) ).
fof(f1883,axiom,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f12342,plain,
spl0_1515,
inference(avatar_split_clause,[],[f3080,f12340]) ).
fof(f3080,plain,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11),
inference(forward_demodulation,[],[f2128,f2127]) ).
fof(f2127,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f2128,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f12338,plain,
spl0_1514,
inference(avatar_split_clause,[],[f3076,f12336]) ).
fof(f3076,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2873,f2846]) ).
fof(f2846,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
inference(definition_unfolding,[],[f2112,f2113]) ).
fof(f2113,axiom,
! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f2112,axiom,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2873,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2124,f2129,f2113,f2129]) ).
fof(f2124,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f12334,plain,
spl0_1513,
inference(avatar_split_clause,[],[f2986,f12332]) ).
fof(f12332,plain,
( spl0_1513
<=> ! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f2986,plain,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1853,f2129]) ).
fof(f1853,axiom,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f12330,plain,
spl0_1512,
inference(avatar_split_clause,[],[f2984,f12328]) ).
fof(f12328,plain,
( spl0_1512
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f2984,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1854,f2129]) ).
fof(f1854,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f12299,plain,
( spl0_1511
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1510 ),
inference(avatar_split_clause,[],[f12295,f12292,f10764,f10443,f6847,f5912,f12297]) ).
fof(f12297,plain,
( spl0_1511
<=> ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f12292,plain,
( spl0_1510
<=> ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f12295,plain,
( ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) )
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1510 ),
inference(forward_demodulation,[],[f12293,f11723]) ).
fof(f12293,plain,
( ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
| ~ spl0_1510 ),
inference(avatar_component_clause,[],[f12292]) ).
fof(f12294,plain,
spl0_1510,
inference(avatar_split_clause,[],[f2968,f12292]) ).
fof(f2968,plain,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f1783,f2544]) ).
fof(f1783,axiom,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f12290,plain,
spl0_1509,
inference(avatar_split_clause,[],[f2932,f12288]) ).
fof(f12288,plain,
( spl0_1509
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f2932,plain,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ),
inference(definition_unfolding,[],[f2117,f2129]) ).
fof(f2117,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f12282,plain,
( spl0_1508
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1507 ),
inference(avatar_split_clause,[],[f12278,f12275,f10764,f10443,f6847,f5912,f12280]) ).
fof(f12280,plain,
( spl0_1508
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f12275,plain,
( spl0_1507
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f12278,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1507 ),
inference(forward_demodulation,[],[f12276,f11723]) ).
fof(f12276,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat)
| ~ spl0_1507 ),
inference(avatar_component_clause,[],[f12275]) ).
fof(f12277,plain,
spl0_1507,
inference(avatar_split_clause,[],[f2874,f12275]) ).
fof(f2874,plain,
! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2527,f2544]) ).
fof(f2527,axiom,
! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f12273,plain,
spl0_1506,
inference(avatar_split_clause,[],[f2872,f12271]) ).
fof(f12271,plain,
( spl0_1506
<=> ! [X13,X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f2872,plain,
! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2589,f2373]) ).
fof(f2589,axiom,
! [X1,X12,X13] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f12269,plain,
spl0_1505,
inference(avatar_split_clause,[],[f2861,f12267]) ).
fof(f12267,plain,
( spl0_1505
<=> ! [X85,X1] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f2861,plain,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2706,f2716]) ).
fof(f2706,axiom,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f12265,plain,
spl0_1504,
inference(avatar_split_clause,[],[f2860,f12263]) ).
fof(f12263,plain,
( spl0_1504
<=> ! [X85,X1] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f2860,plain,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2707,f2716]) ).
fof(f2707,axiom,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f12258,plain,
( spl0_1503
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1500 ),
inference(avatar_split_clause,[],[f12246,f12243,f10764,f10443,f6847,f5912,f12256]) ).
fof(f12256,plain,
( spl0_1503
<=> ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f12243,plain,
( spl0_1500
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f12246,plain,
( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
| ~ spl0_640
| ~ spl0_679
| ~ spl0_1310
| ~ spl0_1388
| ~ spl0_1500 ),
inference(forward_demodulation,[],[f12244,f11723]) ).
fof(f12244,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21)
| ~ spl0_1500 ),
inference(avatar_component_clause,[],[f12243]) ).
fof(f12254,plain,
( ~ spl0_1501
| spl0_1502
| ~ spl0_112
| ~ spl0_1279 ),
inference(avatar_split_clause,[],[f10878,f10317,f3800,f12252,f12248]) ).
fof(f12248,plain,
( spl0_1501
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f12252,plain,
( spl0_1502
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f10317,plain,
( spl0_1279
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f10878,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_112
| ~ spl0_1279 ),
inference(resolution,[],[f10318,f3801]) ).
fof(f10318,plain,
( ! [X48,X1] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1279 ),
inference(avatar_component_clause,[],[f10317]) ).
fof(f12245,plain,
spl0_1500,
inference(avatar_split_clause,[],[f2856,f12243]) ).
fof(f2856,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21),
inference(definition_unfolding,[],[f1163,f2544,f2544]) ).
fof(f1163,axiom,
! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f12241,plain,
spl0_1499,
inference(avatar_split_clause,[],[f2821,f12239]) ).
fof(f12239,plain,
( spl0_1499
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f2821,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_1) ).
fof(f12237,plain,
spl0_1498,
inference(avatar_split_clause,[],[f2820,f12235]) ).
fof(f2820,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__subset__iff_0) ).
fof(f12233,plain,
spl0_1497,
inference(avatar_split_clause,[],[f2815,f12231]) ).
fof(f12231,plain,
( spl0_1497
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f2815,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
fof(f12229,plain,
spl0_1496,
inference(avatar_split_clause,[],[f2814,f12227]) ).
fof(f2814,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
fof(f12225,plain,
spl0_1495,
inference(avatar_split_clause,[],[f2812,f12223]) ).
fof(f12223,plain,
( spl0_1495
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f2812,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
fof(f12221,plain,
spl0_1494,
inference(avatar_split_clause,[],[f2811,f12219]) ).
fof(f12219,plain,
( spl0_1494
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f2811,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
fof(f12217,plain,
spl0_1493,
inference(avatar_split_clause,[],[f2809,f12215]) ).
fof(f12215,plain,
( spl0_1493
<=> ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f2809,axiom,
! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
fof(f12213,plain,
spl0_1492,
inference(avatar_split_clause,[],[f2808,f12211]) ).
fof(f12211,plain,
( spl0_1492
<=> ! [X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f2808,axiom,
! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
fof(f12209,plain,
spl0_1491,
inference(avatar_split_clause,[],[f2806,f12207]) ).
fof(f12207,plain,
( spl0_1491
<=> ! [X102,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f2806,axiom,
! [X88,X102] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
fof(f12200,plain,
spl0_1490,
inference(avatar_split_clause,[],[f2804,f12198]) ).
fof(f12198,plain,
( spl0_1490
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f2804,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
fof(f12196,plain,
spl0_1489,
inference(avatar_split_clause,[],[f2801,f12194]) ).
fof(f12194,plain,
( spl0_1489
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2801,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_1) ).
fof(f12192,plain,
spl0_1488,
inference(avatar_split_clause,[],[f2800,f12190]) ).
fof(f2800,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__iff_0) ).
fof(f12188,plain,
spl0_1487,
inference(avatar_split_clause,[],[f2798,f12186]) ).
fof(f12186,plain,
( spl0_1487
<=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f2798,axiom,
! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Number_0) ).
fof(f12184,plain,
spl0_1486,
inference(avatar_split_clause,[],[f2797,f12182]) ).
fof(f12182,plain,
( spl0_1486
<=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f2797,axiom,
! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Nonce_0) ).
fof(f12180,plain,
spl0_1485,
inference(avatar_split_clause,[],[f2794,f12178]) ).
fof(f12178,plain,
( spl0_1485
<=> ! [X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f2794,axiom,
! [X88,X86] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Hash_0) ).
fof(f12176,plain,
spl0_1484,
inference(avatar_split_clause,[],[f2793,f12174]) ).
fof(f12174,plain,
( spl0_1484
<=> ! [X102,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f2793,axiom,
! [X88,X102] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__insert__Agent_0) ).
fof(f12172,plain,
spl0_1483,
inference(avatar_split_clause,[],[f2725,f12170]) ).
fof(f2725,axiom,
! [X1,X18,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f12168,plain,
spl0_1482,
inference(avatar_split_clause,[],[f2689,f12166]) ).
fof(f12166,plain,
( spl0_1482
<=> ! [X13,X12,X0,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f2689,axiom,
! [X0,X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f12164,plain,
spl0_1481,
inference(avatar_split_clause,[],[f2656,f12162]) ).
fof(f12162,plain,
( spl0_1481
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f2656,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f12154,plain,
spl0_1480,
inference(avatar_split_clause,[],[f2652,f12152]) ).
fof(f12152,plain,
( spl0_1480
<=> ! [X12,X1,X24] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f2652,axiom,
! [X1,X24,X12] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f12150,plain,
spl0_1479,
inference(avatar_split_clause,[],[f2646,f12148]) ).
fof(f12148,plain,
( spl0_1479
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f2646,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f12146,plain,
spl0_1478,
inference(avatar_split_clause,[],[f2645,f12144]) ).
fof(f12144,plain,
( spl0_1478
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f2645,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f12142,plain,
spl0_1477,
inference(avatar_split_clause,[],[f2631,f12140]) ).
fof(f12140,plain,
( spl0_1477
<=> ! [X13,X12,X1] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f2631,axiom,
! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f12138,plain,
spl0_1476,
inference(avatar_split_clause,[],[f2630,f12136]) ).
fof(f12136,plain,
( spl0_1476
<=> ! [X13,X12,X1] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f2630,axiom,
! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f12134,plain,
spl0_1475,
inference(avatar_split_clause,[],[f2622,f12132]) ).
fof(f12132,plain,
( spl0_1475
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f2622,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f12130,plain,
spl0_1474,
inference(avatar_split_clause,[],[f2616,f12128]) ).
fof(f12128,plain,
( spl0_1474
<=> ! [X12,X1,X24] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f2616,axiom,
! [X1,X24,X12] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f12126,plain,
spl0_1473,
inference(avatar_split_clause,[],[f2555,f12124]) ).
fof(f12124,plain,
( spl0_1473
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f2555,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f12122,plain,
spl0_1472,
inference(avatar_split_clause,[],[f2554,f12120]) ).
fof(f12120,plain,
( spl0_1472
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f2554,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f12118,plain,
spl0_1471,
inference(avatar_split_clause,[],[f2552,f12116]) ).
fof(f12116,plain,
( spl0_1471
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f2552,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f12103,plain,
spl0_1470,
inference(avatar_split_clause,[],[f2551,f12101]) ).
fof(f12101,plain,
( spl0_1470
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f2551,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f12099,plain,
spl0_1469,
inference(avatar_split_clause,[],[f2525,f12097]) ).
fof(f12097,plain,
( spl0_1469
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f2525,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f12095,plain,
spl0_1468,
inference(avatar_split_clause,[],[f2524,f12093]) ).
fof(f12093,plain,
( spl0_1468
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f2524,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f12091,plain,
spl0_1467,
inference(avatar_split_clause,[],[f2520,f12089]) ).
fof(f12089,plain,
( spl0_1467
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f2520,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f12087,plain,
spl0_1466,
inference(avatar_split_clause,[],[f2519,f12085]) ).
fof(f12085,plain,
( spl0_1466
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f2519,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f12083,plain,
spl0_1465,
inference(avatar_split_clause,[],[f2387,f12081]) ).
fof(f12081,plain,
( spl0_1465
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f2387,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f12079,plain,
spl0_1464,
inference(avatar_split_clause,[],[f2367,f12077]) ).
fof(f12077,plain,
( spl0_1464
<=> ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f2367,axiom,
! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f12075,plain,
spl0_1463,
inference(avatar_split_clause,[],[f2365,f12073]) ).
fof(f2365,axiom,
! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f12071,plain,
spl0_1462,
inference(avatar_split_clause,[],[f2361,f12069]) ).
fof(f12069,plain,
( spl0_1462
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f2361,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f12067,plain,
spl0_1461,
inference(avatar_split_clause,[],[f2358,f12065]) ).
fof(f12065,plain,
( spl0_1461
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f2358,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f12062,plain,
spl0_1460,
inference(avatar_split_clause,[],[f2347,f12060]) ).
fof(f12060,plain,
( spl0_1460
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f2347,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f12058,plain,
spl0_1459,
inference(avatar_split_clause,[],[f2339,f12056]) ).
fof(f12056,plain,
( spl0_1459
<=> ! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f2339,axiom,
! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f12054,plain,
spl0_1458,
inference(avatar_split_clause,[],[f2295,f12052]) ).
fof(f12052,plain,
( spl0_1458
<=> ! [X0,X21] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f2295,axiom,
! [X21,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f12050,plain,
spl0_1457,
inference(avatar_split_clause,[],[f2282,f12048]) ).
fof(f12048,plain,
( spl0_1457
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f2282,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f12046,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2265,f12044]) ).
fof(f12044,plain,
( spl0_1456
<=> ! [X2,X48,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2265,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f12042,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2264,f12040]) ).
fof(f12040,plain,
( spl0_1455
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2264,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f12038,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2260,f12036]) ).
fof(f12036,plain,
( spl0_1454
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f2260,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f12034,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2259,f12032]) ).
fof(f12032,plain,
( spl0_1453
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f2259,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f12030,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2257,f12028]) ).
fof(f12028,plain,
( spl0_1452
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f2257,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f12026,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2256,f12024]) ).
fof(f12024,plain,
( spl0_1451
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f2256,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f12017,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2254,f12015]) ).
fof(f12015,plain,
( spl0_1450
<=> ! [X48,X1,X0,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f2254,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f12013,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2253,f12011]) ).
fof(f12011,plain,
( spl0_1449
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f2253,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f12009,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2249,f12007]) ).
fof(f12007,plain,
( spl0_1448
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f2249,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f12005,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2248,f12003]) ).
fof(f12003,plain,
( spl0_1447
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2248,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f12001,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2215,f11999]) ).
fof(f11999,plain,
( spl0_1446
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f2215,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f11997,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2212,f11995]) ).
fof(f11995,plain,
( spl0_1445
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f2212,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f11993,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2210,f11991]) ).
fof(f11991,plain,
( spl0_1444
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f2210,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f11989,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2207,f11987]) ).
fof(f11987,plain,
( spl0_1443
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f2207,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f11985,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2206,f11983]) ).
fof(f11983,plain,
( spl0_1442
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f2206,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f11981,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2204,f11979]) ).
fof(f11979,plain,
( spl0_1441
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f2204,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f11977,plain,
( ~ spl0_1440
| ~ spl0_641
| ~ spl0_1128
| ~ spl0_1249 ),
inference(avatar_split_clause,[],[f9806,f9800,f9110,f5917,f11974]) ).
fof(f9800,plain,
( spl0_1249
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f9806,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1128
| ~ spl0_1249 ),
inference(forward_demodulation,[],[f9805,f9111]) ).
fof(f9805,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1249 ),
inference(superposition,[],[f9801,f5919]) ).
fof(f9801,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1249 ),
inference(avatar_component_clause,[],[f9800]) ).
fof(f11972,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2203,f11970]) ).
fof(f11970,plain,
( spl0_1439
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f2203,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f11968,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2202,f11966]) ).
fof(f11966,plain,
( spl0_1438
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f2202,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f11964,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2201,f11962]) ).
fof(f11962,plain,
( spl0_1437
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f2201,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f11960,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2200,f11958]) ).
fof(f11958,plain,
( spl0_1436
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f2200,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f11956,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2184,f11954]) ).
fof(f11954,plain,
( spl0_1435
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f2184,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f11952,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2110,f11950]) ).
fof(f11950,plain,
( spl0_1434
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f2110,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f11948,plain,
spl0_1433,
inference(avatar_split_clause,[],[f2109,f11946]) ).
fof(f11946,plain,
( spl0_1433
<=> ! [X11,X3,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f2109,axiom,
! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f11944,plain,
spl0_1432,
inference(avatar_split_clause,[],[f2045,f11942]) ).
fof(f11942,plain,
( spl0_1432
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f2045,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f11940,plain,
spl0_1431,
inference(avatar_split_clause,[],[f2044,f11938]) ).
fof(f11938,plain,
( spl0_1431
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f2044,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f11936,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1852,f11934]) ).
fof(f11934,plain,
( spl0_1430
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f1852,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f11927,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1799,f11925]) ).
fof(f11925,plain,
( spl0_1429
<=> ! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f1799,axiom,
! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f11923,plain,
spl0_1428,
inference(avatar_split_clause,[],[f1765,f11921]) ).
fof(f11921,plain,
( spl0_1428
<=> ! [X0,X12,X1] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1765,axiom,
! [X0,X1,X12] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f11919,plain,
spl0_1427,
inference(avatar_split_clause,[],[f1748,f11917]) ).
fof(f11917,plain,
( spl0_1427
<=> ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f1748,axiom,
! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f11915,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1742,f11913]) ).
fof(f11913,plain,
( spl0_1426
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f1742,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f11911,plain,
spl0_1425,
inference(avatar_split_clause,[],[f1702,f11909]) ).
fof(f11909,plain,
( spl0_1425
<=> ! [X43,X3,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f1702,axiom,
! [X21,X3,X1,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f11907,plain,
spl0_1424,
inference(avatar_split_clause,[],[f1604,f11905]) ).
fof(f11905,plain,
( spl0_1424
<=> ! [X43,X0,X23,X1] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f1604,axiom,
! [X0,X1,X23,X43] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f11903,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1591,f11901]) ).
fof(f11901,plain,
( spl0_1423
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f1591,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f11899,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1589,f11897]) ).
fof(f11897,plain,
( spl0_1422
<=> ! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f1589,axiom,
! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f11895,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1581,f11893]) ).
fof(f11893,plain,
( spl0_1421
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1581,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f11891,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1580,f11889]) ).
fof(f1580,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f11883,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1578,f11881]) ).
fof(f11881,plain,
( spl0_1419
<=> ! [X59,X43,X15] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f1578,axiom,
! [X59,X15,X43] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f11879,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1576,f11877]) ).
fof(f11877,plain,
( spl0_1418
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f1576,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f11875,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1575,f11873]) ).
fof(f11873,plain,
( spl0_1417
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f1575,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f11871,plain,
spl0_1416,
inference(avatar_split_clause,[],[f1475,f11869]) ).
fof(f11869,plain,
( spl0_1416
<=> ! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f1475,axiom,
! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f11867,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1416,f11865]) ).
fof(f11865,plain,
( spl0_1415
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1416,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f11863,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1305,f11861]) ).
fof(f11861,plain,
( spl0_1414
<=> ! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f1305,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f11859,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1304,f11857]) ).
fof(f11857,plain,
( spl0_1413
<=> ! [X16,X21,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f1304,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f11855,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1291,f11853]) ).
fof(f11853,plain,
( spl0_1412
<=> ! [X12,X1,X18] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1291,axiom,
! [X1,X18,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f11851,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1287,f11849]) ).
fof(f11849,plain,
( spl0_1411
<=> ! [X20,X1,X19] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1287,axiom,
! [X1,X19,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f11847,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1286,f11845]) ).
fof(f11845,plain,
( spl0_1410
<=> ! [X20,X1,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1286,axiom,
! [X1,X19,X20] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f11841,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1285,f11839]) ).
fof(f11839,plain,
( spl0_1409
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1285,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f11837,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1284,f11835]) ).
fof(f11835,plain,
( spl0_1408
<=> ! [X12,X1] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1284,axiom,
! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f11833,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1276,f11831]) ).
fof(f11831,plain,
( spl0_1407
<=> ! [X12,X1] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f1276,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f11829,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1223,f11827]) ).
fof(f11827,plain,
( spl0_1406
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1223,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f11825,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1221,f11823]) ).
fof(f11823,plain,
( spl0_1405
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1221,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f11821,plain,
spl0_1404,
inference(avatar_split_clause,[],[f111,f11819]) ).
fof(f11819,plain,
( spl0_1404
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f111,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f11817,plain,
spl0_1403,
inference(avatar_split_clause,[],[f108,f11815]) ).
fof(f11815,plain,
( spl0_1403
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f108,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11813,plain,
spl0_1402,
inference(avatar_split_clause,[],[f104,f11811]) ).
fof(f11811,plain,
( spl0_1402
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f104,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f11809,plain,
spl0_1401,
inference(avatar_split_clause,[],[f100,f11807]) ).
fof(f11807,plain,
( spl0_1401
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f100,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f11805,plain,
spl0_1400,
inference(avatar_split_clause,[],[f97,f11803]) ).
fof(f11803,plain,
( spl0_1400
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f97,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f11801,plain,
spl0_1399,
inference(avatar_split_clause,[],[f29,f11799]) ).
fof(f11799,plain,
( spl0_1399
<=> ! [X12,X1,X18] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f29,axiom,
! [X1,X18,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11251,plain,
( spl0_1398
| ~ spl0_718
| ~ spl0_1145 ),
inference(avatar_split_clause,[],[f9471,f9178,f7024,f11249]) ).
fof(f11249,plain,
( spl0_1398
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f7024,plain,
( spl0_718
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f9178,plain,
( spl0_1145
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f9471,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_718
| ~ spl0_1145 ),
inference(superposition,[],[f9179,f7025]) ).
fof(f7025,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f7024]) ).
fof(f9179,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f9178]) ).
fof(f11029,plain,
( spl0_1397
| ~ spl0_644
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9388,f9057,f5931,f11027]) ).
fof(f11027,plain,
( spl0_1397
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f5931,plain,
( spl0_644
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f9057,plain,
( spl0_1115
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f9388,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_644
| ~ spl0_1115 ),
inference(resolution,[],[f9058,f5932]) ).
fof(f5932,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f5931]) ).
fof(f9058,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1115 ),
inference(avatar_component_clause,[],[f9057]) ).
fof(f10964,plain,
( spl0_1396
| ~ spl0_644
| ~ spl0_1112 ),
inference(avatar_split_clause,[],[f9378,f9044,f5931,f10962]) ).
fof(f10962,plain,
( spl0_1396
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f9044,plain,
( spl0_1112
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f9378,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_644
| ~ spl0_1112 ),
inference(resolution,[],[f9045,f5932]) ).
fof(f9045,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1112 ),
inference(avatar_component_clause,[],[f9044]) ).
fof(f10828,plain,
( spl0_1395
| ~ spl0_1074
| ~ spl0_1267 ),
inference(avatar_split_clause,[],[f10818,f10269,f8687,f10826]) ).
fof(f10826,plain,
( spl0_1395
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f8687,plain,
( spl0_1074
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f10269,plain,
( spl0_1267
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f10818,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1074
| ~ spl0_1267 ),
inference(resolution,[],[f10270,f8688]) ).
fof(f8688,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1074 ),
inference(avatar_component_clause,[],[f8687]) ).
fof(f10270,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1267 ),
inference(avatar_component_clause,[],[f10269]) ).
fof(f10793,plain,
spl0_1394,
inference(avatar_split_clause,[],[f3204,f10791]) ).
fof(f10791,plain,
( spl0_1394
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f3204,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3203,f2115]) ).
fof(f3203,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3003,f2830]) ).
fof(f3003,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1338,f2129]) ).
fof(f1338,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10789,plain,
spl0_1393,
inference(avatar_split_clause,[],[f3132,f10787]) ).
fof(f10787,plain,
( spl0_1393
<=> ! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f3132,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f3131,f2156]) ).
fof(f3131,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f3130,f2154]) ).
fof(f3130,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f1878,f2156]) ).
fof(f1878,axiom,
! [X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10785,plain,
spl0_1392,
inference(avatar_split_clause,[],[f3125,f10783]) ).
fof(f3125,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3124,f2156]) ).
fof(f3124,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3123,f2154]) ).
fof(f3123,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1328,f2156]) ).
fof(f1328,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10778,plain,
spl0_1391,
inference(avatar_split_clause,[],[f2944,f10776]) ).
fof(f10776,plain,
( spl0_1391
<=> ! [X13,X12,X1] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f2944,plain,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2599,f2373]) ).
fof(f2599,axiom,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10774,plain,
spl0_1390,
inference(avatar_split_clause,[],[f2943,f10772]) ).
fof(f10772,plain,
( spl0_1390
<=> ! [X13,X12,X1] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f2943,plain,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2598,f2373]) ).
fof(f2598,axiom,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10770,plain,
spl0_1389,
inference(avatar_split_clause,[],[f2938,f10768]) ).
fof(f10768,plain,
( spl0_1389
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f2938,plain,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
inference(definition_unfolding,[],[f2346,f2544]) ).
fof(f2346,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10766,plain,
spl0_1388,
inference(avatar_split_clause,[],[f2867,f10764]) ).
fof(f2867,plain,
! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1372,f2544]) ).
fof(f1372,axiom,
! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10762,plain,
spl0_1387,
inference(avatar_split_clause,[],[f2864,f10760]) ).
fof(f10760,plain,
( spl0_1387
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f2864,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1),
inference(definition_unfolding,[],[f2578,f2373]) ).
fof(f2578,axiom,
! [X1,X12] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10758,plain,
spl0_1386,
inference(avatar_split_clause,[],[f2863,f10756]) ).
fof(f10756,plain,
( spl0_1386
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f2863,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2579,f2373]) ).
fof(f2579,axiom,
! [X1,X12] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10754,plain,
spl0_1385,
inference(avatar_split_clause,[],[f2824,f10752]) ).
fof(f2824,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).
fof(f10750,plain,
spl0_1384,
inference(avatar_split_clause,[],[f2823,f10748]) ).
fof(f10748,plain,
( spl0_1384
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f2823,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OBody_0) ).
fof(f10746,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2780,f10744]) ).
fof(f10744,plain,
( spl0_1383
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f2780,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
fof(f10742,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2779,f10740]) ).
fof(f10740,plain,
( spl0_1382
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f2779,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
fof(f10737,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2771,f10735]) ).
fof(f10735,plain,
( spl0_1381
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f2771,axiom,
! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
fof(f10733,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2768,f10731]) ).
fof(f10731,plain,
( spl0_1380
<=> ! [X20,X88] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f2768,axiom,
! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
fof(f10729,plain,
spl0_1379,
inference(avatar_split_clause,[],[f2742,f10727]) ).
fof(f10727,plain,
( spl0_1379
<=> ! [X93,X88] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f2742,axiom,
! [X88,X93] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
fof(f10725,plain,
spl0_1378,
inference(avatar_split_clause,[],[f2729,f10723]) ).
fof(f10723,plain,
( spl0_1378
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f2729,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
fof(f10721,plain,
spl0_1377,
inference(avatar_split_clause,[],[f2728,f10719]) ).
fof(f10719,plain,
( spl0_1377
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f2728,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
fof(f10717,plain,
spl0_1376,
inference(avatar_split_clause,[],[f2703,f10715]) ).
fof(f10715,plain,
( spl0_1376
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f2703,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10713,plain,
spl0_1375,
inference(avatar_split_clause,[],[f2701,f10711]) ).
fof(f10711,plain,
( spl0_1375
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f2701,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10709,plain,
spl0_1374,
inference(avatar_split_clause,[],[f2692,f10707]) ).
fof(f10707,plain,
( spl0_1374
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f2692,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
fof(f10705,plain,
spl0_1373,
inference(avatar_split_clause,[],[f2688,f10703]) ).
fof(f10703,plain,
( spl0_1373
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f2688,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10701,plain,
spl0_1372,
inference(avatar_split_clause,[],[f2676,f10699]) ).
fof(f10699,plain,
( spl0_1372
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f2676,axiom,
! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10693,plain,
spl0_1371,
inference(avatar_split_clause,[],[f2670,f10691]) ).
fof(f10691,plain,
( spl0_1371
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f2670,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10689,plain,
spl0_1370,
inference(avatar_split_clause,[],[f2653,f10687]) ).
fof(f10687,plain,
( spl0_1370
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f2653,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10685,plain,
spl0_1369,
inference(avatar_split_clause,[],[f2628,f10683]) ).
fof(f10683,plain,
( spl0_1369
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f2628,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10681,plain,
spl0_1368,
inference(avatar_split_clause,[],[f2627,f10679]) ).
fof(f10679,plain,
( spl0_1368
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f2627,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10677,plain,
spl0_1367,
inference(avatar_split_clause,[],[f2617,f10675]) ).
fof(f10675,plain,
( spl0_1367
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f2617,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10673,plain,
spl0_1366,
inference(avatar_split_clause,[],[f2614,f10671]) ).
fof(f10671,plain,
( spl0_1366
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f2614,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10669,plain,
spl0_1365,
inference(avatar_split_clause,[],[f2595,f10667]) ).
fof(f10667,plain,
( spl0_1365
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f2595,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10665,plain,
spl0_1364,
inference(avatar_split_clause,[],[f2594,f10663]) ).
fof(f10663,plain,
( spl0_1364
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f2594,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10661,plain,
spl0_1363,
inference(avatar_split_clause,[],[f2592,f10659]) ).
fof(f10659,plain,
( spl0_1363
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f2592,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10657,plain,
spl0_1362,
inference(avatar_split_clause,[],[f2591,f10655]) ).
fof(f10655,plain,
( spl0_1362
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f2591,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10653,plain,
spl0_1361,
inference(avatar_split_clause,[],[f2581,f10651]) ).
fof(f10651,plain,
( spl0_1361
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f2581,axiom,
! [X1,X12,X13] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10649,plain,
spl0_1360,
inference(avatar_split_clause,[],[f2570,f10647]) ).
fof(f10647,plain,
( spl0_1360
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f2570,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10645,plain,
spl0_1359,
inference(avatar_split_clause,[],[f2569,f10643]) ).
fof(f10643,plain,
( spl0_1359
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f2569,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10641,plain,
spl0_1358,
inference(avatar_split_clause,[],[f2568,f10639]) ).
fof(f10639,plain,
( spl0_1358
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f2568,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10637,plain,
spl0_1357,
inference(avatar_split_clause,[],[f2559,f10635]) ).
fof(f10635,plain,
( spl0_1357
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f2559,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10633,plain,
spl0_1356,
inference(avatar_split_clause,[],[f2558,f10631]) ).
fof(f10631,plain,
( spl0_1356
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f2558,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10629,plain,
spl0_1355,
inference(avatar_split_clause,[],[f2557,f10627]) ).
fof(f10627,plain,
( spl0_1355
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f2557,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10625,plain,
spl0_1354,
inference(avatar_split_clause,[],[f2550,f10623]) ).
fof(f10623,plain,
( spl0_1354
<=> ! [X16,X1,X26] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f2550,axiom,
! [X1,X26,X16] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10621,plain,
spl0_1353,
inference(avatar_split_clause,[],[f2546,f10619]) ).
fof(f10619,plain,
( spl0_1353
<=> ! [X14,X26] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f2546,axiom,
! [X26,X14] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10617,plain,
spl0_1352,
inference(avatar_split_clause,[],[f2543,f10615]) ).
fof(f10615,plain,
( spl0_1352
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f2543,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10610,plain,
spl0_1351,
inference(avatar_split_clause,[],[f2537,f10608]) ).
fof(f10608,plain,
( spl0_1351
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f2537,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10606,plain,
spl0_1350,
inference(avatar_split_clause,[],[f2536,f10604]) ).
fof(f10604,plain,
( spl0_1350
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f2536,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10602,plain,
spl0_1349,
inference(avatar_split_clause,[],[f2535,f10600]) ).
fof(f10600,plain,
( spl0_1349
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f2535,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10598,plain,
spl0_1348,
inference(avatar_split_clause,[],[f2531,f10596]) ).
