TSTP Solution File: COM010-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : COM010-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 04:47:12 EDT 2024
% Result : Unsatisfiable 8.02s 1.60s
% Output : Refutation 8.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4237
% Syntax : Number of formulae : 7327 (2740 unt; 0 def)
% Number of atoms : 15918 (2873 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 14738 (6147 ~;6371 |; 0 &)
% (2220 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 2290 (2288 usr;2221 prp; 0-3 aty)
% Number of functors : 228 ( 228 usr; 47 con; 0-18 aty)
% Number of variables : 10552 (10552 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f28331,plain,
$false,
inference(avatar_sat_refutation,[],[f3160,f3165,f3170,f3175,f3180,f3185,f3190,f3195,f3200,f3205,f3210,f3215,f3220,f3225,f3230,f3235,f3240,f3245,f3250,f3255,f3260,f3265,f3270,f3275,f3280,f3285,f3290,f3295,f3300,f3305,f3310,f3315,f3320,f3325,f3330,f3335,f3340,f3345,f3350,f3355,f3360,f3365,f3370,f3375,f3380,f3385,f3390,f3395,f3400,f3405,f3410,f3415,f3420,f3425,f3430,f3435,f3440,f3445,f3450,f3455,f3460,f3465,f3470,f3475,f3480,f3485,f3490,f3495,f3500,f3505,f3510,f3515,f3520,f3525,f3530,f3535,f3540,f3545,f3550,f3555,f3560,f3565,f3570,f3575,f3580,f3585,f3590,f3595,f3600,f3605,f3610,f3615,f3620,f3625,f3630,f3635,f3640,f3645,f3649,f3653,f3658,f3663,f3668,f3673,f3678,f3682,f3687,f3692,f3696,f3700,f3704,f3709,f3714,f3719,f3723,f3727,f3731,f3736,f3740,f3745,f3749,f3753,f3757,f3761,f3765,f3769,f3773,f3777,f3781,f3785,f3789,f3793,f3797,f3801,f3805,f3809,f3813,f3817,f3821,f3825,f3829,f3833,f3837,f3841,f3845,f3849,f3853,f3857,f3861,f3865,f3869,f3873,f3877,f3881,f3885,f3889,f3893,f3897,f3901,f3905,f3909,f3913,f3917,f3921,f3925,f3929,f3933,f3937,f3941,f3945,f3949,f3953,f3957,f3961,f3965,f3969,f3973,f3977,f3981,f3985,f3989,f3993,f3997,f4001,f4005,f4009,f4013,f4017,f4021,f4025,f4029,f4033,f4037,f4041,f4045,f4049,f4053,f4057,f4061,f4065,f4069,f4073,f4077,f4081,f4085,f4089,f4093,f4097,f4101,f4105,f4109,f4113,f4117,f4121,f4125,f4129,f4133,f4137,f4141,f4145,f4149,f4153,f4157,f4161,f4165,f4169,f4173,f4177,f4181,f4185,f4189,f4193,f4197,f4201,f4205,f4209,f4213,f4217,f4221,f4225,f4229,f4233,f4237,f4241,f4245,f4249,f4253,f4257,f4261,f4265,f4269,f4273,f4277,f4281,f4285,f4289,f4293,f4297,f4301,f4305,f4309,f4313,f4317,f4321,f4325,f4329,f4333,f4337,f4341,f4345,f4349,f4353,f4357,f4361,f4365,f4369,f4373,f4377,f4381,f4385,f4389,f4393,f4397,f4401,f4405,f4409,f4413,f4417,f4421,f4425,f4429,f4433,f4437,f4441,f4445,f4449,f4453,f4457,f4461,f4465,f4469,f4473,f4477,f4481,f4485,f4489,f4493,f4497,f4501,f4505,f4509,f4513,f4517,f4521,f4525,f4529,f4533,f4537,f4541,f4545,f4549,f4553,f4557,f4561,f4565,f4569,f4573,f4577,f4581,f4585,f4589,f4593,f4597,f4601,f4605,f4609,f4613,f4617,f4621,f4625,f4629,f4633,f4637,f4641,f4645,f4649,f4653,f4657,f4661,f4665,f4669,f4673,f4677,f4681,f4685,f4689,f4693,f4697,f4701,f4705,f4709,f4713,f4717,f4721,f4725,f4729,f4733,f4737,f4741,f4745,f4749,f4753,f4757,f4761,f4765,f4769,f4773,f4777,f4781,f4785,f4789,f4793,f4797,f4801,f4805,f4809,f4813,f4817,f4821,f4825,f4829,f4833,f4837,f4841,f4845,f4849,f4853,f4857,f4861,f4865,f4869,f4873,f4877,f4881,f4885,f4889,f4893,f4897,f4901,f4905,f4909,f4913,f4917,f4921,f4925,f4929,f4933,f4937,f4941,f4945,f4949,f4953,f4957,f4961,f4965,f4969,f4973,f4977,f4981,f4985,f4989,f4993,f4997,f5001,f5005,f5009,f5013,f5017,f5021,f5025,f5029,f5033,f5037,f5041,f5045,f5049,f5053,f5057,f5061,f5065,f5069,f5073,f5077,f5081,f5085,f5089,f5093,f5097,f5101,f5105,f5109,f5113,f5117,f5121,f5125,f5129,f5133,f5137,f5141,f5145,f5149,f5153,f5157,f5161,f5165,f5169,f5173,f5177,f5181,f5185,f5189,f5193,f5197,f5201,f5205,f5209,f5213,f5217,f5221,f5225,f5229,f5233,f5237,f5241,f5245,f5249,f5253,f5257,f5261,f5265,f5269,f5273,f5277,f5281,f5285,f5289,f5293,f5297,f5301,f5305,f5309,f5313,f5317,f5321,f5325,f5329,f5333,f5337,f5341,f5345,f5349,f5353,f5357,f5361,f5365,f5369,f5373,f5377,f5381,f5385,f5389,f5393,f5397,f5401,f5405,f5409,f5413,f5417,f5421,f5425,f5429,f5433,f5437,f5441,f5445,f5449,f5453,f5457,f5461,f5465,f5469,f5473,f5477,f5481,f5485,f5489,f5493,f5497,f5501,f5505,f5509,f5513,f5517,f5521,f5525,f5529,f5533,f5537,f5541,f5545,f5549,f5553,f5557,f5561,f5565,f5569,f5573,f5577,f5581,f5585,f5589,f5593,f5597,f5601,f5605,f5609,f5613,f5617,f5621,f5625,f5629,f5633,f5637,f5641,f5645,f5649,f5653,f5657,f5661,f5665,f5669,f5673,f5677,f5681,f5685,f5689,f5693,f5697,f5701,f5705,f5709,f5713,f5717,f5721,f5725,f5729,f5733,f5737,f5741,f5745,f5749,f5753,f5757,f5761,f5765,f5769,f5773,f5777,f5781,f5785,f5789,f5793,f5797,f5801,f5805,f5809,f5813,f5817,f5821,f5825,f5829,f5833,f5837,f5841,f5845,f5849,f5853,f5857,f5861,f5865,f5869,f5874,f5879,f5883,f5888,f5895,f5900,f6664,f6668,f6672,f6676,f6681,f6686,f6691,f6695,f6699,f6703,f6708,f6712,f6716,f6720,f6724,f6728,f6732,f6736,f6740,f6745,f6750,f6755,f6760,f6765,f6770,f6775,f6780,f6785,f6790,f6795,f6800,f6805,f6810,f6815,f6820,f6824,f6828,f6832,f6836,f6840,f6845,f6850,f6855,f6859,f6863,f6867,f6871,f6875,f6879,f6884,f6889,f6893,f6898,f6903,f6907,f6911,f6915,f6919,f6923,f6927,f6931,f6935,f6939,f6943,f6947,f6951,f6955,f6959,f6963,f6968,f6972,f6977,f6984,f6993,f6999,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7033,f7037,f7042,f7046,f7050,f7054,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7086,f7090,f7094,f7098,f7102,f7106,f7110,f7114,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7154,f7158,f7162,f7166,f7170,f7174,f7178,f7182,f7186,f7191,f7195,f7199,f7203,f7207,f7211,f7215,f7219,f7223,f7227,f7231,f7235,f7239,f7243,f7247,f7251,f7255,f7259,f7263,f7267,f7271,f7276,f7280,f7285,f7289,f7294,f7298,f7302,f7306,f7310,f7314,f7318,f7322,f7326,f7330,f7334,f7338,f7342,f7346,f7350,f7354,f7358,f7362,f7366,f7370,f7374,f7378,f7382,f7386,f7390,f7394,f7398,f7402,f7406,f7410,f7414,f7418,f7422,f7426,f7430,f7434,f7438,f7442,f7446,f7450,f7454,f7458,f7462,f7466,f7470,f7474,f7478,f7482,f7486,f7490,f7494,f7498,f7502,f7506,f7510,f7514,f7518,f7522,f7526,f7530,f7534,f7539,f7544,f7548,f7552,f7556,f7569,f7605,f7615,f7623,f7642,f7650,f7655,f7659,f7663,f7667,f7671,f7676,f7680,f7684,f7688,f7692,f7696,f7700,f7704,f7708,f7712,f7716,f7721,f7725,f7729,f7733,f7737,f7741,f7745,f7749,f7753,f7757,f7761,f7770,f7774,f7778,f7782,f7786,f7790,f7794,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7838,f7842,f7846,f7850,f7854,f7858,f7862,f7866,f7870,f7874,f7878,f7882,f7886,f7890,f7894,f7898,f7902,f7906,f7911,f7915,f7919,f7923,f7927,f7931,f7936,f7940,f7944,f7948,f7952,f7956,f7960,f7964,f7968,f7972,f7976,f7981,f7985,f7989,f7993,f7997,f8008,f8121,f8125,f8129,f8133,f8137,f8141,f8145,f8150,f8154,f8158,f8162,f8166,f8170,f8174,f8178,f8182,f8186,f8191,f8195,f8199,f8203,f8207,f8211,f8215,f8219,f8223,f8227,f8231,f8235,f8239,f8243,f8247,f8251,f8255,f8259,f8263,f8267,f8271,f8276,f8280,f8284,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8332,f8336,f8340,f8344,f8348,f8352,f8356,f8361,f8365,f8369,f8373,f8377,f8381,f8385,f8389,f8393,f8397,f8401,f8405,f8409,f8413,f8417,f8421,f8425,f8429,f8433,f8437,f8441,f8445,f8449,f8453,f8457,f8495,f8555,f8576,f8623,f8671,f8681,f8685,f8689,f8693,f8697,f8701,f8705,f8709,f8713,f8718,f8722,f8726,f8730,f8734,f8738,f8742,f8746,f8750,f8754,f8758,f8762,f8766,f8770,f8774,f8778,f8782,f8786,f8790,f8794,f8799,f8803,f8807,f8811,f8815,f8819,f8823,f8827,f8831,f8835,f8839,f8843,f8847,f8851,f8855,f8859,f8863,f8867,f8871,f8875,f8879,f8883,f8887,f8892,f8896,f8900,f8904,f8908,f8912,f8916,f8920,f8924,f8928,f8932,f8936,f8940,f8944,f8948,f8952,f8956,f8960,f8965,f8969,f8974,f8978,f8985,f8989,f8993,f8997,f9001,f9020,f9088,f9108,f9166,f9191,f9206,f9224,f9228,f9232,f9236,f9240,f9244,f9248,f9252,f9257,f9261,f9265,f9269,f9273,f9277,f9281,f9285,f9289,f9293,f9297,f9301,f9305,f9309,f9313,f9317,f9321,f9325,f9329,f9333,f9337,f9341,f9345,f9349,f9353,f9357,f9361,f9365,f9369,f9373,f9377,f9381,f9385,f9389,f9393,f9397,f9401,f9405,f9409,f9413,f9417,f9421,f9425,f9429,f9433,f9437,f9441,f9445,f9449,f9453,f9457,f9461,f9465,f9469,f9473,f9477,f9481,f9485,f9489,f9493,f9497,f9502,f9506,f9514,f9518,f9522,f9526,f9530,f9534,f9550,f9572,f9585,f9647,f9690,f9738,f9861,f9919,f9923,f9927,f9931,f9936,f9940,f9944,f9948,f9952,f9956,f9960,f9964,f9968,f9972,f9976,f9985,f9989,f9993,f9997,f10001,f10005,f10009,f10013,f10017,f10021,f10032,f10037,f10041,f10045,f10049,f10053,f10057,f10061,f10065,f10075,f10079,f10083,f10087,f10091,f10095,f10099,f10103,f10107,f10111,f10115,f10119,f10123,f10127,f10131,f10135,f10139,f10143,f10147,f10151,f10155,f10159,f10163,f10167,f10171,f10175,f10179,f10183,f10187,f10191,f10195,f10203,f10207,f10211,f10215,f10219,f10223,f10227,f10231,f10235,f10239,f10243,f10247,f10251,f10255,f10259,f10263,f10267,f10271,f10275,f10279,f10283,f10288,f10292,f10296,f10300,f10304,f10308,f10312,f10316,f10320,f10324,f10328,f10332,f10336,f10340,f10344,f10348,f10352,f10356,f10360,f10364,f10368,f10372,f10376,f10380,f10384,f10388,f10392,f10396,f10400,f10404,f10408,f10412,f10416,f10420,f10424,f10428,f10432,f10638,f10699,f10931,f11297,f11309,f11313,f11317,f11321,f11325,f11329,f11333,f11344,f11348,f11352,f11356,f11360,f11364,f11368,f11372,f11376,f11380,f11399,f11403,f11407,f11411,f11415,f11419,f11423,f11427,f11431,f11435,f11439,f11443,f11447,f11451,f11455,f11459,f11463,f11467,f11471,f11475,f11479,f11483,f11487,f11491,f11495,f11499,f11503,f11507,f11511,f11515,f11519,f11523,f11527,f11531,f11535,f11539,f11543,f11547,f11551,f11555,f11559,f11563,f11567,f11571,f11575,f11579,f11583,f11587,f11591,f11595,f11600,f11604,f11608,f11612,f11616,f11620,f11624,f11628,f11632,f11636,f11640,f11646,f11650,f11654,f11658,f11662,f11666,f11670,f11674,f11678,f11682,f11691,f11698,f11702,f11706,f11710,f11715,f11723,f11727,f11737,f