fof(f10596,plain,
( spl0_1348
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f2531,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10594,plain,
spl0_1347,
inference(avatar_split_clause,[],[f2530,f10592]) ).
fof(f10592,plain,
( spl0_1347
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f2530,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10590,plain,
spl0_1346,
inference(avatar_split_clause,[],[f2529,f10588]) ).
fof(f10588,plain,
( spl0_1346
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f2529,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10586,plain,
spl0_1345,
inference(avatar_split_clause,[],[f2523,f10584]) ).
fof(f10584,plain,
( spl0_1345
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f2523,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10582,plain,
spl0_1344,
inference(avatar_split_clause,[],[f2518,f10580]) ).
fof(f10580,plain,
( spl0_1344
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f2518,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10578,plain,
spl0_1343,
inference(avatar_split_clause,[],[f2517,f10576]) ).
fof(f10576,plain,
( spl0_1343
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f2517,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10574,plain,
spl0_1342,
inference(avatar_split_clause,[],[f2516,f10572]) ).
fof(f10572,plain,
( spl0_1342
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f2516,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10570,plain,
spl0_1341,
inference(avatar_split_clause,[],[f2515,f10568]) ).
fof(f10568,plain,
( spl0_1341
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f2515,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10566,plain,
spl0_1340,
inference(avatar_split_clause,[],[f2514,f10564]) ).
fof(f10564,plain,
( spl0_1340
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f2514,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10562,plain,
spl0_1339,
inference(avatar_split_clause,[],[f2302,f10560]) ).
fof(f10560,plain,
( spl0_1339
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f2302,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10558,plain,
spl0_1338,
inference(avatar_split_clause,[],[f2301,f10556]) ).
fof(f10556,plain,
( spl0_1338
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f2301,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10554,plain,
spl0_1337,
inference(avatar_split_clause,[],[f2300,f10552]) ).
fof(f10552,plain,
( spl0_1337
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f2300,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10550,plain,
spl0_1336,
inference(avatar_split_clause,[],[f2299,f10548]) ).
fof(f10548,plain,
( spl0_1336
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f2299,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10546,plain,
spl0_1335,
inference(avatar_split_clause,[],[f2296,f10544]) ).
fof(f10544,plain,
( spl0_1335
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f2296,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10542,plain,
spl0_1334,
inference(avatar_split_clause,[],[f2289,f10540]) ).
fof(f10540,plain,
( spl0_1334
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f2289,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10538,plain,
spl0_1333,
inference(avatar_split_clause,[],[f2288,f10536]) ).
fof(f10536,plain,
( spl0_1333
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f2288,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10534,plain,
spl0_1332,
inference(avatar_split_clause,[],[f2287,f10532]) ).
fof(f10532,plain,
( spl0_1332
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f2287,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10530,plain,
spl0_1331,
inference(avatar_split_clause,[],[f2286,f10528]) ).
fof(f10528,plain,
( spl0_1331
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f2286,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10526,plain,
spl0_1330,
inference(avatar_split_clause,[],[f2283,f10524]) ).
fof(f10524,plain,
( spl0_1330
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f2283,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10522,plain,
spl0_1329,
inference(avatar_split_clause,[],[f2277,f10520]) ).
fof(f10520,plain,
( spl0_1329
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f2277,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10518,plain,
spl0_1328,
inference(avatar_split_clause,[],[f2276,f10516]) ).
fof(f10516,plain,
( spl0_1328
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f2276,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10514,plain,
spl0_1327,
inference(avatar_split_clause,[],[f2275,f10512]) ).
fof(f10512,plain,
( spl0_1327
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f2275,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10510,plain,
spl0_1326,
inference(avatar_split_clause,[],[f2274,f10508]) ).
fof(f10508,plain,
( spl0_1326
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f2274,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10506,plain,
spl0_1325,
inference(avatar_split_clause,[],[f2234,f10504]) ).
fof(f10504,plain,
( spl0_1325
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f2234,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10502,plain,
spl0_1324,
inference(avatar_split_clause,[],[f2233,f10500]) ).
fof(f10500,plain,
( spl0_1324
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f2233,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10498,plain,
spl0_1323,
inference(avatar_split_clause,[],[f2230,f10496]) ).
fof(f10496,plain,
( spl0_1323
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f2230,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10494,plain,
spl0_1322,
inference(avatar_split_clause,[],[f2229,f10492]) ).
fof(f10492,plain,
( spl0_1322
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f2229,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10490,plain,
( spl0_1321
| ~ spl0_709
| ~ spl0_785
| ~ spl0_1071 ),
inference(avatar_split_clause,[],[f8906,f8675,f7310,f6985,f10487]) ).
fof(f8675,plain,
( spl0_1071
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f8906,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_709
| ~ spl0_785
| ~ spl0_1071 ),
inference(forward_demodulation,[],[f8903,f6987]) ).
fof(f8903,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_785
| ~ spl0_1071 ),
inference(superposition,[],[f8676,f7312]) ).
fof(f8676,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1071 ),
inference(avatar_component_clause,[],[f8675]) ).
fof(f10485,plain,
spl0_1320,
inference(avatar_split_clause,[],[f2227,f10483]) ).
fof(f10483,plain,
( spl0_1320
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f2227,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10481,plain,
spl0_1319,
inference(avatar_split_clause,[],[f2224,f10479]) ).
fof(f10479,plain,
( spl0_1319
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f2224,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10477,plain,
spl0_1318,
inference(avatar_split_clause,[],[f2223,f10475]) ).
fof(f10475,plain,
( spl0_1318
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f2223,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10473,plain,
spl0_1317,
inference(avatar_split_clause,[],[f2222,f10471]) ).
fof(f2222,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10469,plain,
spl0_1316,
inference(avatar_split_clause,[],[f2221,f10467]) ).
fof(f2221,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10465,plain,
spl0_1315,
inference(avatar_split_clause,[],[f2167,f10463]) ).
fof(f10463,plain,
( spl0_1315
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f2167,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10461,plain,
spl0_1314,
inference(avatar_split_clause,[],[f2166,f10459]) ).
fof(f10459,plain,
( spl0_1314
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f2166,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10457,plain,
spl0_1313,
inference(avatar_split_clause,[],[f2086,f10455]) ).
fof(f10455,plain,
( spl0_1313
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f2086,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10453,plain,
spl0_1312,
inference(avatar_split_clause,[],[f2081,f10451]) ).
fof(f10451,plain,
( spl0_1312
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f2081,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10449,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2065,f10447]) ).
fof(f10447,plain,
( spl0_1311
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f2065,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10445,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1850,f10443]) ).
fof(f1850,axiom,
! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10441,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1813,f10439]) ).
fof(f10439,plain,
( spl0_1309
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1813,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10437,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1807,f10435]) ).
fof(f10435,plain,
( spl0_1308
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1807,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10433,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1806,f10431]) ).
fof(f10431,plain,
( spl0_1307
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1806,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10429,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1784,f10427]) ).
fof(f10427,plain,
( spl0_1306
<=> ! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1784,axiom,
! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10425,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1743,f10423]) ).
fof(f10423,plain,
( spl0_1305
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1743,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10421,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1737,f10419]) ).
fof(f10419,plain,
( spl0_1304
<=> ! [X1,X3] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1737,axiom,
! [X3,X1] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10417,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1626,f10415]) ).
fof(f10415,plain,
( spl0_1303
<=> ! [X18,X42,X64,X63,X1] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1626,axiom,
! [X1,X18,X63,X42,X64] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10413,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1625,f10411]) ).
fof(f10411,plain,
( spl0_1302
<=> ! [X18,X42,X64,X63,X1] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1625,axiom,
! [X18,X1,X63,X42,X64] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10409,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1610,f10407]) ).
fof(f10407,plain,
( spl0_1301
<=> ! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1610,axiom,
! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10405,plain,
( spl0_1299
| ~ spl0_1300
| ~ spl0_787
| ~ spl0_1039 ),
inference(avatar_split_clause,[],[f8857,f8546,f7319,f10402,f10399]) ).
fof(f10399,plain,
( spl0_1299
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f10402,plain,
( spl0_1300
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f7319,plain,
( spl0_787
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f8546,plain,
( spl0_1039
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f8857,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_787
| ~ spl0_1039 ),
inference(superposition,[],[f8547,f7320]) ).
fof(f7320,plain,
( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
| ~ spl0_787 ),
inference(avatar_component_clause,[],[f7319]) ).
fof(f8547,plain,
( ! [X3,X0] :
( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1039 ),
inference(avatar_component_clause,[],[f8546]) ).
fof(f10397,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1552,f10395]) ).
fof(f10395,plain,
( spl0_1298
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1552,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10393,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1530,f10391]) ).
fof(f10391,plain,
( spl0_1297
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1530,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10389,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1493,f10387]) ).
fof(f10387,plain,
( spl0_1296
<=> ! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1493,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10385,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1492,f10383]) ).
fof(f10383,plain,
( spl0_1295
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1492,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10381,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1485,f10379]) ).
fof(f10379,plain,
( spl0_1294
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1485,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10376,plain,
( spl0_1293
| ~ spl0_889
| ~ spl0_1292 ),
inference(avatar_split_clause,[],[f10372,f10369,f7801,f10374]) ).
fof(f10374,plain,
( spl0_1293
<=> ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f7801,plain,
( spl0_889
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f10369,plain,
( spl0_1292
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f10372,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_889
| ~ spl0_1292 ),
inference(forward_demodulation,[],[f10370,f7803]) ).
fof(f7803,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_889 ),
inference(avatar_component_clause,[],[f7801]) ).
fof(f10370,plain,
( ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1292 ),
inference(avatar_component_clause,[],[f10369]) ).
fof(f10371,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1484,f10369]) ).
fof(f1484,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10367,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1477,f10365]) ).
fof(f10365,plain,
( spl0_1291
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1477,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10363,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1476,f10361]) ).
fof(f10361,plain,
( spl0_1290
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1476,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10359,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1457,f10357]) ).
fof(f10357,plain,
( spl0_1289
<=> ! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1457,axiom,
! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10355,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1442,f10353]) ).
fof(f10353,plain,
( spl0_1288
<=> ! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1442,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10351,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1413,f10349]) ).
fof(f10349,plain,
( spl0_1287
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1413,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f10347,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1412,f10345]) ).
fof(f10345,plain,
( spl0_1286
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1412,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f10343,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1409,f10341]) ).
fof(f10341,plain,
( spl0_1285
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1409,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f10339,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1408,f10337]) ).
fof(f10337,plain,
( spl0_1284
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1408,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f10335,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1406,f10333]) ).
fof(f10333,plain,
( spl0_1283
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1406,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f10331,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1400,f10329]) ).
fof(f10329,plain,
( spl0_1282
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f1400,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f10327,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1399,f10325]) ).
fof(f10325,plain,
( spl0_1281
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1399,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f10323,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1398,f10321]) ).
fof(f10321,plain,
( spl0_1280
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1398,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f10319,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1397,f10317]) ).
fof(f1397,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f10315,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1361,f10313]) ).
fof(f10313,plain,
( spl0_1278
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1361,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f10311,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1356,f10309]) ).
fof(f10309,plain,
( spl0_1277
<=> ! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1356,axiom,
! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f10307,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1342,f10305]) ).
fof(f10305,plain,
( spl0_1276
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1342,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f10303,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1341,f10301]) ).
fof(f10301,plain,
( spl0_1275
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1341,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f10299,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1243,f10297]) ).
fof(f10297,plain,
( spl0_1274
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1243,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f10295,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1233,f10293]) ).
fof(f10293,plain,
( spl0_1273
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1233,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f10291,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1232,f10289]) ).
fof(f10289,plain,
( spl0_1272
<=> ! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1232,axiom,
! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f10287,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1191,f10285]) ).
fof(f10285,plain,
( spl0_1271
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1191,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f10283,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1189,f10281]) ).
fof(f10281,plain,
( spl0_1270
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f1189,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f10279,plain,
( spl0_1269
| ~ spl0_753
| ~ spl0_1004 ),
inference(avatar_split_clause,[],[f8764,f8405,f7182,f10277]) ).
fof(f10277,plain,
( spl0_1269
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f7182,plain,
( spl0_753
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f8405,plain,
( spl0_1004
<=> ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f8764,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_753
| ~ spl0_1004 ),
inference(superposition,[],[f8406,f7183]) ).
fof(f7183,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_753 ),
inference(avatar_component_clause,[],[f7182]) ).
fof(f8406,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_1004 ),
inference(avatar_component_clause,[],[f8405]) ).
fof(f10275,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1185,f10273]) ).
fof(f10273,plain,
( spl0_1268
<=> ! [X2,X18,X27,X1] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1185,axiom,
! [X2,X18,X1,X27] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f10271,plain,
spl0_1267,
inference(avatar_split_clause,[],[f110,f10269]) ).
fof(f110,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10267,plain,
spl0_1266,
inference(avatar_split_clause,[],[f109,f10265]) ).
fof(f10265,plain,
( spl0_1266
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f109,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10263,plain,
spl0_1265,
inference(avatar_split_clause,[],[f49,f10261]) ).
fof(f10261,plain,
( spl0_1265
<=> ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f49,axiom,
! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10259,plain,
spl0_1264,
inference(avatar_split_clause,[],[f2,f10257]) ).
fof(f10257,plain,
( spl0_1264
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10255,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1,f10253]) ).
fof(f10253,plain,
( spl0_1263
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10157,plain,
( ~ spl0_1261
| spl0_1262
| ~ spl0_775
| ~ spl0_1223 ),
inference(avatar_split_clause,[],[f10068,f9695,f7270,f10155,f10151]) ).
fof(f10151,plain,
( spl0_1261
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f10155,plain,
( spl0_1262
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f7270,plain,
( spl0_775
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f9695,plain,
( spl0_1223
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f10068,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_775
| ~ spl0_1223 ),
inference(trivial_inequality_removal,[],[f10061]) ).
fof(f10061,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_775
| ~ spl0_1223 ),
inference(superposition,[],[f9696,f7271]) ).
fof(f7271,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_775 ),
inference(avatar_component_clause,[],[f7270]) ).
fof(f9696,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1223 ),
inference(avatar_component_clause,[],[f9695]) ).
fof(f9931,plain,
( spl0_1260
| ~ spl0_52
| ~ spl0_984 ),
inference(avatar_split_clause,[],[f8329,f8198,f3508,f9928]) ).
fof(f8198,plain,
( spl0_984
<=> ! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f8329,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_984 ),
inference(resolution,[],[f8199,f3510]) ).
fof(f8199,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_984 ),
inference(avatar_component_clause,[],[f8198]) ).
fof(f9881,plain,
( spl0_1259
| ~ spl0_879
| ~ spl0_968 ),
inference(avatar_split_clause,[],[f8311,f8131,f7699,f9878]) ).
fof(f9878,plain,
( spl0_1259
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f8311,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_879
| ~ spl0_968 ),
inference(superposition,[],[f7700,f8133]) ).
fof(f9872,plain,
( spl0_1258
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1182 ),
inference(avatar_split_clause,[],[f9533,f9530,f8526,f3508,f9870]) ).
fof(f9870,plain,
( spl0_1258
<=> ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f9530,plain,
( spl0_1182
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f9533,plain,
( ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1182 ),
inference(forward_demodulation,[],[f9531,f8848]) ).
fof(f9531,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) )
| ~ spl0_1182 ),
inference(avatar_component_clause,[],[f9530]) ).
fof(f9838,plain,
( spl0_1257
| ~ spl0_87
| ~ spl0_956 ),
inference(avatar_split_clause,[],[f8295,f8083,f3683,f9836]) ).
fof(f9836,plain,
( spl0_1257
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f3683,plain,
( spl0_87
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f8083,plain,
( spl0_956
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f8295,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_87
| ~ spl0_956 ),
inference(resolution,[],[f8084,f3685]) ).
fof(f3685,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_87 ),
inference(avatar_component_clause,[],[f3683]) ).
fof(f8084,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_956 ),
inference(avatar_component_clause,[],[f8083]) ).
fof(f9834,plain,
spl0_1256,
inference(avatar_split_clause,[],[f3150,f9832]) ).
fof(f9832,plain,
( spl0_1256
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f3150,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ),
inference(forward_demodulation,[],[f2970,f2831]) ).
fof(f2970,plain,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2096,f2544]) ).
fof(f2096,axiom,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9830,plain,
spl0_1255,
inference(avatar_split_clause,[],[f3149,f9828]) ).
fof(f9828,plain,
( spl0_1255
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f3149,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f2969,f2831]) ).
fof(f2969,plain,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2095,f2544]) ).
fof(f2095,axiom,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9826,plain,
spl0_1254,
inference(avatar_split_clause,[],[f3145,f9824]) ).
fof(f9824,plain,
( spl0_1254
<=> ! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f3145,plain,
! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ),
inference(forward_demodulation,[],[f2958,f2831]) ).
fof(f2958,plain,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2340,f2544]) ).
fof(f2340,axiom,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9822,plain,
spl0_1253,
inference(avatar_split_clause,[],[f3079,f9820]) ).
fof(f3079,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2882,f2831]) ).
fof(f2882,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2764,f2544]) ).
fof(f2764,axiom,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__5_0) ).
fof(f9818,plain,
spl0_1252,
inference(avatar_split_clause,[],[f3075,f9816]) ).
fof(f3075,plain,
! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2871,f2867]) ).
fof(f2871,plain,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(definition_unfolding,[],[f38,f2544]) ).
fof(f38,axiom,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9814,plain,
spl0_1251,
inference(avatar_split_clause,[],[f3071,f9812]) ).
fof(f9812,plain,
( spl0_1251
<=> ! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f3071,plain,
! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2869,f2846]) ).
fof(f2869,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2131,f2113,f2113]) ).
fof(f2131,axiom,
! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9810,plain,
spl0_1250,
inference(avatar_split_clause,[],[f2870,f9808]) ).
fof(f9808,plain,
( spl0_1250
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f2870,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f2123,f2129,f2129]) ).
fof(f2123,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9802,plain,
( spl0_1249
| ~ spl0_1248 ),
inference(avatar_split_clause,[],[f9798,f9795,f9800]) ).
fof(f9795,plain,
( spl0_1248
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f9798,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1248 ),
inference(forward_demodulation,[],[f9796,f2867]) ).
fof(f9796,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1248 ),
inference(avatar_component_clause,[],[f9795]) ).
fof(f9797,plain,
spl0_1248,
inference(avatar_split_clause,[],[f2859,f9795]) ).
fof(f2859,plain,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1394,f2544]) ).
fof(f1394,axiom,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9793,plain,
( spl0_1247
| ~ spl0_53
| ~ spl0_956 ),
inference(avatar_split_clause,[],[f8294,f8083,f3513,f9791]) ).
fof(f3513,plain,
( spl0_53
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f8294,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_53
| ~ spl0_956 ),
inference(resolution,[],[f8084,f3515]) ).
fof(f3515,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f3513]) ).
fof(f9789,plain,
spl0_1246,
inference(avatar_split_clause,[],[f2822,f9787]) ).
fof(f9787,plain,
( spl0_1246
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f2822,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__synthD__dest_0) ).
fof(f9785,plain,
spl0_1245,
inference(avatar_split_clause,[],[f2817,f9783]) ).
fof(f9783,plain,
( spl0_1245
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f2817,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OHash_0) ).
fof(f9781,plain,
spl0_1244,
inference(avatar_split_clause,[],[f2783,f9779]) ).
fof(f9779,plain,
( spl0_1244
<=> ! [X88,X7] :
( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f2783,axiom,
! [X88,X7] :
( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONonce__synth__eq_0) ).
fof(f9777,plain,
spl0_1243,
inference(avatar_split_clause,[],[f2777,f9775]) ).
fof(f9775,plain,
( spl0_1243
<=> ! [X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f2777,axiom,
! [X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OKey__synth__eq_0) ).
fof(f9773,plain,
spl0_1242,
inference(avatar_split_clause,[],[f2715,f9771]) ).
fof(f9771,plain,
( spl0_1242
<=> ! [X5,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f2715,axiom,
! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9769,plain,
spl0_1241,
inference(avatar_split_clause,[],[f2713,f9767]) ).
fof(f9767,plain,
( spl0_1241
<=> ! [X5,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f2713,axiom,
! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9765,plain,
spl0_1240,
inference(avatar_split_clause,[],[f2685,f9763]) ).
fof(f9763,plain,
( spl0_1240
<=> ! [X18,X12,X27,X1] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f2685,axiom,
! [X18,X1,X27,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9761,plain,
spl0_1239,
inference(avatar_split_clause,[],[f2642,f9759]) ).
fof(f9759,plain,
( spl0_1239
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f2642,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9757,plain,
spl0_1238,
inference(avatar_split_clause,[],[f2641,f9755]) ).
fof(f9755,plain,
( spl0_1238
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f2641,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9753,plain,
spl0_1237,
inference(avatar_split_clause,[],[f2583,f9751]) ).
fof(f9751,plain,
( spl0_1237
<=> ! [X12,X1,X4] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f2583,axiom,
! [X1,X4,X12] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9749,plain,
( spl0_1236
| ~ spl0_87
| ~ spl0_955 ),
inference(avatar_split_clause,[],[f8289,f8079,f3683,f9747]) ).
fof(f9747,plain,
( spl0_1236
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f8079,plain,
( spl0_955
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f8289,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_87
| ~ spl0_955 ),
inference(resolution,[],[f8080,f3685]) ).
fof(f8080,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_955 ),
inference(avatar_component_clause,[],[f8079]) ).
fof(f9745,plain,
spl0_1235,
inference(avatar_split_clause,[],[f2582,f9743]) ).
fof(f9743,plain,
( spl0_1235
<=> ! [X12,X1,X4] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f2582,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9741,plain,
spl0_1234,
inference(avatar_split_clause,[],[f2545,f9739]) ).
fof(f9739,plain,
( spl0_1234
<=> ! [X14,X26] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f2545,axiom,
! [X26,X14] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9737,plain,
spl0_1233,
inference(avatar_split_clause,[],[f2542,f9735]) ).
fof(f9735,plain,
( spl0_1233
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f2542,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9733,plain,
spl0_1232,
inference(avatar_split_clause,[],[f2522,f9731]) ).
fof(f9731,plain,
( spl0_1232
<=> ! [X18,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f2522,axiom,
! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9729,plain,
spl0_1231,
inference(avatar_split_clause,[],[f2271,f9727]) ).
fof(f9727,plain,
( spl0_1231
<=> ! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f2271,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
fof(f9725,plain,
spl0_1230,
inference(avatar_split_clause,[],[f2270,f9723]) ).
fof(f9723,plain,
( spl0_1230
<=> ! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f2270,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
fof(f9721,plain,
spl0_1229,
inference(avatar_split_clause,[],[f2252,f9719]) ).
fof(f9719,plain,
( spl0_1229
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f2252,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9717,plain,
spl0_1228,
inference(avatar_split_clause,[],[f2245,f9715]) ).
fof(f9715,plain,
( spl0_1228
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f2245,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9713,plain,
spl0_1227,
inference(avatar_split_clause,[],[f2244,f9711]) ).
fof(f9711,plain,
( spl0_1227
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f2244,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9709,plain,
spl0_1226,
inference(avatar_split_clause,[],[f2240,f9707]) ).
fof(f9707,plain,
( spl0_1226
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f2240,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9705,plain,
( spl0_1225
| ~ spl0_53
| ~ spl0_955 ),
inference(avatar_split_clause,[],[f8288,f8079,f3513,f9703]) ).
fof(f9703,plain,
( spl0_1225
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f8288,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_955 ),
inference(resolution,[],[f8080,f3515]) ).
fof(f9701,plain,
spl0_1224,
inference(avatar_split_clause,[],[f2239,f9699]) ).
fof(f9699,plain,
( spl0_1224
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f2239,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9697,plain,
spl0_1223,
inference(avatar_split_clause,[],[f2199,f9695]) ).
fof(f2199,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9693,plain,
spl0_1222,
inference(avatar_split_clause,[],[f2183,f9691]) ).
fof(f2183,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9689,plain,
spl0_1221,
inference(avatar_split_clause,[],[f2181,f9687]) ).
fof(f9687,plain,
( spl0_1221
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2181,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9685,plain,
spl0_1220,
inference(avatar_split_clause,[],[f2179,f9683]) ).
fof(f9683,plain,
( spl0_1220
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f2179,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9681,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2178,f9679]) ).
fof(f9679,plain,
( spl0_1219
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f2178,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9677,plain,
spl0_1218,
inference(avatar_split_clause,[],[f2147,f9675]) ).
fof(f9675,plain,
( spl0_1218
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f2147,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9673,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2127,f9671]) ).
fof(f9669,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2104,f9667]) ).
fof(f9667,plain,
( spl0_1216
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f2104,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9665,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2103,f9663]) ).
fof(f9663,plain,
( spl0_1215
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f2103,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9661,plain,
( spl0_1214
| ~ spl0_91
| ~ spl0_952 ),
inference(avatar_split_clause,[],[f8284,f8067,f3703,f9659]) ).
fof(f9659,plain,
( spl0_1214
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f3703,plain,
( spl0_91
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f8067,plain,
( spl0_952
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f8284,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_91
| ~ spl0_952 ),
inference(resolution,[],[f8068,f3705]) ).
fof(f3705,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f3703]) ).
fof(f8068,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_952 ),
inference(avatar_component_clause,[],[f8067]) ).
fof(f9657,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2079,f9655]) ).
fof(f9655,plain,
( spl0_1213
<=> ! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f2079,axiom,
! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9653,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2078,f9651]) ).
fof(f9651,plain,
( spl0_1212
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f2078,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9649,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2030,f9647]) ).
fof(f9647,plain,
( spl0_1211
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f2030,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9645,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2029,f9643]) ).
fof(f9643,plain,
( spl0_1210
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f2029,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9641,plain,
spl0_1209,
inference(avatar_split_clause,[],[f1851,f9639]) ).
fof(f9639,plain,
( spl0_1209
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1851,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9637,plain,
spl0_1208,
inference(avatar_split_clause,[],[f1814,f9635]) ).
fof(f9635,plain,
( spl0_1208
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f1814,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9633,plain,
spl0_1207,
inference(avatar_split_clause,[],[f1761,f9631]) ).
fof(f9631,plain,
( spl0_1207
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f1761,axiom,
! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osingleton__rev__conv_1) ).
fof(f9629,plain,
spl0_1206,
inference(avatar_split_clause,[],[f1731,f9627]) ).
fof(f9627,plain,
( spl0_1206
<=> ! [X0,X1,X21] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1731,axiom,
! [X21,X0,X1] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9625,plain,
spl0_1205,
inference(avatar_split_clause,[],[f1712,f9623]) ).
fof(f9623,plain,
( spl0_1205
<=> ! [X41,X0,X3,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f1712,axiom,
! [X41,X3,X0,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9621,plain,
spl0_1204,
inference(avatar_split_clause,[],[f1613,f9619]) ).
fof(f9619,plain,
( spl0_1204
<=> ! [X43,X59] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1613,axiom,
! [X59,X43] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9617,plain,
( spl0_1203
| ~ spl0_27
| ~ spl0_952 ),
inference(avatar_split_clause,[],[f8283,f8067,f3383,f9615]) ).
fof(f9615,plain,
( spl0_1203
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f3383,plain,
( spl0_27
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f8283,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_952 ),
inference(resolution,[],[f8068,f3385]) ).
fof(f3385,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f3383]) ).
fof(f9613,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1609,f9611]) ).
fof(f9611,plain,
( spl0_1202
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1609,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9609,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1608,f9607]) ).
fof(f9607,plain,
( spl0_1201
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1608,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9605,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1595,f9603]) ).
fof(f9603,plain,
( spl0_1200
<=> ! [X1,X23,X3] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1595,axiom,
! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9601,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1594,f9599]) ).
fof(f9599,plain,
( spl0_1199
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1594,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9597,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1593,f9595]) ).
fof(f9595,plain,
( spl0_1198
<=> ! [X60,X1] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f1593,axiom,
! [X1,X60] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9593,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1584,f9591]) ).
fof(f1584,axiom,
! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9589,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1583,f9587]) ).
fof(f9587,plain,
( spl0_1196
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1583,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9585,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1582,f9583]) ).
fof(f9583,plain,
( spl0_1195
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1582,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9581,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1539,f9579]) ).
fof(f9579,plain,
( spl0_1194
<=> ! [X0,X1,X3] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1539,axiom,
! [X3,X0,X1] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9577,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1463,f9575]) ).
fof(f9575,plain,
( spl0_1193
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1463,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9573,plain,
( spl0_1192
| ~ spl0_91
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8282,f8063,f3703,f9571]) ).
fof(f9571,plain,
( spl0_1192
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f8063,plain,
( spl0_951
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f8282,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_91
| ~ spl0_951 ),
inference(resolution,[],[f8064,f3705]) ).
fof(f8064,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_951 ),
inference(avatar_component_clause,[],[f8063]) ).
fof(f9569,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1462,f9567]) ).
fof(f9567,plain,
( spl0_1191
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1462,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9565,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1455,f9563]) ).
fof(f9563,plain,
( spl0_1190
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1455,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9561,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1454,f9559]) ).
fof(f9559,plain,
( spl0_1189
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f1454,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9557,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1418,f9555]) ).
fof(f9555,plain,
( spl0_1188
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1418,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9553,plain,
spl0_1187,
inference(avatar_split_clause,[],[f1354,f9551]) ).
fof(f9551,plain,
( spl0_1187
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1354,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9549,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1353,f9547]) ).
fof(f9547,plain,
( spl0_1186
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1353,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9545,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1352,f9543]) ).
fof(f9543,plain,
( spl0_1185
<=> ! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1352,axiom,
! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9541,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1351,f9539]) ).
fof(f9539,plain,
( spl0_1184
<=> ! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1351,axiom,
! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9537,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1348,f9535]) ).
fof(f9535,plain,
( spl0_1183
<=> ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f1348,axiom,
! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f9532,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1345,f9530]) ).
fof(f1345,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9528,plain,
( spl0_1181
| ~ spl0_27
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8281,f8063,f3383,f9526]) ).
fof(f9526,plain,
( spl0_1181
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f8281,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_951 ),
inference(resolution,[],[f8064,f3385]) ).
fof(f9524,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1310,f9522]) ).
fof(f9522,plain,
( spl0_1180
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1310,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9520,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1307,f9518]) ).
fof(f9518,plain,
( spl0_1179
<=> ! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1307,axiom,
! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9516,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1236,f9514]) ).
fof(f9514,plain,
( spl0_1178
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1236,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9512,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1234,f9510]) ).
fof(f9510,plain,
( spl0_1177
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1234,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9508,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1178,f9506]) ).
fof(f1178,axiom,
! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9504,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1166,f9502]) ).
fof(f9502,plain,
( spl0_1175
<=> ! [X0,X1,X40] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f1166,axiom,
! [X40,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9489,plain,
( spl0_1174
| ~ spl0_64
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8276,f8047,f3568,f9487]) ).
fof(f9487,plain,
( spl0_1174
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f3568,plain,
( spl0_64
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f8047,plain,
( spl0_947
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f8276,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_64
| ~ spl0_947 ),
inference(resolution,[],[f8048,f3570]) ).
fof(f3570,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_64 ),
inference(avatar_component_clause,[],[f3568]) ).
fof(f8048,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f8047]) ).
fof(f9478,plain,
( spl0_1173
| ~ spl0_15
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8275,f8047,f3323,f9476]) ).
fof(f9476,plain,
( spl0_1173
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f3323,plain,
( spl0_15
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f8275,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_15
| ~ spl0_947 ),
inference(resolution,[],[f8048,f3325]) ).
fof(f3325,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f3323]) ).
fof(f9461,plain,
( spl0_1172
| ~ spl0_64
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8274,f8043,f3568,f9459]) ).
fof(f9459,plain,
( spl0_1172
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f8043,plain,
( spl0_946
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f8274,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_64
| ~ spl0_946 ),
inference(resolution,[],[f8044,f3570]) ).
fof(f8044,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f8043]) ).
fof(f9419,plain,
( spl0_1171
| ~ spl0_15
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8273,f8043,f3323,f9417]) ).
fof(f9417,plain,
( spl0_1171
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f8273,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_15
| ~ spl0_946 ),
inference(resolution,[],[f8044,f3325]) ).
fof(f9387,plain,
( spl0_1170
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1114 ),
inference(avatar_split_clause,[],[f9055,f9052,f8526,f3508,f9385]) ).
fof(f9385,plain,
( spl0_1170
<=> ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f9052,plain,
( spl0_1114
<=> ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f9055,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_1034
| ~ spl0_1114 ),
inference(forward_demodulation,[],[f9053,f8848]) ).
fof(f9053,plain,
( ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint)
| ~ spl0_1114 ),
inference(avatar_component_clause,[],[f9052]) ).
fof(f9337,plain,
( spl0_1169
| spl0_677
| ~ spl0_1100 ),
inference(avatar_split_clause,[],[f9324,f8996,f6838,f9334]) ).
fof(f9334,plain,
( spl0_1169
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f6838,plain,
( spl0_677
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f8996,plain,
( spl0_1100
<=> ! [X12,X1] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f9324,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_677
| ~ spl0_1100 ),
inference(resolution,[],[f8997,f6840]) ).
fof(f6840,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_677 ),
inference(avatar_component_clause,[],[f6838]) ).
fof(f8997,plain,
( ! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_0 = c_Finite__Set_Ocard(X12,X1) )
| ~ spl0_1100 ),
inference(avatar_component_clause,[],[f8996]) ).
fof(f9280,plain,
( spl0_1168
| ~ spl0_641
| ~ spl0_1128
| ~ spl0_1161 ),
inference(avatar_split_clause,[],[f9249,f9244,f9110,f5917,f9277]) ).
fof(f9277,plain,
( spl0_1168
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f9244,plain,
( spl0_1161
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f9249,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1128
| ~ spl0_1161 ),
inference(forward_demodulation,[],[f9248,f9111]) ).
fof(f9248,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1161 ),
inference(superposition,[],[f9245,f5919]) ).
fof(f9245,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1161 ),
inference(avatar_component_clause,[],[f9244]) ).
fof(f9273,plain,
spl0_1167,
inference(avatar_split_clause,[],[f3199,f9271]) ).
fof(f9271,plain,
( spl0_1167
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f3199,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(inner_rewriting,[],[f3198]) ).
fof(f3198,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3197,f2115]) ).
fof(f3197,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2999,f2830]) ).
fof(f2999,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1337,f2129]) ).
fof(f1337,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f9269,plain,
spl0_1166,
inference(avatar_split_clause,[],[f3082,f9267]) ).
fof(f9267,plain,
( spl0_1166
<=> ! [X96,X90] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f3082,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
inference(forward_demodulation,[],[f3081,f3079]) ).
fof(f3081,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2896,f2831]) ).
fof(f2896,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2766,f2544]) ).
fof(f2766,axiom,
! [X90,X96] : c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__7_0) ).
fof(f9265,plain,
spl0_1165,
inference(avatar_split_clause,[],[f3078,f9263]) ).
fof(f9263,plain,
( spl0_1165
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f3078,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2876,f2831]) ).
fof(f2876,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1210,f2544]) ).
fof(f1210,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f9261,plain,
spl0_1164,
inference(avatar_split_clause,[],[f3077,f9259]) ).
fof(f9259,plain,
( spl0_1164
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f3077,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2875,f2831]) ).
fof(f2875,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1209,f2544]) ).
fof(f1209,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f9257,plain,
spl0_1163,
inference(avatar_split_clause,[],[f2950,f9255]) ).
fof(f9255,plain,
( spl0_1163
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f2950,plain,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2279,f2544]) ).
fof(f2279,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9253,plain,
spl0_1162,
inference(avatar_split_clause,[],[f2940,f9251]) ).
fof(f9251,plain,
( spl0_1162
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f2940,plain,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2278,f2544]) ).
fof(f2278,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9246,plain,
( spl0_1161
| ~ spl0_1159 ),
inference(avatar_split_clause,[],[f9238,f9235,f9244]) ).
fof(f9235,plain,
( spl0_1159
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f9238,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1159 ),
inference(forward_demodulation,[],[f9236,f2867]) ).
fof(f9236,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1159 ),
inference(avatar_component_clause,[],[f9235]) ).
fof(f9242,plain,
( spl0_1160
| ~ spl0_9
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8269,f8039,f3293,f9240]) ).
fof(f9240,plain,
( spl0_1160
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f8039,plain,
( spl0_945
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f8269,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_9
| ~ spl0_945 ),
inference(resolution,[],[f8040,f3295]) ).
fof(f8040,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_945 ),
inference(avatar_component_clause,[],[f8039]) ).
fof(f9237,plain,
spl0_1159,
inference(avatar_split_clause,[],[f2858,f9235]) ).
fof(f2858,plain,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1388,f2544]) ).
fof(f1388,axiom,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f9233,plain,
( spl0_1158
| ~ spl0_802
| ~ spl0_1157 ),
inference(avatar_split_clause,[],[f9229,f9226,f7379,f9231]) ).
fof(f9231,plain,
( spl0_1158
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f7379,plain,
( spl0_802
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f9226,plain,
( spl0_1157
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f9229,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
| ~ spl0_802
| ~ spl0_1157 ),
inference(forward_demodulation,[],[f9227,f7380]) ).
fof(f7380,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7379]) ).
fof(f9227,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1)
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f9226]) ).
fof(f9228,plain,
spl0_1157,
inference(avatar_split_clause,[],[f2832,f9226]) ).
fof(f2832,plain,
! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2709,f2716]) ).
fof(f2709,axiom,
! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f9224,plain,
spl0_1156,
inference(avatar_split_clause,[],[f2759,f9222]) ).
fof(f9222,plain,
( spl0_1156
<=> ! [X89,X96,X97,X90] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2759,axiom,
! [X90,X89,X96,X97] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
fof(f9220,plain,
spl0_1155,
inference(avatar_split_clause,[],[f2758,f9218]) ).
fof(f9218,plain,
( spl0_1155
<=> ! [X96,X97,X90,X89] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f2758,axiom,
! [X90,X89,X96,X97] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
fof(f9216,plain,
spl0_1154,
inference(avatar_split_clause,[],[f2757,f9214]) ).
fof(f9214,plain,
( spl0_1154
<=> ! [X100,X101,X98,X99] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f2757,axiom,
! [X101,X98,X99,X100] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
fof(f9212,plain,
spl0_1153,
inference(avatar_split_clause,[],[f2756,f9210]) ).
fof(f9210,plain,
( spl0_1153
<=> ! [X101,X98,X100,X99] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f2756,axiom,
! [X101,X98,X99,X100] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
fof(f9208,plain,
spl0_1152,
inference(avatar_split_clause,[],[f2748,f9206]) ).
fof(f9206,plain,
( spl0_1152
<=> ! [X87,X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f2748,axiom,
! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
fof(f9204,plain,
spl0_1151,
inference(avatar_split_clause,[],[f2671,f9202]) ).
fof(f9202,plain,
( spl0_1151
<=> ! [X12,X1] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f2671,axiom,
! [X1,X12] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f9200,plain,
( spl0_1150
| ~ spl0_9
| ~ spl0_944 ),
inference(avatar_split_clause,[],[f8268,f8035,f3293,f9198]) ).
fof(f9198,plain,
( spl0_1150
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f8035,plain,
( spl0_944
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f8268,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_9
| ~ spl0_944 ),
inference(resolution,[],[f8036,f3295]) ).
fof(f8036,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_944 ),
inference(avatar_component_clause,[],[f8035]) ).
fof(f9196,plain,
spl0_1149,
inference(avatar_split_clause,[],[f2654,f9194]) ).
fof(f9194,plain,
( spl0_1149
<=> ! [X12,X1] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f2654,axiom,
! [X1,X12] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f9192,plain,
spl0_1148,
inference(avatar_split_clause,[],[f2618,f9190]) ).
fof(f9190,plain,
( spl0_1148
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f2618,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f9188,plain,
spl0_1147,
inference(avatar_split_clause,[],[f2615,f9186]) ).
fof(f9186,plain,
( spl0_1147
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f2615,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f9184,plain,
spl0_1146,
inference(avatar_split_clause,[],[f2388,f9182]) ).
fof(f2388,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f9180,plain,
spl0_1145,
inference(avatar_split_clause,[],[f2383,f9178]) ).
fof(f2383,axiom,
! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f9176,plain,
spl0_1144,
inference(avatar_split_clause,[],[f2366,f9174]) ).
fof(f9174,plain,
( spl0_1144
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f2366,axiom,
! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f9172,plain,
spl0_1143,
inference(avatar_split_clause,[],[f2364,f9170]) ).
fof(f9170,plain,
( spl0_1143
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f2364,axiom,
! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f9168,plain,
spl0_1142,
inference(avatar_split_clause,[],[f2342,f9166]) ).
fof(f9166,plain,
( spl0_1142
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f2342,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f9164,plain,
spl0_1141,
inference(avatar_split_clause,[],[f2341,f9162]) ).
fof(f9162,plain,
( spl0_1141
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f2341,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f9160,plain,
spl0_1140,
inference(avatar_split_clause,[],[f2294,f9158]) ).
fof(f9158,plain,
( spl0_1140
<=> ! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f2294,axiom,
! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f9156,plain,
( spl0_1139
| ~ spl0_4
| ~ spl0_943 ),
inference(avatar_split_clause,[],[f8266,f8031,f3268,f9154]) ).
fof(f9154,plain,
( spl0_1139
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f3268,plain,
( spl0_4
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f8031,plain,
( spl0_943
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f8266,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_4
| ~ spl0_943 ),
inference(resolution,[],[f8032,f3270]) ).
fof(f3270,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3268]) ).
fof(f8032,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_943 ),
inference(avatar_component_clause,[],[f8031]) ).
fof(f9152,plain,
spl0_1138,
inference(avatar_split_clause,[],[f2281,f9150]) ).
fof(f9150,plain,
( spl0_1138
<=> ! [X0,X3] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f2281,axiom,
! [X3,X0] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f9148,plain,
spl0_1137,
inference(avatar_split_clause,[],[f2247,f9146]) ).
fof(f9146,plain,
( spl0_1137
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f2247,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f9144,plain,
spl0_1136,
inference(avatar_split_clause,[],[f2225,f9142]) ).
fof(f9142,plain,
( spl0_1136
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f2225,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f9140,plain,
spl0_1135,
inference(avatar_split_clause,[],[f2213,f9138]) ).
fof(f9138,plain,
( spl0_1135
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f2213,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f9136,plain,
spl0_1134,
inference(avatar_split_clause,[],[f2211,f9134]) ).
fof(f9134,plain,
( spl0_1134
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f2211,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f9132,plain,
spl0_1133,
inference(avatar_split_clause,[],[f2197,f9130]) ).
fof(f9130,plain,
( spl0_1133
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f2197,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f9128,plain,
spl0_1132,
inference(avatar_split_clause,[],[f2172,f9126]) ).
fof(f9126,plain,
( spl0_1132
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f2172,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
fof(f9124,plain,
spl0_1131,
inference(avatar_split_clause,[],[f2171,f9122]) ).
fof(f9122,plain,
( spl0_1131
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2171,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f9120,plain,
spl0_1130,
inference(avatar_split_clause,[],[f2039,f9118]) ).
fof(f9118,plain,
( spl0_1130
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f2039,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f9116,plain,
spl0_1129,
inference(avatar_split_clause,[],[f2038,f9114]) ).
fof(f2038,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f9112,plain,
( spl0_1128
| ~ spl0_4
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8264,f8027,f3268,f9110]) ).
fof(f8027,plain,
( spl0_942
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8264,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_4
| ~ spl0_942 ),
inference(resolution,[],[f8028,f3270]) ).
fof(f8028,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f8027]) ).
fof(f9108,plain,
spl0_1127,
inference(avatar_split_clause,[],[f1849,f9106]) ).
fof(f1849,axiom,
! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f9104,plain,
spl0_1126,
inference(avatar_split_clause,[],[f1832,f9102]) ).
fof(f9102,plain,
( spl0_1126
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f1832,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f9100,plain,
spl0_1125,
inference(avatar_split_clause,[],[f1803,f9098]) ).
fof(f9098,plain,
( spl0_1125
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f1803,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f9096,plain,
spl0_1124,
inference(avatar_split_clause,[],[f1759,f9094]) ).
fof(f9094,plain,
( spl0_1124
<=> ! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f1759,axiom,
! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f9092,plain,
spl0_1123,
inference(avatar_split_clause,[],[f1730,f9090]) ).
fof(f9090,plain,
( spl0_1123
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f1730,axiom,
! [X1,X25,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f9088,plain,
spl0_1122,
inference(avatar_split_clause,[],[f1603,f9086]) ).
fof(f9086,plain,
( spl0_1122
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f1603,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f9084,plain,
spl0_1121,
inference(avatar_split_clause,[],[f1548,f9082]) ).
fof(f9082,plain,
( spl0_1121
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f1548,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f9080,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1541,f9078]) ).
fof(f9078,plain,
( spl0_1120
<=> ! [X54,X57,X55,X56] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1541,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f9076,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1540,f9074]) ).
fof(f9074,plain,
( spl0_1119
<=> ! [X55,X54,X56,X57] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1540,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f9072,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1509,f9070]) ).
fof(f9070,plain,
( spl0_1118
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1509,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f9068,plain,
( spl0_1117
| ~ spl0_708
| ~ spl0_883
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f8253,f8011,f7716,f6980,f9065]) ).
fof(f9065,plain,
( spl0_1117
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f8011,plain,
( spl0_938
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f8253,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_708
| ~ spl0_883
| ~ spl0_938 ),
inference(forward_demodulation,[],[f8251,f6982]) ).
fof(f8251,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_883
| ~ spl0_938 ),
inference(superposition,[],[f8012,f7718]) ).
fof(f8012,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f8011]) ).
fof(f9063,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1488,f9061]) ).
fof(f9061,plain,
( spl0_1116
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1488,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f9059,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1487,f9057]) ).
fof(f1487,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f9054,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1467,f9052]) ).
fof(f1467,axiom,
! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f9050,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1440,f9048]) ).
fof(f9048,plain,
( spl0_1113
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1440,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f9046,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1439,f9044]) ).
fof(f1439,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f9042,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1430,f9040]) ).
fof(f9040,plain,
( spl0_1111
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f1430,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f9038,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1429,f9036]) ).
fof(f9036,plain,
( spl0_1110
<=> ! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1429,axiom,
! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f9034,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1428,f9032]) ).
fof(f9032,plain,
( spl0_1109
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1428,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f9030,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1427,f9028]) ).
fof(f9028,plain,
( spl0_1108
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f1427,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f9026,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1426,f9024]) ).
fof(f9024,plain,
( spl0_1107
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1426,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f9022,plain,
( spl0_1106
| ~ spl0_82
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8231,f7929,f3658,f9020]) ).
fof(f9020,plain,
( spl0_1106
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f3658,plain,
( spl0_82
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f7929,plain,
( spl0_918
<=> ! [X1,X3] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f8231,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_82
| ~ spl0_918 ),
inference(resolution,[],[f7930,f3660]) ).
fof(f3660,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_82 ),
inference(avatar_component_clause,[],[f3658]) ).
fof(f7930,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f7929]) ).
fof(f9018,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1425,f9016]) ).
fof(f9016,plain,
( spl0_1105
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1425,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f9014,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1407,f9012]) ).
fof(f9012,plain,
( spl0_1104
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1407,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f9010,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1395,f9008]) ).
fof(f9008,plain,
( spl0_1103
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X48
| c_0 != c_IntDef_Oof__int(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1395,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X48
| c_0 != c_IntDef_Oof__int(X48,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
fof(f9006,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1390,f9004]) ).
fof(f9004,plain,
( spl0_1102
<=> ! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1390,axiom,
! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f9002,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1389,f9000]) ).
fof(f9000,plain,
( spl0_1101
<=> ! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1389,axiom,
! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8998,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1279,f8996]) ).
fof(f1279,axiom,
! [X1,X12] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8994,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1275,f8992]) ).
fof(f8992,plain,
( spl0_1099
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1275,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8990,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1265,f8988]) ).
fof(f8988,plain,
( spl0_1098
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1265,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8986,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1235,f8984]) ).
fof(f8984,plain,
( spl0_1097
<=> ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1235,axiom,
! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8982,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1224,f8980]) ).
fof(f8980,plain,
( spl0_1096
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1224,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8978,plain,
( spl0_1095
| ~ spl0_24
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8230,f7929,f3368,f8976]) ).
fof(f8976,plain,
( spl0_1095
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f3368,plain,
( spl0_24
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f8230,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_24
| ~ spl0_918 ),
inference(resolution,[],[f7930,f3370]) ).
fof(f3370,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f3368]) ).
fof(f8974,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1216,f8972]) ).
fof(f8972,plain,
( spl0_1094
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f1216,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8970,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1201,f8968]) ).
fof(f8968,plain,
( spl0_1093
<=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1201,axiom,
! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb_0) ).
fof(f8966,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1200,f8964]) ).
fof(f8964,plain,
( spl0_1092
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f1200,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf_0) ).
fof(f8962,plain,
spl0_1091,
inference(avatar_split_clause,[],[f1199,f8960]) ).
fof(f8960,plain,
( spl0_1091
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f1199,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Atom_0) ).
fof(f8958,plain,
spl0_1090,
inference(avatar_split_clause,[],[f1180,f8956]) ).
fof(f8956,plain,
( spl0_1090
<=> ! [X2,X27,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f1180,axiom,
! [X2,X1,X27] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8954,plain,
spl0_1089,
inference(avatar_split_clause,[],[f1179,f8952]) ).
fof(f8952,plain,
( spl0_1089
<=> ! [X2,X1,X18] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1179,axiom,
! [X2,X18,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8950,plain,
spl0_1088,
inference(avatar_split_clause,[],[f1175,f8948]) ).
fof(f8948,plain,
( spl0_1088
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f1175,axiom,
! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8946,plain,
spl0_1087,
inference(avatar_split_clause,[],[f1170,f8944]) ).
fof(f8944,plain,
( spl0_1087
<=> ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f1170,axiom,
! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8942,plain,
spl0_1086,
inference(avatar_split_clause,[],[f1169,f8940]) ).
fof(f8940,plain,
( spl0_1086
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f1169,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8938,plain,
spl0_1085,
inference(avatar_split_clause,[],[f1168,f8936]) ).
fof(f8936,plain,
( spl0_1085
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f1168,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8933,plain,
spl0_1084,
inference(avatar_split_clause,[],[f105,f8931]) ).
fof(f8931,plain,
( spl0_1084
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f105,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8929,plain,
spl0_1083,
inference(avatar_split_clause,[],[f103,f8927]) ).
fof(f8927,plain,
( spl0_1083
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f103,axiom,
! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8925,plain,
spl0_1082,
inference(avatar_split_clause,[],[f102,f8923]) ).
fof(f8923,plain,
( spl0_1082
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f102,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8892,plain,
( spl0_1081
| ~ spl0_804
| ~ spl0_1049 ),
inference(avatar_split_clause,[],[f8870,f8587,f7387,f8890]) ).
fof(f8890,plain,
( spl0_1081
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f7387,plain,
( spl0_804
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f8870,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_804
| ~ spl0_1049 ),
inference(superposition,[],[f7388,f8588]) ).
fof(f7388,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_804 ),
inference(avatar_component_clause,[],[f7387]) ).
fof(f8867,plain,
( spl0_1080
| ~ spl0_887
| ~ spl0_1031 ),
inference(avatar_split_clause,[],[f8831,f8514,f7757,f8865]) ).
fof(f8865,plain,
( spl0_1080
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f7757,plain,
( spl0_887
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f8514,plain,
( spl0_1031
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f8831,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_887
| ~ spl0_1031 ),
inference(resolution,[],[f8515,f7758]) ).
fof(f7758,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_887 ),
inference(avatar_component_clause,[],[f7757]) ).
fof(f8515,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1031 ),
inference(avatar_component_clause,[],[f8514]) ).
fof(f8820,plain,
( spl0_1079
| ~ spl0_804
| ~ spl0_1023 ),
inference(avatar_split_clause,[],[f8815,f8482,f7387,f8818]) ).
fof(f8818,plain,
( spl0_1079
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f8815,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_804
| ~ spl0_1023 ),
inference(superposition,[],[f7388,f8483]) ).
fof(f8801,plain,
( spl0_1078
| ~ spl0_89
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8229,f7925,f3693,f8799]) ).
fof(f8799,plain,
( spl0_1078
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f3693,plain,
( spl0_89
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f7925,plain,
( spl0_917
<=> ! [X1,X3] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f8229,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_89
| ~ spl0_917 ),
inference(resolution,[],[f7926,f3695]) ).
fof(f3695,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f3693]) ).
fof(f7926,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f7925]) ).
fof(f8773,plain,
( spl0_1077
| ~ spl0_25
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8228,f7925,f3373,f8771]) ).
fof(f8771,plain,
( spl0_1077
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f3373,plain,
( spl0_25
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f8228,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_25
| ~ spl0_917 ),
inference(resolution,[],[f7926,f3375]) ).
fof(f3375,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f3373]) ).
fof(f8697,plain,
spl0_1076,
inference(avatar_split_clause,[],[f3148,f8695]) ).
fof(f8695,plain,
( spl0_1076
<=> ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f3148,plain,
! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2966,f2831]) ).
fof(f2966,plain,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1346,f2544]) ).
fof(f1346,axiom,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8693,plain,
spl0_1075,
inference(avatar_split_clause,[],[f3138,f8691]) ).
fof(f8691,plain,
( spl0_1075
<=> ! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f3138,plain,
! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2951,f2831]) ).
fof(f2951,plain,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1347,f2544]) ).
fof(f1347,axiom,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8689,plain,
( ~ spl0_74
| spl0_1074
| ~ spl0_675
| ~ spl0_915 ),
inference(avatar_split_clause,[],[f8227,f7917,f6830,f8687,f3618]) ).
fof(f3618,plain,
( spl0_74
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f6830,plain,
( spl0_675
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f7917,plain,
( spl0_915
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f8227,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_675
| ~ spl0_915 ),
inference(superposition,[],[f7918,f6831]) ).
fof(f6831,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_675 ),
inference(avatar_component_clause,[],[f6830]) ).
fof(f7918,plain,
( ! [X21,X1] :
( c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) )
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f7917]) ).
fof(f8685,plain,
spl0_1073,
inference(avatar_split_clause,[],[f3135,f8683]) ).
fof(f8683,plain,
( spl0_1073
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f3135,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ),
inference(forward_demodulation,[],[f2947,f2831]) ).
fof(f2947,plain,
! [X21,X15] :
( c_1 = X21
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2093,f2544]) ).
fof(f2093,axiom,
! [X21,X15] :
( c_1 = X21
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
fof(f8681,plain,
spl0_1072,
inference(avatar_split_clause,[],[f3133,f8679]) ).
fof(f8679,plain,
( spl0_1072
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f3133,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f2945,f2831]) ).
fof(f2945,plain,
! [X21,X15] :
( c_1 = X15
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2092,f2544]) ).
fof(f2092,axiom,
! [X21,X15] :
( c_1 = X15
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_0) ).
fof(f8677,plain,
spl0_1071,
inference(avatar_split_clause,[],[f2862,f8675]) ).
fof(f2862,plain,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f2132,f2113]) ).
fof(f2132,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8673,plain,
spl0_1070,
inference(avatar_split_clause,[],[f2851,f8671]) ).
fof(f8671,plain,
( spl0_1070
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f2851,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2603,f2373]) ).
fof(f2603,axiom,
! [X3,X1] : c_inter(X3,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8669,plain,
spl0_1069,
inference(avatar_split_clause,[],[f2850,f8667]) ).
fof(f8667,plain,
( spl0_1069
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f2850,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2601,f2373]) ).
fof(f2601,axiom,
! [X3,X1] : c_inter(c_UNIV,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8665,plain,
spl0_1068,
inference(avatar_split_clause,[],[f2849,f8663]) ).
fof(f8663,plain,
( spl0_1068
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f2849,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3,
inference(definition_unfolding,[],[f2602,f2373]) ).
fof(f2602,axiom,
! [X3,X1] : c_inter(X3,c_UNIV,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8661,plain,
spl0_1067,
inference(avatar_split_clause,[],[f2843,f8659]) ).
fof(f8659,plain,
( spl0_1067
<=> ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f2843,plain,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1160,f2544]) ).
fof(f1160,axiom,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8657,plain,
spl0_1066,
inference(avatar_split_clause,[],[f2818,f8655]) ).
fof(f8655,plain,
( spl0_1066
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f2818,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
fof(f8653,plain,
spl0_1065,
inference(avatar_split_clause,[],[f2787,f8651]) ).
fof(f8651,plain,
( spl0_1065
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f2787,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
fof(f8649,plain,
spl0_1064,
inference(avatar_split_clause,[],[f2767,f8647]) ).
fof(f8647,plain,
( spl0_1064
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f2767,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
fof(f8645,plain,
( spl0_1063
| ~ spl0_826
| ~ spl0_844 ),
inference(avatar_split_clause,[],[f7764,f7559,f7487,f8643]) ).
fof(f8643,plain,
( spl0_1063
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f7487,plain,
( spl0_826
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f7559,plain,
( spl0_844
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f7764,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_826
| ~ spl0_844 ),
inference(resolution,[],[f7560,f7488]) ).
fof(f7488,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_826 ),
inference(avatar_component_clause,[],[f7487]) ).
fof(f7560,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f7559]) ).
fof(f8641,plain,
spl0_1062,
inference(avatar_split_clause,[],[f2750,f8639]) ).
fof(f8639,plain,
( spl0_1062
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f2750,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
fof(f8637,plain,
spl0_1061,
inference(avatar_split_clause,[],[f2749,f8635]) ).
fof(f8635,plain,
( spl0_1061
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f2749,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
fof(f8633,plain,
spl0_1060,
inference(avatar_split_clause,[],[f2747,f8631]) ).
fof(f8631,plain,
( spl0_1060
<=> ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f2747,axiom,
! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
fof(f8629,plain,
spl0_1059,
inference(avatar_split_clause,[],[f2746,f8627]) ).
fof(f8627,plain,
( spl0_1059
<=> ! [X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f2746,axiom,
! [X88,X86] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
fof(f8625,plain,
spl0_1058,
inference(avatar_split_clause,[],[f2744,f8623]) ).
fof(f8623,plain,
( spl0_1058
<=> ! [X12,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f2744,axiom,
! [X88,X12] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
fof(f8621,plain,
spl0_1057,
inference(avatar_split_clause,[],[f2718,f8619]) ).
fof(f8619,plain,
( spl0_1057
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f2718,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8617,plain,
spl0_1056,
inference(avatar_split_clause,[],[f2717,f8615]) ).
fof(f8615,plain,
( spl0_1056
<=> ! [X5,X1] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f2717,axiom,
! [X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8613,plain,
spl0_1055,
inference(avatar_split_clause,[],[f2702,f8611]) ).
fof(f8611,plain,
( spl0_1055
<=> ! [X2,X27,X1,X18] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f2702,axiom,
! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__not__Inr_0) ).
fof(f8609,plain,
spl0_1054,
inference(avatar_split_clause,[],[f2667,f8607]) ).
fof(f8607,plain,
( spl0_1054
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f2667,axiom,
! [X3,X1] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8605,plain,
spl0_1053,
inference(avatar_split_clause,[],[f2659,f8603]) ).
fof(f8603,plain,
( spl0_1053
<=> ! [X12,X1] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f2659,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8601,plain,
( spl0_1052
| ~ spl0_825
| ~ spl0_844 ),
inference(avatar_split_clause,[],[f7763,f7559,f7483,f8599]) ).
fof(f8599,plain,
( spl0_1052
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f7483,plain,
( spl0_825
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f7763,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_825
| ~ spl0_844 ),
inference(resolution,[],[f7560,f7484]) ).
fof(f7484,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_825 ),
inference(avatar_component_clause,[],[f7483]) ).
fof(f8597,plain,
spl0_1051,
inference(avatar_split_clause,[],[f2636,f8595]) ).
fof(f8595,plain,
( spl0_1051
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f2636,axiom,
! [X1,X12,X13] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8593,plain,
spl0_1050,
inference(avatar_split_clause,[],[f2635,f8591]) ).
fof(f8591,plain,
( spl0_1050
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f2635,axiom,
! [X1,X12,X13] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8589,plain,
spl0_1049,
inference(avatar_split_clause,[],[f2626,f8587]) ).
fof(f2626,axiom,
! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8585,plain,
spl0_1048,
inference(avatar_split_clause,[],[f2390,f8583]) ).
fof(f8583,plain,
( spl0_1048
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f2390,axiom,
! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8581,plain,
spl0_1047,
inference(avatar_split_clause,[],[f2389,f8579]) ).
fof(f8579,plain,
( spl0_1047
<=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f2389,axiom,
! [X3,X1] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8577,plain,
spl0_1046,
inference(avatar_split_clause,[],[f2382,f8575]) ).
fof(f8575,plain,
( spl0_1046
<=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f2382,axiom,
! [X2,X3,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8573,plain,
spl0_1045,
inference(avatar_split_clause,[],[f2298,f8571]) ).
fof(f8571,plain,
( spl0_1045
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f2298,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8569,plain,
spl0_1044,
inference(avatar_split_clause,[],[f2297,f8567]) ).
fof(f8567,plain,
( spl0_1044
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f2297,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8565,plain,
spl0_1043,
inference(avatar_split_clause,[],[f2293,f8563]) ).
fof(f8563,plain,
( spl0_1043
<=> ! [X0,X21] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f2293,axiom,
! [X21,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8561,plain,
spl0_1042,
inference(avatar_split_clause,[],[f2285,f8559]) ).
fof(f8559,plain,
( spl0_1042
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f2285,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8557,plain,
( spl0_1041
| ~ spl0_640
| ~ spl0_841 ),
inference(avatar_split_clause,[],[f7752,f7547,f5912,f8554]) ).
fof(f8554,plain,
( spl0_1041
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f7547,plain,
( spl0_841
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f7752,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_640
| ~ spl0_841 ),
inference(superposition,[],[f7548,f5914]) ).
fof(f7548,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f7547]) ).
fof(f8552,plain,
spl0_1040,
inference(avatar_split_clause,[],[f2284,f8550]) ).
fof(f8550,plain,
( spl0_1040
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f2284,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8548,plain,
spl0_1039,
inference(avatar_split_clause,[],[f2280,f8546]) ).
fof(f2280,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8544,plain,
spl0_1038,
inference(avatar_split_clause,[],[f2216,f8542]) ).
fof(f2216,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8540,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2154,f8538]) ).
fof(f8538,plain,
( spl0_1037
<=> ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f8536,plain,
spl0_1036,
inference(avatar_split_clause,[],[f2150,f8534]) ).
fof(f8534,plain,
( spl0_1036
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f2150,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8532,plain,
spl0_1035,
inference(avatar_split_clause,[],[f2136,f8530]) ).
fof(f8530,plain,
( spl0_1035
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f2136,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8528,plain,
spl0_1034,
inference(avatar_split_clause,[],[f2118,f8526]) ).
fof(f2118,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8524,plain,
spl0_1033,
inference(avatar_split_clause,[],[f2032,f8522]) ).
fof(f8522,plain,
( spl0_1033
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f2032,axiom,
! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8520,plain,
spl0_1032,
inference(avatar_split_clause,[],[f2031,f8518]) ).