11769,f11773,f11777,f11781,f11785,f11789,f11793,f12451,f12700,f12817,f12877,f12881,f12885,f12889,f12893,f12897,f12901,f12905,f12909,f12913,f12917,f12921,f12925,f12929,f12933,f12937,f12941,f12945,f12949,f12953,f12957,f12961,f12965,f12969,f12973,f12977,f12981,f12985,f12989,f12993,f12997,f13001,f13005,f13009,f13013,f13018,f13022,f13026,f13030,f13034,f13038,f13042,f13046,f13050,f13054,f13062,f13066,f13070,f13074,f13078,f13082,f13086,f13090,f13094,f13098,f13102,f13106,f13110,f13114,f13118,f13122,f13126,f13130,f13134,f13138,f13142,f13151,f13155,f13159,f13163,f13167,f13171,f13175,f13180,f13189,f13196,f13200,f13204,f13410,f13563,f13681,f14169,f14173,f14177,f14181,f14185,f14189,f14193,f14197,f14201,f14205,f14209,f14213,f14217,f14221,f14226,f14230,f14234,f14238,f14242,f14246,f14250,f14254,f14258,f14262,f14266,f14270,f14274,f14278,f14282,f14286,f14290,f14294,f14298,f14302,f14306,f14311,f14315,f14319,f14323,f14327,f14331,f14335,f14339,f14343,f14347,f14351,f14356,f14360,f14364,f14368,f14372,f14376,f14380,f14384,f14388,f14392,f14396,f14400,f14404,f14408,f14412,f14417,f14441,f14446,f14464,f14478,f14498,f14502,f14506,f14510,f14514,f14518,f14522,f14526,f14530,f14534,f14538,f14655,f14893,f15093,f15181,f15544,f15548,f15552,f15556,f15560,f15564,f15568,f15572,f15576,f15580,f15584,f15602,f15606,f15610,f15614,f15618,f15622,f15626,f15630,f15634,f15639,f15643,f15647,f15651,f15655,f15659,f15663,f15667,f15671,f15675,f15679,f15683,f15687,f15691,f15695,f15699,f15703,f15707,f15711,f15715,f15719,f15723,f15727,f15735,f15739,f15743,f15747,f15751,f15755,f15759,f15763,f15767,f15771,f15775,f15779,f15783,f15787,f15791,f15795,f15799,f15804,f15832,f15837,f15842,f15900,f15905,f16000,f16005,f16104,f16109,f16139,f16143,f16148,f16165,f16170,f16178,f16183,f16191,f16197,f16201,f16207,f16211,f16215,f16221,f16227,f16231,f16235,f16239,f16243,f16249,f16253,f16286,f16290,f16304,f16386,f16540,f16696,f16777,f17040,f17270,f17426,f17430,f17435,f17439,f17443,f17447,f17451,f17455,f17459,f17463,f17467,f17471,f17475,f17483,f17487,f17491,f17495,f17499,f17503,f17507,f17511,f17515,f17519,f17523,f17527,f17531,f17535,f17539,f17543,f17547,f17551,f17555,f17559,f17563,f17567,f17571,f17575,f17579,f17583,f17587,f17591,f17595,f17599,f17603,f17607,f17611,f17615,f17619,f17623,f17627,f17631,f17635,f17639,f17643,f17649,f17675,f17679,f17685,f17770,f17775,f17798,f17802,f17806,f17811,f17818,f17823,f17828,f17833,f17838,f17843,f17847,f17851,f17855,f17860,f17882,f17886,f17890,f17895,f17900,f17905,f17910,f17916,f17921,f17927,f17932,f17945,f17949,f17954,f17967,f17971,f17975,f17979,f17983,f18137,f18528,f18865,f18869,f18877,f18881,f18885,f18889,f18893,f18899,f18905,f18909,f18913,f18917,f18921,f18925,f18929,f18933,f18937,f18941,f18945,f18949,f18953,f18957,f18968,f18972,f18976,f18980,f18984,f18988,f18992,f18996,f19000,f19004,f19009,f19013,f19019,f19335,f19340,f19344,f20014,f20018,f20022,f20035,f20039,f20043,f20048,f20052,f20056,f20060,f20064,f20068,f20072,f20090,f20094,f20098,f20102,f20106,f20162,f20195,f20619,f20623,f20627,f20631,f20635,f20640,f20644,f20648,f20652,f20656,f20660,f20664,f20668,f20672,f20676,f20680,f20721,f20725,f20729,f20734,f20739,f20745,f20766,f20771,f20828,f20832,f20836,f20841,f20862,f20867,f20888,f20892,f20899,f20904,f21221,f21225,f21334,f21338,f21344,f21348,f21352,f21356,f21360,f21364,f21368,f21372,f21376,f21380,f21390,f21394,f21398,f21402,f21406,f21410,f21414,f21418,f21422,f21426,f21431,f21435,f21439,f21443,f21447,f21451,f21455,f21459,f21463,f21467,f21471,f21476,f21480,f21484,f21488,f21492,f21496,f21500,f21504,f21508,f21512,f21516,f21523,f21527,f21531,f21535,f21539,f21543,f21547,f21551,f21555,f21559,f21567,f21571,f21575,f21579,f21583,f21587,f21594,f21614,f21621,f21644,f21648,f21652,f21656,f21662,f21723,f21727,f21731,f21771,f21775,f21779,f21783,f21787,f21792,f21819,f21825,f22062,f22066,f22254,f22691,f22695,f22699,f22703,f22707,f22711,f22715,f22719,f22723,f22727,f22731,f22735,f22739,f22743,f22748,f22752,f22756,f22760,f22764,f22768,f22772,f22776,f22780,f22784,f22788,f22795,f22799,f22803,f22807,f22811,f22815,f22954,f23405,f23529,f23533,f23537,f23541,f23545,f23549,f23553,f23557,f23561,f23565,f23569,f23573,f23577,f23581,f23585,f23589,f23594,f23598,f23602,f23606,f23610,f23614,f23619,f23644,f23649,f23699,f23703,f23707,f23712,f24437,f24441,f24445,f24449,f24454,f24458,f24463,f24468,f24472,f24476,f24480,f24484,f24488,f24492,f24496,f24500,f24506,f24512,f24594,f24598,f24602,f24606,f24611,f24644,f24648,f24705,f24709,f24731,f25094,f25142,f25146,f25150,f25154,f25158,f25197,f25292,f25296,f25300,f25304,f25308,f25312,f25316,f25320,f25324,f25328,f25332,f25336,f25340,f25344,f25348,f25355,f25736,f25740,f25744,f25748,f25752,f25757,f25762,f25902,f25906,f25910,f25914,f25918,f25922,f25926,f25930,f25934,f25938,f25942,f25946,f25950,f25954,f25958,f25962,f25966,f25970,f25974,f25978,f25982,f25986,f25990,f25994,f25998,f26002,f26006,f26012,f26016,f26024,f26030,f26038,f26044,f26060,f26066,f26070,f26119,f26125,f26138,f26143,f26281,f26672,f26908,f26912,f26936,f26940,f26944,f26948,f26952,f26957,f27057,f27061,f27065,f27069,f27073,f27082,f27086,f27390,f27403,f27478,f27482,f27486,f27490,f27494,f27498,f27502,f27516,f27538,f27678,f27704,f27708,f27712,f27856,f27861,f27866,f27873,f27878,f27882,f27886,f27890,f27894,f27898,f27902,f27906,f27933,f27975,f27979,f27983,f27987,f27991,f27995,f27999,f28003,f28099,f28156,f28161,f28165,f28194,f28198,f28202,f28206,f28210,f28214,f28218,f28223,f28228,f28233,f28330]) ).
fof(f28330,plain,
( spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_2216 ),
inference(avatar_split_clause,[],[f28323,f28212,f3172,f3167,f3162,f3157]) ).
fof(f3157,plain,
( spl0_1
<=> v_F = v_G ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f3162,plain,
( spl0_2
<=> c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f3167,plain,
( spl0_3
<=> c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f3172,plain,
( spl0_4
<=> c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f28212,plain,
( spl0_2216
<=> ! [X5,X1] : c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(X1,X5),c_Pair(c_UNITY_OActs(X1,X5),c_UNITY_OAllowedActs(X1,X5),tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5)))),tc_set(X5),tc_prod(tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5))))),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f28323,plain,
( v_F = v_G
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_2216 ),
inference(forward_demodulation,[],[f28322,f28213]) ).
fof(f28213,plain,
( ! [X1,X5] : c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(X1,X5),c_Pair(c_UNITY_OActs(X1,X5),c_UNITY_OAllowedActs(X1,X5),tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5)))),tc_set(X5),tc_prod(tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5))))),X5) = X1
| ~ spl0_2216 ),
inference(avatar_component_clause,[],[f28212]) ).
fof(f28322,plain,
( v_G = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_F,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a)
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_2216 ),
inference(forward_demodulation,[],[f28321,f3169]) ).
fof(f3169,plain,
( c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f3167]) ).
fof(f28321,plain,
( v_G = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_F,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a)
| ~ spl0_2
| ~ spl0_4
| ~ spl0_2216 ),
inference(forward_demodulation,[],[f28318,f3174]) ).
fof(f3174,plain,
( c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f3172]) ).
fof(f28318,plain,
( v_G = c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(v_F,t_a),c_Pair(c_UNITY_OActs(v_G,t_a),c_UNITY_OAllowedActs(v_G,t_a),tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a)))),tc_set(t_a),tc_prod(tc_set(tc_set(tc_prod(t_a,t_a))),tc_set(tc_set(tc_prod(t_a,t_a))))),t_a)
| ~ spl0_2
| ~ spl0_2216 ),
inference(superposition,[],[f28213,f3164]) ).
fof(f3164,plain,
( c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f3162]) ).
fof(f28233,plain,
spl0_2220,
inference(avatar_split_clause,[],[f3121,f28231]) ).
fof(f28231,plain,
( spl0_2220
<=> ! [X29,X28] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).
fof(f3121,plain,
! [X28,X29] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f287,f297]) ).
fof(f297,axiom,
! [X32,X13] : c_IntDiv_OnegateSnd(c_Pair(X32,X13,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X32,c_uminus(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f287,axiom,
! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__number__of_0) ).
fof(f28228,plain,
spl0_2219,
inference(avatar_split_clause,[],[f3120,f28226]) ).
fof(f28226,plain,
( spl0_2219
<=> ! [X29,X28] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f3120,plain,
! [X28,X29] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f277,f297]) ).
fof(f277,axiom,
! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
fof(f28223,plain,
spl0_2218,
inference(avatar_split_clause,[],[f3119,f28221]) ).
fof(f28221,plain,
( spl0_2218
<=> ! [X29,X28] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f3119,plain,
! [X28,X29] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f284,f297]) ).
fof(f284,axiom,
! [X28,X29] :
( ~ c_lessequals(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__neg__number__of_0) ).
fof(f28218,plain,
spl0_2217,
inference(avatar_split_clause,[],[f3118,f28216]) ).
fof(f28216,plain,
( spl0_2217
<=> ! [X29,X28] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f3118,plain,
! [X28,X29] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f274,f297]) ).
fof(f274,axiom,
! [X28,X29] :
( ~ c_lessequals(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
fof(f28214,plain,
spl0_2216,
inference(avatar_split_clause,[],[f2736,f28212]) ).