fof(f8518,plain,
( spl0_1032
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f2031,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8516,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1786,f8514]) ).
fof(f1786,axiom,
! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8512,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1758,f8510]) ).
fof(f8510,plain,
( spl0_1030
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1758,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8508,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1757,f8506]) ).
fof(f8506,plain,
( spl0_1029
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1757,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8504,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1754,f8502]) ).
fof(f8502,plain,
( spl0_1028
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f1754,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8500,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1744,f8498]) ).
fof(f8498,plain,
( spl0_1027
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1744,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8496,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1740,f8494]) ).
fof(f8494,plain,
( spl0_1026
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1740,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8492,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1720,f8490]) ).
fof(f8490,plain,
( spl0_1025
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1720,axiom,
! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8488,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1692,f8486]) ).
fof(f8486,plain,
( spl0_1024
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1692,axiom,
! [X3,X1,X23] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8484,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1639,f8482]) ).
fof(f8480,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1607,f8478]) ).
fof(f8478,plain,
( spl0_1022
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1607,axiom,
! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8476,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1597,f8474]) ).
fof(f8474,plain,
( spl0_1021
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1597,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8472,plain,
( ~ spl0_52
| spl0_1020
| ~ spl0_859
| ~ spl0_972 ),
inference(avatar_split_clause,[],[f8305,f8148,f7619,f8469,f3508]) ).
fof(f8469,plain,
( spl0_1020
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f7619,plain,
( spl0_859
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f8148,plain,
( spl0_972
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f8305,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_859
| ~ spl0_972 ),
inference(superposition,[],[f7620,f8150]) ).
fof(f8150,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_972 ),
inference(avatar_component_clause,[],[f8148]) ).
fof(f7620,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f7619]) ).
fof(f8467,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1565,f8465]) ).
fof(f8465,plain,
( spl0_1019
<=> ! [X1,X23,X58] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1565,axiom,
! [X58,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8463,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1564,f8461]) ).
fof(f8461,plain,
( spl0_1018
<=> ! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1564,axiom,
! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8459,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1563,f8457]) ).
fof(f8457,plain,
( spl0_1017
<=> ! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1563,axiom,
! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8455,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1560,f8453]) ).
fof(f8453,plain,
( spl0_1016
<=> ! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1560,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8451,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1559,f8449]) ).
fof(f8449,plain,
( spl0_1015
<=> ! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1559,axiom,
! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8447,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1556,f8445]) ).
fof(f8445,plain,
( spl0_1014
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1556,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8443,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1555,f8441]) ).
fof(f8441,plain,
( spl0_1013
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1555,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8439,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1553,f8437]) ).
fof(f8437,plain,
( spl0_1012
<=> ! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1553,axiom,
! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8435,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1533,f8433]) ).
fof(f8433,plain,
( spl0_1011
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1533,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8431,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1528,f8429]) ).
fof(f8429,plain,
( spl0_1010
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f1528,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
fof(f8427,plain,
spl0_1009,
inference(avatar_split_clause,[],[f1527,f8425]) ).
fof(f8425,plain,
( spl0_1009
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f1527,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f8423,plain,
spl0_1008,
inference(avatar_split_clause,[],[f1497,f8421]) ).
fof(f8421,plain,
( spl0_1008
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1497,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8419,plain,
spl0_1007,
inference(avatar_split_clause,[],[f1496,f8417]) ).
fof(f8417,plain,
( spl0_1007
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1496,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8415,plain,
spl0_1006,
inference(avatar_split_clause,[],[f1483,f8413]) ).
fof(f1483,axiom,
! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8411,plain,
spl0_1005,
inference(avatar_split_clause,[],[f1471,f8409]) ).
fof(f8409,plain,
( spl0_1005
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1471,axiom,
! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8407,plain,
spl0_1004,
inference(avatar_split_clause,[],[f1441,f8405]) ).
fof(f1441,axiom,
! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8403,plain,
spl0_1003,
inference(avatar_split_clause,[],[f1423,f8401]) ).
fof(f8401,plain,
( spl0_1003
<=> ! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1423,axiom,
! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8399,plain,
spl0_1002,
inference(avatar_split_clause,[],[f1422,f8397]) ).
fof(f8397,plain,
( spl0_1002
<=> ! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1422,axiom,
! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8395,plain,
spl0_1001,
inference(avatar_split_clause,[],[f1421,f8393]) ).
fof(f8393,plain,
( spl0_1001
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f1421,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8391,plain,
spl0_1000,
inference(avatar_split_clause,[],[f1420,f8389]) ).
fof(f8389,plain,
( spl0_1000
<=> ! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1420,axiom,
! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8387,plain,
( ~ spl0_999
| ~ spl0_804
| ~ spl0_968 ),
inference(avatar_split_clause,[],[f8312,f8131,f7387,f8384]) ).
fof(f8384,plain,
( spl0_999
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f8312,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_804
| ~ spl0_968 ),
inference(superposition,[],[f7388,f8133]) ).
fof(f8382,plain,
spl0_998,
inference(avatar_split_clause,[],[f1380,f8380]) ).
fof(f8380,plain,
( spl0_998
<=> ! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f1380,axiom,
! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8378,plain,
spl0_997,
inference(avatar_split_clause,[],[f1379,f8376]) ).
fof(f8376,plain,
( spl0_997
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f1379,axiom,
! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8374,plain,
spl0_996,
inference(avatar_split_clause,[],[f1349,f8372]) ).
fof(f8372,plain,
( spl0_996
<=> ! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1349,axiom,
! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8370,plain,
spl0_995,
inference(avatar_split_clause,[],[f1244,f8368]) ).
fof(f8368,plain,
( spl0_995
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1244,axiom,
! [X1,X5,X12] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
fof(f8366,plain,
spl0_994,
inference(avatar_split_clause,[],[f1242,f8364]) ).
fof(f8364,plain,
( spl0_994
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f1242,axiom,
! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8362,plain,
spl0_993,
inference(avatar_split_clause,[],[f1240,f8360]) ).
fof(f8360,plain,
( spl0_993
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f1240,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8358,plain,
spl0_992,
inference(avatar_split_clause,[],[f1238,f8356]) ).
fof(f8356,plain,
( spl0_992
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f1238,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8354,plain,
spl0_991,
inference(avatar_split_clause,[],[f1195,f8352]) ).
fof(f8352,plain,
( spl0_991
<=> ! [X2,X16,X1,X18] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f1195,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f8350,plain,
spl0_990,
inference(avatar_split_clause,[],[f1190,f8348]) ).
fof(f8348,plain,
( spl0_990
<=> ! [X2,X1,X7,X9] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f1190,axiom,
! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f8346,plain,
spl0_989,
inference(avatar_split_clause,[],[f63,f8344]) ).
fof(f8344,plain,
( spl0_989
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f63,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8341,plain,
spl0_988,
inference(avatar_split_clause,[],[f62,f8339]) ).
fof(f8339,plain,
( spl0_988
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f62,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8337,plain,
spl0_987,
inference(avatar_split_clause,[],[f35,f8335]) ).
fof(f8335,plain,
( spl0_987
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f35,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8333,plain,
spl0_986,
inference(avatar_split_clause,[],[f34,f8331]) ).
fof(f8331,plain,
( spl0_986
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f34,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8210,plain,
( spl0_985
| ~ spl0_40
| ~ spl0_869 ),
inference(avatar_split_clause,[],[f7798,f7659,f3448,f8207]) ).
fof(f8207,plain,
( spl0_985
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f3448,plain,
( spl0_40
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f7659,plain,
( spl0_869
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f7798,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_40
| ~ spl0_869 ),
inference(resolution,[],[f7660,f3450]) ).
fof(f3450,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_40 ),
inference(avatar_component_clause,[],[f3448]) ).
fof(f7660,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_869 ),
inference(avatar_component_clause,[],[f7659]) ).
fof(f8200,plain,
spl0_984,
inference(avatar_split_clause,[],[f3122,f8198]) ).
fof(f3122,plain,
! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2170,f2156]) ).
fof(f2170,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f8196,plain,
( spl0_983
| ~ spl0_40
| ~ spl0_868 ),
inference(avatar_split_clause,[],[f7797,f7655,f3448,f8193]) ).
fof(f8193,plain,
( spl0_983
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f7655,plain,
( spl0_868
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f7797,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_40
| ~ spl0_868 ),
inference(resolution,[],[f7656,f3450]) ).
fof(f7656,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_868 ),
inference(avatar_component_clause,[],[f7655]) ).
fof(f8191,plain,
spl0_982,
inference(avatar_split_clause,[],[f3070,f8189]) ).
fof(f8189,plain,
( spl0_982
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f3070,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2866,f2831]) ).
fof(f2866,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X15,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1300,f2544]) ).
fof(f1300,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X15,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f8187,plain,
spl0_981,
inference(avatar_split_clause,[],[f3069,f8185]) ).
fof(f8185,plain,
( spl0_981
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f3069,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2865,f2831]) ).
fof(f2865,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1299,f2544]) ).
fof(f1299,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f8183,plain,
spl0_980,
inference(avatar_split_clause,[],[f2837,f8181]) ).
fof(f8181,plain,
( spl0_980
<=> ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f2837,plain,
! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f67,f2544]) ).
fof(f67,axiom,
! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f8179,plain,
spl0_979,
inference(avatar_split_clause,[],[f2836,f8177]) ).
fof(f8177,plain,
( spl0_979
<=> ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f2836,plain,
! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f65,f2544]) ).
fof(f65,axiom,
! [X21] : c_less(X21,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f8175,plain,
spl0_978,
inference(avatar_split_clause,[],[f2755,f8173]) ).
fof(f8173,plain,
( spl0_978
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f2755,axiom,
! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
fof(f8171,plain,
spl0_977,
inference(avatar_split_clause,[],[f2754,f8169]) ).
fof(f8169,plain,
( spl0_977
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f2754,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
fof(f8167,plain,
spl0_976,
inference(avatar_split_clause,[],[f2753,f8165]) ).
fof(f8165,plain,
( spl0_976
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f2753,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
fof(f8163,plain,
spl0_975,
inference(avatar_split_clause,[],[f2752,f8161]) ).
fof(f8161,plain,
( spl0_975
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2752,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
fof(f8159,plain,
spl0_974,
inference(avatar_split_clause,[],[f2751,f8157]) ).
fof(f8157,plain,
( spl0_974
<=> ! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2751,axiom,
! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
fof(f8155,plain,
spl0_973,
inference(avatar_split_clause,[],[f2741,f8153]) ).
fof(f8153,plain,
( spl0_973
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2741,axiom,
! [X91,X92] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
fof(f8151,plain,
( spl0_972
| ~ spl0_52
| ~ spl0_865 ),
inference(avatar_split_clause,[],[f7794,f7643,f3508,f8148]) ).
fof(f7643,plain,
( spl0_865
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f7794,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_865 ),
inference(resolution,[],[f7644,f3510]) ).
fof(f7644,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_865 ),
inference(avatar_component_clause,[],[f7643]) ).
fof(f8146,plain,
spl0_971,
inference(avatar_split_clause,[],[f2736,f8144]) ).
fof(f8144,plain,
( spl0_971
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2736,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).
fof(f8142,plain,
spl0_970,
inference(avatar_split_clause,[],[f2699,f8140]) ).
fof(f8140,plain,
( spl0_970
<=> ! [X12,X1] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f2699,axiom,
! [X1,X12] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f8138,plain,
spl0_969,
inference(avatar_split_clause,[],[f2660,f8136]) ).
fof(f2660,axiom,
! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f8134,plain,
spl0_968,
inference(avatar_split_clause,[],[f2534,f8131]) ).
fof(f2534,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
fof(f8129,plain,
spl0_967,
inference(avatar_split_clause,[],[f2492,f8127]) ).
fof(f8127,plain,
( spl0_967
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f2492,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f8125,plain,
spl0_966,
inference(avatar_split_clause,[],[f2491,f8123]) ).
fof(f8123,plain,
( spl0_966
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f2491,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f8121,plain,
spl0_965,
inference(avatar_split_clause,[],[f2474,f8119]) ).
fof(f8119,plain,
( spl0_965
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f2474,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f8117,plain,
spl0_964,
inference(avatar_split_clause,[],[f2473,f8115]) ).
fof(f8115,plain,
( spl0_964
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2473,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f8113,plain,
spl0_963,
inference(avatar_split_clause,[],[f2470,f8111]) ).
fof(f8111,plain,
( spl0_963
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2470,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f8109,plain,
spl0_962,
inference(avatar_split_clause,[],[f2469,f8107]) ).
fof(f8107,plain,
( spl0_962
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2469,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f8105,plain,
spl0_961,
inference(avatar_split_clause,[],[f2379,f8103]) ).
fof(f8103,plain,
( spl0_961
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2379,axiom,
! [X3,X1] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f8101,plain,
spl0_960,
inference(avatar_split_clause,[],[f2377,f8099]) ).
fof(f8099,plain,
( spl0_960
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2377,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f8097,plain,
spl0_959,
inference(avatar_split_clause,[],[f2371,f8095]) ).
fof(f8095,plain,
( spl0_959
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2371,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f8093,plain,
spl0_958,
inference(avatar_split_clause,[],[f2369,f8091]) ).
fof(f8091,plain,
( spl0_958
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2369,axiom,
! [X3,X1] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f8089,plain,
spl0_957,
inference(avatar_split_clause,[],[f2357,f8087]) ).
fof(f8087,plain,
( spl0_957
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2357,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f8085,plain,
spl0_956,
inference(avatar_split_clause,[],[f2354,f8083]) ).
fof(f2354,axiom,
! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f8081,plain,
spl0_955,
inference(avatar_split_clause,[],[f2353,f8079]) ).
fof(f2353,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f8077,plain,
spl0_954,
inference(avatar_split_clause,[],[f2292,f8075]) ).
fof(f8075,plain,
( spl0_954
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2292,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f8073,plain,
spl0_953,
inference(avatar_split_clause,[],[f2291,f8071]) ).
fof(f8071,plain,
( spl0_953
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2291,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f8069,plain,
spl0_952,
inference(avatar_split_clause,[],[f2267,f8067]) ).
fof(f2267,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f8065,plain,
spl0_951,
inference(avatar_split_clause,[],[f2262,f8063]) ).
fof(f2262,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f8061,plain,
spl0_950,
inference(avatar_split_clause,[],[f2251,f8059]) ).
fof(f8059,plain,
( spl0_950
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f2251,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f8057,plain,
spl0_949,
inference(avatar_split_clause,[],[f2250,f8055]) ).
fof(f8055,plain,
( spl0_949
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2250,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f8053,plain,
spl0_948,
inference(avatar_split_clause,[],[f2241,f8051]) ).
fof(f2241,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f8049,plain,
spl0_947,
inference(avatar_split_clause,[],[f2218,f8047]) ).
fof(f2218,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f8045,plain,
spl0_946,
inference(avatar_split_clause,[],[f2217,f8043]) ).
fof(f2217,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f8041,plain,
spl0_945,
inference(avatar_split_clause,[],[f2205,f8039]) ).
fof(f2205,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f8037,plain,
spl0_944,
inference(avatar_split_clause,[],[f2198,f8035]) ).
fof(f2198,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f8033,plain,
spl0_943,
inference(avatar_split_clause,[],[f2196,f8031]) ).
fof(f2196,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f8029,plain,
spl0_942,
inference(avatar_split_clause,[],[f2185,f8027]) ).
fof(f2185,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f8025,plain,
spl0_941,
inference(avatar_split_clause,[],[f2182,f8023]) ).
fof(f8023,plain,
( spl0_941
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f2182,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f8021,plain,
spl0_940,
inference(avatar_split_clause,[],[f2180,f8019]) ).
fof(f8019,plain,
( spl0_940
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f2180,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f8017,plain,
spl0_939,
inference(avatar_split_clause,[],[f2177,f8015]) ).
fof(f8015,plain,
( spl0_939
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f2177,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f8013,plain,
spl0_938,
inference(avatar_split_clause,[],[f2153,f8011]) ).
fof(f2153,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f8009,plain,
spl0_937,
inference(avatar_split_clause,[],[f1865,f8007]) ).
fof(f8007,plain,
( spl0_937
<=> ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1865,axiom,
! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f8005,plain,
spl0_936,
inference(avatar_split_clause,[],[f1818,f8003]) ).
fof(f8003,plain,
( spl0_936
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1818,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f8001,plain,
spl0_935,
inference(avatar_split_clause,[],[f1815,f7999]) ).
fof(f7999,plain,
( spl0_935
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1815,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7997,plain,
spl0_934,
inference(avatar_split_clause,[],[f1805,f7995]) ).
fof(f7995,plain,
( spl0_934
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1805,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7993,plain,
spl0_933,
inference(avatar_split_clause,[],[f1779,f7991]) ).
fof(f7991,plain,
( spl0_933
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1779,axiom,
! [X3,X41,X0] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7989,plain,
spl0_932,
inference(avatar_split_clause,[],[f1750,f7987]) ).
fof(f7987,plain,
( spl0_932
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1750,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
fof(f7985,plain,
( ~ spl0_930
| spl0_931
| ~ spl0_707
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f7788,f7619,f6975,f7982,f7978]) ).
fof(f7978,plain,
( spl0_930
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f7982,plain,
( spl0_931
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f7788,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_707
| ~ spl0_859 ),
inference(superposition,[],[f7620,f6977]) ).
fof(f7976,plain,
spl0_929,
inference(avatar_split_clause,[],[f1735,f7974]) ).
fof(f7974,plain,
( spl0_929
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1735,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7972,plain,
spl0_928,
inference(avatar_split_clause,[],[f1717,f7970]) ).
fof(f7970,plain,
( spl0_928
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1717,axiom,
! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f7968,plain,
spl0_927,
inference(avatar_split_clause,[],[f1588,f7966]) ).
fof(f7966,plain,
( spl0_927
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1588,axiom,
! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7964,plain,
spl0_926,
inference(avatar_split_clause,[],[f1579,f7962]) ).
fof(f7962,plain,
( spl0_926
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1579,axiom,
! [X3,X1,X23] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7960,plain,
spl0_925,
inference(avatar_split_clause,[],[f1562,f7958]) ).
fof(f7958,plain,
( spl0_925
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f1562,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7956,plain,
spl0_924,
inference(avatar_split_clause,[],[f1561,f7954]) ).
fof(f7954,plain,
( spl0_924
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f1561,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7952,plain,
spl0_923,
inference(avatar_split_clause,[],[f1550,f7950]) ).
fof(f7950,plain,
( spl0_923
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1550,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7948,plain,
spl0_922,
inference(avatar_split_clause,[],[f1549,f7946]) ).
fof(f7946,plain,
( spl0_922
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f1549,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7944,plain,
spl0_921,
inference(avatar_split_clause,[],[f1537,f7942]) ).
fof(f7942,plain,
( spl0_921
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f1537,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7940,plain,
spl0_920,
inference(avatar_split_clause,[],[f1513,f7938]) ).
fof(f7938,plain,
( spl0_920
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1513,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7936,plain,
( spl0_919
| ~ spl0_48
| ~ spl0_852 ),
inference(avatar_split_clause,[],[f7768,f7591,f3488,f7933]) ).
fof(f7933,plain,
( spl0_919
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f3488,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f7591,plain,
( spl0_852
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f7768,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_48
| ~ spl0_852 ),
inference(resolution,[],[f7592,f3490]) ).
fof(f3490,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_48 ),
inference(avatar_component_clause,[],[f3488]) ).
fof(f7592,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_852 ),
inference(avatar_component_clause,[],[f7591]) ).
fof(f7931,plain,
spl0_918,
inference(avatar_split_clause,[],[f1499,f7929]) ).
fof(f1499,axiom,
! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7927,plain,
spl0_917,
inference(avatar_split_clause,[],[f1498,f7925]) ).
fof(f1498,axiom,
! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7923,plain,
spl0_916,
inference(avatar_split_clause,[],[f1490,f7921]) ).
fof(f7921,plain,
( spl0_916
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1490,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f7919,plain,
spl0_915,
inference(avatar_split_clause,[],[f1419,f7917]) ).
fof(f1419,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7915,plain,
spl0_914,
inference(avatar_split_clause,[],[f1392,f7913]) ).
fof(f1392,axiom,
! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7911,plain,
spl0_913,
inference(avatar_split_clause,[],[f1385,f7909]) ).
fof(f7909,plain,
( spl0_913
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1385,axiom,
! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7907,plain,
spl0_912,
inference(avatar_split_clause,[],[f1376,f7905]) ).
fof(f7905,plain,
( spl0_912
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1376,axiom,
! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7903,plain,
spl0_911,
inference(avatar_split_clause,[],[f1375,f7901]) ).
fof(f1375,axiom,
! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7899,plain,
spl0_910,
inference(avatar_split_clause,[],[f1308,f7897]) ).
fof(f7897,plain,
( spl0_910
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1308,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7895,plain,
spl0_909,
inference(avatar_split_clause,[],[f1298,f7893]) ).
fof(f7893,plain,
( spl0_909
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1298,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7891,plain,
( spl0_908
| ~ spl0_21
| ~ spl0_851 ),
inference(avatar_split_clause,[],[f7766,f7587,f3353,f7888]) ).
fof(f7888,plain,
( spl0_908
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f3353,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f7587,plain,
( spl0_851
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f7766,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_21
| ~ spl0_851 ),
inference(resolution,[],[f7588,f3355]) ).
fof(f3355,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f3353]) ).
fof(f7588,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_851 ),
inference(avatar_component_clause,[],[f7587]) ).
fof(f7886,plain,
spl0_907,
inference(avatar_split_clause,[],[f1297,f7884]) ).
fof(f7884,plain,
( spl0_907
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1297,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7882,plain,
spl0_906,
inference(avatar_split_clause,[],[f1177,f7880]) ).
fof(f7880,plain,
( spl0_906
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1177,axiom,
! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7878,plain,
spl0_905,
inference(avatar_split_clause,[],[f1171,f7876]) ).
fof(f7876,plain,
( spl0_905
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f1171,axiom,
! [X40,X1] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7873,plain,
spl0_904,
inference(avatar_split_clause,[],[f1167,f7871]) ).
fof(f7871,plain,
( spl0_904
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f1167,axiom,
! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7869,plain,
spl0_903,
inference(avatar_split_clause,[],[f252,f7867]) ).
fof(f7867,plain,
( spl0_903
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f252,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f7865,plain,
spl0_902,
inference(avatar_split_clause,[],[f246,f7863]) ).
fof(f7863,plain,
( spl0_902
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f246,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f7861,plain,
spl0_901,
inference(avatar_split_clause,[],[f196,f7859]) ).
fof(f7859,plain,
( spl0_901
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f196,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f7857,plain,
spl0_900,
inference(avatar_split_clause,[],[f94,f7855]) ).
fof(f7855,plain,
( spl0_900
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f94,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f7853,plain,
spl0_899,
inference(avatar_split_clause,[],[f93,f7851]) ).
fof(f7851,plain,
( spl0_899
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f93,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f7849,plain,
spl0_898,
inference(avatar_split_clause,[],[f92,f7847]) ).
fof(f7847,plain,
( spl0_898
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f92,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f7845,plain,
( spl0_897
| ~ spl0_22
| ~ spl0_843 ),
inference(avatar_split_clause,[],[f7760,f7555,f3358,f7842]) ).
fof(f7842,plain,
( spl0_897
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f3358,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f7555,plain,
( spl0_843
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f7760,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_22
| ~ spl0_843 ),
inference(resolution,[],[f7556,f3360]) ).
fof(f3360,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f3358]) ).
fof(f7556,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_843 ),
inference(avatar_component_clause,[],[f7555]) ).
fof(f7840,plain,
spl0_896,
inference(avatar_split_clause,[],[f91,f7838]) ).
fof(f7838,plain,
( spl0_896
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f91,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7836,plain,
spl0_895,
inference(avatar_split_clause,[],[f89,f7834]) ).
fof(f7834,plain,
( spl0_895
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f89,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f7832,plain,
spl0_894,
inference(avatar_split_clause,[],[f88,f7830]) ).
fof(f7830,plain,
( spl0_894
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f88,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7828,plain,
spl0_893,
inference(avatar_split_clause,[],[f87,f7826]) ).
fof(f7826,plain,
( spl0_893
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f87,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f7824,plain,
spl0_892,
inference(avatar_split_clause,[],[f86,f7822]) ).
fof(f7822,plain,
( spl0_892
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f86,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7820,plain,
spl0_891,
inference(avatar_split_clause,[],[f37,f7818]) ).
fof(f37,axiom,
! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7812,plain,
( spl0_890
| ~ spl0_50
| ~ spl0_842 ),
inference(avatar_split_clause,[],[f7755,f7551,f3498,f7809]) ).
fof(f7809,plain,
( spl0_890
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f3498,plain,
( spl0_50
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f7551,plain,
( spl0_842
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f7755,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_50
| ~ spl0_842 ),
inference(resolution,[],[f7552,f3500]) ).
fof(f3500,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f3498]) ).
fof(f7552,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_842 ),
inference(avatar_component_clause,[],[f7551]) ).
fof(f7804,plain,
( spl0_889
| ~ spl0_641
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f7749,f7539,f5917,f7801]) ).
fof(f7539,plain,
( spl0_839
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f7749,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_839 ),
inference(superposition,[],[f7540,f5919]) ).
fof(f7540,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_839 ),
inference(avatar_component_clause,[],[f7539]) ).
fof(f7793,plain,
( spl0_888
| ~ spl0_640
| ~ spl0_839 ),
inference(avatar_split_clause,[],[f7748,f7539,f5912,f7790]) ).
fof(f7790,plain,
( spl0_888
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f7748,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_839 ),
inference(superposition,[],[f7540,f5914]) ).
fof(f7759,plain,
( spl0_887
| ~ spl0_822
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f7742,f7515,f7462,f7757]) ).
fof(f7462,plain,
( spl0_822
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f7742,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_822
| ~ spl0_833 ),
inference(superposition,[],[f7516,f7463]) ).
fof(f7463,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_822 ),
inference(avatar_component_clause,[],[f7462]) ).
fof(f7731,plain,
spl0_886,
inference(avatar_split_clause,[],[f3147,f7729]) ).
fof(f7729,plain,
( spl0_886
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f3147,plain,
! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f3146,f2831]) ).
fof(f3146,plain,
! [X15] :
( c_1 = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2965,f2831]) ).
fof(f2965,plain,
! [X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1227,f2544,f2544]) ).
fof(f1227,axiom,
! [X15] :
( c_Suc(c_0) = X15
| ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7727,plain,
spl0_885,
inference(avatar_split_clause,[],[f3057,f7725]) ).
fof(f7725,plain,
( spl0_885
<=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f3057,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1),
inference(forward_demodulation,[],[f2842,f2386]) ).
fof(f2386,axiom,
! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2842,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X1),X13,X1,X1),
inference(definition_unfolding,[],[f2604,f2373]) ).
fof(f2604,axiom,
! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7723,plain,
spl0_884,
inference(avatar_split_clause,[],[f2846,f7721]) ).
fof(f7719,plain,
spl0_883,
inference(avatar_split_clause,[],[f2844,f7716]) ).
fof(f2844,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2133,f2113]) ).
fof(f2133,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7714,plain,
spl0_882,
inference(avatar_split_clause,[],[f2831,f7711]) ).
fof(f7711,plain,
( spl0_882
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f7709,plain,
spl0_881,
inference(avatar_split_clause,[],[f2827,f7707]) ).
fof(f7707,plain,
( spl0_881
<=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2827,plain,
! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2025,f2544]) ).
fof(f2025,axiom,
! [X15] : c_0 != c_Suc(X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OZero__not__Suc_0) ).
fof(f7705,plain,
spl0_880,
inference(avatar_split_clause,[],[f2705,f7703]) ).
fof(f7703,plain,
( spl0_880
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2705,axiom,
! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7701,plain,
spl0_879,
inference(avatar_split_clause,[],[f2684,f7699]) ).
fof(f2684,axiom,
! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7697,plain,
spl0_878,
inference(avatar_split_clause,[],[f2668,f7695]) ).
fof(f7695,plain,
( spl0_878
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2668,axiom,
! [X1,X12] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7693,plain,
spl0_877,
inference(avatar_split_clause,[],[f2648,f7691]) ).
fof(f7691,plain,
( spl0_877
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2648,axiom,
! [X3,X1] : c_Union(c_Pow(X3,X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7689,plain,
spl0_876,
inference(avatar_split_clause,[],[f2590,f7687]) ).
fof(f7687,plain,
( spl0_876
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2590,axiom,
! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7685,plain,
spl0_875,
inference(avatar_split_clause,[],[f2588,f7683]) ).
fof(f7683,plain,
( spl0_875
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f2588,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7681,plain,
spl0_874,
inference(avatar_split_clause,[],[f2587,f7679]) ).
fof(f7679,plain,
( spl0_874
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2587,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7677,plain,
spl0_873,
inference(avatar_split_clause,[],[f2549,f7675]) ).
fof(f7675,plain,
( spl0_873
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2549,axiom,
! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7673,plain,
spl0_872,
inference(avatar_split_clause,[],[f2394,f7671]) ).
fof(f7671,plain,
( spl0_872
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2394,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7669,plain,
spl0_871,
inference(avatar_split_clause,[],[f2374,f7667]) ).
fof(f7667,plain,
( spl0_871
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2374,axiom,
! [X2,X1,X85] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7665,plain,
spl0_870,
inference(avatar_split_clause,[],[f2372,f7663]) ).
fof(f7663,plain,
( spl0_870
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2372,axiom,
! [X3,X1] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7661,plain,
spl0_869,
inference(avatar_split_clause,[],[f2243,f7659]) ).
fof(f2243,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7657,plain,
spl0_868,
inference(avatar_split_clause,[],[f2238,f7655]) ).
fof(f2238,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7653,plain,
spl0_867,
inference(avatar_split_clause,[],[f2220,f7651]) ).
fof(f7651,plain,
( spl0_867
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2220,axiom,
! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
fof(f7649,plain,
spl0_866,
inference(avatar_split_clause,[],[f2176,f7647]) ).
fof(f7647,plain,
( spl0_866
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2176,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7645,plain,
spl0_865,
inference(avatar_split_clause,[],[f2169,f7643]) ).
fof(f2169,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7641,plain,
spl0_864,
inference(avatar_split_clause,[],[f2162,f7639]) ).
fof(f7639,plain,
( spl0_864
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2162,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7637,plain,
spl0_863,
inference(avatar_split_clause,[],[f2161,f7635]) ).
fof(f7635,plain,
( spl0_863
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2161,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7633,plain,
spl0_862,
inference(avatar_split_clause,[],[f2158,f7631]) ).
fof(f7631,plain,
( spl0_862
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2158,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7629,plain,
spl0_861,
inference(avatar_split_clause,[],[f2157,f7627]) ).
fof(f7627,plain,
( spl0_861
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2157,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7625,plain,
spl0_860,
inference(avatar_split_clause,[],[f2144,f7623]) ).
fof(f7623,plain,
( spl0_860
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2144,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7621,plain,
spl0_859,
inference(avatar_split_clause,[],[f2143,f7619]) ).
fof(f2143,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7617,plain,
spl0_858,
inference(avatar_split_clause,[],[f2089,f7615]) ).
fof(f7615,plain,
( spl0_858
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f2089,axiom,
! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7613,plain,
spl0_857,
inference(avatar_split_clause,[],[f2088,f7611]) ).
fof(f2088,axiom,
! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7609,plain,
spl0_856,
inference(avatar_split_clause,[],[f2087,f7607]) ).
fof(f7607,plain,
( spl0_856
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2087,axiom,
! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7605,plain,
spl0_855,
inference(avatar_split_clause,[],[f2048,f7603]) ).
fof(f7603,plain,
( spl0_855
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2048,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7601,plain,
spl0_854,
inference(avatar_split_clause,[],[f2042,f7599]) ).
fof(f2042,axiom,
! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7597,plain,
spl0_853,
inference(avatar_split_clause,[],[f2040,f7595]) ).
fof(f7595,plain,
( spl0_853
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2040,axiom,
! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7593,plain,
spl0_852,
inference(avatar_split_clause,[],[f1812,f7591]) ).
fof(f1812,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f7589,plain,
spl0_851,
inference(avatar_split_clause,[],[f1808,f7587]) ).
fof(f1808,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7585,plain,
spl0_850,
inference(avatar_split_clause,[],[f1790,f7583]) ).
fof(f7583,plain,
( spl0_850
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1790,axiom,
! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7581,plain,
spl0_849,
inference(avatar_split_clause,[],[f1788,f7579]) ).
fof(f7579,plain,
( spl0_849
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1788,axiom,
! [X82,X41,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7577,plain,
spl0_848,
inference(avatar_split_clause,[],[f1732,f7575]) ).
fof(f7575,plain,
( spl0_848
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1732,axiom,
! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7573,plain,
spl0_847,
inference(avatar_split_clause,[],[f1711,f7571]) ).
fof(f7571,plain,
( spl0_847
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1711,axiom,
! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7569,plain,
spl0_846,
inference(avatar_split_clause,[],[f1631,f7567]) ).
fof(f7567,plain,
( spl0_846
<=> ! [X41,X43,X47] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1631,axiom,
! [X41,X47,X43] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7565,plain,
spl0_845,
inference(avatar_split_clause,[],[f1542,f7563]) ).
fof(f7563,plain,
( spl0_845
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1542,axiom,
! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7561,plain,
spl0_844,
inference(avatar_split_clause,[],[f1478,f7559]) ).
fof(f1478,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7557,plain,
spl0_843,
inference(avatar_split_clause,[],[f1401,f7555]) ).
fof(f1401,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7553,plain,
spl0_842,
inference(avatar_split_clause,[],[f1396,f7551]) ).
fof(f1396,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
fof(f7549,plain,
spl0_841,
inference(avatar_split_clause,[],[f1387,f7547]) ).
fof(f1387,axiom,
! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7545,plain,
spl0_840,
inference(avatar_split_clause,[],[f1373,f7543]) ).
fof(f7543,plain,
( spl0_840
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f1373,axiom,
! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7541,plain,
spl0_839,
inference(avatar_split_clause,[],[f1367,f7539]) ).
fof(f1367,axiom,
! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7537,plain,
spl0_838,
inference(avatar_split_clause,[],[f1253,f7535]) ).
fof(f7535,plain,
( spl0_838
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f1253,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7533,plain,
spl0_837,
inference(avatar_split_clause,[],[f1252,f7531]) ).
fof(f7531,plain,
( spl0_837
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f1252,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7529,plain,
spl0_836,
inference(avatar_split_clause,[],[f1249,f7527]) ).
fof(f7527,plain,
( spl0_836
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f1249,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7525,plain,
spl0_835,
inference(avatar_split_clause,[],[f1248,f7523]) ).
fof(f7523,plain,
( spl0_835
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f1248,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7521,plain,
spl0_834,
inference(avatar_split_clause,[],[f1225,f7519]) ).
fof(f7519,plain,
( spl0_834
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f1225,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7517,plain,
spl0_833,
inference(avatar_split_clause,[],[f1215,f7515]) ).
fof(f1215,axiom,
! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7513,plain,
spl0_832,
inference(avatar_split_clause,[],[f1202,f7511]) ).
fof(f7511,plain,
( spl0_832
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f1202,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7509,plain,
spl0_831,
inference(avatar_split_clause,[],[f1181,f7507]) ).
fof(f7507,plain,
( spl0_831
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f1181,axiom,
! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7505,plain,
spl0_830,
inference(avatar_split_clause,[],[f95,f7503]) ).
fof(f7503,plain,
( spl0_830
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f95,axiom,
! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7501,plain,
spl0_829,
inference(avatar_split_clause,[],[f90,f7499]) ).
fof(f7499,plain,
( spl0_829
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f90,axiom,
! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7497,plain,
spl0_828,
inference(avatar_split_clause,[],[f61,f7495]) ).
fof(f7495,plain,
( spl0_828
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f61,axiom,
! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7493,plain,
spl0_827,
inference(avatar_split_clause,[],[f45,f7491]) ).
fof(f7491,plain,
( spl0_827
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f45,axiom,
! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7489,plain,
spl0_826,
inference(avatar_split_clause,[],[f42,f7487]) ).
fof(f42,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7485,plain,
spl0_825,
inference(avatar_split_clause,[],[f41,f7483]) ).
fof(f41,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7481,plain,
spl0_824,
inference(avatar_split_clause,[],[f26,f7479]) ).
fof(f7479,plain,
( spl0_824
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f26,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7477,plain,
spl0_823,
inference(avatar_split_clause,[],[f25,f7475]) ).
fof(f7475,plain,
( spl0_823
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f25,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7464,plain,
spl0_822,
inference(avatar_split_clause,[],[f3067,f7462]) ).
fof(f3067,plain,
! [X3] : c_div(X3,c_1,tc_nat) = X3,
inference(forward_demodulation,[],[f2857,f2831]) ).
fof(f2857,plain,
! [X3] : c_div(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X3,
inference(definition_unfolding,[],[f1214,f2544]) ).
fof(f1214,axiom,
! [X3] : c_div(X3,c_Suc(c_0),tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7460,plain,
spl0_821,
inference(avatar_split_clause,[],[f3065,f7457]) ).
fof(f7457,plain,
( spl0_821
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f3065,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2854,f2831]) ).
fof(f2854,plain,
c_times(c_1,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2094,f2544]) ).
fof(f2094,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
fof(f7455,plain,
spl0_820,
inference(avatar_split_clause,[],[f3063,f7453]) ).
fof(f7453,plain,
( spl0_820
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f3063,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
inference(forward_demodulation,[],[f2853,f2831]) ).
fof(f2853,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1231,f2544]) ).
fof(f1231,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7451,plain,
spl0_819,
inference(avatar_split_clause,[],[f3062,f7448]) ).
fof(f3062,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f1867,f2156]) ).
fof(f1867,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7446,plain,
spl0_818,
inference(avatar_split_clause,[],[f3060,f7444]) ).
fof(f7444,plain,
( spl0_818
<=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f3060,plain,
! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3,
inference(forward_demodulation,[],[f2848,f1514]) ).
fof(f1514,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
fof(f2848,plain,
! [X41,X3] : c_append(c_List_Orev(c_List_Olist_ONil,X41),X3,X41) = X3,
inference(definition_unfolding,[],[f1586,f1585]) ).
fof(f1586,axiom,
! [X3,X41] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7442,plain,
spl0_817,
inference(avatar_split_clause,[],[f3058,f7439]) ).
fof(f7439,plain,
( spl0_817
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f3058,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2845,f2156]) ).
fof(f2845,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2125,f2129]) ).
fof(f2125,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7437,plain,
spl0_816,
inference(avatar_split_clause,[],[f2825,f7435]) ).
fof(f2825,axiom,
! [X88] : c_lessequals(X88,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Osynth__increasing_0) ).
fof(f7433,plain,
spl0_815,
inference(avatar_split_clause,[],[f2805,f7431]) ).
fof(f7431,plain,
( spl0_815
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2805,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
fof(f7429,plain,
spl0_814,
inference(avatar_split_clause,[],[f2803,f7427]) ).
fof(f7427,plain,
( spl0_814
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2803,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
fof(f7425,plain,
spl0_813,
inference(avatar_split_clause,[],[f2799,f7423]) ).
fof(f7423,plain,
( spl0_813
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2799,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__parts_0) ).
fof(f7421,plain,
spl0_812,
inference(avatar_split_clause,[],[f2792,f7419]) ).
fof(f7419,plain,
( spl0_812
<=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2792,axiom,
! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__idem_0) ).
fof(f7417,plain,
spl0_811,
inference(avatar_split_clause,[],[f2785,f7415]) ).
fof(f7415,plain,
( spl0_811
<=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f2785,axiom,
! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_ONumber__synth_0) ).
fof(f7413,plain,
spl0_810,
inference(avatar_split_clause,[],[f2772,f7411]) ).
fof(f7411,plain,
( spl0_810
<=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f2772,axiom,
! [X88,X12] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OAgent__synth_0) ).
fof(f7409,plain,
spl0_809,
inference(avatar_split_clause,[],[f2763,f7407]) ).
fof(f2763,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).
fof(f7405,plain,
spl0_808,
inference(avatar_split_clause,[],[f2762,f7403]) ).
fof(f2762,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).
fof(f7401,plain,
spl0_807,
inference(avatar_split_clause,[],[f2761,f7399]) ).
fof(f2761,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).
fof(f7397,plain,
spl0_806,
inference(avatar_split_clause,[],[f2760,f7395]) ).
fof(f2760,axiom,
! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).
fof(f7393,plain,
spl0_805,
inference(avatar_split_clause,[],[f2738,f7391]) ).
fof(f7391,plain,
( spl0_805
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2738,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).
fof(f7389,plain,
spl0_804,
inference(avatar_split_clause,[],[f2673,f7387]) ).
fof(f2673,axiom,
! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
fof(f7385,plain,
spl0_803,
inference(avatar_split_clause,[],[f2639,f7383]) ).
fof(f7383,plain,
( spl0_803
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2639,axiom,
! [X3,X1] : c_union(X3,c_emptyset,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7381,plain,
spl0_802,
inference(avatar_split_clause,[],[f2638,f7379]) ).
fof(f2638,axiom,
! [X3,X1] : c_union(c_emptyset,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7377,plain,
spl0_801,
inference(avatar_split_clause,[],[f2634,f7375]) ).
fof(f7375,plain,
( spl0_801
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7373,plain,
spl0_800,
inference(avatar_split_clause,[],[f2633,f7371]) ).
fof(f7371,plain,
( spl0_800
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2633,axiom,
! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7369,plain,
spl0_799,
inference(avatar_split_clause,[],[f2632,f7367]) ).
fof(f2632,axiom,
! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7365,plain,
spl0_798,
inference(avatar_split_clause,[],[f2580,f7363]) ).
fof(f7363,plain,
( spl0_798
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2580,axiom,
! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7361,plain,
spl0_797,
inference(avatar_split_clause,[],[f2576,f7359]) ).
fof(f7359,plain,
( spl0_797
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2576,axiom,
! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7357,plain,
spl0_796,
inference(avatar_split_clause,[],[f2511,f7355]) ).
fof(f7355,plain,
( spl0_796
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2511,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7353,plain,
spl0_795,
inference(avatar_split_clause,[],[f2499,f7351]) ).
fof(f7351,plain,
( spl0_795
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2499,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7349,plain,
spl0_794,
inference(avatar_split_clause,[],[f2494,f7347]) ).
fof(f7347,plain,
( spl0_794
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2494,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7345,plain,
spl0_793,
inference(avatar_split_clause,[],[f2493,f7343]) ).
fof(f7343,plain,
( spl0_793
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2493,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7341,plain,
spl0_792,
inference(avatar_split_clause,[],[f2381,f7339]) ).
fof(f7339,plain,
( spl0_792
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2381,axiom,
! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7337,plain,
spl0_791,
inference(avatar_split_clause,[],[f2380,f7335]) ).
fof(f7335,plain,
( spl0_791
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2380,axiom,
! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7333,plain,
spl0_790,
inference(avatar_split_clause,[],[f2378,f7331]) ).
fof(f7331,plain,
( spl0_790
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2378,axiom,
! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7329,plain,
spl0_789,
inference(avatar_split_clause,[],[f2370,f7327]) ).
fof(f7327,plain,
( spl0_789
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2370,axiom,
! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7325,plain,
spl0_788,
inference(avatar_split_clause,[],[f2368,f7323]) ).
fof(f7323,plain,
( spl0_788
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2368,axiom,
! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7321,plain,
spl0_787,
inference(avatar_split_clause,[],[f2344,f7319]) ).
fof(f2344,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7317,plain,
spl0_786,
inference(avatar_split_clause,[],[f2269,f7315]) ).
fof(f7315,plain,
( spl0_786
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f2269,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7313,plain,
spl0_785,
inference(avatar_split_clause,[],[f2156,f7310]) ).
fof(f7308,plain,
spl0_784,
inference(avatar_split_clause,[],[f2102,f7306]) ).
fof(f2102,axiom,
! [X3] : c_minus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7304,plain,
spl0_783,
inference(avatar_split_clause,[],[f2100,f7302]) ).
fof(f2100,axiom,
! [X3] : c_plus(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7300,plain,
spl0_782,
inference(avatar_split_clause,[],[f2098,f7298]) ).
fof(f7298,plain,
( spl0_782
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f2098,axiom,
! [X21] : c_0 = c_times(c_0,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7296,plain,
spl0_781,
inference(avatar_split_clause,[],[f2056,f7294]) ).
fof(f7294,plain,
( spl0_781
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f2056,axiom,
! [X15] : c_0 = c_times(X15,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7292,plain,
spl0_780,
inference(avatar_split_clause,[],[f2054,f7290]) ).
fof(f7290,plain,
( spl0_780
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f2054,axiom,
! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7288,plain,
spl0_779,
inference(avatar_split_clause,[],[f2053,f7286]) ).
fof(f7286,plain,
( spl0_779
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f2053,axiom,
! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7284,plain,
spl0_778,
inference(avatar_split_clause,[],[f2051,f7282]) ).
fof(f7282,plain,
( spl0_778
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2051,axiom,
! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7280,plain,
spl0_777,
inference(avatar_split_clause,[],[f2050,f7278]) ).
fof(f7278,plain,
( spl0_777
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2050,axiom,
! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7276,plain,
spl0_776,
inference(avatar_split_clause,[],[f2041,f7274]) ).
fof(f2041,axiom,
! [X15] : c_0 = c_minus(X15,X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7272,plain,
spl0_775,
inference(avatar_split_clause,[],[f2034,f7270]) ).
fof(f2034,axiom,
! [X21] : c_0 = c_minus(c_0,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7268,plain,
spl0_774,
inference(avatar_split_clause,[],[f2026,f7266]) ).
fof(f2026,axiom,
! [X3] : c_plus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7264,plain,
spl0_773,
inference(avatar_split_clause,[],[f1763,f7262]) ).
fof(f7262,plain,
( spl0_773
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f1763,axiom,
! [X1,X12] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7260,plain,
spl0_772,
inference(avatar_split_clause,[],[f1762,f7258]) ).
fof(f7258,plain,
( spl0_772
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1762,axiom,
! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7256,plain,
spl0_771,
inference(avatar_split_clause,[],[f1747,f7254]) ).
fof(f7254,plain,
( spl0_771
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1747,axiom,
! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
fof(f7252,plain,
spl0_770,
inference(avatar_split_clause,[],[f1741,f7250]) ).
fof(f7250,plain,
( spl0_770
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f1741,axiom,
! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7248,plain,
spl0_769,
inference(avatar_split_clause,[],[f1722,f7246]) ).
fof(f1722,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7244,plain,
spl0_768,
inference(avatar_split_clause,[],[f1719,f7242]) ).
fof(f7242,plain,
( spl0_768
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1719,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7240,plain,
spl0_767,
inference(avatar_split_clause,[],[f1707,f7238]) ).
fof(f1707,axiom,
! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7236,plain,
spl0_766,
inference(avatar_split_clause,[],[f1689,f7234]) ).
fof(f7234,plain,
( spl0_766
<=> ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f1689,axiom,
! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onot__Cons__self_0) ).
fof(f7232,plain,
spl0_765,
inference(avatar_split_clause,[],[f1628,f7230]) ).
fof(f7230,plain,
( spl0_765
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1628,axiom,
! [X65,X41] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7228,plain,
spl0_764,
inference(avatar_split_clause,[],[f1624,f7226]) ).
fof(f7226,plain,
( spl0_764
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f1624,axiom,
! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f7224,plain,
spl0_763,
inference(avatar_split_clause,[],[f1615,f7222]) ).
fof(f7222,plain,
( spl0_763
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1615,axiom,
! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7220,plain,
spl0_762,
inference(avatar_split_clause,[],[f1598,f7218]) ).
fof(f7218,plain,
( spl0_762
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f1598,axiom,
! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7216,plain,
spl0_761,
inference(avatar_split_clause,[],[f1569,f7214]) ).
fof(f7214,plain,
( spl0_761
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1569,axiom,
! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7212,plain,
spl0_760,
inference(avatar_split_clause,[],[f1568,f7210]) ).
fof(f7210,plain,
( spl0_760
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1568,axiom,
! [X21,X41] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7208,plain,
spl0_759,
inference(avatar_split_clause,[],[f1494,f7206]) ).
fof(f7206,plain,
( spl0_759
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1494,axiom,
! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7204,plain,
spl0_758,
inference(avatar_split_clause,[],[f1491,f7202]) ).
fof(f7202,plain,
( spl0_758
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1491,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7200,plain,
spl0_757,
inference(avatar_split_clause,[],[f1489,f7198]) ).
fof(f7198,plain,
( spl0_757
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f1489,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7196,plain,
spl0_756,
inference(avatar_split_clause,[],[f1474,f7194]) ).
fof(f7194,plain,
( spl0_756
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f1474,axiom,
! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7192,plain,
spl0_755,
inference(avatar_split_clause,[],[f1466,f7190]) ).
fof(f7190,plain,
( spl0_755
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f1466,axiom,
! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7188,plain,
spl0_754,
inference(avatar_split_clause,[],[f1464,f7186]) ).
fof(f7186,plain,
( spl0_754
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f1464,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7184,plain,
spl0_753,
inference(avatar_split_clause,[],[f1432,f7182]) ).
fof(f1432,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7180,plain,
spl0_752,
inference(avatar_split_clause,[],[f1364,f7178]) ).
fof(f7178,plain,
( spl0_752
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f1364,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7176,plain,
spl0_751,
inference(avatar_split_clause,[],[f1363,f7174]) ).
fof(f7174,plain,
( spl0_751
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1363,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7172,plain,
spl0_750,
inference(avatar_split_clause,[],[f1358,f7170]) ).
fof(f7170,plain,
( spl0_750
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f1358,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7168,plain,
spl0_749,
inference(avatar_split_clause,[],[f1357,f7166]) ).
fof(f7166,plain,
( spl0_749
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f1357,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7164,plain,
spl0_748,
inference(avatar_split_clause,[],[f1350,f7161]) ).
fof(f7161,plain,
( spl0_748
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f1350,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f7159,plain,
spl0_747,
inference(avatar_split_clause,[],[f1245,f7157]) ).
fof(f7157,plain,
( spl0_747
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f1245,axiom,
! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
fof(f7155,plain,
spl0_746,
inference(avatar_split_clause,[],[f1241,f7153]) ).
fof(f7153,plain,
( spl0_746
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f1241,axiom,
! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7151,plain,
spl0_745,
inference(avatar_split_clause,[],[f1230,f7149]) ).
fof(f1230,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7147,plain,
spl0_744,
inference(avatar_split_clause,[],[f1213,f7145]) ).
fof(f7145,plain,
( spl0_744
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1213,axiom,
! [X15] : c_0 = c_div(c_0,X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7143,plain,
spl0_743,
inference(avatar_split_clause,[],[f1212,f7141]) ).
fof(f7141,plain,
( spl0_743
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f1212,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7139,plain,
spl0_742,
inference(avatar_split_clause,[],[f1211,f7137]) ).
fof(f7137,plain,
( spl0_742
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f1211,axiom,
! [X18] : c_0 = c_div(X18,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7135,plain,
spl0_741,
inference(avatar_split_clause,[],[f1183,f7133]) ).
fof(f7133,plain,
( spl0_741
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1183,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7131,plain,
spl0_740,
inference(avatar_split_clause,[],[f1182,f7129]) ).
fof(f7129,plain,
( spl0_740
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1182,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7127,plain,
spl0_739,
inference(avatar_split_clause,[],[f1176,f7125]) ).
fof(f7125,plain,
( spl0_739
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1176,axiom,
! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f7123,plain,
spl0_738,
inference(avatar_split_clause,[],[f68,f7121]) ).
fof(f7121,plain,
( spl0_738
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7119,plain,
( spl0_737
| ~ spl0_640
| ~ spl0_680 ),
inference(avatar_split_clause,[],[f7101,f6851,f5912,f7116]) ).
fof(f7116,plain,
( spl0_737
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f6851,plain,
( spl0_680
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f7101,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_680 ),
inference(superposition,[],[f6852,f5914]) ).
fof(f6852,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_680 ),
inference(avatar_component_clause,[],[f6851]) ).
fof(f7112,plain,
( ~ spl0_736
| ~ spl0_641
| ~ spl0_678 ),
inference(avatar_split_clause,[],[f7098,f6843,f5917,f7109]) ).
fof(f7109,plain,
( spl0_736
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f6843,plain,
( spl0_678
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f7098,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_678 ),
inference(superposition,[],[f6844,f5919]) ).
fof(f6844,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_678 ),
inference(avatar_component_clause,[],[f6843]) ).
fof(f7107,plain,
( ~ spl0_735
| ~ spl0_640
| ~ spl0_678 ),
inference(avatar_split_clause,[],[f7097,f6843,f5912,f7104]) ).
fof(f7104,plain,
( spl0_735
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f7097,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_678 ),
inference(superposition,[],[f6844,f5914]) ).
fof(f7096,plain,
spl0_734,
inference(avatar_split_clause,[],[f3064,f7093]) ).
fof(f7093,plain,
( spl0_734
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f3064,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1391,f1374]) ).
fof(f1374,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f1391,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f7091,plain,
spl0_733,
inference(avatar_split_clause,[],[f3059,f7089]) ).
fof(f7089,plain,
( spl0_733
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f3059,plain,
! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
inference(forward_demodulation,[],[f2847,f2831]) ).
fof(f2847,plain,
! [X3] : c_Binomial_Obinomial(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X3,
inference(definition_unfolding,[],[f1161,f2544]) ).
fof(f1161,axiom,
! [X3] : c_Binomial_Obinomial(X3,c_Suc(c_0)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f7087,plain,
spl0_732,
inference(avatar_split_clause,[],[f2830,f7084]) ).
fof(f7082,plain,
spl0_731,
inference(avatar_split_clause,[],[f2740,f7080]) ).
fof(f7080,plain,
( spl0_731
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2740,axiom,
! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
fof(f7078,plain,
spl0_730,
inference(avatar_split_clause,[],[f2739,f7075]) ).
fof(f7075,plain,
( spl0_730
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2739,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).
fof(f7073,plain,
spl0_729,
inference(avatar_split_clause,[],[f2737,f7070]) ).
fof(f7070,plain,
( spl0_729
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2737,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).
fof(f7068,plain,
spl0_728,
inference(avatar_split_clause,[],[f2714,f7066]) ).
fof(f7066,plain,
( spl0_728
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2714,axiom,
! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f7064,plain,
spl0_727,
inference(avatar_split_clause,[],[f2698,f7062]) ).
fof(f7062,plain,
( spl0_727
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f2698,axiom,
! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f7060,plain,
spl0_726,
inference(avatar_split_clause,[],[f2691,f7058]) ).
fof(f7058,plain,
( spl0_726
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2691,axiom,
! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f7056,plain,
spl0_725,
inference(avatar_split_clause,[],[f2651,f7054]) ).
fof(f7054,plain,
( spl0_725
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f7052,plain,
spl0_724,
inference(avatar_split_clause,[],[f2649,f7050]) ).
fof(f7050,plain,
( spl0_724
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f7048,plain,
spl0_723,
inference(avatar_split_clause,[],[f2625,f7046]) ).
fof(f7046,plain,
( spl0_723
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f7044,plain,
spl0_722,
inference(avatar_split_clause,[],[f2619,f7042]) ).
fof(f7042,plain,
( spl0_722
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f7040,plain,
spl0_721,
inference(avatar_split_clause,[],[f2612,f7038]) ).
fof(f7038,plain,
( spl0_721
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f7036,plain,
spl0_720,
inference(avatar_split_clause,[],[f2567,f7033]) ).
fof(f7033,plain,
( spl0_720
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2567,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f7031,plain,
spl0_719,
inference(avatar_split_clause,[],[f2528,f7028]) ).
fof(f7028,plain,
( spl0_719
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2528,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f7026,plain,
spl0_718,
inference(avatar_split_clause,[],[f2386,f7024]) ).
fof(f7022,plain,
spl0_717,
inference(avatar_split_clause,[],[f2164,f7019]) ).
fof(f7019,plain,
( spl0_717
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f2164,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__2_0) ).
fof(f7017,plain,
spl0_716,
inference(avatar_split_clause,[],[f2163,f7014]) ).
fof(f7014,plain,
( spl0_716
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2163,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__1_0) ).
fof(f7012,plain,
spl0_715,
inference(avatar_split_clause,[],[f2152,f7010]) ).
fof(f7010,plain,
( spl0_715
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f2152,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f7008,plain,
spl0_714,
inference(avatar_split_clause,[],[f2151,f7006]) ).
fof(f7006,plain,
( spl0_714
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f2151,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f7004,plain,
spl0_713,
inference(avatar_split_clause,[],[f2135,f7002]) ).
fof(f7002,plain,
( spl0_713
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f2135,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f7000,plain,
spl0_712,
inference(avatar_split_clause,[],[f2130,f6998]) ).
fof(f2130,axiom,
! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6996,plain,
spl0_711,
inference(avatar_split_clause,[],[f2115,f6994]) ).
fof(f6994,plain,
( spl0_711
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f6992,plain,
spl0_710,
inference(avatar_split_clause,[],[f2114,f6990]) ).
fof(f6988,plain,
spl0_709,
inference(avatar_split_clause,[],[f2106,f6985]) ).
fof(f2106,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
fof(f6983,plain,
spl0_708,
inference(avatar_split_clause,[],[f2105,f6980]) ).
fof(f2105,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
fof(f6978,plain,
spl0_707,
inference(avatar_split_clause,[],[f1866,f6975]) ).
fof(f1866,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f6973,plain,
spl0_706,
inference(avatar_split_clause,[],[f1785,f6971]) ).
fof(f6971,plain,
( spl0_706
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f1785,axiom,
! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6969,plain,
spl0_705,
inference(avatar_split_clause,[],[f1778,f6967]) ).
fof(f6967,plain,
( spl0_705
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1778,axiom,
! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6965,plain,
spl0_704,
inference(avatar_split_clause,[],[f1751,f6963]) ).
fof(f6963,plain,
( spl0_704
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f1751,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
fof(f6961,plain,
spl0_703,
inference(avatar_split_clause,[],[f1736,f6959]) ).
fof(f6959,plain,
( spl0_703
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f1736,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6957,plain,
spl0_702,
inference(avatar_split_clause,[],[f1716,f6955]) ).
fof(f6955,plain,
( spl0_702
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1716,axiom,
! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
fof(f6953,plain,
spl0_701,
inference(avatar_split_clause,[],[f1688,f6950]) ).
fof(f6950,plain,
( spl0_701
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f1688,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__9_0) ).
fof(f6948,plain,
spl0_700,
inference(avatar_split_clause,[],[f1687,f6945]) ).
fof(f6945,plain,
( spl0_700
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1687,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__8_0) ).
fof(f6943,plain,
spl0_699,
inference(avatar_split_clause,[],[f1686,f6940]) ).
fof(f6940,plain,
( spl0_699
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1686,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__7_0) ).
fof(f6938,plain,
spl0_698,
inference(avatar_split_clause,[],[f1685,f6935]) ).
fof(f6935,plain,
( spl0_698
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1685,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__6_0) ).
fof(f6933,plain,
spl0_697,
inference(avatar_split_clause,[],[f1684,f6930]) ).
fof(f6930,plain,
( spl0_697
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1684,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__5_0) ).
fof(f6928,plain,
spl0_696,
inference(avatar_split_clause,[],[f1683,f6925]) ).
fof(f6925,plain,
( spl0_696
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1683,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__4_0) ).
fof(f6923,plain,
spl0_695,
inference(avatar_split_clause,[],[f1682,f6920]) ).
fof(f6920,plain,
( spl0_695
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1682,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__3_0) ).
fof(f6918,plain,
spl0_694,
inference(avatar_split_clause,[],[f1681,f6915]) ).
fof(f6915,plain,
( spl0_694
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1681,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__2_0) ).
fof(f6913,plain,
spl0_693,
inference(avatar_split_clause,[],[f1680,f6910]) ).
fof(f6910,plain,
( spl0_693
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1680,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__1_0) ).
fof(f6908,plain,
spl0_692,
inference(avatar_split_clause,[],[f1679,f6905]) ).
fof(f6905,plain,
( spl0_692
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1679,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__16_0) ).
fof(f6903,plain,
spl0_691,
inference(avatar_split_clause,[],[f1678,f6900]) ).
fof(f6900,plain,
( spl0_691
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1678,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__15_0) ).
fof(f6898,plain,
spl0_690,
inference(avatar_split_clause,[],[f1677,f6895]) ).
fof(f6895,plain,
( spl0_690
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1677,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__14_0) ).
fof(f6893,plain,
spl0_689,
inference(avatar_split_clause,[],[f1676,f6890]) ).
fof(f6890,plain,
( spl0_689
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1676,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__13_0) ).
fof(f6888,plain,
spl0_688,
inference(avatar_split_clause,[],[f1675,f6885]) ).
fof(f6885,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1675,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__12_0) ).
fof(f6883,plain,
spl0_687,
inference(avatar_split_clause,[],[f1674,f6880]) ).
fof(f6880,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1674,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__11_0) ).
fof(f6878,plain,
spl0_686,
inference(avatar_split_clause,[],[f1673,f6875]) ).
fof(f6875,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1673,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__10_0) ).
fof(f6873,plain,
spl0_685,
inference(avatar_split_clause,[],[f1638,f6871]) ).
fof(f6871,plain,
( spl0_685
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1638,axiom,
! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6869,plain,
spl0_684,
inference(avatar_split_clause,[],[f1567,f6867]) ).
fof(f6867,plain,
( spl0_684
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1567,axiom,
! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6865,plain,
spl0_683,
inference(avatar_split_clause,[],[f1543,f6863]) ).
fof(f6863,plain,
( spl0_683
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1543,axiom,
! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6861,plain,
spl0_682,
inference(avatar_split_clause,[],[f1536,f6859]) ).
fof(f6859,plain,
( spl0_682
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1536,axiom,
! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6857,plain,
spl0_681,
inference(avatar_split_clause,[],[f1514,f6855]) ).
fof(f6855,plain,
( spl0_681
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f6853,plain,
spl0_680,
inference(avatar_split_clause,[],[f1424,f6851]) ).
fof(f1424,axiom,
! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6849,plain,
spl0_679,
inference(avatar_split_clause,[],[f1384,f6847]) ).
fof(f1384,axiom,
! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6845,plain,
spl0_678,
inference(avatar_split_clause,[],[f1378,f6843]) ).
fof(f1378,axiom,
! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6841,plain,
~ spl0_677,
inference(avatar_split_clause,[],[f1309,f6838]) ).
fof(f1309,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
fof(f6836,plain,
spl0_676,
inference(avatar_split_clause,[],[f1296,f6834]) ).
fof(f6834,plain,
( spl0_676
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6832,plain,
spl0_675,
inference(avatar_split_clause,[],[f1295,f6830]) ).
fof(f1295,axiom,
! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6828,plain,
spl0_674,
inference(avatar_split_clause,[],[f1278,f6826]) ).