fof(f2736,axiom,
! [X1,X5] : c_UNITY_Omk__program(c_Pair(c_UNITY_OInit(X1,X5),c_Pair(c_UNITY_OActs(X1,X5),c_UNITY_OAllowedActs(X1,X5),tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5)))),tc_set(X5),tc_prod(tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5))))),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Osurjective__mk__program_0) ).
fof(f28210,plain,
( spl0_2215
| ~ spl0_1620
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25088,f24728,f15542,f28208]) ).
fof(f28208,plain,
( spl0_2215
<=> ! [X0,X1] : c_IntDef_ONats = c_insert(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).
fof(f15542,plain,
( spl0_1620
<=> ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f24728,plain,
( spl0_2083
<=> c_UNIV = c_IntDef_ONats ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f25088,plain,
( ! [X0,X1] : c_IntDef_ONats = c_insert(X0,c_IntDef_ONats,X1)
| ~ spl0_1620
| ~ spl0_2083 ),
inference(superposition,[],[f15543,f24730]) ).
fof(f24730,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_2083 ),
inference(avatar_component_clause,[],[f24728]) ).
fof(f15543,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_1620 ),
inference(avatar_component_clause,[],[f15542]) ).
fof(f28206,plain,
spl0_2214,
inference(avatar_split_clause,[],[f463,f28204]) ).
fof(f28204,plain,
( spl0_2214
<=> ! [X48,X3,X13,X5,X1] :
( ~ c_in(c_Pair(X48,X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X3,X48,X5),c_List_Olist_OCons(X3,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f463,axiom,
! [X3,X48,X1,X5,X13] :
( ~ c_in(c_Pair(X48,X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X3,X48,X5),c_List_Olist_OCons(X3,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_3) ).
fof(f28202,plain,
spl0_2213,
inference(avatar_split_clause,[],[f346,f28200]) ).
fof(f28200,plain,
( spl0_2213
<=> ! [X35,X34,X13,X5,X3] :
( ~ c_in(c_Pair(X34,X35,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X3,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f346,axiom,
! [X3,X34,X35,X5,X13] :
( ~ c_in(c_Pair(X34,X35,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5)))
| c_in(c_Pair(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X3,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_5) ).
fof(f28198,plain,
spl0_2212,
inference(avatar_split_clause,[],[f29,f28196]) ).
fof(f28196,plain,
( spl0_2212
<=> ! [X10,X13,X14,X5] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X13,X14,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X13,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),c_Relation_ODomain(X14,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f29,axiom,
! [X10,X14,X5,X13] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X13,X14,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X13,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),c_Relation_ODomain(X14,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f28194,plain,
spl0_2211,
inference(avatar_split_clause,[],[f28,f28192]) ).
fof(f28192,plain,
( spl0_2211
<=> ! [X10,X13,X14,X5] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X13,X14,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X13,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),c_Relation_ODomain(X14,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f28,axiom,
! [X10,X14,X5,X13] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X13,X14,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X13,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),c_Relation_ODomain(X14,tc_set(tc_Datatype__Universe_Onode(X5,X10)),tc_set(tc_Datatype__Universe_Onode(X5,X10))),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f28165,plain,
( spl0_2210
| ~ spl0_1716
| ~ spl0_2208 ),
inference(avatar_split_clause,[],[f28157,f28154,f16537,f28163]) ).
fof(f28163,plain,
( spl0_2210
<=> ! [X28] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f16537,plain,
( spl0_1716
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f28154,plain,
( spl0_2208
<=> ! [X28] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f28157,plain,
( ! [X28] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1716
| ~ spl0_2208 ),
inference(forward_demodulation,[],[f28155,f16539]) ).
fof(f16539,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_1716 ),
inference(avatar_component_clause,[],[f16537]) ).
fof(f28155,plain,
( ! [X28] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2208 ),
inference(avatar_component_clause,[],[f28154]) ).
fof(f28161,plain,
spl0_2209,
inference(avatar_split_clause,[],[f546,f28159]) ).
fof(f28159,plain,
( spl0_2209
<=> ! [X17,X34,X10,X5,X35] :
( ~ c_less(X17,c_Nat_Osize(X35,tc_List_Olist(X10)),tc_nat)
| ~ c_less(X17,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Ozip(X34,X35,X5,X10),X17,tc_prod(X5,X10)) = c_Pair(c_List_Onth(X34,X17,X5),c_List_Onth(X35,X17,X10),X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f546,axiom,
! [X10,X17,X34,X35,X5] :
( ~ c_less(X17,c_Nat_Osize(X35,tc_List_Olist(X10)),tc_nat)
| ~ c_less(X17,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Ozip(X34,X35,X5,X10),X17,tc_prod(X5,X10)) = c_Pair(c_List_Onth(X34,X17,X5),c_List_Onth(X35,X17,X10),X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__zip_0) ).
fof(f28156,plain,
spl0_2208,
inference(avatar_split_clause,[],[f290,f28154]) ).
fof(f290,axiom,
! [X28] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
fof(f28099,plain,
( spl0_2207
| ~ spl0_794
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25081,f24728,f7249,f28097]) ).
fof(f28097,plain,
( spl0_2207
<=> ! [X0,X1] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f7249,plain,
( spl0_794
<=> ! [X20,X5] : c_UNIV = c_union(X20,c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f25081,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,X1)
| ~ spl0_794
| ~ spl0_2083 ),
inference(superposition,[],[f7250,f24730]) ).
fof(f7250,plain,
( ! [X5,X20] : c_UNIV = c_union(X20,c_UNIV,X5)
| ~ spl0_794 ),
inference(avatar_component_clause,[],[f7249]) ).
fof(f28003,plain,
spl0_2206,
inference(avatar_split_clause,[],[f1653,f28001]) ).
fof(f28001,plain,
( spl0_2206
<=> ! [X5,X8,X9,X13,X78,X14,X10,X19] :
( ~ c_in(c_Pair(X9,X19,X10,X78),X13,tc_prod(X10,X78))
| ~ c_in(c_Pair(X8,X9,X5,X10),X14,tc_prod(X5,X10))
| c_in(c_Pair(X8,X19,X5,X78),c_Relation_Orel__comp(X13,X14,X10,X78,X5),tc_prod(X5,X78)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).
fof(f1653,axiom,
! [X10,X78,X8,X19,X9,X14,X5,X13] :
( ~ c_in(c_Pair(X9,X19,X10,X78),X13,tc_prod(X10,X78))
| ~ c_in(c_Pair(X8,X9,X5,X10),X14,tc_prod(X5,X10))
| c_in(c_Pair(X8,X19,X5,X78),c_Relation_Orel__comp(X13,X14,X10,X78,X5),tc_prod(X5,X78)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compI_0) ).
fof(f27999,plain,
spl0_2205,
inference(avatar_split_clause,[],[f1621,f27997]) ).
fof(f27997,plain,
( spl0_2205
<=> ! [X35,X34,X13,X5,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X13,X34,X1,X35,X5),c_Main_Olistrel__Cons2__2(X13,X34,X1,X35,X5),X5) = X34
| ~ c_in(c_Pair(X34,c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f1621,axiom,
! [X1,X34,X35,X5,X13] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X13,X34,X1,X35,X5),c_Main_Olistrel__Cons2__2(X13,X34,X1,X35,X5),X5) = X34
| ~ c_in(c_Pair(X34,c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_0) ).
fof(f27995,plain,
spl0_2204,
inference(avatar_split_clause,[],[f1618,f27993]) ).
fof(f27993,plain,
( spl0_2204
<=> ! [X35,X34,X13,X5,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X13,X34,X1,X35,X5),c_Main_Olistrel__Cons1__2(X13,X34,X1,X35,X5),X5) = X34
| ~ c_in(c_Pair(c_List_Olist_OCons(X1,X35,X5),X34,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f1618,axiom,
! [X1,X34,X35,X5,X13] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X13,X34,X1,X35,X5),c_Main_Olistrel__Cons1__2(X13,X34,X1,X35,X5),X5) = X34
| ~ c_in(c_Pair(c_List_Olist_OCons(X1,X35,X5),X34,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_0) ).
fof(f27991,plain,
spl0_2203,
inference(avatar_split_clause,[],[f460,f27989]) ).
fof(f27989,plain,
( spl0_2203
<=> ! [X5,X3,X13,X9,X8,X1] :
( X8 = X9
| c_in(c_Pair(X8,X9,X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X3,X5),c_List_Olist_OCons(X9,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f460,axiom,
! [X3,X1,X8,X9,X5,X13] :
( X8 = X9
| c_in(c_Pair(X8,X9,X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X8,X3,X5),c_List_Olist_OCons(X9,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_0) ).
fof(f27987,plain,
( spl0_2202
| ~ spl0_793
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25080,f24728,f7245,f27985]) ).
fof(f27985,plain,
( spl0_2202
<=> ! [X0,X1] : c_IntDef_ONats = c_union(c_IntDef_ONats,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f7245,plain,
( spl0_793
<=> ! [X5,X24] : c_UNIV = c_union(c_UNIV,X24,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f25080,plain,
( ! [X0,X1] : c_IntDef_ONats = c_union(c_IntDef_ONats,X0,X1)
| ~ spl0_793
| ~ spl0_2083 ),
inference(superposition,[],[f7246,f24730]) ).
fof(f7246,plain,
( ! [X24,X5] : c_UNIV = c_union(c_UNIV,X24,X5)
| ~ spl0_793 ),
inference(avatar_component_clause,[],[f7245]) ).
fof(f27983,plain,
spl0_2201,
inference(avatar_split_clause,[],[f341,f27981]) ).
fof(f27981,plain,
( spl0_2201
<=> ! [X3,X34,X13,X5,X35,X1] :
( X1 = X3
| c_in(c_Pair(X3,X1,X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f341,axiom,
! [X3,X1,X34,X5,X35,X13] :
( X1 = X3
| c_in(c_Pair(X3,X1,X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_0) ).
fof(f27979,plain,
spl0_2200,
inference(avatar_split_clause,[],[f224,f27977]) ).
fof(f27977,plain,
( spl0_2200
<=> ! [X3,X31,X29,X1] :
( c_plus(X3,X29,tc_nat) != c_plus(X31,X1,tc_nat)
| c_in(c_Pair(c_Pair(X3,X1,tc_nat,tc_nat),c_Pair(X31,X29,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f224,axiom,
! [X31,X3,X29,X1] :
( c_plus(X3,X29,tc_nat) != c_plus(X31,X1,tc_nat)
| c_in(c_Pair(c_Pair(X3,X1,tc_nat,tc_nat),c_Pair(X31,X29,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_1) ).
fof(f27975,plain,
spl0_2199,
inference(avatar_split_clause,[],[f223,f27973]) ).
fof(f27973,plain,
( spl0_2199
<=> ! [X3,X31,X29,X1] :
( c_plus(X3,X29,tc_nat) = c_plus(X31,X1,tc_nat)
| ~ c_in(c_Pair(c_Pair(X3,X1,tc_nat,tc_nat),c_Pair(X31,X29,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f223,axiom,
! [X31,X3,X29,X1] :
( c_plus(X3,X29,tc_nat) = c_plus(X31,X1,tc_nat)
| ~ c_in(c_Pair(c_Pair(X3,X1,tc_nat,tc_nat),c_Pair(X31,X29,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel__iff_0) ).
fof(f27933,plain,
( spl0_2198
| ~ spl0_791
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25079,f24728,f7237,f27931]) ).
fof(f27931,plain,
( spl0_2198
<=> ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f7237,plain,
( spl0_791
<=> ! [X5] : c_emptyset = c_uminus(c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f25079,plain,
( ! [X0] : c_emptyset = c_uminus(c_IntDef_ONats,tc_set(X0))
| ~ spl0_791
| ~ spl0_2083 ),
inference(superposition,[],[f7238,f24730]) ).
fof(f7238,plain,
( ! [X5] : c_emptyset = c_uminus(c_UNIV,tc_set(X5))
| ~ spl0_791 ),
inference(avatar_component_clause,[],[f7237]) ).
fof(f27906,plain,
( spl0_2197
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2189 ),
inference(avatar_split_clause,[],[f27874,f27871,f11561,f8914,f27904]) ).
fof(f27904,plain,
( spl0_2197
<=> ! [X29,X28] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f8914,plain,
( spl0_1109
<=> ! [X5,X1,X8,X10] : c_snd(c_Pair(X8,X1,X10,X5),X10,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f11561,plain,
( spl0_1407
<=> ! [X5,X30,X10] : c_Pair(c_Main_Osurj__pair__1(X30,X5,X10),c_Main_Osurj__pair__2(X30,X5,X10),X5,X10) = X30 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f27871,plain,
( spl0_2189
<=> ! [X29,X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f27874,plain,
( ! [X28,X29] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2189 ),
inference(forward_demodulation,[],[f27872,f12533]) ).
fof(f12533,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1109
| ~ spl0_1407 ),
inference(superposition,[],[f8915,f11562]) ).