fof(f6826,plain,
( spl0_674
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f1278,axiom,
! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6824,plain,
spl0_673,
inference(avatar_split_clause,[],[f1255,f6821]) ).
fof(f6821,plain,
( spl0_673
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1255,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f6819,plain,
spl0_672,
inference(avatar_split_clause,[],[f1254,f6816]) ).
fof(f6816,plain,
( spl0_672
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1254,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f6814,plain,
spl0_671,
inference(avatar_split_clause,[],[f1184,f6811]) ).
fof(f6811,plain,
( spl0_671
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f1184,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Osize_0) ).
fof(f6809,plain,
spl0_670,
inference(avatar_split_clause,[],[f1173,f6807]) ).
fof(f6807,plain,
( spl0_670
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1173,axiom,
! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f6805,plain,
spl0_669,
inference(avatar_split_clause,[],[f1172,f6803]) ).
fof(f6803,plain,
( spl0_669
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1172,axiom,
! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6801,plain,
spl0_668,
inference(avatar_split_clause,[],[f1165,f6799]) ).
fof(f6799,plain,
( spl0_668
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1165,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,X21),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6797,plain,
spl0_667,
inference(avatar_split_clause,[],[f1164,f6795]) ).
fof(f6795,plain,
( spl0_667
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f1164,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f6793,plain,
spl0_666,
inference(avatar_split_clause,[],[f250,f6791]) ).
fof(f6791,plain,
( spl0_666
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f250,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6789,plain,
spl0_665,
inference(avatar_split_clause,[],[f128,f6787]) ).
fof(f6787,plain,
( spl0_665
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f128,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6785,plain,
( ~ spl0_664
| ~ spl0_641
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f6759,f5927,f5917,f6782]) ).
fof(f6782,plain,
( spl0_664
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f5927,plain,
( spl0_643
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f6759,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_643 ),
inference(superposition,[],[f5928,f5919]) ).
fof(f5928,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f5927]) ).
fof(f6780,plain,
spl0_663,
inference(avatar_split_clause,[],[f112,f6778]) ).
fof(f112,axiom,
! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6776,plain,
spl0_662,
inference(avatar_split_clause,[],[f101,f6774]) ).
fof(f6774,plain,
( spl0_662
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f101,axiom,
! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6772,plain,
spl0_661,
inference(avatar_split_clause,[],[f44,f6770]) ).
fof(f6770,plain,
( spl0_661
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f44,axiom,
! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6768,plain,
spl0_660,
inference(avatar_split_clause,[],[f28,f6766]) ).
fof(f6766,plain,
( spl0_660
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f28,axiom,
! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6764,plain,
( ~ spl0_659
| ~ spl0_640
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f6758,f5927,f5912,f6761]) ).
fof(f6761,plain,
( spl0_659
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f6758,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_643 ),
inference(superposition,[],[f5928,f5914]) ).
fof(f5997,plain,
spl0_658,
inference(avatar_split_clause,[],[f3074,f5994]) ).
fof(f5994,plain,
( spl0_658
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3074,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1486,f1464]) ).
fof(f1486,axiom,
! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f5992,plain,
spl0_657,
inference(avatar_split_clause,[],[f3055,f5990]) ).
fof(f5990,plain,
( spl0_657
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f3055,plain,
! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
inference(forward_demodulation,[],[f2835,f2831]) ).
fof(f2835,plain,
! [X16] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X16,tc_nat),
inference(definition_unfolding,[],[f24,f2544]) ).
fof(f24,axiom,
! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f5988,plain,
spl0_656,
inference(avatar_split_clause,[],[f3053,f5985]) ).
fof(f5985,plain,
( spl0_656
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f3053,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1377,f1374]) ).
fof(f1377,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f5983,plain,
spl0_655,
inference(avatar_split_clause,[],[f3052,f5980]) ).
fof(f5980,plain,
( spl0_655
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f3052,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2833,f2831]) ).
fof(f2833,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1344,f2544]) ).
fof(f1344,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5978,plain,
spl0_654,
inference(avatar_split_clause,[],[f2791,f5975]) ).
fof(f5975,plain,
( spl0_654
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2791,axiom,
c_emptyset = c_Message_Oanalz(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__empty_0) ).
fof(f5973,plain,
spl0_653,
inference(avatar_split_clause,[],[f2770,f5970]) ).
fof(f5970,plain,
( spl0_653
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
fof(f5968,plain,
spl0_652,
inference(avatar_split_clause,[],[f2743,f5965]) ).
fof(f5965,plain,
( spl0_652
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
fof(f5963,plain,
spl0_651,
inference(avatar_split_clause,[],[f2735,f5961]) ).
fof(f5961,plain,
( spl0_651
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2735,axiom,
! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).
fof(f5959,plain,
spl0_650,
inference(avatar_split_clause,[],[f2730,f5957]) ).
fof(f5957,plain,
( spl0_650
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2730,axiom,
! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).
fof(f5955,plain,
spl0_649,
inference(avatar_split_clause,[],[f2672,f5953]) ).
fof(f5953,plain,
( spl0_649
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f5951,plain,
spl0_648,
inference(avatar_split_clause,[],[f2155,f5948]) ).
fof(f5948,plain,
( spl0_648
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2155,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f5946,plain,
spl0_647,
inference(avatar_split_clause,[],[f2091,f5944]) ).
fof(f5944,plain,
( spl0_647
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f5942,plain,
spl0_646,
inference(avatar_split_clause,[],[f2049,f5939]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f5937,plain,
spl0_645,
inference(avatar_split_clause,[],[f1709,f5935]) ).
fof(f5935,plain,
( spl0_645
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1709,axiom,
! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f5933,plain,
spl0_644,
inference(avatar_split_clause,[],[f1482,f5931]) ).
fof(f1482,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f5929,plain,
spl0_643,
inference(avatar_split_clause,[],[f1393,f5927]) ).
fof(f1393,axiom,
! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f5925,plain,
spl0_642,
inference(avatar_split_clause,[],[f1386,f5922]) ).
fof(f5922,plain,
( spl0_642
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f5920,plain,
spl0_641,
inference(avatar_split_clause,[],[f1374,f5917]) ).
fof(f5915,plain,
spl0_640,
inference(avatar_split_clause,[],[f1371,f5912]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f5910,plain,
spl0_639,
inference(avatar_split_clause,[],[f1229,f5908]) ).
fof(f5908,plain,
( spl0_639
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1229,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f5906,plain,
spl0_638,
inference(avatar_split_clause,[],[f1159,f5904]) ).
fof(f5904,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1159,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5902,plain,
spl0_637,
inference(avatar_split_clause,[],[f1158,f5900]) ).
fof(f5900,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1158,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5898,plain,
spl0_636,
inference(avatar_split_clause,[],[f1157,f5896]) ).
fof(f5896,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1157,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5894,plain,
spl0_635,
inference(avatar_split_clause,[],[f1156,f5892]) ).
fof(f5892,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1156,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5890,plain,
spl0_634,
inference(avatar_split_clause,[],[f1155,f5888]) ).
fof(f5888,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1155,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5886,plain,
spl0_633,
inference(avatar_split_clause,[],[f1154,f5884]) ).
fof(f5884,plain,
( spl0_633
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1154,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5882,plain,
spl0_632,
inference(avatar_split_clause,[],[f1153,f5880]) ).
fof(f5880,plain,
( spl0_632
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f1153,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5878,plain,
spl0_631,
inference(avatar_split_clause,[],[f1148,f5876]) ).
fof(f5876,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1148,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5874,plain,
spl0_630,
inference(avatar_split_clause,[],[f1147,f5872]) ).
fof(f5872,plain,
( spl0_630
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1147,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5870,plain,
spl0_629,
inference(avatar_split_clause,[],[f1146,f5868]) ).
fof(f5868,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f1146,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5866,plain,
spl0_628,
inference(avatar_split_clause,[],[f1145,f5864]) ).
fof(f5864,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1145,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5862,plain,
spl0_627,
inference(avatar_split_clause,[],[f1144,f5860]) ).
fof(f5860,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1144,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5858,plain,
spl0_626,
inference(avatar_split_clause,[],[f1143,f5856]) ).
fof(f5856,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1143,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5854,plain,
spl0_625,
inference(avatar_split_clause,[],[f1140,f5852]) ).
fof(f5852,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1140,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5850,plain,
spl0_624,
inference(avatar_split_clause,[],[f1139,f5848]) ).
fof(f5848,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1139,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5846,plain,
spl0_623,
inference(avatar_split_clause,[],[f1138,f5844]) ).
fof(f5844,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1138,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5842,plain,
spl0_622,
inference(avatar_split_clause,[],[f1135,f5840]) ).
fof(f5840,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1135,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5838,plain,
spl0_621,
inference(avatar_split_clause,[],[f1132,f5836]) ).
fof(f5836,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1132,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5834,plain,
spl0_620,
inference(avatar_split_clause,[],[f1131,f5832]) ).
fof(f5832,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1131,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5830,plain,
spl0_619,
inference(avatar_split_clause,[],[f1130,f5828]) ).
fof(f5828,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1130,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5826,plain,
spl0_618,
inference(avatar_split_clause,[],[f1129,f5824]) ).
fof(f5824,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1129,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5822,plain,
spl0_617,
inference(avatar_split_clause,[],[f1126,f5820]) ).
fof(f5820,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1126,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5818,plain,
spl0_616,
inference(avatar_split_clause,[],[f1125,f5816]) ).
fof(f5816,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1125,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5814,plain,
spl0_615,
inference(avatar_split_clause,[],[f1120,f5812]) ).
fof(f5812,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1120,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5810,plain,
spl0_614,
inference(avatar_split_clause,[],[f1117,f5808]) ).
fof(f5808,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1117,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5806,plain,
spl0_613,
inference(avatar_split_clause,[],[f1116,f5804]) ).
fof(f5804,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1116,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5802,plain,
spl0_612,
inference(avatar_split_clause,[],[f1115,f5800]) ).
fof(f5800,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1115,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5798,plain,
spl0_611,
inference(avatar_split_clause,[],[f1113,f5796]) ).
fof(f5796,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1113,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5794,plain,
spl0_610,
inference(avatar_split_clause,[],[f1107,f5792]) ).
fof(f5792,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1107,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5790,plain,
spl0_609,
inference(avatar_split_clause,[],[f1099,f5788]) ).
fof(f5788,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1099,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5786,plain,
spl0_608,
inference(avatar_split_clause,[],[f1098,f5784]) ).
fof(f5784,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1098,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5782,plain,
spl0_607,
inference(avatar_split_clause,[],[f1097,f5780]) ).
fof(f5780,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1097,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5778,plain,
spl0_606,
inference(avatar_split_clause,[],[f1096,f5776]) ).
fof(f5776,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1096,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5774,plain,
spl0_605,
inference(avatar_split_clause,[],[f1095,f5772]) ).
fof(f5772,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1095,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5770,plain,
spl0_604,
inference(avatar_split_clause,[],[f1093,f5768]) ).
fof(f5768,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f1093,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5766,plain,
spl0_603,
inference(avatar_split_clause,[],[f1092,f5764]) ).
fof(f5764,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1092,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5762,plain,
spl0_602,
inference(avatar_split_clause,[],[f1091,f5760]) ).
fof(f5760,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1091,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5758,plain,
spl0_601,
inference(avatar_split_clause,[],[f1090,f5756]) ).
fof(f5756,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1090,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5754,plain,
spl0_600,
inference(avatar_split_clause,[],[f1089,f5752]) ).
fof(f5752,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1089,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5750,plain,
spl0_599,
inference(avatar_split_clause,[],[f1084,f5748]) ).
fof(f5748,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1084,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5746,plain,
spl0_598,
inference(avatar_split_clause,[],[f1083,f5744]) ).
fof(f5744,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1083,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5742,plain,
spl0_597,
inference(avatar_split_clause,[],[f1082,f5740]) ).
fof(f5740,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1082,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5738,plain,
spl0_596,
inference(avatar_split_clause,[],[f1080,f5736]) ).
fof(f5736,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1080,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5734,plain,
spl0_595,
inference(avatar_split_clause,[],[f1078,f5732]) ).
fof(f5732,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1078,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5730,plain,
spl0_594,
inference(avatar_split_clause,[],[f1073,f5728]) ).
fof(f5728,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1073,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5726,plain,
spl0_593,
inference(avatar_split_clause,[],[f1072,f5724]) ).
fof(f5724,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1072,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5722,plain,
spl0_592,
inference(avatar_split_clause,[],[f1071,f5720]) ).
fof(f5720,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1071,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5718,plain,
spl0_591,
inference(avatar_split_clause,[],[f1070,f5716]) ).
fof(f5716,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1070,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5714,plain,
spl0_590,
inference(avatar_split_clause,[],[f1068,f5712]) ).
fof(f5712,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1068,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5710,plain,
spl0_589,
inference(avatar_split_clause,[],[f1067,f5708]) ).
fof(f5708,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1067,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5706,plain,
spl0_588,
inference(avatar_split_clause,[],[f1062,f5704]) ).
fof(f5704,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1062,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5702,plain,
spl0_587,
inference(avatar_split_clause,[],[f1059,f5700]) ).
fof(f5700,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1059,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5698,plain,
spl0_586,
inference(avatar_split_clause,[],[f1058,f5696]) ).
fof(f5696,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1058,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5694,plain,
spl0_585,
inference(avatar_split_clause,[],[f1057,f5692]) ).
fof(f5692,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1057,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5690,plain,
spl0_584,
inference(avatar_split_clause,[],[f1056,f5688]) ).
fof(f5688,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1056,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5686,plain,
spl0_583,
inference(avatar_split_clause,[],[f1053,f5684]) ).
fof(f5684,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1053,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5682,plain,
spl0_582,
inference(avatar_split_clause,[],[f1052,f5680]) ).
fof(f5680,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1052,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5678,plain,
spl0_581,
inference(avatar_split_clause,[],[f1051,f5676]) ).
fof(f5676,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1051,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5674,plain,
spl0_580,
inference(avatar_split_clause,[],[f1050,f5672]) ).
fof(f5672,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1050,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5670,plain,
spl0_579,
inference(avatar_split_clause,[],[f1049,f5668]) ).
fof(f5668,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1049,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5666,plain,
spl0_578,
inference(avatar_split_clause,[],[f1048,f5664]) ).
fof(f5664,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1048,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5662,plain,
spl0_577,
inference(avatar_split_clause,[],[f1047,f5660]) ).
fof(f5660,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1047,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5658,plain,
spl0_576,
inference(avatar_split_clause,[],[f1046,f5656]) ).
fof(f5656,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1046,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5654,plain,
spl0_575,
inference(avatar_split_clause,[],[f1044,f5652]) ).
fof(f5652,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1044,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5650,plain,
spl0_574,
inference(avatar_split_clause,[],[f1043,f5648]) ).
fof(f5648,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1043,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5646,plain,
spl0_573,
inference(avatar_split_clause,[],[f1042,f5644]) ).
fof(f5644,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1042,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5642,plain,
spl0_572,
inference(avatar_split_clause,[],[f1041,f5640]) ).
fof(f5640,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1041,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5638,plain,
spl0_571,
inference(avatar_split_clause,[],[f1040,f5636]) ).
fof(f5636,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1040,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5634,plain,
spl0_570,
inference(avatar_split_clause,[],[f1035,f5632]) ).
fof(f5632,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1035,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5630,plain,
spl0_569,
inference(avatar_split_clause,[],[f1034,f5628]) ).
fof(f5628,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f1034,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5626,plain,
spl0_568,
inference(avatar_split_clause,[],[f1033,f5624]) ).
fof(f5624,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1033,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5622,plain,
spl0_567,
inference(avatar_split_clause,[],[f1030,f5620]) ).
fof(f5620,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1030,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5618,plain,
spl0_566,
inference(avatar_split_clause,[],[f1027,f5616]) ).
fof(f5616,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1027,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5614,plain,
spl0_565,
inference(avatar_split_clause,[],[f1026,f5612]) ).
fof(f5612,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1026,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5610,plain,
spl0_564,
inference(avatar_split_clause,[],[f1024,f5608]) ).
fof(f5608,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f1024,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5606,plain,
spl0_563,
inference(avatar_split_clause,[],[f1023,f5604]) ).
fof(f5604,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f1023,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5602,plain,
spl0_562,
inference(avatar_split_clause,[],[f1022,f5600]) ).
fof(f5600,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1022,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5598,plain,
spl0_561,
inference(avatar_split_clause,[],[f1021,f5596]) ).
fof(f5596,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1021,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5594,plain,
spl0_560,
inference(avatar_split_clause,[],[f1018,f5592]) ).
fof(f5592,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1018,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5590,plain,
spl0_559,
inference(avatar_split_clause,[],[f1017,f5588]) ).
fof(f5588,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1017,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5586,plain,
spl0_558,
inference(avatar_split_clause,[],[f989,f5584]) ).
fof(f5584,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f989,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5582,plain,
spl0_557,
inference(avatar_split_clause,[],[f987,f5580]) ).
fof(f5580,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f987,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5578,plain,
spl0_556,
inference(avatar_split_clause,[],[f984,f5576]) ).
fof(f5576,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f984,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5574,plain,
spl0_555,
inference(avatar_split_clause,[],[f983,f5572]) ).
fof(f5572,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f983,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5570,plain,
spl0_554,
inference(avatar_split_clause,[],[f982,f5568]) ).
fof(f5568,plain,
( spl0_554
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f982,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5566,plain,
spl0_553,
inference(avatar_split_clause,[],[f981,f5564]) ).
fof(f5564,plain,
( spl0_553
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f981,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5562,plain,
spl0_552,
inference(avatar_split_clause,[],[f980,f5560]) ).
fof(f5560,plain,
( spl0_552
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f980,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5558,plain,
spl0_551,
inference(avatar_split_clause,[],[f979,f5556]) ).
fof(f5556,plain,
( spl0_551
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f979,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5554,plain,
spl0_550,
inference(avatar_split_clause,[],[f977,f5552]) ).
fof(f5552,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f977,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5550,plain,
spl0_549,
inference(avatar_split_clause,[],[f976,f5548]) ).
fof(f5548,plain,
( spl0_549
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f976,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5546,plain,
spl0_548,
inference(avatar_split_clause,[],[f974,f5544]) ).
fof(f5544,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f974,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5542,plain,
spl0_547,
inference(avatar_split_clause,[],[f971,f5540]) ).
fof(f5540,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f971,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5538,plain,
spl0_546,
inference(avatar_split_clause,[],[f970,f5536]) ).
fof(f5536,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f970,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5534,plain,
spl0_545,
inference(avatar_split_clause,[],[f968,f5532]) ).
fof(f5532,plain,
( spl0_545
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f968,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5530,plain,
spl0_544,
inference(avatar_split_clause,[],[f967,f5528]) ).
fof(f5528,plain,
( spl0_544
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f967,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5526,plain,
spl0_543,
inference(avatar_split_clause,[],[f966,f5524]) ).
fof(f5524,plain,
( spl0_543
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f966,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5522,plain,
spl0_542,
inference(avatar_split_clause,[],[f965,f5520]) ).
fof(f5520,plain,
( spl0_542
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f965,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5518,plain,
spl0_541,
inference(avatar_split_clause,[],[f964,f5516]) ).
fof(f5516,plain,
( spl0_541
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f964,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5514,plain,
spl0_540,
inference(avatar_split_clause,[],[f963,f5512]) ).
fof(f5512,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f963,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5510,plain,
spl0_539,
inference(avatar_split_clause,[],[f962,f5508]) ).
fof(f5508,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f962,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5506,plain,
spl0_538,
inference(avatar_split_clause,[],[f961,f5504]) ).
fof(f5504,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f961,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5502,plain,
spl0_537,
inference(avatar_split_clause,[],[f957,f5500]) ).
fof(f5500,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f957,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5498,plain,
spl0_536,
inference(avatar_split_clause,[],[f956,f5496]) ).
fof(f5496,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f956,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5494,plain,
spl0_535,
inference(avatar_split_clause,[],[f955,f5492]) ).
fof(f5492,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f955,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5490,plain,
spl0_534,
inference(avatar_split_clause,[],[f954,f5488]) ).
fof(f5488,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f954,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5486,plain,
spl0_533,
inference(avatar_split_clause,[],[f949,f5484]) ).
fof(f5484,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f949,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5482,plain,
spl0_532,
inference(avatar_split_clause,[],[f947,f5480]) ).
fof(f5480,plain,
( spl0_532
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f947,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5478,plain,
spl0_531,
inference(avatar_split_clause,[],[f946,f5476]) ).
fof(f5476,plain,
( spl0_531
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f946,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5474,plain,
spl0_530,
inference(avatar_split_clause,[],[f945,f5472]) ).
fof(f5472,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f945,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5470,plain,
spl0_529,
inference(avatar_split_clause,[],[f944,f5468]) ).
fof(f5468,plain,
( spl0_529
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f944,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5466,plain,
spl0_528,
inference(avatar_split_clause,[],[f942,f5464]) ).
fof(f5464,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f942,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5462,plain,
spl0_527,
inference(avatar_split_clause,[],[f941,f5460]) ).
fof(f5460,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f941,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5458,plain,
spl0_526,
inference(avatar_split_clause,[],[f940,f5456]) ).
fof(f5456,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f940,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5454,plain,
spl0_525,
inference(avatar_split_clause,[],[f939,f5452]) ).
fof(f5452,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f939,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5450,plain,
spl0_524,
inference(avatar_split_clause,[],[f938,f5448]) ).
fof(f5448,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f938,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5446,plain,
spl0_523,
inference(avatar_split_clause,[],[f937,f5444]) ).
fof(f5444,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f937,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5442,plain,
spl0_522,
inference(avatar_split_clause,[],[f936,f5440]) ).
fof(f5440,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f936,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5438,plain,
spl0_521,
inference(avatar_split_clause,[],[f935,f5436]) ).
fof(f5436,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f935,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5434,plain,
spl0_520,
inference(avatar_split_clause,[],[f934,f5432]) ).
fof(f5432,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f934,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5430,plain,
spl0_519,
inference(avatar_split_clause,[],[f933,f5428]) ).
fof(f5428,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f933,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5426,plain,
spl0_518,
inference(avatar_split_clause,[],[f932,f5424]) ).
fof(f5424,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f932,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5422,plain,
spl0_517,
inference(avatar_split_clause,[],[f931,f5420]) ).
fof(f5420,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f931,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5418,plain,
spl0_516,
inference(avatar_split_clause,[],[f930,f5416]) ).
fof(f5416,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f930,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5414,plain,
spl0_515,
inference(avatar_split_clause,[],[f929,f5412]) ).
fof(f5412,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f929,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5410,plain,
spl0_514,
inference(avatar_split_clause,[],[f928,f5408]) ).
fof(f5408,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f928,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5406,plain,
spl0_513,
inference(avatar_split_clause,[],[f927,f5404]) ).
fof(f5404,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f927,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5402,plain,
spl0_512,
inference(avatar_split_clause,[],[f926,f5400]) ).
fof(f5400,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f926,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5398,plain,
spl0_511,
inference(avatar_split_clause,[],[f925,f5396]) ).
fof(f5396,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f925,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5394,plain,
spl0_510,
inference(avatar_split_clause,[],[f924,f5392]) ).
fof(f5392,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f924,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5390,plain,
spl0_509,
inference(avatar_split_clause,[],[f923,f5388]) ).
fof(f5388,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f923,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5386,plain,
spl0_508,
inference(avatar_split_clause,[],[f922,f5384]) ).
fof(f5384,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f922,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5382,plain,
spl0_507,
inference(avatar_split_clause,[],[f921,f5380]) ).
fof(f5380,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f921,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5378,plain,
spl0_506,
inference(avatar_split_clause,[],[f920,f5376]) ).
fof(f5376,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f920,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5374,plain,
spl0_505,
inference(avatar_split_clause,[],[f919,f5372]) ).
fof(f5372,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f919,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5370,plain,
spl0_504,
inference(avatar_split_clause,[],[f918,f5368]) ).
fof(f5368,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f918,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5366,plain,
spl0_503,
inference(avatar_split_clause,[],[f917,f5364]) ).
fof(f5364,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f917,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5362,plain,
spl0_502,
inference(avatar_split_clause,[],[f916,f5360]) ).
fof(f5360,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f916,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5358,plain,
spl0_501,
inference(avatar_split_clause,[],[f915,f5356]) ).
fof(f5356,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f915,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5354,plain,
spl0_500,
inference(avatar_split_clause,[],[f914,f5352]) ).
fof(f5352,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f914,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5350,plain,
spl0_499,
inference(avatar_split_clause,[],[f913,f5348]) ).
fof(f5348,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f913,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5346,plain,
spl0_498,
inference(avatar_split_clause,[],[f912,f5344]) ).
fof(f5344,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f912,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5342,plain,
spl0_497,
inference(avatar_split_clause,[],[f911,f5340]) ).
fof(f5340,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f911,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5338,plain,
spl0_496,
inference(avatar_split_clause,[],[f910,f5336]) ).
fof(f5336,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f910,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5334,plain,
spl0_495,
inference(avatar_split_clause,[],[f909,f5332]) ).
fof(f5332,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f909,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5330,plain,
spl0_494,
inference(avatar_split_clause,[],[f908,f5328]) ).
fof(f5328,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f908,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5326,plain,
spl0_493,
inference(avatar_split_clause,[],[f905,f5324]) ).
fof(f5324,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f905,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5322,plain,
spl0_492,
inference(avatar_split_clause,[],[f903,f5320]) ).
fof(f5320,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f903,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5318,plain,
spl0_491,
inference(avatar_split_clause,[],[f902,f5316]) ).
fof(f5316,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f902,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5314,plain,
spl0_490,
inference(avatar_split_clause,[],[f900,f5312]) ).
fof(f5312,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f900,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5310,plain,
spl0_489,
inference(avatar_split_clause,[],[f897,f5308]) ).
fof(f5308,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f897,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5306,plain,
spl0_488,
inference(avatar_split_clause,[],[f896,f5304]) ).
fof(f5304,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f896,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5302,plain,
spl0_487,
inference(avatar_split_clause,[],[f895,f5300]) ).
fof(f5300,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f895,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5298,plain,
spl0_486,
inference(avatar_split_clause,[],[f893,f5296]) ).
fof(f5296,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f893,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5294,plain,
spl0_485,
inference(avatar_split_clause,[],[f892,f5292]) ).
fof(f5292,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f892,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5290,plain,
spl0_484,
inference(avatar_split_clause,[],[f891,f5288]) ).
fof(f5288,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f891,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5286,plain,
spl0_483,
inference(avatar_split_clause,[],[f888,f5284]) ).
fof(f5284,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f888,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5282,plain,
spl0_482,
inference(avatar_split_clause,[],[f887,f5280]) ).
fof(f5280,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f887,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5278,plain,
spl0_481,
inference(avatar_split_clause,[],[f886,f5276]) ).
fof(f5276,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f886,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5274,plain,
spl0_480,
inference(avatar_split_clause,[],[f885,f5272]) ).
fof(f5272,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f885,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5270,plain,
spl0_479,
inference(avatar_split_clause,[],[f883,f5268]) ).
fof(f5268,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f883,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5266,plain,
spl0_478,
inference(avatar_split_clause,[],[f882,f5264]) ).
fof(f5264,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f882,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5262,plain,
spl0_477,
inference(avatar_split_clause,[],[f881,f5260]) ).
fof(f5260,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f881,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5258,plain,
spl0_476,
inference(avatar_split_clause,[],[f880,f5256]) ).
fof(f5256,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f880,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5254,plain,
spl0_475,
inference(avatar_split_clause,[],[f879,f5252]) ).
fof(f5252,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f879,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5250,plain,
spl0_474,
inference(avatar_split_clause,[],[f878,f5248]) ).
fof(f5248,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f878,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5246,plain,
spl0_473,
inference(avatar_split_clause,[],[f877,f5244]) ).
fof(f5244,plain,
( spl0_473
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f877,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5242,plain,
spl0_472,
inference(avatar_split_clause,[],[f876,f5240]) ).
fof(f5240,plain,
( spl0_472
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f876,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5238,plain,
spl0_471,
inference(avatar_split_clause,[],[f875,f5236]) ).
fof(f5236,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f875,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5234,plain,
spl0_470,
inference(avatar_split_clause,[],[f874,f5232]) ).
fof(f5232,plain,
( spl0_470
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f874,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5230,plain,
spl0_469,
inference(avatar_split_clause,[],[f873,f5228]) ).
fof(f5228,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f873,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5226,plain,
spl0_468,
inference(avatar_split_clause,[],[f872,f5224]) ).
fof(f5224,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f872,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5222,plain,
spl0_467,
inference(avatar_split_clause,[],[f871,f5220]) ).
fof(f5220,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f871,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5218,plain,
spl0_466,
inference(avatar_split_clause,[],[f870,f5216]) ).
fof(f5216,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f870,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5214,plain,
spl0_465,
inference(avatar_split_clause,[],[f869,f5212]) ).
fof(f5212,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f869,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5210,plain,
spl0_464,
inference(avatar_split_clause,[],[f868,f5208]) ).
fof(f5208,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f868,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5206,plain,
spl0_463,
inference(avatar_split_clause,[],[f867,f5204]) ).
fof(f5204,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f867,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5202,plain,
spl0_462,
inference(avatar_split_clause,[],[f865,f5200]) ).
fof(f5200,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f865,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5198,plain,
spl0_461,
inference(avatar_split_clause,[],[f864,f5196]) ).
fof(f5196,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f864,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5194,plain,
spl0_460,
inference(avatar_split_clause,[],[f863,f5192]) ).
fof(f5192,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f863,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5190,plain,
spl0_459,
inference(avatar_split_clause,[],[f862,f5188]) ).
fof(f5188,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f862,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5186,plain,
spl0_458,
inference(avatar_split_clause,[],[f861,f5184]) ).
fof(f5184,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f861,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5182,plain,
spl0_457,
inference(avatar_split_clause,[],[f856,f5180]) ).
fof(f5180,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f856,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5178,plain,
spl0_456,
inference(avatar_split_clause,[],[f855,f5176]) ).
fof(f5176,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f855,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5174,plain,
spl0_455,
inference(avatar_split_clause,[],[f854,f5172]) ).
fof(f5172,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f854,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5170,plain,
spl0_454,
inference(avatar_split_clause,[],[f853,f5168]) ).
fof(f5168,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f853,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5166,plain,
spl0_453,
inference(avatar_split_clause,[],[f852,f5164]) ).
fof(f5164,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f852,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5162,plain,
spl0_452,
inference(avatar_split_clause,[],[f851,f5160]) ).
fof(f5160,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f851,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5158,plain,
spl0_451,
inference(avatar_split_clause,[],[f850,f5156]) ).
fof(f5156,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f850,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5154,plain,
spl0_450,
inference(avatar_split_clause,[],[f849,f5152]) ).
fof(f5152,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f849,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5150,plain,
spl0_449,
inference(avatar_split_clause,[],[f847,f5148]) ).
fof(f5148,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f847,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5146,plain,
spl0_448,
inference(avatar_split_clause,[],[f846,f5144]) ).
fof(f5144,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f846,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5142,plain,
spl0_447,
inference(avatar_split_clause,[],[f845,f5140]) ).
fof(f5140,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f845,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5138,plain,
spl0_446,
inference(avatar_split_clause,[],[f844,f5136]) ).
fof(f5136,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f844,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5134,plain,
spl0_445,
inference(avatar_split_clause,[],[f843,f5132]) ).
fof(f5132,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f843,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5130,plain,
spl0_444,
inference(avatar_split_clause,[],[f842,f5128]) ).
fof(f5128,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f842,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5126,plain,
spl0_443,
inference(avatar_split_clause,[],[f840,f5124]) ).
fof(f5124,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f840,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5122,plain,
spl0_442,
inference(avatar_split_clause,[],[f839,f5120]) ).
fof(f5120,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f839,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5118,plain,
spl0_441,
inference(avatar_split_clause,[],[f838,f5116]) ).
fof(f5116,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f838,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5114,plain,
spl0_440,
inference(avatar_split_clause,[],[f837,f5112]) ).
fof(f5112,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f837,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5110,plain,
spl0_439,
inference(avatar_split_clause,[],[f836,f5108]) ).
fof(f5108,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f836,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5106,plain,
spl0_438,
inference(avatar_split_clause,[],[f835,f5104]) ).
fof(f5104,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f835,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5102,plain,
spl0_437,
inference(avatar_split_clause,[],[f834,f5100]) ).
fof(f5100,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f834,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5098,plain,
spl0_436,
inference(avatar_split_clause,[],[f833,f5096]) ).
fof(f5096,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f833,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5094,plain,
spl0_435,
inference(avatar_split_clause,[],[f832,f5092]) ).
fof(f5092,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f832,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5090,plain,
spl0_434,
inference(avatar_split_clause,[],[f831,f5088]) ).
fof(f5088,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f831,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5086,plain,
spl0_433,
inference(avatar_split_clause,[],[f830,f5084]) ).
fof(f5084,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f830,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5082,plain,
spl0_432,
inference(avatar_split_clause,[],[f829,f5080]) ).
fof(f5080,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f829,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5078,plain,
spl0_431,
inference(avatar_split_clause,[],[f828,f5076]) ).
fof(f5076,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f828,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5074,plain,
spl0_430,
inference(avatar_split_clause,[],[f827,f5072]) ).
fof(f5072,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f827,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5070,plain,
spl0_429,
inference(avatar_split_clause,[],[f826,f5068]) ).
fof(f5068,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f826,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5066,plain,
spl0_428,
inference(avatar_split_clause,[],[f825,f5064]) ).
fof(f5064,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f825,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5062,plain,
spl0_427,
inference(avatar_split_clause,[],[f824,f5060]) ).
fof(f5060,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f824,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5058,plain,
spl0_426,
inference(avatar_split_clause,[],[f823,f5056]) ).
fof(f5056,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f823,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5054,plain,
spl0_425,
inference(avatar_split_clause,[],[f822,f5052]) ).
fof(f5052,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f822,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5050,plain,
spl0_424,
inference(avatar_split_clause,[],[f821,f5048]) ).
fof(f5048,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f821,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5046,plain,
spl0_423,
inference(avatar_split_clause,[],[f820,f5044]) ).
fof(f5044,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f820,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5042,plain,
spl0_422,
inference(avatar_split_clause,[],[f819,f5040]) ).
fof(f5040,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f819,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5038,plain,
spl0_421,
inference(avatar_split_clause,[],[f816,f5036]) ).
fof(f5036,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f816,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5034,plain,
spl0_420,
inference(avatar_split_clause,[],[f814,f5032]) ).
fof(f5032,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f814,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5030,plain,
spl0_419,
inference(avatar_split_clause,[],[f812,f5028]) ).
fof(f5028,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f812,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5026,plain,
spl0_418,
inference(avatar_split_clause,[],[f809,f5024]) ).
fof(f5024,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f809,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5022,plain,
spl0_417,
inference(avatar_split_clause,[],[f808,f5020]) ).
fof(f5020,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f808,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5018,plain,
spl0_416,
inference(avatar_split_clause,[],[f807,f5016]) ).
fof(f5016,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f807,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5014,plain,
spl0_415,
inference(avatar_split_clause,[],[f806,f5012]) ).
fof(f5012,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f806,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5010,plain,
spl0_414,
inference(avatar_split_clause,[],[f804,f5008]) ).
fof(f5008,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f804,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5006,plain,
spl0_413,
inference(avatar_split_clause,[],[f803,f5004]) ).
fof(f5004,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f803,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f5002,plain,
spl0_412,
inference(avatar_split_clause,[],[f802,f5000]) ).
fof(f5000,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f802,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4998,plain,
spl0_411,
inference(avatar_split_clause,[],[f801,f4996]) ).
fof(f4996,plain,
( spl0_411
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f801,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4994,plain,
spl0_410,
inference(avatar_split_clause,[],[f800,f4992]) ).
fof(f4992,plain,
( spl0_410
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f800,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4990,plain,
spl0_409,
inference(avatar_split_clause,[],[f799,f4988]) ).
fof(f4988,plain,
( spl0_409
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f799,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4986,plain,
spl0_408,
inference(avatar_split_clause,[],[f798,f4984]) ).
fof(f4984,plain,
( spl0_408
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f798,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4982,plain,
spl0_407,
inference(avatar_split_clause,[],[f797,f4980]) ).
fof(f4980,plain,
( spl0_407
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f797,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4978,plain,
spl0_406,
inference(avatar_split_clause,[],[f796,f4976]) ).
fof(f4976,plain,
( spl0_406
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f796,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4974,plain,
spl0_405,
inference(avatar_split_clause,[],[f732,f4972]) ).
fof(f4972,plain,
( spl0_405
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f732,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4970,plain,
spl0_404,
inference(avatar_split_clause,[],[f729,f4968]) ).
fof(f4968,plain,
( spl0_404
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f729,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4966,plain,
spl0_403,
inference(avatar_split_clause,[],[f728,f4964]) ).
fof(f4964,plain,
( spl0_403
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f728,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4962,plain,
spl0_402,
inference(avatar_split_clause,[],[f727,f4960]) ).
fof(f4960,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f727,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4958,plain,
spl0_401,
inference(avatar_split_clause,[],[f726,f4956]) ).
fof(f4956,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f726,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4954,plain,
spl0_400,
inference(avatar_split_clause,[],[f725,f4952]) ).
fof(f4952,plain,
( spl0_400
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f725,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4950,plain,
spl0_399,
inference(avatar_split_clause,[],[f724,f4948]) ).
fof(f4948,plain,
( spl0_399
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f724,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4946,plain,
spl0_398,
inference(avatar_split_clause,[],[f723,f4944]) ).
fof(f4944,plain,
( spl0_398
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f723,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4942,plain,
spl0_397,
inference(avatar_split_clause,[],[f722,f4940]) ).
fof(f4940,plain,
( spl0_397
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f722,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4938,plain,
spl0_396,
inference(avatar_split_clause,[],[f721,f4936]) ).
fof(f4936,plain,
( spl0_396
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f721,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4934,plain,
spl0_395,
inference(avatar_split_clause,[],[f720,f4932]) ).
fof(f4932,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f720,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4930,plain,
spl0_394,
inference(avatar_split_clause,[],[f719,f4928]) ).
fof(f4928,plain,
( spl0_394
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f719,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4926,plain,
spl0_393,
inference(avatar_split_clause,[],[f718,f4924]) ).
fof(f4924,plain,
( spl0_393
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f718,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4922,plain,
spl0_392,
inference(avatar_split_clause,[],[f716,f4920]) ).
fof(f4920,plain,
( spl0_392
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f716,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4918,plain,
spl0_391,
inference(avatar_split_clause,[],[f715,f4916]) ).
fof(f4916,plain,
( spl0_391
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f715,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4914,plain,
spl0_390,
inference(avatar_split_clause,[],[f714,f4912]) ).
fof(f4912,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f714,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4910,plain,
spl0_389,
inference(avatar_split_clause,[],[f713,f4908]) ).
fof(f4908,plain,
( spl0_389
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f713,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4906,plain,
spl0_388,
inference(avatar_split_clause,[],[f712,f4904]) ).
fof(f4904,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f712,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4902,plain,
spl0_387,
inference(avatar_split_clause,[],[f711,f4900]) ).
fof(f4900,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f711,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4898,plain,
spl0_386,
inference(avatar_split_clause,[],[f710,f4896]) ).
fof(f4896,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f710,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4894,plain,
spl0_385,
inference(avatar_split_clause,[],[f709,f4892]) ).
fof(f4892,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f709,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4890,plain,
spl0_384,
inference(avatar_split_clause,[],[f706,f4888]) ).
fof(f4888,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f706,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4886,plain,
spl0_383,
inference(avatar_split_clause,[],[f705,f4884]) ).
fof(f4884,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f705,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4882,plain,
spl0_382,
inference(avatar_split_clause,[],[f704,f4880]) ).
fof(f4880,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f704,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4878,plain,
spl0_381,
inference(avatar_split_clause,[],[f703,f4876]) ).
fof(f4876,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f703,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4874,plain,
spl0_380,
inference(avatar_split_clause,[],[f702,f4872]) ).
fof(f4872,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f702,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4870,plain,
spl0_379,
inference(avatar_split_clause,[],[f701,f4868]) ).
fof(f4868,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f701,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4866,plain,
spl0_378,
inference(avatar_split_clause,[],[f700,f4864]) ).
fof(f4864,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f700,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4862,plain,
spl0_377,
inference(avatar_split_clause,[],[f698,f4860]) ).
fof(f4860,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f698,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4858,plain,
spl0_376,
inference(avatar_split_clause,[],[f697,f4856]) ).
fof(f4856,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f697,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4854,plain,
spl0_375,
inference(avatar_split_clause,[],[f696,f4852]) ).
fof(f4852,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f696,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4850,plain,
spl0_374,
inference(avatar_split_clause,[],[f695,f4848]) ).
fof(f4848,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f695,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4846,plain,
spl0_373,
inference(avatar_split_clause,[],[f694,f4844]) ).
fof(f4844,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f694,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4842,plain,
spl0_372,
inference(avatar_split_clause,[],[f693,f4840]) ).
fof(f4840,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f693,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4838,plain,
spl0_371,
inference(avatar_split_clause,[],[f692,f4836]) ).
fof(f4836,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f692,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4834,plain,
spl0_370,
inference(avatar_split_clause,[],[f691,f4832]) ).
fof(f4832,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f691,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4830,plain,
spl0_369,
inference(avatar_split_clause,[],[f688,f4828]) ).
fof(f4828,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f688,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4826,plain,
spl0_368,
inference(avatar_split_clause,[],[f686,f4824]) ).
fof(f4824,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f686,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4822,plain,
spl0_367,
inference(avatar_split_clause,[],[f685,f4820]) ).
fof(f4820,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f685,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4818,plain,
spl0_366,
inference(avatar_split_clause,[],[f683,f4816]) ).
fof(f4816,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f683,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4814,plain,
spl0_365,
inference(avatar_split_clause,[],[f680,f4812]) ).
fof(f4812,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f680,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4810,plain,
spl0_364,
inference(avatar_split_clause,[],[f679,f4808]) ).
fof(f4808,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f679,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4806,plain,
spl0_363,
inference(avatar_split_clause,[],[f678,f4804]) ).
fof(f4804,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f678,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4802,plain,
spl0_362,
inference(avatar_split_clause,[],[f677,f4800]) ).
fof(f4800,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f677,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4798,plain,
spl0_361,
inference(avatar_split_clause,[],[f676,f4796]) ).
fof(f4796,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f676,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4794,plain,
spl0_360,
inference(avatar_split_clause,[],[f675,f4792]) ).
fof(f4792,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f675,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4790,plain,
spl0_359,
inference(avatar_split_clause,[],[f674,f4788]) ).
fof(f4788,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f674,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4786,plain,
spl0_358,
inference(avatar_split_clause,[],[f673,f4784]) ).
fof(f4784,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f673,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4782,plain,
spl0_357,
inference(avatar_split_clause,[],[f672,f4780]) ).
fof(f4780,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f672,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4778,plain,
spl0_356,
inference(avatar_split_clause,[],[f671,f4776]) ).
fof(f4776,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f671,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4774,plain,
spl0_355,
inference(avatar_split_clause,[],[f670,f4772]) ).
fof(f4772,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f670,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4770,plain,
spl0_354,
inference(avatar_split_clause,[],[f668,f4768]) ).
fof(f4768,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f668,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4766,plain,
spl0_353,
inference(avatar_split_clause,[],[f666,f4764]) ).
fof(f4764,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f666,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4762,plain,
spl0_352,
inference(avatar_split_clause,[],[f663,f4760]) ).
fof(f4760,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f663,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4758,plain,
spl0_351,
inference(avatar_split_clause,[],[f661,f4756]) ).
fof(f4756,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f661,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4754,plain,
spl0_350,
inference(avatar_split_clause,[],[f659,f4752]) ).
fof(f4752,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f659,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4750,plain,
spl0_349,
inference(avatar_split_clause,[],[f656,f4748]) ).
fof(f4748,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f656,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4746,plain,
spl0_348,
inference(avatar_split_clause,[],[f655,f4744]) ).
fof(f4744,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f655,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4742,plain,
spl0_347,
inference(avatar_split_clause,[],[f654,f4740]) ).
fof(f4740,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f654,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4738,plain,
spl0_346,
inference(avatar_split_clause,[],[f653,f4736]) ).
fof(f4736,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f653,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4734,plain,
spl0_345,
inference(avatar_split_clause,[],[f651,f4732]) ).
fof(f4732,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f651,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4730,plain,
spl0_344,
inference(avatar_split_clause,[],[f650,f4728]) ).
fof(f4728,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f650,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4726,plain,
spl0_343,
inference(avatar_split_clause,[],[f649,f4724]) ).
fof(f4724,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f649,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4722,plain,
spl0_342,
inference(avatar_split_clause,[],[f648,f4720]) ).
fof(f4720,plain,
( spl0_342
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f648,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4718,plain,
spl0_341,
inference(avatar_split_clause,[],[f647,f4716]) ).
fof(f4716,plain,
( spl0_341
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f647,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4714,plain,
spl0_340,
inference(avatar_split_clause,[],[f646,f4712]) ).
fof(f4712,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f646,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4710,plain,
spl0_339,
inference(avatar_split_clause,[],[f645,f4708]) ).
fof(f4708,plain,
( spl0_339
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f645,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4706,plain,
spl0_338,
inference(avatar_split_clause,[],[f644,f4704]) ).
fof(f4704,plain,
( spl0_338
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f644,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4702,plain,
spl0_337,
inference(avatar_split_clause,[],[f643,f4700]) ).
fof(f4700,plain,
( spl0_337
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f643,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4698,plain,
spl0_336,
inference(avatar_split_clause,[],[f607,f4696]) ).
fof(f4696,plain,
( spl0_336
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f607,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4694,plain,
spl0_335,
inference(avatar_split_clause,[],[f606,f4692]) ).
fof(f4692,plain,
( spl0_335
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f606,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4690,plain,
spl0_334,
inference(avatar_split_clause,[],[f605,f4688]) ).
fof(f4688,plain,
( spl0_334
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f605,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4686,plain,
spl0_333,
inference(avatar_split_clause,[],[f604,f4684]) ).
fof(f4684,plain,
( spl0_333
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f604,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4682,plain,
spl0_332,
inference(avatar_split_clause,[],[f603,f4680]) ).
fof(f4680,plain,
( spl0_332
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f603,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4678,plain,
spl0_331,
inference(avatar_split_clause,[],[f601,f4676]) ).
fof(f4676,plain,
( spl0_331
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f601,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4674,plain,
spl0_330,
inference(avatar_split_clause,[],[f600,f4672]) ).
fof(f4672,plain,
( spl0_330
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f600,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4670,plain,
spl0_329,
inference(avatar_split_clause,[],[f599,f4668]) ).
fof(f4668,plain,
( spl0_329
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f599,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4666,plain,
spl0_328,
inference(avatar_split_clause,[],[f598,f4664]) ).
fof(f4664,plain,
( spl0_328
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f598,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4662,plain,
spl0_327,
inference(avatar_split_clause,[],[f597,f4660]) ).
fof(f4660,plain,
( spl0_327
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f597,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4658,plain,
spl0_326,
inference(avatar_split_clause,[],[f596,f4656]) ).
fof(f4656,plain,
( spl0_326
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f596,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4654,plain,
spl0_325,
inference(avatar_split_clause,[],[f595,f4652]) ).
fof(f4652,plain,
( spl0_325
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f595,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4650,plain,
spl0_324,
inference(avatar_split_clause,[],[f592,f4648]) ).
fof(f4648,plain,
( spl0_324
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f592,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4646,plain,
spl0_323,
inference(avatar_split_clause,[],[f591,f4644]) ).
fof(f4644,plain,
( spl0_323
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f591,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4642,plain,
spl0_322,
inference(avatar_split_clause,[],[f586,f4640]) ).
fof(f4640,plain,
( spl0_322
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f586,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4638,plain,
spl0_321,
inference(avatar_split_clause,[],[f585,f4636]) ).
fof(f4636,plain,
( spl0_321
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f585,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4634,plain,
spl0_320,
inference(avatar_split_clause,[],[f582,f4632]) ).
fof(f4632,plain,
( spl0_320
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f582,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4630,plain,
spl0_319,
inference(avatar_split_clause,[],[f581,f4628]) ).
fof(f4628,plain,
( spl0_319
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f581,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4626,plain,
spl0_318,
inference(avatar_split_clause,[],[f579,f4624]) ).
fof(f4624,plain,
( spl0_318
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f579,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4622,plain,
spl0_317,
inference(avatar_split_clause,[],[f578,f4620]) ).
fof(f4620,plain,
( spl0_317
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f578,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4618,plain,
spl0_316,
inference(avatar_split_clause,[],[f577,f4616]) ).
fof(f4616,plain,
( spl0_316
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f577,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4614,plain,
spl0_315,
inference(avatar_split_clause,[],[f576,f4612]) ).
fof(f4612,plain,
( spl0_315
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f576,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4610,plain,
spl0_314,
inference(avatar_split_clause,[],[f575,f4608]) ).
fof(f4608,plain,
( spl0_314
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f575,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4606,plain,
spl0_313,
inference(avatar_split_clause,[],[f574,f4604]) ).
fof(f4604,plain,
( spl0_313
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f574,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4602,plain,
spl0_312,
inference(avatar_split_clause,[],[f570,f4600]) ).
fof(f4600,plain,
( spl0_312
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f570,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4598,plain,
spl0_311,
inference(avatar_split_clause,[],[f568,f4596]) ).
fof(f4596,plain,
( spl0_311
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f568,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4594,plain,
spl0_310,
inference(avatar_split_clause,[],[f565,f4592]) ).
fof(f4592,plain,
( spl0_310
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f565,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4590,plain,
spl0_309,
inference(avatar_split_clause,[],[f562,f4588]) ).
fof(f4588,plain,
( spl0_309
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f562,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4586,plain,
spl0_308,
inference(avatar_split_clause,[],[f561,f4584]) ).
fof(f4584,plain,
( spl0_308
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f561,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4582,plain,
spl0_307,
inference(avatar_split_clause,[],[f559,f4580]) ).
fof(f4580,plain,
( spl0_307
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f559,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4578,plain,
spl0_306,
inference(avatar_split_clause,[],[f558,f4576]) ).
fof(f4576,plain,
( spl0_306
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f558,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4574,plain,
spl0_305,
inference(avatar_split_clause,[],[f557,f4572]) ).
fof(f4572,plain,
( spl0_305
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f557,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4570,plain,
spl0_304,
inference(avatar_split_clause,[],[f554,f4568]) ).
fof(f4568,plain,
( spl0_304
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f554,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4566,plain,
spl0_303,
inference(avatar_split_clause,[],[f553,f4564]) ).
fof(f4564,plain,
( spl0_303
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f553,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4562,plain,
spl0_302,
inference(avatar_split_clause,[],[f551,f4560]) ).
fof(f4560,plain,
( spl0_302
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f551,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4558,plain,
spl0_301,
inference(avatar_split_clause,[],[f545,f4556]) ).
fof(f4556,plain,
( spl0_301
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f545,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4554,plain,
spl0_300,
inference(avatar_split_clause,[],[f544,f4552]) ).
fof(f4552,plain,
( spl0_300
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f544,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4550,plain,
spl0_299,
inference(avatar_split_clause,[],[f542,f4548]) ).
fof(f4548,plain,
( spl0_299
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f542,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4546,plain,
spl0_298,
inference(avatar_split_clause,[],[f541,f4544]) ).
fof(f4544,plain,
( spl0_298
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f541,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4542,plain,
spl0_297,
inference(avatar_split_clause,[],[f534,f4540]) ).
fof(f4540,plain,
( spl0_297
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f534,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4538,plain,
spl0_296,
inference(avatar_split_clause,[],[f533,f4536]) ).
fof(f4536,plain,
( spl0_296
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f533,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4534,plain,
spl0_295,
inference(avatar_split_clause,[],[f531,f4532]) ).
fof(f4532,plain,
( spl0_295
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f531,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4530,plain,
spl0_294,
inference(avatar_split_clause,[],[f530,f4528]) ).
fof(f4528,plain,
( spl0_294
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f530,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4526,plain,
spl0_293,
inference(avatar_split_clause,[],[f529,f4524]) ).
fof(f4524,plain,
( spl0_293
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f529,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4522,plain,
spl0_292,
inference(avatar_split_clause,[],[f527,f4520]) ).
fof(f4520,plain,
( spl0_292
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f527,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4518,plain,
spl0_291,
inference(avatar_split_clause,[],[f526,f4516]) ).
fof(f4516,plain,
( spl0_291
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f526,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4514,plain,
spl0_290,
inference(avatar_split_clause,[],[f525,f4512]) ).
fof(f4512,plain,
( spl0_290
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f525,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4510,plain,
spl0_289,
inference(avatar_split_clause,[],[f524,f4508]) ).
fof(f4508,plain,
( spl0_289
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f524,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4506,plain,
spl0_288,
inference(avatar_split_clause,[],[f523,f4504]) ).
fof(f4504,plain,
( spl0_288
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f523,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4502,plain,
spl0_287,
inference(avatar_split_clause,[],[f522,f4500]) ).
fof(f4500,plain,
( spl0_287
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f522,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4498,plain,
spl0_286,
inference(avatar_split_clause,[],[f521,f4496]) ).
fof(f4496,plain,
( spl0_286
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f521,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4494,plain,
spl0_285,
inference(avatar_split_clause,[],[f520,f4492]) ).
fof(f4492,plain,
( spl0_285
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f520,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4490,plain,
spl0_284,
inference(avatar_split_clause,[],[f519,f4488]) ).
fof(f4488,plain,
( spl0_284
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f519,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4486,plain,
spl0_283,
inference(avatar_split_clause,[],[f518,f4484]) ).
fof(f4484,plain,
( spl0_283
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f518,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4482,plain,
spl0_282,
inference(avatar_split_clause,[],[f515,f4480]) ).
fof(f4480,plain,
( spl0_282
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f515,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4478,plain,
spl0_281,
inference(avatar_split_clause,[],[f513,f4476]) ).
fof(f4476,plain,
( spl0_281
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f513,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4474,plain,
spl0_280,
inference(avatar_split_clause,[],[f511,f4472]) ).
fof(f4472,plain,
( spl0_280
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f511,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4470,plain,
spl0_279,
inference(avatar_split_clause,[],[f508,f4468]) ).
fof(f4468,plain,
( spl0_279
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f508,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4466,plain,
spl0_278,
inference(avatar_split_clause,[],[f507,f4464]) ).
fof(f4464,plain,
( spl0_278
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f507,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4462,plain,
spl0_277,
inference(avatar_split_clause,[],[f506,f4460]) ).
fof(f4460,plain,
( spl0_277
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f506,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4458,plain,
spl0_276,
inference(avatar_split_clause,[],[f503,f4456]) ).
fof(f4456,plain,
( spl0_276
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f503,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4454,plain,
spl0_275,
inference(avatar_split_clause,[],[f500,f4452]) ).
fof(f4452,plain,
( spl0_275
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f500,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4450,plain,
spl0_274,
inference(avatar_split_clause,[],[f499,f4448]) ).
fof(f4448,plain,
( spl0_274
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f499,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4446,plain,
spl0_273,
inference(avatar_split_clause,[],[f497,f4444]) ).
fof(f4444,plain,
( spl0_273
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f497,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4442,plain,
spl0_272,
inference(avatar_split_clause,[],[f496,f4440]) ).
fof(f4440,plain,
( spl0_272
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f496,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4438,plain,
spl0_271,
inference(avatar_split_clause,[],[f495,f4436]) ).
fof(f4436,plain,
( spl0_271
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f495,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4434,plain,
spl0_270,
inference(avatar_split_clause,[],[f494,f4432]) ).
fof(f4432,plain,
( spl0_270
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f494,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4430,plain,
spl0_269,
inference(avatar_split_clause,[],[f493,f4428]) ).
fof(f4428,plain,
( spl0_269
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f493,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4426,plain,
spl0_268,
inference(avatar_split_clause,[],[f491,f4424]) ).
fof(f4424,plain,
( spl0_268
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f491,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4422,plain,
spl0_267,
inference(avatar_split_clause,[],[f488,f4420]) ).
fof(f4420,plain,
( spl0_267
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f488,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4418,plain,
spl0_266,
inference(avatar_split_clause,[],[f487,f4416]) ).
fof(f4416,plain,
( spl0_266
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f487,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4414,plain,
spl0_265,
inference(avatar_split_clause,[],[f483,f4412]) ).
fof(f4412,plain,
( spl0_265
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f483,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4410,plain,
spl0_264,
inference(avatar_split_clause,[],[f481,f4408]) ).
fof(f4408,plain,
( spl0_264
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f481,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4406,plain,
spl0_263,
inference(avatar_split_clause,[],[f473,f4404]) ).
fof(f4404,plain,
( spl0_263
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f473,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4402,plain,
spl0_262,
inference(avatar_split_clause,[],[f472,f4400]) ).
fof(f4400,plain,
( spl0_262
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f472,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4398,plain,
spl0_261,
inference(avatar_split_clause,[],[f471,f4396]) ).
fof(f4396,plain,
( spl0_261
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f471,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4394,plain,
spl0_260,
inference(avatar_split_clause,[],[f470,f4392]) ).
fof(f4392,plain,
( spl0_260
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f470,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4390,plain,
spl0_259,
inference(avatar_split_clause,[],[f469,f4388]) ).
fof(f4388,plain,
( spl0_259
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f469,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4386,plain,
spl0_258,
inference(avatar_split_clause,[],[f468,f4384]) ).
fof(f4384,plain,
( spl0_258
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f468,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4382,plain,
spl0_257,
inference(avatar_split_clause,[],[f467,f4380]) ).
fof(f4380,plain,
( spl0_257
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4378,plain,
spl0_256,
inference(avatar_split_clause,[],[f466,f4376]) ).
fof(f4376,plain,
( spl0_256
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f466,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4374,plain,
spl0_255,
inference(avatar_split_clause,[],[f465,f4372]) ).
fof(f4372,plain,
( spl0_255
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f465,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4370,plain,
spl0_254,
inference(avatar_split_clause,[],[f464,f4368]) ).
fof(f4368,plain,
( spl0_254
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f464,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4366,plain,
spl0_253,
inference(avatar_split_clause,[],[f463,f4364]) ).
fof(f4364,plain,
( spl0_253
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f463,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4362,plain,
spl0_252,
inference(avatar_split_clause,[],[f462,f4360]) ).
fof(f4360,plain,
( spl0_252
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f462,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4358,plain,
spl0_251,
inference(avatar_split_clause,[],[f461,f4356]) ).
fof(f4356,plain,
( spl0_251
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f461,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4354,plain,
spl0_250,
inference(avatar_split_clause,[],[f460,f4352]) ).
fof(f4352,plain,
( spl0_250
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f460,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4350,plain,
spl0_249,
inference(avatar_split_clause,[],[f459,f4348]) ).
fof(f4348,plain,
( spl0_249
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f459,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4346,plain,
spl0_248,
inference(avatar_split_clause,[],[f458,f4344]) ).
fof(f4344,plain,
( spl0_248
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f458,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4342,plain,
spl0_247,
inference(avatar_split_clause,[],[f457,f4340]) ).
fof(f4340,plain,
( spl0_247
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f457,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4338,plain,
spl0_246,
inference(avatar_split_clause,[],[f454,f4336]) ).
fof(f4336,plain,
( spl0_246
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4334,plain,
spl0_245,
inference(avatar_split_clause,[],[f453,f4332]) ).
fof(f4332,plain,
( spl0_245
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4330,plain,
spl0_244,
inference(avatar_split_clause,[],[f452,f4328]) ).
fof(f4328,plain,
( spl0_244
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4326,plain,
spl0_243,
inference(avatar_split_clause,[],[f451,f4324]) ).
fof(f4324,plain,
( spl0_243
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f451,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4322,plain,
spl0_242,
inference(avatar_split_clause,[],[f450,f4320]) ).
fof(f4320,plain,
( spl0_242
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f450,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4318,plain,
spl0_241,
inference(avatar_split_clause,[],[f449,f4316]) ).
fof(f4316,plain,
( spl0_241
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4314,plain,
spl0_240,
inference(avatar_split_clause,[],[f446,f4312]) ).
fof(f4312,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f446,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4310,plain,
spl0_239,
inference(avatar_split_clause,[],[f445,f4308]) ).
fof(f4308,plain,
( spl0_239
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f445,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4306,plain,
spl0_238,
inference(avatar_split_clause,[],[f441,f4304]) ).
fof(f4304,plain,
( spl0_238
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f441,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4302,plain,
spl0_237,
inference(avatar_split_clause,[],[f440,f4300]) ).
fof(f4300,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f440,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4298,plain,
spl0_236,
inference(avatar_split_clause,[],[f439,f4296]) ).
fof(f4296,plain,
( spl0_236
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f439,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4294,plain,
spl0_235,
inference(avatar_split_clause,[],[f436,f4292]) ).
fof(f4292,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f436,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4290,plain,
spl0_234,
inference(avatar_split_clause,[],[f434,f4288]) ).
fof(f4288,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f434,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4286,plain,
spl0_233,
inference(avatar_split_clause,[],[f433,f4284]) ).
fof(f4284,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f433,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4282,plain,
spl0_232,
inference(avatar_split_clause,[],[f432,f4280]) ).
fof(f4280,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f432,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4278,plain,
spl0_231,
inference(avatar_split_clause,[],[f431,f4276]) ).
fof(f4276,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f431,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4274,plain,
spl0_230,
inference(avatar_split_clause,[],[f430,f4272]) ).
fof(f4272,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f430,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4270,plain,
spl0_229,
inference(avatar_split_clause,[],[f426,f4268]) ).
fof(f4268,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f426,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4266,plain,
spl0_228,
inference(avatar_split_clause,[],[f425,f4264]) ).
fof(f4264,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f425,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4262,plain,
spl0_227,
inference(avatar_split_clause,[],[f424,f4260]) ).
fof(f4260,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f424,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4258,plain,
spl0_226,
inference(avatar_split_clause,[],[f421,f4256]) ).
fof(f4256,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f421,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4254,plain,
spl0_225,
inference(avatar_split_clause,[],[f419,f4252]) ).
fof(f4252,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f419,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4250,plain,
spl0_224,
inference(avatar_split_clause,[],[f417,f4248]) ).
fof(f4248,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f417,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4246,plain,
spl0_223,
inference(avatar_split_clause,[],[f416,f4244]) ).
fof(f4244,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f416,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4242,plain,
spl0_222,
inference(avatar_split_clause,[],[f415,f4240]) ).
fof(f4240,plain,
( spl0_222
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f415,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4238,plain,
spl0_221,
inference(avatar_split_clause,[],[f414,f4236]) ).
fof(f4236,plain,
( spl0_221
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f414,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4234,plain,
spl0_220,
inference(avatar_split_clause,[],[f413,f4232]) ).
fof(f4232,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f413,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4230,plain,
spl0_219,
inference(avatar_split_clause,[],[f411,f4228]) ).
fof(f4228,plain,
( spl0_219
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f411,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4226,plain,
spl0_218,
inference(avatar_split_clause,[],[f410,f4224]) ).