fof(f11562,plain,
( ! [X10,X5,X30] : c_Pair(c_Main_Osurj__pair__1(X30,X5,X10),c_Main_Osurj__pair__2(X30,X5,X10),X5,X10) = X30
| ~ spl0_1407 ),
inference(avatar_component_clause,[],[f11561]) ).
fof(f8915,plain,
( ! [X10,X1,X8,X5] : c_snd(c_Pair(X8,X1,X10,X5),X10,X5) = X1
| ~ spl0_1109 ),
inference(avatar_component_clause,[],[f8914]) ).
fof(f27872,plain,
( ! [X28,X29] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2189 ),
inference(avatar_component_clause,[],[f27871]) ).
fof(f27902,plain,
( spl0_2196
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2188 ),
inference(avatar_split_clause,[],[f27867,f27864,f11561,f8914,f27900]) ).
fof(f27900,plain,
( spl0_2196
<=> ! [X29,X28] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f27864,plain,
( spl0_2188
<=> ! [X29,X28] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).
fof(f27867,plain,
( ! [X28,X29] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2188 ),
inference(forward_demodulation,[],[f27865,f12533]) ).
fof(f27865,plain,
( ! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2188 ),
inference(avatar_component_clause,[],[f27864]) ).
fof(f27898,plain,
( spl0_2195
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2187 ),
inference(avatar_split_clause,[],[f27862,f27859,f11561,f8910,f27896]) ).
fof(f27896,plain,
( spl0_2195
<=> ! [X29,X28] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f8910,plain,
( spl0_1108
<=> ! [X5,X10,X9,X1] : c_fst(c_Pair(X1,X9,X5,X10),X5,X10) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f27859,plain,
( spl0_2187
<=> ! [X29,X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f27862,plain,
( ! [X28,X29] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2187 ),
inference(forward_demodulation,[],[f27860,f12534]) ).
fof(f12534,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__1(X0,X1,X2) = c_fst(X0,X1,X2)
| ~ spl0_1108
| ~ spl0_1407 ),
inference(superposition,[],[f8911,f11562]) ).
fof(f8911,plain,
( ! [X10,X1,X9,X5] : c_fst(c_Pair(X1,X9,X5,X10),X5,X10) = X1
| ~ spl0_1108 ),
inference(avatar_component_clause,[],[f8910]) ).
fof(f27860,plain,
( ! [X28,X29] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2187 ),
inference(avatar_component_clause,[],[f27859]) ).
fof(f27894,plain,
( spl0_2194
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2186 ),
inference(avatar_split_clause,[],[f27857,f27854,f11561,f8910,f27892]) ).
fof(f27892,plain,
( spl0_2194
<=> ! [X29,X28] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f27854,plain,
( spl0_2186
<=> ! [X29,X28] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f27857,plain,
( ! [X28,X29] :
( c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2186 ),
inference(forward_demodulation,[],[f27855,f12534]) ).
fof(f27855,plain,
( ! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2186 ),
inference(avatar_component_clause,[],[f27854]) ).
fof(f27890,plain,
spl0_2193,
inference(avatar_split_clause,[],[f2733,f27888]) ).
fof(f27888,plain,
( spl0_2193
<=> ! [X88,X5,X87,X1] : c_UNITY_OInit(c_UNITY_Omk__program(c_Pair(X1,c_Pair(X87,X88,tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5)))),tc_set(X5),tc_prod(tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5))))),X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f2733,axiom,
! [X1,X88,X87,X5] : c_UNITY_OInit(c_UNITY_Omk__program(c_Pair(X1,c_Pair(X87,X88,tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5)))),tc_set(X5),tc_prod(tc_set(tc_set(tc_prod(X5,X5))),tc_set(tc_set(tc_prod(X5,X5))))),X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_OInit__eq_0) ).
fof(f27886,plain,
spl0_2192,
inference(avatar_split_clause,[],[f1623,f27884]) ).
fof(f27884,plain,
( spl0_2192
<=> ! [X35,X34,X13,X5,X1] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X13,X34,X1,X35,X5),X1,X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(X34,c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f1623,axiom,
! [X1,X34,X35,X5,X13] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X13,X34,X1,X35,X5),X1,X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(X34,c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons2_2) ).
fof(f27882,plain,
spl0_2191,
inference(avatar_split_clause,[],[f1620,f27880]) ).
fof(f27880,plain,
( spl0_2191
<=> ! [X35,X34,X13,X5,X1] :
( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X13,X34,X1,X35,X5),X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X1,X35,X5),X34,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f1620,axiom,
! [X1,X34,X35,X5,X13] :
( c_in(c_Pair(X1,c_Main_Olistrel__Cons1__1(X13,X34,X1,X35,X5),X5,X5),X13,tc_prod(X5,X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X1,X35,X5),X34,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Cons1_2) ).
fof(f27878,plain,
spl0_2190,
inference(avatar_split_clause,[],[f343,f27876]) ).
fof(f27876,plain,
( spl0_2190
<=> ! [X3,X34,X13,X5,X35,X1] :
( X1 = X3
| c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(X35,tc_List_Olist(X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f343,axiom,
! [X3,X1,X34,X5,X35,X13] :
( X1 = X3
| c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(X35,tc_List_Olist(X5))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X1,X35,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OCons__in__lex_2) ).
fof(f27873,plain,
spl0_2189,
inference(avatar_split_clause,[],[f289,f27871]) ).
fof(f289,axiom,
! [X28,X29] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__number__of_0) ).
fof(f27866,plain,
spl0_2188,
inference(avatar_split_clause,[],[f285,f27864]) ).
fof(f285,axiom,
! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__neg__pos__number__of_0) ).
fof(f27861,plain,
spl0_2187,
inference(avatar_split_clause,[],[f279,f27859]) ).
fof(f279,axiom,
! [X28,X29] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
fof(f27856,plain,
spl0_2186,
inference(avatar_split_clause,[],[f275,f27854]) ).
fof(f275,axiom,
! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
fof(f27712,plain,
spl0_2185,
inference(avatar_split_clause,[],[f1651,f27710]) ).
fof(f27710,plain,
( spl0_2185
<=> ! [X10,X77,X14,X78,X13,X5] :
( ~ c_in(X77,c_Relation_Orel__comp(X13,X14,X78,X10,X5),tc_prod(X5,X10))
| c_in(c_Pair(c_Main_Orel__compE__1(X13,X14,X77,X78,X10,X5),c_Main_Orel__compE__2(X13,X14,X77,X78,X10,X5),X5,X78),X14,tc_prod(X5,X78)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f1651,axiom,
! [X10,X78,X14,X77,X5,X13] :
( ~ c_in(X77,c_Relation_Orel__comp(X13,X14,X78,X10,X5),tc_prod(X5,X10))
| c_in(c_Pair(c_Main_Orel__compE__1(X13,X14,X77,X78,X10,X5),c_Main_Orel__compE__2(X13,X14,X77,X78,X10,X5),X5,X78),X14,tc_prod(X5,X78)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_1) ).
fof(f27708,plain,
spl0_2184,
inference(avatar_split_clause,[],[f1650,f27706]) ).
fof(f27706,plain,
( spl0_2184
<=> ! [X10,X77,X14,X78,X13,X5] :
( ~ c_in(X77,c_Relation_Orel__comp(X13,X14,X78,X10,X5),tc_prod(X5,X10))
| c_in(c_Pair(c_Main_Orel__compE__2(X13,X14,X77,X78,X10,X5),c_Main_Orel__compE__3(X13,X14,X77,X78,X10,X5),X78,X10),X13,tc_prod(X78,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f1650,axiom,
! [X10,X78,X14,X77,X5,X13] :
( ~ c_in(X77,c_Relation_Orel__comp(X13,X14,X78,X10,X5),tc_prod(X5,X10))
| c_in(c_Pair(c_Main_Orel__compE__2(X13,X14,X77,X78,X10,X5),c_Main_Orel__compE__3(X13,X14,X77,X78,X10,X5),X78,X10),X13,tc_prod(X78,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_0) ).
fof(f27704,plain,
spl0_2183,
inference(avatar_split_clause,[],[f1588,f27702]) ).
fof(f27702,plain,
( spl0_2183
<=> ! [X24,X10,X20,X31,X5] :
( ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__2(X24,X31,X5,X10),X24,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__1(X20,X31,X5,X10),X20,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f1588,axiom,
! [X31,X10,X24,X5,X20] :
( ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__2(X24,X31,X5,X10),X24,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__1(X20,X31,X5,X10),X20,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_3) ).
fof(f27678,plain,
spl0_2182,
inference(avatar_split_clause,[],[f311,f27676]) ).
fof(f27676,plain,
( spl0_2182
<=> ! [X29,X9,X28] :
( c_Numeral_Obit_OB0 = X9
| c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X29,X9),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f311,axiom,
! [X28,X29,X9] :
( c_Numeral_Obit_OB0 = X9
| c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X29,X9),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f27538,plain,
spl0_2181,
inference(avatar_split_clause,[],[f3027,f27536]) ).
fof(f27536,plain,
( spl0_2181
<=> ! [X29,X18] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f3027,plain,
! [X29,X18] : c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3026,f997]) ).
fof(f997,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
fof(f3026,plain,
! [X29,X18] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3025,f2792]) ).
fof(f2792,plain,
! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat),
inference(definition_unfolding,[],[f942,f1385,f1385]) ).
fof(f1385,axiom,
! [X31] : c_Suc(X31) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X31,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f942,axiom,
! [X2,X18] : c_Suc(c_plus(X18,X2,tc_nat)) = c_plus(c_Suc(X18),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f3025,plain,
! [X29,X18] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2842,f2992]) ).
fof(f2992,plain,
! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2991,f997]) ).
fof(f2991,plain,
! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X2,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,[],[f2990,f995]) ).
fof(f995,axiom,
! [X28] : c_Numeral_Obin__succ(c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X28),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f2990,plain,
! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X2,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,[],[f2811,f997]) ).
fof(f2811,plain,
! [X2] : c_plus(X2,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(X2,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f723,f1385,f1385]) ).
fof(f723,axiom,
! [X2] : c_Suc(c_Suc(X2)) = c_plus(X2,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/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
fof(f2842,plain,
! [X29,X18] : c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(definition_unfolding,[],[f721,f1385,f1385,f1385]) ).
fof(f721,axiom,
! [X29,X18] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X18))),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f27516,plain,
( spl0_2180
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2179 ),
inference(avatar_split_clause,[],[f27504,f27500,f19017,f10406,f10097,f6714,f3706,f27514]) ).
fof(f27514,plain,
( spl0_2180
<=> ! [X29,X18] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f3706,plain,
( spl0_112
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f6714,plain,
( spl0_670
<=> ! [X1] : c_IntDef_Onat(c_IntDef_Oint(X1)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f10097,plain,
( spl0_1261
<=> ! [X2,X18] : c_IntDef_Oint(c_plus(X18,X2,tc_nat)) = c_plus(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f10406,plain,
( spl0_1338
<=> ! [X18] : c_plus(c_1,c_IntDef_Oint(X18),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f19017,plain,
( spl0_1852
<=> ! [X2] : c_plus(X2,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,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f27500,plain,
( spl0_2179
<=> ! [X29,X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f27504,plain,
( ! [X29,X18] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(c_1,c_plus(c_1,X18,tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2179 ),
inference(forward_demodulation,[],[f27503,f19018]) ).
fof(f19018,plain,
( ! [X2] : c_plus(X2,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,X2,tc_nat),tc_nat)
| ~ spl0_1852 ),
inference(avatar_component_clause,[],[f19017]) ).
fof(f27503,plain,
( ! [X29,X18] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_1,c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2179 ),
inference(forward_demodulation,[],[f27501,f11227]) ).
fof(f11227,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338 ),
inference(forward_demodulation,[],[f11226,f6715]) ).
fof(f6715,plain,
( ! [X1] : c_IntDef_Onat(c_IntDef_Oint(X1)) = X1
| ~ spl0_670 ),
inference(avatar_component_clause,[],[f6714]) ).
fof(f11226,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_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338 ),
inference(forward_demodulation,[],[f11188,f10666]) ).
fof(f10666,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_112
| ~ spl0_1261 ),
inference(superposition,[],[f10098,f3708]) ).
fof(f3708,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3706]) ).
fof(f10098,plain,
( ! [X2,X18] : c_IntDef_Oint(c_plus(X18,X2,tc_nat)) = c_plus(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint)
| ~ spl0_1261 ),
inference(avatar_component_clause,[],[f10097]) ).
fof(f11188,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_670
| ~ spl0_1338 ),
inference(superposition,[],[f6715,f10407]) ).
fof(f10407,plain,
( ! [X18] : c_plus(c_1,c_IntDef_Oint(X18),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat))
| ~ spl0_1338 ),
inference(avatar_component_clause,[],[f10406]) ).
fof(f27501,plain,
( ! [X29,X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ spl0_2179 ),
inference(avatar_component_clause,[],[f27500]) ).
fof(f27502,plain,
spl0_2179,
inference(avatar_split_clause,[],[f3024,f27500]) ).