fof(f4224,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f410,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4222,plain,
spl0_217,
inference(avatar_split_clause,[],[f407,f4220]) ).
fof(f4220,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f407,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4218,plain,
spl0_216,
inference(avatar_split_clause,[],[f405,f4216]) ).
fof(f4216,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f405,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4214,plain,
spl0_215,
inference(avatar_split_clause,[],[f404,f4212]) ).
fof(f4212,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f404,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4210,plain,
spl0_214,
inference(avatar_split_clause,[],[f403,f4208]) ).
fof(f4208,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f403,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4206,plain,
spl0_213,
inference(avatar_split_clause,[],[f402,f4204]) ).
fof(f4204,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f402,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4202,plain,
spl0_212,
inference(avatar_split_clause,[],[f401,f4200]) ).
fof(f4200,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f401,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4198,plain,
spl0_211,
inference(avatar_split_clause,[],[f400,f4196]) ).
fof(f4196,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f400,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4194,plain,
spl0_210,
inference(avatar_split_clause,[],[f399,f4192]) ).
fof(f4192,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f399,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4190,plain,
spl0_209,
inference(avatar_split_clause,[],[f398,f4188]) ).
fof(f4188,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f398,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4186,plain,
spl0_208,
inference(avatar_split_clause,[],[f397,f4184]) ).
fof(f4184,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f397,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4182,plain,
spl0_207,
inference(avatar_split_clause,[],[f394,f4180]) ).
fof(f4180,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f394,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4178,plain,
spl0_206,
inference(avatar_split_clause,[],[f393,f4176]) ).
fof(f4176,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f393,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4174,plain,
spl0_205,
inference(avatar_split_clause,[],[f392,f4172]) ).
fof(f4172,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f392,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4170,plain,
spl0_204,
inference(avatar_split_clause,[],[f391,f4168]) ).
fof(f4168,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f391,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4166,plain,
spl0_203,
inference(avatar_split_clause,[],[f390,f4164]) ).
fof(f4164,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f390,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4162,plain,
spl0_202,
inference(avatar_split_clause,[],[f389,f4160]) ).
fof(f4160,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f389,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4158,plain,
spl0_201,
inference(avatar_split_clause,[],[f387,f4156]) ).
fof(f4156,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f387,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4154,plain,
spl0_200,
inference(avatar_split_clause,[],[f385,f4152]) ).
fof(f4152,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f385,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4150,plain,
spl0_199,
inference(avatar_split_clause,[],[f384,f4148]) ).
fof(f4148,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f384,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4146,plain,
spl0_198,
inference(avatar_split_clause,[],[f383,f4144]) ).
fof(f4144,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f383,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4142,plain,
spl0_197,
inference(avatar_split_clause,[],[f382,f4140]) ).
fof(f4140,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f382,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4138,plain,
spl0_196,
inference(avatar_split_clause,[],[f379,f4136]) ).
fof(f4136,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f379,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4134,plain,
spl0_195,
inference(avatar_split_clause,[],[f377,f4132]) ).
fof(f4132,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f377,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4130,plain,
spl0_194,
inference(avatar_split_clause,[],[f376,f4128]) ).
fof(f4128,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f376,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4126,plain,
spl0_193,
inference(avatar_split_clause,[],[f375,f4124]) ).
fof(f4124,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f375,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4122,plain,
spl0_192,
inference(avatar_split_clause,[],[f374,f4120]) ).
fof(f4120,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f374,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4118,plain,
spl0_191,
inference(avatar_split_clause,[],[f373,f4116]) ).
fof(f4116,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f373,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4114,plain,
spl0_190,
inference(avatar_split_clause,[],[f372,f4112]) ).
fof(f4112,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f372,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4110,plain,
spl0_189,
inference(avatar_split_clause,[],[f371,f4108]) ).
fof(f4108,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f371,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4106,plain,
spl0_188,
inference(avatar_split_clause,[],[f370,f4104]) ).
fof(f4104,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f370,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4102,plain,
spl0_187,
inference(avatar_split_clause,[],[f368,f4100]) ).
fof(f4100,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f368,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4098,plain,
spl0_186,
inference(avatar_split_clause,[],[f366,f4096]) ).
fof(f4096,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f366,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4094,plain,
spl0_185,
inference(avatar_split_clause,[],[f365,f4092]) ).
fof(f4092,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f365,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4090,plain,
spl0_184,
inference(avatar_split_clause,[],[f364,f4088]) ).
fof(f4088,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f364,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4086,plain,
spl0_183,
inference(avatar_split_clause,[],[f363,f4084]) ).
fof(f4084,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f363,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4082,plain,
spl0_182,
inference(avatar_split_clause,[],[f360,f4080]) ).
fof(f4080,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f360,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4078,plain,
spl0_181,
inference(avatar_split_clause,[],[f358,f4076]) ).
fof(f4076,plain,
( spl0_181
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f358,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4074,plain,
spl0_180,
inference(avatar_split_clause,[],[f357,f4072]) ).
fof(f4072,plain,
( spl0_180
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f357,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4070,plain,
spl0_179,
inference(avatar_split_clause,[],[f356,f4068]) ).
fof(f4068,plain,
( spl0_179
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f356,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4066,plain,
spl0_178,
inference(avatar_split_clause,[],[f355,f4064]) ).
fof(f4064,plain,
( spl0_178
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f355,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4062,plain,
spl0_177,
inference(avatar_split_clause,[],[f354,f4060]) ).
fof(f4060,plain,
( spl0_177
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f354,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4058,plain,
spl0_176,
inference(avatar_split_clause,[],[f353,f4056]) ).
fof(f4056,plain,
( spl0_176
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f353,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4054,plain,
spl0_175,
inference(avatar_split_clause,[],[f352,f4052]) ).
fof(f4052,plain,
( spl0_175
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f352,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4050,plain,
spl0_174,
inference(avatar_split_clause,[],[f350,f4048]) ).
fof(f4048,plain,
( spl0_174
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f350,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4046,plain,
spl0_173,
inference(avatar_split_clause,[],[f348,f4044]) ).
fof(f4044,plain,
( spl0_173
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f348,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4042,plain,
spl0_172,
inference(avatar_split_clause,[],[f347,f4040]) ).
fof(f4040,plain,
( spl0_172
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f347,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4038,plain,
spl0_171,
inference(avatar_split_clause,[],[f346,f4036]) ).
fof(f4036,plain,
( spl0_171
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f346,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4034,plain,
spl0_170,
inference(avatar_split_clause,[],[f345,f4032]) ).
fof(f4032,plain,
( spl0_170
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f345,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4030,plain,
spl0_169,
inference(avatar_split_clause,[],[f344,f4028]) ).
fof(f4028,plain,
( spl0_169
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f344,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4026,plain,
spl0_168,
inference(avatar_split_clause,[],[f343,f4024]) ).
fof(f4024,plain,
( spl0_168
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f343,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4022,plain,
spl0_167,
inference(avatar_split_clause,[],[f340,f4020]) ).
fof(f4020,plain,
( spl0_167
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f340,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4018,plain,
spl0_166,
inference(avatar_split_clause,[],[f338,f4016]) ).
fof(f4016,plain,
( spl0_166
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f338,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4014,plain,
spl0_165,
inference(avatar_split_clause,[],[f337,f4012]) ).
fof(f4012,plain,
( spl0_165
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f337,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4010,plain,
spl0_164,
inference(avatar_split_clause,[],[f336,f4008]) ).
fof(f4008,plain,
( spl0_164
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f336,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4006,plain,
spl0_163,
inference(avatar_split_clause,[],[f335,f4004]) ).
fof(f4004,plain,
( spl0_163
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f335,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4002,plain,
spl0_162,
inference(avatar_split_clause,[],[f334,f4000]) ).
fof(f4000,plain,
( spl0_162
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f334,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3998,plain,
spl0_161,
inference(avatar_split_clause,[],[f333,f3996]) ).
fof(f3996,plain,
( spl0_161
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f333,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3994,plain,
spl0_160,
inference(avatar_split_clause,[],[f332,f3992]) ).
fof(f3992,plain,
( spl0_160
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f332,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3990,plain,
spl0_159,
inference(avatar_split_clause,[],[f330,f3988]) ).
fof(f3988,plain,
( spl0_159
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f330,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3986,plain,
spl0_158,
inference(avatar_split_clause,[],[f328,f3984]) ).
fof(f3984,plain,
( spl0_158
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f328,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3982,plain,
spl0_157,
inference(avatar_split_clause,[],[f327,f3980]) ).
fof(f3980,plain,
( spl0_157
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f327,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3978,plain,
spl0_156,
inference(avatar_split_clause,[],[f326,f3976]) ).
fof(f3976,plain,
( spl0_156
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f326,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3974,plain,
spl0_155,
inference(avatar_split_clause,[],[f323,f3972]) ).
fof(f3972,plain,
( spl0_155
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f323,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3970,plain,
spl0_154,
inference(avatar_split_clause,[],[f321,f3968]) ).
fof(f3968,plain,
( spl0_154
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f321,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3966,plain,
spl0_153,
inference(avatar_split_clause,[],[f320,f3964]) ).
fof(f3964,plain,
( spl0_153
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f320,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3962,plain,
spl0_152,
inference(avatar_split_clause,[],[f319,f3960]) ).
fof(f3960,plain,
( spl0_152
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f319,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3958,plain,
spl0_151,
inference(avatar_split_clause,[],[f318,f3956]) ).
fof(f3956,plain,
( spl0_151
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f318,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3954,plain,
spl0_150,
inference(avatar_split_clause,[],[f314,f3952]) ).
fof(f3952,plain,
( spl0_150
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f314,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3950,plain,
spl0_149,
inference(avatar_split_clause,[],[f307,f3948]) ).
fof(f3948,plain,
( spl0_149
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f307,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3946,plain,
spl0_148,
inference(avatar_split_clause,[],[f299,f3944]) ).
fof(f3944,plain,
( spl0_148
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f299,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3942,plain,
spl0_147,
inference(avatar_split_clause,[],[f298,f3940]) ).
fof(f3940,plain,
( spl0_147
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f298,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3938,plain,
spl0_146,
inference(avatar_split_clause,[],[f293,f3936]) ).
fof(f3936,plain,
( spl0_146
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f293,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3934,plain,
spl0_145,
inference(avatar_split_clause,[],[f291,f3932]) ).
fof(f3932,plain,
( spl0_145
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f291,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3930,plain,
spl0_144,
inference(avatar_split_clause,[],[f289,f3928]) ).
fof(f3928,plain,
( spl0_144
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f289,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3926,plain,
spl0_143,
inference(avatar_split_clause,[],[f288,f3924]) ).
fof(f3924,plain,
( spl0_143
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f288,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3922,plain,
spl0_142,
inference(avatar_split_clause,[],[f285,f3920]) ).
fof(f3920,plain,
( spl0_142
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f285,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3918,plain,
spl0_141,
inference(avatar_split_clause,[],[f283,f3916]) ).
fof(f3916,plain,
( spl0_141
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f283,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3914,plain,
spl0_140,
inference(avatar_split_clause,[],[f282,f3912]) ).
fof(f3912,plain,
( spl0_140
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f282,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3910,plain,
spl0_139,
inference(avatar_split_clause,[],[f281,f3908]) ).
fof(f3908,plain,
( spl0_139
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f281,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3906,plain,
spl0_138,
inference(avatar_split_clause,[],[f280,f3904]) ).
fof(f3904,plain,
( spl0_138
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f280,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3902,plain,
spl0_137,
inference(avatar_split_clause,[],[f279,f3900]) ).
fof(f3900,plain,
( spl0_137
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f279,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3898,plain,
spl0_136,
inference(avatar_split_clause,[],[f278,f3896]) ).
fof(f3896,plain,
( spl0_136
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f278,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3894,plain,
spl0_135,
inference(avatar_split_clause,[],[f277,f3892]) ).
fof(f3892,plain,
( spl0_135
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f277,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3890,plain,
spl0_134,
inference(avatar_split_clause,[],[f276,f3888]) ).
fof(f3888,plain,
( spl0_134
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f276,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3886,plain,
spl0_133,
inference(avatar_split_clause,[],[f275,f3884]) ).
fof(f3884,plain,
( spl0_133
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f275,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3882,plain,
spl0_132,
inference(avatar_split_clause,[],[f274,f3880]) ).
fof(f3880,plain,
( spl0_132
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f274,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3878,plain,
spl0_131,
inference(avatar_split_clause,[],[f272,f3876]) ).
fof(f3876,plain,
( spl0_131
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f272,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3874,plain,
spl0_130,
inference(avatar_split_clause,[],[f271,f3872]) ).
fof(f3872,plain,
( spl0_130
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f271,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3870,plain,
spl0_129,
inference(avatar_split_clause,[],[f270,f3868]) ).
fof(f3868,plain,
( spl0_129
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f270,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3866,plain,
spl0_128,
inference(avatar_split_clause,[],[f269,f3864]) ).
fof(f3864,plain,
( spl0_128
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f269,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3862,plain,
spl0_127,
inference(avatar_split_clause,[],[f268,f3860]) ).
fof(f3860,plain,
( spl0_127
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f268,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3858,plain,
spl0_126,
inference(avatar_split_clause,[],[f267,f3856]) ).
fof(f3856,plain,
( spl0_126
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f267,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3854,plain,
spl0_125,
inference(avatar_split_clause,[],[f266,f3852]) ).
fof(f3852,plain,
( spl0_125
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f266,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3850,plain,
spl0_124,
inference(avatar_split_clause,[],[f264,f3848]) ).
fof(f3848,plain,
( spl0_124
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f264,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3846,plain,
spl0_123,
inference(avatar_split_clause,[],[f263,f3844]) ).
fof(f3844,plain,
( spl0_123
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f263,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3842,plain,
spl0_122,
inference(avatar_split_clause,[],[f260,f3840]) ).
fof(f3840,plain,
( spl0_122
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f260,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3838,plain,
spl0_121,
inference(avatar_split_clause,[],[f259,f3836]) ).
fof(f3836,plain,
( spl0_121
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f259,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3834,plain,
spl0_120,
inference(avatar_split_clause,[],[f258,f3832]) ).
fof(f3832,plain,
( spl0_120
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f258,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3830,plain,
spl0_119,
inference(avatar_split_clause,[],[f257,f3828]) ).
fof(f3828,plain,
( spl0_119
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3826,plain,
spl0_118,
inference(avatar_split_clause,[],[f256,f3824]) ).
fof(f3824,plain,
( spl0_118
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3822,plain,
spl0_117,
inference(avatar_split_clause,[],[f255,f3820]) ).
fof(f3820,plain,
( spl0_117
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f255,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3818,plain,
spl0_116,
inference(avatar_split_clause,[],[f254,f3816]) ).
fof(f3816,plain,
( spl0_116
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f254,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3814,plain,
spl0_115,
inference(avatar_split_clause,[],[f253,f3812]) ).
fof(f3812,plain,
( spl0_115
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f253,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3810,plain,
spl0_114,
inference(avatar_split_clause,[],[f98,f3808]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3806,plain,
spl0_113,
inference(avatar_split_clause,[],[f66,f3804]) ).
fof(f3804,plain,
( spl0_113
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3802,plain,
spl0_112,
inference(avatar_split_clause,[],[f64,f3800]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3798,plain,
spl0_111,
inference(avatar_split_clause,[],[f40,f3796]) ).
fof(f3796,plain,
( spl0_111
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f40,axiom,
! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3794,plain,
spl0_110,
inference(avatar_split_clause,[],[f39,f3792]) ).
fof(f3792,plain,
( spl0_110
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f39,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3790,plain,
spl0_109,
inference(avatar_split_clause,[],[f23,f3788]) ).
fof(f3788,plain,
( spl0_109
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f23,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3786,plain,
~ spl0_108,
inference(avatar_split_clause,[],[f2732,f3783]) ).
fof(f3783,plain,
( spl0_108
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2732,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).
fof(f3781,plain,
~ spl0_107,
inference(avatar_split_clause,[],[f2629,f3778]) ).
fof(f3778,plain,
( spl0_107
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3776,plain,
~ spl0_106,
inference(avatar_split_clause,[],[f2310,f3773]) ).
fof(f3773,plain,
( spl0_106
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3771,plain,
spl0_105,
inference(avatar_split_clause,[],[f2303,f3768]) ).
fof(f3768,plain,
( spl0_105
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3766,plain,
spl0_104,
inference(avatar_split_clause,[],[f2290,f3763]) ).
fof(f3763,plain,
( spl0_104
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3761,plain,
~ spl0_103,
inference(avatar_split_clause,[],[f2159,f3758]) ).
fof(f3758,plain,
( spl0_103
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f2159,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3756,plain,
spl0_102,
inference(avatar_split_clause,[],[f1706,f3754]) ).
fof(f3754,plain,
( spl0_102
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1706,axiom,
! [X41] : c_List_Onull(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3752,plain,
spl0_101,
inference(avatar_split_clause,[],[f1551,f3750]) ).
fof(f3750,plain,
( spl0_101
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1551,axiom,
! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3748,plain,
~ spl0_100,
inference(avatar_split_clause,[],[f1370,f3745]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3743,plain,
~ spl0_99,
inference(avatar_split_clause,[],[f1250,f3740]) ).
fof(f3740,plain,
( spl0_99
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1250,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3738,plain,
spl0_98,
inference(avatar_split_clause,[],[f249,f3736]) ).
fof(f3736,plain,
( spl0_98
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3734,plain,
spl0_97,
inference(avatar_split_clause,[],[f248,f3732]) ).
fof(f3732,plain,
( spl0_97
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3730,plain,
spl0_96,
inference(avatar_split_clause,[],[f126,f3727]) ).
fof(f3727,plain,
( spl0_96
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f126,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3725,plain,
spl0_95,
inference(avatar_split_clause,[],[f124,f3722]) ).
fof(f3722,plain,
( spl0_95
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f124,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3720,plain,
spl0_94,
inference(avatar_split_clause,[],[f123,f3718]) ).
fof(f3718,plain,
( spl0_94
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f123,axiom,
! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3716,plain,
~ spl0_93,
inference(avatar_split_clause,[],[f2826,f3713]) ).
fof(f2826,axiom,
~ c_lessequals(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3711,plain,
spl0_92,
inference(avatar_split_clause,[],[f244,f3708]) ).
fof(f3708,plain,
( spl0_92
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3706,plain,
spl0_91,
inference(avatar_split_clause,[],[f243,f3703]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3701,plain,
spl0_90,
inference(avatar_split_clause,[],[f242,f3698]) ).
fof(f3698,plain,
( spl0_90
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3696,plain,
spl0_89,
inference(avatar_split_clause,[],[f241,f3693]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3691,plain,
spl0_88,
inference(avatar_split_clause,[],[f239,f3688]) ).
fof(f3688,plain,
( spl0_88
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3686,plain,
spl0_87,
inference(avatar_split_clause,[],[f238,f3683]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3681,plain,
spl0_86,
inference(avatar_split_clause,[],[f236,f3678]) ).
fof(f3678,plain,
( spl0_86
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3676,plain,
spl0_85,
inference(avatar_split_clause,[],[f235,f3673]) ).
fof(f3673,plain,
( spl0_85
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3671,plain,
spl0_84,
inference(avatar_split_clause,[],[f234,f3668]) ).
fof(f3668,plain,
( spl0_84
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3666,plain,
spl0_83,
inference(avatar_split_clause,[],[f233,f3663]) ).
fof(f3663,plain,
( spl0_83
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3661,plain,
spl0_82,
inference(avatar_split_clause,[],[f232,f3658]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3656,plain,
spl0_81,
inference(avatar_split_clause,[],[f231,f3653]) ).
fof(f3653,plain,
( spl0_81
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3651,plain,
spl0_80,
inference(avatar_split_clause,[],[f230,f3648]) ).
fof(f3648,plain,
( spl0_80
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3646,plain,
spl0_79,
inference(avatar_split_clause,[],[f229,f3643]) ).
fof(f3643,plain,
( spl0_79
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3641,plain,
spl0_78,
inference(avatar_split_clause,[],[f228,f3638]) ).
fof(f3638,plain,
( spl0_78
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3636,plain,
spl0_77,
inference(avatar_split_clause,[],[f227,f3633]) ).
fof(f3633,plain,
( spl0_77
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3631,plain,
spl0_76,
inference(avatar_split_clause,[],[f226,f3628]) ).
fof(f3628,plain,
( spl0_76
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3626,plain,
spl0_75,
inference(avatar_split_clause,[],[f225,f3623]) ).
fof(f3623,plain,
( spl0_75
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3621,plain,
spl0_74,
inference(avatar_split_clause,[],[f224,f3618]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3616,plain,
spl0_73,
inference(avatar_split_clause,[],[f223,f3613]) ).
fof(f3613,plain,
( spl0_73
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3611,plain,
spl0_72,
inference(avatar_split_clause,[],[f222,f3608]) ).
fof(f3608,plain,
( spl0_72
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3606,plain,
spl0_71,
inference(avatar_split_clause,[],[f221,f3603]) ).
fof(f3603,plain,
( spl0_71
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3601,plain,
spl0_70,
inference(avatar_split_clause,[],[f220,f3598]) ).
fof(f3598,plain,
( spl0_70
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3596,plain,
spl0_69,
inference(avatar_split_clause,[],[f219,f3593]) ).
fof(f3593,plain,
( spl0_69
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3591,plain,
spl0_68,
inference(avatar_split_clause,[],[f218,f3588]) ).
fof(f3588,plain,
( spl0_68
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3586,plain,
spl0_67,
inference(avatar_split_clause,[],[f217,f3583]) ).
fof(f3583,plain,
( spl0_67
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3581,plain,
spl0_66,
inference(avatar_split_clause,[],[f216,f3578]) ).
fof(f3578,plain,
( spl0_66
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3576,plain,
spl0_65,
inference(avatar_split_clause,[],[f215,f3573]) ).
fof(f3573,plain,
( spl0_65
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3571,plain,
spl0_64,
inference(avatar_split_clause,[],[f214,f3568]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3566,plain,
spl0_63,
inference(avatar_split_clause,[],[f213,f3563]) ).
fof(f3563,plain,
( spl0_63
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3561,plain,
spl0_62,
inference(avatar_split_clause,[],[f212,f3558]) ).
fof(f3558,plain,
( spl0_62
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3556,plain,
spl0_61,
inference(avatar_split_clause,[],[f211,f3553]) ).
fof(f3553,plain,
( spl0_61
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3551,plain,
spl0_60,
inference(avatar_split_clause,[],[f210,f3548]) ).
fof(f3548,plain,
( spl0_60
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3546,plain,
spl0_59,
inference(avatar_split_clause,[],[f209,f3543]) ).
fof(f3543,plain,
( spl0_59
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3541,plain,
spl0_58,
inference(avatar_split_clause,[],[f208,f3538]) ).
fof(f3538,plain,
( spl0_58
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3536,plain,
spl0_57,
inference(avatar_split_clause,[],[f203,f3533]) ).
fof(f3533,plain,
( spl0_57
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3531,plain,
spl0_56,
inference(avatar_split_clause,[],[f198,f3528]) ).
fof(f3528,plain,
( spl0_56
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3526,plain,
spl0_55,
inference(avatar_split_clause,[],[f195,f3523]) ).
fof(f3523,plain,
( spl0_55
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3521,plain,
spl0_54,
inference(avatar_split_clause,[],[f194,f3518]) ).
fof(f3518,plain,
( spl0_54
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3516,plain,
spl0_53,
inference(avatar_split_clause,[],[f189,f3513]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3511,plain,
spl0_52,
inference(avatar_split_clause,[],[f186,f3508]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3506,plain,
spl0_51,
inference(avatar_split_clause,[],[f184,f3503]) ).
fof(f3503,plain,
( spl0_51
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3501,plain,
spl0_50,
inference(avatar_split_clause,[],[f183,f3498]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3496,plain,
spl0_49,
inference(avatar_split_clause,[],[f182,f3493]) ).
fof(f3493,plain,
( spl0_49
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3491,plain,
spl0_48,
inference(avatar_split_clause,[],[f181,f3488]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3486,plain,
spl0_47,
inference(avatar_split_clause,[],[f180,f3483]) ).
fof(f3483,plain,
( spl0_47
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f180,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3481,plain,
spl0_46,
inference(avatar_split_clause,[],[f178,f3478]) ).
fof(f3478,plain,
( spl0_46
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f178,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3476,plain,
spl0_45,
inference(avatar_split_clause,[],[f177,f3473]) ).
fof(f3473,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f177,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3471,plain,
spl0_44,
inference(avatar_split_clause,[],[f176,f3468]) ).
fof(f3468,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f176,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3466,plain,
spl0_43,
inference(avatar_split_clause,[],[f175,f3463]) ).
fof(f3463,plain,
( spl0_43
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3461,plain,
spl0_42,
inference(avatar_split_clause,[],[f174,f3458]) ).
fof(f3458,plain,
( spl0_42
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f174,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3456,plain,
spl0_41,
inference(avatar_split_clause,[],[f173,f3453]) ).
fof(f3453,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f173,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3451,plain,
spl0_40,
inference(avatar_split_clause,[],[f172,f3448]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3446,plain,
spl0_39,
inference(avatar_split_clause,[],[f171,f3443]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3441,plain,
spl0_38,
inference(avatar_split_clause,[],[f170,f3438]) ).
fof(f3438,plain,
( spl0_38
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f170,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3436,plain,
spl0_37,
inference(avatar_split_clause,[],[f169,f3433]) ).
fof(f3433,plain,
( spl0_37
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f169,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3431,plain,
spl0_36,
inference(avatar_split_clause,[],[f168,f3428]) ).
fof(f3428,plain,
( spl0_36
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f168,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3426,plain,
spl0_35,
inference(avatar_split_clause,[],[f167,f3423]) ).
fof(f3423,plain,
( spl0_35
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f167,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3421,plain,
spl0_34,
inference(avatar_split_clause,[],[f166,f3418]) ).
fof(f3418,plain,
( spl0_34
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f166,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3416,plain,
spl0_33,
inference(avatar_split_clause,[],[f165,f3413]) ).
fof(f3413,plain,
( spl0_33
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f165,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3411,plain,
spl0_32,
inference(avatar_split_clause,[],[f164,f3408]) ).
fof(f3408,plain,
( spl0_32
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f164,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3406,plain,
spl0_31,
inference(avatar_split_clause,[],[f162,f3403]) ).
fof(f3403,plain,
( spl0_31
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f162,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3401,plain,
spl0_30,
inference(avatar_split_clause,[],[f161,f3398]) ).
fof(f3398,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3396,plain,
spl0_29,
inference(avatar_split_clause,[],[f160,f3393]) ).
fof(f3393,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f160,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3391,plain,
spl0_28,
inference(avatar_split_clause,[],[f159,f3388]) ).
fof(f3388,plain,
( spl0_28
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3386,plain,
spl0_27,
inference(avatar_split_clause,[],[f158,f3383]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3381,plain,
spl0_26,
inference(avatar_split_clause,[],[f157,f3378]) ).
fof(f3378,plain,
( spl0_26
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3376,plain,
spl0_25,
inference(avatar_split_clause,[],[f156,f3373]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3371,plain,
spl0_24,
inference(avatar_split_clause,[],[f155,f3368]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3366,plain,
spl0_23,
inference(avatar_split_clause,[],[f154,f3363]) ).
fof(f3363,plain,
( spl0_23
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3361,plain,
spl0_22,
inference(avatar_split_clause,[],[f153,f3358]) ).
fof(f153,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3356,plain,
spl0_21,
inference(avatar_split_clause,[],[f151,f3353]) ).
fof(f151,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3351,plain,
spl0_20,
inference(avatar_split_clause,[],[f150,f3348]) ).
fof(f3348,plain,
( spl0_20
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3346,plain,
spl0_19,
inference(avatar_split_clause,[],[f149,f3343]) ).
fof(f3343,plain,
( spl0_19
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f149,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3341,plain,
spl0_18,
inference(avatar_split_clause,[],[f148,f3338]) ).
fof(f3338,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f148,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3336,plain,
spl0_17,
inference(avatar_split_clause,[],[f147,f3333]) ).
fof(f3333,plain,
( spl0_17
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3331,plain,
spl0_16,
inference(avatar_split_clause,[],[f146,f3328]) ).
fof(f3328,plain,
( spl0_16
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3326,plain,
spl0_15,
inference(avatar_split_clause,[],[f145,f3323]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3321,plain,
spl0_14,
inference(avatar_split_clause,[],[f144,f3318]) ).
fof(f3318,plain,
( spl0_14
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f144,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3316,plain,
spl0_13,
inference(avatar_split_clause,[],[f143,f3313]) ).
fof(f3313,plain,
( spl0_13
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3311,plain,
spl0_12,
inference(avatar_split_clause,[],[f142,f3308]) ).
fof(f3308,plain,
( spl0_12
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f142,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3306,plain,
spl0_11,
inference(avatar_split_clause,[],[f140,f3303]) ).
fof(f3303,plain,
( spl0_11
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3301,plain,
spl0_10,
inference(avatar_split_clause,[],[f139,f3298]) ).
fof(f3298,plain,
( spl0_10
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f139,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3296,plain,
spl0_9,
inference(avatar_split_clause,[],[f138,f3293]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3291,plain,
spl0_8,
inference(avatar_split_clause,[],[f137,f3288]) ).
fof(f3288,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3286,plain,
spl0_7,
inference(avatar_split_clause,[],[f136,f3283]) ).
fof(f3283,plain,
( spl0_7
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3281,plain,
spl0_6,
inference(avatar_split_clause,[],[f135,f3278]) ).
fof(f3278,plain,
( spl0_6
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f135,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3276,plain,
spl0_5,
inference(avatar_split_clause,[],[f134,f3273]) ).
fof(f3273,plain,
( spl0_5
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3271,plain,
spl0_4,
inference(avatar_split_clause,[],[f133,f3268]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3266,plain,
spl0_3,
inference(avatar_split_clause,[],[f132,f3263]) ).
fof(f3263,plain,
( spl0_3
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3261,plain,
spl0_2,
inference(avatar_split_clause,[],[f131,f3258]) ).
fof(f3258,plain,
( spl0_2
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3256,plain,
spl0_1,
inference(avatar_split_clause,[],[f130,f3253]) ).
fof(f3253,plain,
( spl0_1
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV273-1 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.35 % Computer : n003.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 300
% 0.12/0.35 % DateTime : Fri May 3 21:15:53 EDT 2024
% 0.12/0.35 % CPUTime :
% 0.12/0.36 % (31910)Running in auto input_syntax mode. Trying TPTP
% 0.19/0.47 % (31912)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.19/0.47 % (31913)WARNING: value z3 for option sas not known
% 0.19/0.47 % (31913)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)
% 0.19/0.47 % (31917)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)
% 0.19/0.47 % (31916)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)
% 0.19/0.47 % (31914)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.19/0.47 % (31915)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.19/0.47 % (31911)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 1.44/0.72 TRYING [1]
% 4.17/1.07 % (31915)First to succeed.
% 4.62/1.13 % (31915)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-31910"
% 4.62/1.14 % (31915)Refutation found. Thanks to Tanya!
% 4.62/1.14 % SZS status Unsatisfiable for theBenchmark
% 4.62/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 4.98/1.19 % (31915)------------------------------
% 4.98/1.19 % (31915)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.98/1.19 % (31915)Termination reason: Refutation
% 4.98/1.19
% 4.98/1.19 % (31915)Memory used [KB]: 12270
% 4.98/1.19 % (31915)Time elapsed: 0.659 s
% 4.98/1.19 % (31915)Instructions burned: 1293 (million)
% 4.98/1.19 % (31910)Success in time 0.825 s
%------------------------------------------------------------------------------