fof(f3024,plain,
! [X29,X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3023,f997]) ).
fof(f3023,plain,
! [X29,X18] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3022,f2792]) ).
fof(f3022,plain,
! [X29,X18] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2841,f2992]) ).
fof(f2841,plain,
! [X29,X18] : c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
inference(definition_unfolding,[],[f720,f1385,f1385,f1385]) ).
fof(f720,axiom,
! [X29,X18] : c_div(c_Suc(c_Suc(c_Suc(X18))),c_Numeral_Onumber__of(X29,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X18,tc_nat),c_Numeral_Onumber__of(X29,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f27498,plain,
spl0_2178,
inference(avatar_split_clause,[],[f2919,f27496]) ).
fof(f27496,plain,
( spl0_2178
<=> ! [X3,X13,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f2919,plain,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1565,f1557]) ).
fof(f1557,axiom,
! [X5,X13] : c_Transitive__Closure_Ortrancl(X13,X5) = c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f1565,axiom,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Ortrancl(X13,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f27494,plain,
spl0_2177,
inference(avatar_split_clause,[],[f2918,f27492]) ).
fof(f27492,plain,
( spl0_2177
<=> ! [X3,X13,X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X13,X5)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f2918,plain,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Oacyclic(X13,X5)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1562,f1557]) ).
fof(f1562,axiom,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Oacyclic(X13,X5)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Ortrancl(X13,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f27490,plain,
spl0_2176,
inference(avatar_split_clause,[],[f1587,f27488]) ).
fof(f27488,plain,
( spl0_2176
<=> ! [X24,X10,X31,X5,X20] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X24,X31,X5,X10),X5,X10) = X31
| ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__1(X20,X31,X5,X10),X20,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f1587,axiom,
! [X31,X10,X24,X5,X20] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X24,X31,X5,X10),X5,X10) = X31
| ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__1(X20,X31,X5,X10),X20,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_2) ).
fof(f27486,plain,
spl0_2175,
inference(avatar_split_clause,[],[f1586,f27484]) ).
fof(f27484,plain,
( spl0_2175
<=> ! [X31,X10,X20,X5,X24] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X20,X31,X5,X10),X5,X10) = X31
| ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__2(X24,X31,X5,X10),X24,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f1586,axiom,
! [X31,X10,X24,X5,X20] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X20,X31,X5,X10),X5,X10) = X31
| ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OusumE__2(X24,X31,X5,X10),X24,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_1) ).
fof(f27482,plain,
spl0_2174,
inference(avatar_split_clause,[],[f462,f27480]) ).
fof(f27480,plain,
( spl0_2174
<=> ! [X5,X3,X13,X9,X8,X1] :
( ~ c_in(c_Pair(X8,X9,X5,X5),X13,tc_prod(X5,X5))
| c_in(c_Pair(c_List_Olist_OCons(X8,X3,X5),c_List_Olist_OCons(X9,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f462,axiom,
! [X3,X1,X8,X9,X5,X13] :
( ~ c_in(c_Pair(X8,X9,X5,X5),X13,tc_prod(X5,X5))
| c_in(c_Pair(c_List_Olist_OCons(X8,X3,X5),c_List_Olist_OCons(X9,X1,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__cons__cons_2) ).
fof(f27478,plain,
spl0_2173,
inference(avatar_split_clause,[],[f301,f27476]) ).
fof(f27476,plain,
( spl0_2173
<=> ! [X29,X28] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f301,axiom,
! [X28,X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f27403,plain,
spl0_2172,
inference(avatar_split_clause,[],[f2890,f27401]) ).
fof(f27401,plain,
( spl0_2172
<=> ! [X5,X34,X29,X3] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),X5) = c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f2890,plain,
! [X3,X29,X34,X5] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),X5) = c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),tc_nat),X5),X5) ),
inference(definition_unfolding,[],[f609,f607,f607]) ).
fof(f607,axiom,
! [X2,X5,X67] : c_List_Osublist(X67,c_SetInterval_OlessThan(X2,tc_nat),X5) = c_List_Otake(X2,X67,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__upt__eq__take_0) ).
fof(f609,axiom,
! [X3,X29,X34,X5] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X29,tc_nat),c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Olist_OCons(X3,c_List_Otake(c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__Cons__number__of_1) ).
fof(f27390,plain,
spl0_2171,
inference(avatar_split_clause,[],[f1585,f27388]) ).
fof(f27388,plain,
( spl0_2171
<=> ! [X24,X10,X31,X5,X20] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X24,X31,X5,X10),X5,X10) = X31
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X20,X31,X5,X10),X5,X10) = X31
| ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).
fof(f1585,axiom,
! [X31,X10,X24,X5,X20] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X24,X31,X5,X10),X5,X10) = X31
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X20,X31,X5,X10),X5,X10) = X31
| ~ c_in(X31,c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OusumE_0) ).
fof(f27086,plain,
spl0_2170,
inference(avatar_split_clause,[],[f2838,f27084]) ).
fof(f27084,plain,
( spl0_2170
<=> ! [X35,X34,X5,X2] : c_List_Osublist(c_append(X34,X35,X5),c_SetInterval_OlessThan(X2,tc_nat),X5) = c_append(c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),c_List_Osublist(X35,c_SetInterval_OlessThan(c_minus(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat),tc_nat),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f2838,plain,
! [X2,X34,X35,X5] : c_List_Osublist(c_append(X34,X35,X5),c_SetInterval_OlessThan(X2,tc_nat),X5) = c_append(c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),c_List_Osublist(X35,c_SetInterval_OlessThan(c_minus(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat),tc_nat),X5),X5),
inference(definition_unfolding,[],[f612,f607,f607,f607]) ).
fof(f612,axiom,
! [X2,X34,X35,X5] : c_List_Otake(X2,c_append(X34,X35,X5),X5) = c_append(c_List_Otake(X2,X34,X5),c_List_Otake(c_minus(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat),X35,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__append_0) ).
fof(f27082,plain,
spl0_2169,
inference(avatar_split_clause,[],[f1683,f27080]) ).
fof(f27080,plain,
( spl0_2169
<=> ! [X24,X10,X20,X31,X5] :
( ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X24,X31,X10,X5),X10,X5) = X31
| c_Sum__Type_OInl(c_Main_OPlusE__1(X20,X31,X5,X10),X5,X10) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f1683,axiom,
! [X31,X10,X24,X5,X20] :
( ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X24,X31,X10,X5),X10,X5) = X31
| c_Sum__Type_OInl(c_Main_OPlusE__1(X20,X31,X5,X10),X5,X10) = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_0) ).
fof(f27073,plain,
spl0_2168,
inference(avatar_split_clause,[],[f1652,f27071]) ).
fof(f27071,plain,
( spl0_2168
<=> ! [X10,X77,X14,X78,X13,X5] :
( ~ c_in(X77,c_Relation_Orel__comp(X13,X14,X78,X10,X5),tc_prod(X5,X10))
| c_Pair(c_Main_Orel__compE__1(X13,X14,X77,X78,X10,X5),c_Main_Orel__compE__3(X13,X14,X77,X78,X10,X5),X5,X10) = X77 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f1652,axiom,
! [X10,X78,X14,X77,X5,X13] :
( ~ c_in(X77,c_Relation_Orel__comp(X13,X14,X78,X10,X5),tc_prod(X5,X10))
| c_Pair(c_Main_Orel__compE__1(X13,X14,X77,X78,X10,X5),c_Main_Orel__compE__3(X13,X14,X77,X78,X10,X5),X5,X10) = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Orel__compE_2) ).
fof(f27069,plain,
spl0_2167,
inference(avatar_split_clause,[],[f839,f27067]) ).
fof(f27067,plain,
( spl0_2167
<=> ! [X29,X9,X8,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f839,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f27065,plain,
spl0_2166,
inference(avatar_split_clause,[],[f833,f27063]) ).
fof(f27063,plain,
( spl0_2166
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
fof(f833,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f27061,plain,
spl0_2165,
inference(avatar_split_clause,[],[f827,f27059]) ).
fof(f27059,plain,
( spl0_2165
<=> ! [X29,X9,X8,X10] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f827,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f27057,plain,
spl0_2164,
inference(avatar_split_clause,[],[f821,f27055]) ).
fof(f27055,plain,
( spl0_2164
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f821,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f26957,plain,
( spl0_2163
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_2162 ),
inference(avatar_split_clause,[],[f26953,f26950,f19017,f7180,f7144,f26955]) ).
fof(f26955,plain,
( spl0_2163
<=> ! [X2,X5,X8] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_plus(c_1,c_1,tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_plus(c_1,c_1,tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f7144,plain,
( spl0_768
<=> ! [X1] : c_plus(X1,c_0,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f7180,plain,
( spl0_777
<=> ! [X1] : c_plus(c_0,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f26950,plain,
( spl0_2162
<=> ! [X2,X5,X8] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f26953,plain,
( ! [X2,X8,X5] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_plus(c_1,c_1,tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_plus(c_1,c_1,tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) )
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_2162 ),
inference(forward_demodulation,[],[f26951,f19100]) ).
fof(f19100,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_1,tc_nat)
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852 ),
inference(forward_demodulation,[],[f19021,f7145]) ).
fof(f7145,plain,
( ! [X1] : c_plus(X1,c_0,tc_nat) = X1
| ~ spl0_768 ),
inference(avatar_component_clause,[],[f7144]) ).
fof(f19021,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_plus(c_1,c_plus(c_1,c_0,tc_nat),tc_nat)
| ~ spl0_777
| ~ spl0_1852 ),
inference(superposition,[],[f19018,f7181]) ).
fof(f7181,plain,
( ! [X1] : c_plus(c_0,X1,tc_nat) = X1
| ~ spl0_777 ),
inference(avatar_component_clause,[],[f7180]) ).
fof(f26951,plain,
( ! [X2,X8,X5] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) )
| ~ spl0_2162 ),
inference(avatar_component_clause,[],[f26950]) ).
fof(f26952,plain,
spl0_2162,
inference(avatar_split_clause,[],[f3115,f26950]) ).
fof(f3115,plain,
! [X2,X8,X5] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(forward_demodulation,[],[f3114,f997]) ).
fof(f3114,plain,
! [X2,X8,X5] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(forward_demodulation,[],[f3113,f995]) ).
fof(f3113,plain,
! [X2,X8,X5] :
( c_Nat_Opower(c_uminus(X8,X5),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X2,tc_nat),X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5) ),
inference(forward_demodulation,[],[f716,f997]) ).
fof(f716,axiom,
! [X2,X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Nat_Opower(c_uminus(X8,X5),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2,tc_nat),X5) = c_Nat_Opower(X8,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__minus__even_0) ).
fof(f26948,plain,
spl0_2161,
inference(avatar_split_clause,[],[f2906,f26946]) ).
fof(f26946,plain,
( spl0_2161
<=> ! [X3,X13,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f2906,plain,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1564,f1557]) ).
fof(f1564,axiom,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Ortrancl(X13,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f26944,plain,
spl0_2160,
inference(avatar_split_clause,[],[f2905,f26942]) ).
fof(f26942,plain,
( spl0_2160
<=> ! [X3,X13,X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f2905,plain,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1561,f1557]) ).
fof(f1561,axiom,
! [X3,X1,X5,X13] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5)
| ~ c_in(c_Pair(X3,X1,X5,X5),c_Transitive__Closure_Ortrancl(X13,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f26940,plain,
spl0_2159,
inference(avatar_split_clause,[],[f2812,f26938]) ).
fof(f26938,plain,
( spl0_2159
<=> ! [X5,X72] : c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f2812,plain,
! [X72,X5] : c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Relation_Orel__comp(c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5,X5),
inference(definition_unfolding,[],[f1552,f1557,f1557,f1557]) ).
fof(f1552,axiom,
! [X72,X5] : c_Transitive__Closure_Ortrancl(X72,X5) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X72,X5),c_Transitive__Closure_Ortrancl(X72,X5),X5,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f26936,plain,
spl0_2158,
inference(avatar_split_clause,[],[f1584,f26934]) ).
fof(f26934,plain,
( spl0_2158
<=> ! [X24,X11,X10,X12,X5,X20] :
( ~ c_in(X12,X24,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| ~ c_in(X11,X20,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Datatype__Universe_OScons(X11,X12,X5,X10),c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f1584,axiom,
! [X10,X11,X24,X5,X12,X20] :
( ~ c_in(X12,X24,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| ~ c_in(X11,X20,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Datatype__Universe_OScons(X11,X12,X5,X10),c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodI_0) ).
fof(f26912,plain,
( spl0_2157
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2153 ),
inference(avatar_split_clause,[],[f26144,f26141,f11561,f8914,f26910]) ).
fof(f26910,plain,
( spl0_2157
<=> ! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).
fof(f26141,plain,
( spl0_2153
<=> ! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f26144,plain,
( ! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2153 ),
inference(forward_demodulation,[],[f26142,f12533]) ).
fof(f26142,plain,
( ! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2153 ),
inference(avatar_component_clause,[],[f26141]) ).
fof(f26908,plain,
( spl0_2156
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2152 ),
inference(avatar_split_clause,[],[f26139,f26136,f11561,f8910,f26906]) ).
fof(f26906,plain,
( spl0_2156
<=> ! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f26136,plain,
( spl0_2152
<=> ! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f26139,plain,
( ! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2152 ),
inference(forward_demodulation,[],[f26137,f12534]) ).
fof(f26137,plain,
( ! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2152 ),
inference(avatar_component_clause,[],[f26136]) ).
fof(f26672,plain,
( spl0_2155
| ~ spl0_1131
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25086,f24728,f9085,f26669]) ).
fof(f26669,plain,
( spl0_2155
<=> c_0 = c_Finite__Set_Ocard(c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f9085,plain,
( spl0_1131
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f25086,plain,
( c_0 = c_Finite__Set_Ocard(c_IntDef_ONats,tc_nat)
| ~ spl0_1131
| ~ spl0_2083 ),
inference(superposition,[],[f9087,f24730]) ).
fof(f9087,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| ~ spl0_1131 ),
inference(avatar_component_clause,[],[f9085]) ).
fof(f26281,plain,
( spl0_2154
| ~ spl0_718
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25078,f24728,f6929,f26279]) ).
fof(f26279,plain,
( spl0_2154
<=> ! [X0,X1] : c_lessequals(X0,c_IntDef_ONats,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f6929,plain,
( spl0_718
<=> ! [X20,X5] : c_lessequals(X20,c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f25078,plain,
( ! [X0,X1] : c_lessequals(X0,c_IntDef_ONats,tc_set(X1))
| ~ spl0_718
| ~ spl0_2083 ),
inference(superposition,[],[f6930,f24730]) ).
fof(f6930,plain,
( ! [X5,X20] : c_lessequals(X20,c_UNIV,tc_set(X5))
| ~ spl0_718 ),
inference(avatar_component_clause,[],[f6929]) ).
fof(f26143,plain,
spl0_2153,
inference(avatar_split_clause,[],[f3072,f26141]) ).
fof(f3072,plain,
! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f286,f297]) ).
fof(f286,axiom,
! [X28] :
( ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
fof(f26138,plain,
spl0_2152,
inference(avatar_split_clause,[],[f3071,f26136]) ).
fof(f3071,plain,
! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f276,f297]) ).
fof(f276,axiom,
! [X28] :
( ~ c_less(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
fof(f26125,plain,
( spl0_2151
| ~ spl0_112
| ~ spl0_670
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2150 ),
inference(avatar_split_clause,[],[f26121,f26117,f19017,f10406,f10097,f7180,f7144,f6714,f3706,f26123]) ).
fof(f26123,plain,
( spl0_2151
<=> ! [X18] : c_div(c_plus(X18,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X18,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f26117,plain,
( spl0_2150
<=> ! [X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f26121,plain,
( ! [X18] : c_div(c_plus(X18,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat) = c_plus(c_1,c_div(X18,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2150 ),
inference(forward_demodulation,[],[f26120,f11227]) ).
fof(f26120,plain,
( ! [X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X18,c_plus(c_1,c_1,tc_nat),tc_nat),c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_2150 ),
inference(forward_demodulation,[],[f26118,f19100]) ).
fof(f26118,plain,
( ! [X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2150 ),
inference(avatar_component_clause,[],[f26117]) ).
fof(f26119,plain,
spl0_2150,
inference(avatar_split_clause,[],[f3021,f26117]) ).
fof(f3021,plain,
! [X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(c_plus(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3020,f2992]) ).
fof(f3020,plain,
! [X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3019,f997]) ).
fof(f3019,plain,
! [X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3018,f995]) ).
fof(f3018,plain,
! [X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2840,f997]) ).
fof(f2840,plain,
! [X18] : c_div(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_div(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f725,f1385,f1385,f1385]) ).
fof(f725,axiom,
! [X18] : c_div(c_Suc(c_Suc(X18)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X18,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/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
fof(f26070,plain,
( spl0_2149
| ~ spl0_715
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25077,f24728,f6917,f26068]) ).
fof(f26068,plain,
( spl0_2149
<=> ! [X0] : c_IntDef_ONats = c_Union(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f6917,plain,
( spl0_715
<=> ! [X5] : c_UNIV = c_Union(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f25077,plain,
( ! [X0] : c_IntDef_ONats = c_Union(c_IntDef_ONats,X0)
| ~ spl0_715
| ~ spl0_2083 ),
inference(superposition,[],[f6918,f24730]) ).
fof(f6918,plain,
( ! [X5] : c_UNIV = c_Union(c_UNIV,X5)
| ~ spl0_715 ),
inference(avatar_component_clause,[],[f6917]) ).
fof(f26066,plain,
( spl0_2148
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2147 ),
inference(avatar_split_clause,[],[f26062,f26058,f19017,f10406,f10097,f6714,f3706,f26064]) ).
fof(f26064,plain,
( spl0_2148
<=> ! [X2,X18] : c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_1,c_plus(c_1,c_plus(c_1,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f26058,plain,
( spl0_2147
<=> ! [X2,X18] : c_Divides_Oop_Amod(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f26062,plain,
( ! [X2,X18] : c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_1,c_plus(c_1,c_plus(c_1,X2,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2147 ),
inference(forward_demodulation,[],[f26061,f19018]) ).
fof(f26061,plain,
( ! [X2,X18] : c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_1,c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2147 ),
inference(forward_demodulation,[],[f26059,f11227]) ).
fof(f26059,plain,
( ! [X2,X18] : c_Divides_Oop_Amod(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat)
| ~ spl0_2147 ),
inference(avatar_component_clause,[],[f26058]) ).
fof(f26060,plain,
spl0_2147,
inference(avatar_split_clause,[],[f3013,f26058]) ).
fof(f3013,plain,
! [X2,X18] : c_Divides_Oop_Amod(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3012,f997]) ).
fof(f3012,plain,
! [X2,X18] : c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3011,f2792]) ).
fof(f3011,plain,
! [X2,X18] : c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2835,f2992]) ).
fof(f2835,plain,
! [X2,X18] : c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_Divides_Oop_Amod(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f818,f1385,f1385,f1385]) ).
fof(f818,axiom,
! [X2,X18] : c_Divides_Oop_Amod(X18,c_Suc(c_Suc(c_Suc(X2))),tc_nat) = c_Divides_Oop_Amod(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f26044,plain,
( spl0_2146
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2145 ),
inference(avatar_split_clause,[],[f26040,f26036,f19017,f10406,f10097,f6714,f3706,f26042]) ).
fof(f26042,plain,
( spl0_2146
<=> ! [X2,X18] : c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X18,c_plus(c_1,c_plus(c_1,c_plus(c_1,X2,tc_nat),tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f26036,plain,
( spl0_2145
<=> ! [X2,X18] : c_div(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f26040,plain,
( ! [X2,X18] : c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X18,c_plus(c_1,c_plus(c_1,c_plus(c_1,X2,tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2145 ),
inference(forward_demodulation,[],[f26039,f19018]) ).
fof(f26039,plain,
( ! [X2,X18] : c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X18,c_plus(c_1,c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2145 ),
inference(forward_demodulation,[],[f26037,f11227]) ).
fof(f26037,plain,
( ! [X2,X18] : c_div(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat)
| ~ spl0_2145 ),
inference(avatar_component_clause,[],[f26036]) ).
fof(f26038,plain,
spl0_2145,
inference(avatar_split_clause,[],[f3010,f26036]) ).
fof(f3010,plain,
! [X2,X18] : c_div(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3009,f997]) ).
fof(f3009,plain,
! [X2,X18] : c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f3008,f2792]) ).
fof(f3008,plain,
! [X2,X18] : c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X18,c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2834,f2992]) ).
fof(f2834,plain,
! [X2,X18] : c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat) = c_div(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f726,f1385,f1385,f1385]) ).
fof(f726,axiom,
! [X2,X18] : c_div(X18,c_Suc(c_Suc(c_Suc(X2))),tc_nat) = c_div(X18,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f26030,plain,
( spl0_2144
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2143 ),
inference(avatar_split_clause,[],[f26026,f26022,f19017,f10406,f10097,f6714,f3706,f26028]) ).
fof(f26028,plain,
( spl0_2144
<=> ! [X10,X11,X0,X5] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),X11,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f26022,plain,
( spl0_2143
<=> ! [X10,X11,X0,X5] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f26026,plain,
( ! [X10,X0,X11,X5] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),X11,X5,X10),X5,X10)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2143 ),
inference(forward_demodulation,[],[f26025,f11227]) ).
fof(f26025,plain,
( ! [X10,X0,X11,X5] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10)
| ~ spl0_1852
| ~ spl0_2143 ),
inference(forward_demodulation,[],[f26023,f19018]) ).
fof(f26023,plain,
( ! [X10,X0,X11,X5] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10)
| ~ spl0_2143 ),
inference(avatar_component_clause,[],[f26022]) ).
fof(f26024,plain,
spl0_2143,
inference(avatar_split_clause,[],[f3007,f26022]) ).
fof(f3007,plain,
! [X10,X0,X11,X5] : c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10),
inference(forward_demodulation,[],[f2833,f2992]) ).
fof(f2833,plain,
! [X10,X0,X11,X5] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10),
inference(definition_unfolding,[],[f46,f1385,f1385,f1385]) ).
fof(f46,axiom,
! [X10,X0,X11,X5] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X0)),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X0),X11,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f26016,plain,
( spl0_2142
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2140 ),
inference(avatar_split_clause,[],[f26008,f26004,f19017,f10406,f10097,f6714,f3706,f26014]) ).
fof(f26014,plain,
( spl0_2142
<=> ! [X10,X11,X0,X5] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),X11,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f26004,plain,
( spl0_2140
<=> ! [X10,X11,X0,X5] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f26008,plain,
( ! [X10,X0,X11,X5] : c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),X11,X5,X10),X5,X10)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1852
| ~ spl0_2140 ),
inference(forward_demodulation,[],[f26007,f11227]) ).
fof(f26007,plain,
( ! [X10,X0,X11,X5] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,c_plus(c_1,X0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10)
| ~ spl0_1852
| ~ spl0_2140 ),
inference(forward_demodulation,[],[f26005,f19018]) ).
fof(f26005,plain,
( ! [X10,X0,X11,X5] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10)
| ~ spl0_2140 ),
inference(avatar_component_clause,[],[f26004]) ).
fof(f26012,plain,
( spl0_2141
| ~ spl0_714
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25076,f24728,f6913,f26010]) ).
fof(f26010,plain,
( spl0_2141
<=> ! [X0] : c_IntDef_ONats = c_Pow(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f6913,plain,
( spl0_714
<=> ! [X5] : c_UNIV = c_Pow(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f25076,plain,
( ! [X0] : c_IntDef_ONats = c_Pow(c_IntDef_ONats,X0)
| ~ spl0_714
| ~ spl0_2083 ),
inference(superposition,[],[f6914,f24730]) ).
fof(f6914,plain,
( ! [X5] : c_UNIV = c_Pow(c_UNIV,X5)
| ~ spl0_714 ),
inference(avatar_component_clause,[],[f6913]) ).
fof(f26006,plain,
spl0_2140,
inference(avatar_split_clause,[],[f3006,f26004]) ).
fof(f3006,plain,
! [X10,X0,X11,X5] : c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10),
inference(forward_demodulation,[],[f2832,f2992]) ).
fof(f2832,plain,
! [X10,X0,X11,X5] : c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),X11,X5,X10),X5,X10),
inference(definition_unfolding,[],[f45,f1385,f1385,f1385]) ).
fof(f45,axiom,
! [X10,X0,X11,X5] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X0)),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X0),X11,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f26002,plain,
spl0_2139,
inference(avatar_split_clause,[],[f1685,f26000]) ).
fof(f26000,plain,
( spl0_2139
<=> ! [X31,X10,X20,X5,X24] :
( c_in(c_Main_OPlusE__1(X20,X31,X5,X10),X20,X5)
| ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X24,X31,X10,X5),X10,X5) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f1685,axiom,
! [X31,X10,X24,X5,X20] :
( c_in(c_Main_OPlusE__1(X20,X31,X5,X10),X20,X5)
| ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X24,X31,X10,X5),X10,X5) = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_2) ).
fof(f25998,plain,
spl0_2138,
inference(avatar_split_clause,[],[f1684,f25996]) ).
fof(f25996,plain,
( spl0_2138
<=> ! [X24,X10,X31,X5,X20] :
( c_in(c_Main_OPlusE__2(X24,X31,X10,X5),X24,X10)
| ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X20,X31,X5,X10),X5,X10) = X31 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f1684,axiom,
! [X31,X10,X24,X5,X20] :
( c_in(c_Main_OPlusE__2(X24,X31,X10,X5),X24,X10)
| ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X20,X31,X5,X10),X5,X10) = X31 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_1) ).
fof(f25994,plain,
spl0_2137,
inference(avatar_split_clause,[],[f1581,f25992]) ).
fof(f25992,plain,
( spl0_2137
<=> ! [X24,X10,X20,X5,X19] :
( ~ c_in(X19,c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X20,X24,X19,X5,X10),c_Main_OuprodE__2(X20,X24,X19,X5,X10),X5,X10) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f1581,axiom,
! [X10,X19,X24,X5,X20] :
( ~ c_in(X19,c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X20,X24,X19,X5,X10),c_Main_OuprodE__2(X20,X24,X19,X5,X10),X5,X10) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_0) ).
fof(f25990,plain,
spl0_2136,
inference(avatar_split_clause,[],[f844,f25988]) ).
fof(f25988,plain,
( spl0_2136
<=> ! [X9,X10,X29,X19] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Osemiring(X10)
| c_times(c_Numeral_Onumber__of(X29,X10),c_plus(X9,X19,X10),X10) = c_plus(c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),c_times(c_Numeral_Onumber__of(X29,X10),X19,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f844,axiom,
! [X10,X29,X19,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Osemiring(X10)
| c_times(c_Numeral_Onumber__of(X29,X10),c_plus(X9,X19,X10),X10) = c_plus(c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),c_times(c_Numeral_Onumber__of(X29,X10),X19,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f25986,plain,
spl0_2135,
inference(avatar_split_clause,[],[f843,f25984]) ).
fof(f25984,plain,
( spl0_2135
<=> ! [X9,X10,X29,X19] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Oring(X10)
| c_times(c_Numeral_Onumber__of(X29,X10),c_minus(X9,X19,X10),X10) = c_minus(c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),c_times(c_Numeral_Onumber__of(X29,X10),X19,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f843,axiom,
! [X10,X29,X19,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Oring(X10)
| c_times(c_Numeral_Onumber__of(X29,X10),c_minus(X9,X19,X10),X10) = c_minus(c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),c_times(c_Numeral_Onumber__of(X29,X10),X19,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f25982,plain,
spl0_2134,
inference(avatar_split_clause,[],[f841,f25980]) ).
fof(f25980,plain,
( spl0_2134
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f841,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f25978,plain,
spl0_2133,
inference(avatar_split_clause,[],[f840,f25976]) ).
fof(f25976,plain,
( spl0_2133
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X9,X8,X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f840,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X9,X8,X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f25974,plain,
spl0_2132,
inference(avatar_split_clause,[],[f838,f25972]) ).
fof(f25972,plain,
( spl0_2132
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X9,X8,X10)
| ~ c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f838,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X9,X8,X10)
| ~ c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f25970,plain,
spl0_2131,
inference(avatar_split_clause,[],[f837,f25968]) ).
fof(f25968,plain,
( spl0_2131
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X8,X9,X10)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f837,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X8,X9,X10)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f25966,plain,
( spl0_2130
| ~ spl0_712
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25075,f24728,f6905,f25964]) ).
fof(f25964,plain,
( spl0_2130
<=> ! [X0] : c_emptyset = c_Inter(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f6905,plain,
( spl0_712
<=> ! [X5] : c_emptyset = c_Inter(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f25075,plain,
( ! [X0] : c_emptyset = c_Inter(c_IntDef_ONats,X0)
| ~ spl0_712
| ~ spl0_2083 ),
inference(superposition,[],[f6906,f24730]) ).
fof(f6906,plain,
( ! [X5] : c_emptyset = c_Inter(c_UNIV,X5)
| ~ spl0_712 ),
inference(avatar_component_clause,[],[f6905]) ).
fof(f25962,plain,
spl0_2129,
inference(avatar_split_clause,[],[f835,f25960]) ).
fof(f25960,plain,
( spl0_2129
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f835,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f25958,plain,
spl0_2128,
inference(avatar_split_clause,[],[f834,f25956]) ).
fof(f25956,plain,
( spl0_2128
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X9,X8,X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f834,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X9,X8,X10)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f25954,plain,
spl0_2127,
inference(avatar_split_clause,[],[f832,f25952]) ).
fof(f25952,plain,
( spl0_2127
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X9,X8,X10)
| ~ c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f832,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X9,X8,X10)
| ~ c_lessequals(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f25950,plain,
spl0_2126,
inference(avatar_split_clause,[],[f831,f25948]) ).
fof(f25948,plain,
( spl0_2126
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X8,X9,X10)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f831,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_less(X8,X9,X10)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f25946,plain,
spl0_2125,
inference(avatar_split_clause,[],[f829,f25944]) ).
fof(f25944,plain,
( spl0_2125
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f829,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f25942,plain,
spl0_2124,
inference(avatar_split_clause,[],[f828,f25940]) ).
fof(f25940,plain,
( spl0_2124
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X9,X8,X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f828,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X9,X8,X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f25938,plain,
spl0_2123,
inference(avatar_split_clause,[],[f826,f25936]) ).
fof(f25936,plain,
( spl0_2123
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X9,X8,X10)
| ~ c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f826,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X9,X8,X10)
| ~ c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f25934,plain,
spl0_2122,
inference(avatar_split_clause,[],[f825,f25932]) ).
fof(f25932,plain,
( spl0_2122
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X8,X9,X10)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).
fof(f825,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X8,X9,X10)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f25930,plain,
spl0_2121,
inference(avatar_split_clause,[],[f823,f25928]) ).
fof(f25928,plain,
( spl0_2121
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).
fof(f823,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f25926,plain,
spl0_2120,
inference(avatar_split_clause,[],[f822,f25924]) ).
fof(f25924,plain,
( spl0_2120
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X9,X8,X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).
fof(f822,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X9,X8,X10)
| c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f25922,plain,
( spl0_2119
| ~ spl0_676
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25074,f24728,f6738,f25920]) ).
fof(f25920,plain,
( spl0_2119
<=> ! [X0] : c_IntDef_ONats = c_List_Olists(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).
fof(f6738,plain,
( spl0_676
<=> ! [X5] : c_UNIV = c_List_Olists(c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f25074,plain,
( ! [X0] : c_IntDef_ONats = c_List_Olists(c_IntDef_ONats,X0)
| ~ spl0_676
| ~ spl0_2083 ),
inference(superposition,[],[f6739,f24730]) ).
fof(f6739,plain,
( ! [X5] : c_UNIV = c_List_Olists(c_UNIV,X5)
| ~ spl0_676 ),
inference(avatar_component_clause,[],[f6738]) ).
fof(f25918,plain,
spl0_2118,
inference(avatar_split_clause,[],[f820,f25916]) ).
fof(f25916,plain,
( spl0_2118
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X9,X8,X10)
| ~ c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).
fof(f820,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X9,X8,X10)
| ~ c_less(c_Numeral_Onumber__of(X29,X10),c_0,X10)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f25914,plain,
spl0_2117,
inference(avatar_split_clause,[],[f819,f25912]) ).
fof(f25912,plain,
( spl0_2117
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X8,X9,X10)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).
fof(f819,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| c_lessequals(X8,X9,X10)
| ~ c_less(c_0,c_Numeral_Onumber__of(X29,X10),X10)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f25910,plain,
spl0_2116,
inference(avatar_split_clause,[],[f789,f25908]) ).
fof(f25908,plain,
( spl0_2116
<=> ! [X9,X10,X29,X8] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Osemiring(X10)
| c_times(c_plus(X8,X9,X10),c_Numeral_Onumber__of(X29,X10),X10) = c_plus(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).
fof(f789,axiom,
! [X10,X29,X8,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Osemiring(X10)
| c_times(c_plus(X8,X9,X10),c_Numeral_Onumber__of(X29,X10),X10) = c_plus(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f25906,plain,
spl0_2115,
inference(avatar_split_clause,[],[f788,f25904]) ).
fof(f25904,plain,
( spl0_2115
<=> ! [X9,X10,X29,X8] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Oring(X10)
| c_times(c_minus(X8,X9,X10),c_Numeral_Onumber__of(X29,X10),X10) = c_minus(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).
fof(f788,axiom,
! [X10,X29,X8,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_Ring__and__Field_Oring(X10)
| c_times(c_minus(X8,X9,X10),c_Numeral_Onumber__of(X29,X10),X10) = c_minus(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f25902,plain,
spl0_2114,
inference(avatar_split_clause,[],[f703,f25900]) ).
fof(f25900,plain,
( spl0_2114
<=> ! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f703,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_2) ).
fof(f25762,plain,
( ~ spl0_2113
| spl0_668
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25073,f24728,f6705,f25759]) ).
fof(f25759,plain,
( spl0_2113
<=> c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f6705,plain,
( spl0_668
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f25073,plain,
( ~ c_in(c_IntDef_ONats,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_668
| ~ spl0_2083 ),
inference(superposition,[],[f6707,f24730]) ).
fof(f6707,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_668 ),
inference(avatar_component_clause,[],[f6705]) ).
fof(f25757,plain,
( spl0_2112
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2111 ),
inference(avatar_split_clause,[],[f25753,f25750,f10406,f10097,f6714,f3706,f25755]) ).
fof(f25755,plain,
( spl0_2112
<=> ! [X10,X11,X0,X12,X5] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X0,X11,X5,X10),c_Datatype__Universe_Ontrunc(X0,X12,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_OScons(X11,X12,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f25750,plain,
( spl0_2111
<=> ! [X10,X11,X0,X12,X5] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X0,X11,X5,X10),c_Datatype__Universe_Ontrunc(X0,X12,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OScons(X11,X12,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f25753,plain,
( ! [X10,X0,X11,X5,X12] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X0,X11,X5,X10),c_Datatype__Universe_Ontrunc(X0,X12,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_OScons(X11,X12,X5,X10),X5,X10)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2111 ),
inference(forward_demodulation,[],[f25751,f11227]) ).
fof(f25751,plain,
( ! [X10,X0,X11,X5,X12] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X0,X11,X5,X10),c_Datatype__Universe_Ontrunc(X0,X12,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OScons(X11,X12,X5,X10),X5,X10)
| ~ spl0_2111 ),
inference(avatar_component_clause,[],[f25750]) ).
fof(f25752,plain,
spl0_2111,
inference(avatar_split_clause,[],[f2839,f25750]) ).
fof(f2839,plain,
! [X10,X0,X11,X5,X12] : c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X0,X11,X5,X10),c_Datatype__Universe_Ontrunc(X0,X12,X5,X10),X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OScons(X11,X12,X5,X10),X5,X10),
inference(definition_unfolding,[],[f49,f1385]) ).
fof(f49,axiom,
! [X10,X0,X11,X5,X12] : c_Datatype__Universe_Ontrunc(c_Suc(X0),c_Datatype__Universe_OScons(X11,X12,X5,X10),X5,X10) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X0,X11,X5,X10),c_Datatype__Universe_Ontrunc(X0,X12,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f25748,plain,
spl0_2110,
inference(avatar_split_clause,[],[f1645,f25746]) ).
fof(f25746,plain,
( spl0_2110
<=> ! [X10,X13,X5,X76] :
( ~ c_in(X76,c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10))
| c_in(c_Pair(c_Main_OconverseE__1(X13,X76,X10,X5),c_Main_OconverseE__2(X13,X76,X10,X5),X10,X5),X13,tc_prod(X10,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f1645,axiom,
! [X10,X76,X5,X13] :
( ~ c_in(X76,c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10))
| c_in(c_Pair(c_Main_OconverseE__1(X13,X76,X10,X5),c_Main_OconverseE__2(X13,X76,X10,X5),X10,X5),X13,tc_prod(X10,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_0) ).
fof(f25744,plain,
spl0_2109,
inference(avatar_split_clause,[],[f1172,f25742]) ).
fof(f25742,plain,
( spl0_2109
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X3,X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f1172,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X3,X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f25740,plain,
spl0_2108,
inference(avatar_split_clause,[],[f1162,f25738]) ).
fof(f25738,plain,
( spl0_2108
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X3,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f1162,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X3,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f25736,plain,
spl0_2107,
inference(avatar_split_clause,[],[f310,f25734]) ).
fof(f25734,plain,
( spl0_2107
<=> ! [X29,X9,X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X29,X9),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f310,axiom,
! [X28,X29,X9] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X29,X9),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
fof(f25355,plain,
( spl0_2106
| ~ spl0_127
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25072,f24728,f3771,f25353]) ).
fof(f25353,plain,
( spl0_2106
<=> ! [X0,X1] : c_in(X0,c_IntDef_ONats,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).
fof(f3771,plain,
( spl0_127
<=> ! [X5,X3] : c_in(X3,c_UNIV,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f25072,plain,
( ! [X0,X1] : c_in(X0,c_IntDef_ONats,X1)
| ~ spl0_127
| ~ spl0_2083 ),
inference(superposition,[],[f3772,f24730]) ).
fof(f3772,plain,
( ! [X3,X5] : c_in(X3,c_UNIV,X5)
| ~ spl0_127 ),
inference(avatar_component_clause,[],[f3771]) ).
fof(f25348,plain,
spl0_2105,
inference(avatar_split_clause,[],[f2960,f25346]) ).
fof(f25346,plain,
( spl0_2105
<=> ! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f2960,plain,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f681,f970]) ).
fof(f970,axiom,
! [X28] : c_Numeral_Obin__minus(X28) = c_Numeral_Obin__mult(c_Numeral_OMin,X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f681,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f25344,plain,
spl0_2104,
inference(avatar_split_clause,[],[f2959,f25342]) ).
fof(f25342,plain,
( spl0_2104
<=> ! [X29,X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) != c_Numeral_Onumber__of(X70,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f2959,plain,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) != c_Numeral_Onumber__of(X70,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f680,f970]) ).
fof(f680,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) != c_Numeral_Onumber__of(X70,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f25340,plain,
spl0_2103,
inference(avatar_split_clause,[],[f2958,f25338]) ).
fof(f25338,plain,
( spl0_2103
<=> ! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f2958,plain,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f685,f970]) ).
fof(f685,axiom,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f25336,plain,
spl0_2102,
inference(avatar_split_clause,[],[f2957,f25334]) ).
fof(f25334,plain,
( spl0_2102
<=> ! [X29,X70] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f2957,plain,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f683,f970]) ).
fof(f683,axiom,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f25332,plain,
spl0_2101,
inference(avatar_split_clause,[],[f2955,f25330]) ).
fof(f25330,plain,
( spl0_2101
<=> ! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).
fof(f2955,plain,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f687,f970]) ).
fof(f687,axiom,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f25328,plain,
spl0_2100,
inference(avatar_split_clause,[],[f1686,f25326]) ).
fof(f25326,plain,
( spl0_2100
<=> ! [X24,X10,X31,X5,X20] :
( c_in(c_Main_OPlusE__2(X24,X31,X10,X5),X24,X10)
| c_in(c_Main_OPlusE__1(X20,X31,X5,X10),X20,X5)
| ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f1686,axiom,
! [X31,X10,X24,X5,X20] :
( c_in(c_Main_OPlusE__2(X24,X31,X10,X5),X24,X10)
| c_in(c_Main_OPlusE__1(X20,X31,X5,X10),X20,X5)
| ~ c_in(X31,c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OPlusE_3) ).
fof(f25324,plain,
spl0_2099,
inference(avatar_split_clause,[],[f842,f25322]) ).
fof(f25322,plain,
( spl0_2099
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| ~ c_less(X9,X8,X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f842,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| ~ c_less(X9,X8,X10)
| c_less(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f25320,plain,
spl0_2098,
inference(avatar_split_clause,[],[f836,f25318]) ).
fof(f25318,plain,
( spl0_2098
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| ~ c_less(X9,X8,X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).
fof(f836,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_less(X8,X9,X10)
| ~ c_less(X9,X8,X10)
| c_less(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f25316,plain,
spl0_2097,
inference(avatar_split_clause,[],[f830,f25314]) ).
fof(f25314,plain,
( spl0_2097
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).
fof(f830,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10)
| c_lessequals(c_times(X8,c_Numeral_Onumber__of(X29,X10),X10),c_times(X9,c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f25312,plain,
spl0_2096,
inference(avatar_split_clause,[],[f824,f25310]) ).
fof(f25310,plain,
( spl0_2096
<=> ! [X9,X10,X29,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f824,axiom,
! [X10,X29,X8,X9] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X10)
| ~ class_Numeral_Onumber(X10)
| ~ c_lessequals(X8,X9,X10)
| ~ c_lessequals(X9,X8,X10)
| c_lessequals(c_times(c_Numeral_Onumber__of(X29,X10),X8,X10),c_times(c_Numeral_Onumber__of(X29,X10),X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f25308,plain,
spl0_2095,
inference(avatar_split_clause,[],[f635,f25306]) ).
fof(f25306,plain,
( spl0_2095
<=> ! [X35,X34,X10,X5,X3] :
( c_in(X3,c_List_Oset(X34,X5),X5)
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X10))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X34,X35,X5,X10),X3,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f635,axiom,
! [X3,X10,X34,X5,X35] :
( c_in(X3,c_List_Oset(X34,X5),X5)
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X10))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X34,X35,X5,X10),X3,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_1) ).
fof(f25304,plain,
spl0_2094,
inference(avatar_split_clause,[],[f634,f25302]) ).
fof(f25302,plain,
( spl0_2094
<=> ! [X35,X34,X10,X5,X3] :
( ~ c_in(X3,c_List_Oset(X34,X5),X5)
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X10))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X34,X35,X5,X10),X3,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f634,axiom,
! [X3,X10,X34,X5,X35] :
( ~ c_in(X3,c_List_Oset(X34,X5),X5)
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X10))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X34,X35,X5,X10),X3,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Map_Omap__of__zip__is__None_0) ).
fof(f25300,plain,
spl0_2093,
inference(avatar_split_clause,[],[f630,f25298]) ).
fof(f25298,plain,
( spl0_2093
<=> ! [X35,X34,X10,X3,X5,X1] : c_List_Ozip(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X1,X35,X10),X5,X10) = c_List_Olist_OCons(c_Pair(X3,X1,X5,X10),c_List_Ozip(X34,X35,X5,X10),tc_prod(X5,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f630,axiom,
! [X3,X10,X1,X34,X5,X35] : c_List_Ozip(c_List_Olist_OCons(X3,X34,X5),c_List_Olist_OCons(X1,X35,X10),X5,X10) = c_List_Olist_OCons(c_Pair(X3,X1,X5,X10),c_List_Ozip(X34,X35,X5,X10),tc_prod(X5,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Cons__Cons_0) ).
fof(f25296,plain,
spl0_2092,
inference(avatar_split_clause,[],[f457,f25294]) ).
fof(f25294,plain,
( spl0_2092
<=> ! [X13,X5,X1] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X5),c_Main_Olexord__Nil__left__2(X1,X5),X5) = X1
| ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f457,axiom,
! [X1,X5,X13] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X1,X5),c_Main_Olexord__Nil__left__2(X1,X5),X5) = X1
| ~ c_in(c_Pair(c_List_Olist_ONil,X1,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_0) ).
fof(f25292,plain,
spl0_2091,
inference(avatar_split_clause,[],[f299,f25290]) ).
fof(f25290,plain,
( spl0_2091
<=> ! [X28] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f299,axiom,
! [X28] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f25197,plain,
( spl0_2090
| ~ spl0_1456
| ~ spl0_2083 ),
inference(avatar_split_clause,[],[f25087,f24728,f12815,f25195]) ).
fof(f25195,plain,
( spl0_2090
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_IntDef_ONats,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f12815,plain,
( spl0_1456
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f25087,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_IntDef_ONats,X0)
| ~ spl0_1456
| ~ spl0_2083 ),
inference(superposition,[],[f12816,f24730]) ).
fof(f12816,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_1456 ),
inference(avatar_component_clause,[],[f12815]) ).
fof(f25158,plain,
spl0_2089,
inference(avatar_split_clause,[],[f2954,f25156]) ).
fof(f25156,plain,
( spl0_2089
<=> ! [X34,X5,X35] :
( ~ c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(X35,X5)
| c_List_Odistinct(c_append(X34,X35,X5),X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X34,X5),X5),c_List_Oset(X35,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f2954,plain,
! [X34,X5,X35] :
( ~ c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(X35,X5)
| c_List_Odistinct(c_append(X34,X35,X5),X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X34,X5),X5),c_List_Oset(X35,X5),X5,X5) ),
inference(definition_unfolding,[],[f399,f1214]) ).
fof(f1214,axiom,
! [X24,X5,X20] : c_inter(X20,X24,X5) = c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f399,axiom,
! [X34,X5,X35] :
( ~ c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(X35,X5)
| c_List_Odistinct(c_append(X34,X35,X5),X5)
| c_emptyset != c_inter(c_List_Oset(X34,X5),c_List_Oset(X35,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_3) ).
fof(f25154,plain,
spl0_2088,
inference(avatar_split_clause,[],[f2926,f25152]) ).
fof(f25152,plain,
( spl0_2088
<=> ! [X24,X20,X5,X8] :
( c_in(X8,X24,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),X24,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f2926,plain,
! [X8,X24,X5,X20] :
( c_in(X8,X24,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),X24,X5,X5) ),
inference(definition_unfolding,[],[f1520,f1214,f1214]) ).
fof(f1520,axiom,
! [X8,X24,X5,X20] :
( c_in(X8,X24,X5)
| c_emptyset != c_inter(X20,X24,X5)
| c_emptyset = c_inter(c_insert(X8,X20,X5),X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_2) ).
fof(f25150,plain,
spl0_2087,
inference(avatar_split_clause,[],[f2924,f25148]) ).
fof(f25148,plain,
( spl0_2087
<=> ! [X24,X9,X20,X5] :
( c_in(X9,X20,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f2924,plain,
! [X9,X24,X5,X20] :
( c_in(X9,X20,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5) ),
inference(definition_unfolding,[],[f1507,f1214,f1214]) ).
fof(f1507,axiom,
! [X9,X24,X5,X20] :
( c_in(X9,X20,X5)
| c_emptyset != c_inter(X20,X24,X5)
| c_emptyset = c_inter(X20,c_insert(X9,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_2) ).
fof(f25146,plain,
spl0_2086,
inference(avatar_split_clause,[],[f633,f25144]) ).
fof(f25144,plain,
( spl0_2086
<=> ! [X3,X45,X10,X5,X17,X1] : c_List_Ozip(c_List_Oreplicate(X17,X3,X5),c_List_Oreplicate(X45,X1,X10),X5,X10) = c_List_Oreplicate(c_Orderings_Omin(X17,X45,tc_nat),c_Pair(X3,X1,X5,X10),tc_prod(X5,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f633,axiom,
! [X3,X10,X1,X45,X17,X5] : c_List_Ozip(c_List_Oreplicate(X17,X3,X5),c_List_Oreplicate(X45,X1,X10),X5,X10) = c_List_Oreplicate(c_Orderings_Omin(X17,X45,tc_nat),c_Pair(X3,X1,X5,X10),tc_prod(X5,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__replicate_0) ).
fof(f25142,plain,
spl0_2085,
inference(avatar_split_clause,[],[f539,f25140]) ).
fof(f25140,plain,
( spl0_2085
<=> ! [X17,X34,X5,X2] :
( ~ c_lessequals(c_plus(X2,X17,tc_nat),c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Odrop(X2,X34,X5),X17,X5) = c_List_Onth(X34,c_plus(X2,X17,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f539,axiom,
! [X2,X17,X34,X5] :
( ~ c_lessequals(c_plus(X2,X17,tc_nat),c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Odrop(X2,X34,X5),X17,X5) = c_List_Onth(X34,c_plus(X2,X17,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__drop_0) ).
fof(f25094,plain,
( spl0_2084
| ~ spl0_56
| ~ spl0_1443
| ~ spl0_2080 ),
inference(avatar_split_clause,[],[f24649,f24646,f11721,f3432,f25092]) ).
fof(f25092,plain,
( spl0_2084
<=> ! [X70,X29] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f3432,plain,
( spl0_56
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f11721,plain,
( spl0_1443
<=> ! [X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X28),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f24646,plain,
( spl0_2080
<=> ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f24649,plain,
( ! [X70,X29] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) )
| ~ spl0_56
| ~ spl0_1443
| ~ spl0_2080 ),
inference(forward_demodulation,[],[f24647,f12807]) ).
fof(f12807,plain,
( ! [X0] : c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X0),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_1443 ),
inference(resolution,[],[f11722,f3434]) ).
fof(f3434,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f3432]) ).
fof(f11722,plain,
( ! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X28),X5) )
| ~ spl0_1443 ),
inference(avatar_component_clause,[],[f11721]) ).
fof(f24647,plain,
( ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) )
| ~ spl0_2080 ),
inference(avatar_component_clause,[],[f24646]) ).
fof(f24731,plain,
( spl0_2083
| ~ spl0_792
| ~ spl0_796
| ~ spl0_1420
| ~ spl0_1671
| ~ spl0_2070 ),
inference(avatar_split_clause,[],[f24640,f24494,f15761,f11614,f7257,f7241,f24728]) ).
fof(f7241,plain,
( spl0_792
<=> ! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f7257,plain,
( spl0_796
<=> ! [X5,X1] : c_union(c_emptyset,X1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f11614,plain,
( spl0_1420
<=> ! [X20,X5,X24] : c_union(c_minus(X24,X20,tc_set(X5)),X20,X5) = c_union(X24,X20,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f15761,plain,
( spl0_1671
<=> ! [X20,X5,X24] : c_uminus(c_minus(X20,X24,tc_set(X5)),tc_set(X5)) = c_union(c_uminus(X20,tc_set(X5)),X24,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f24494,plain,
( spl0_2070
<=> ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f24640,plain,
( c_UNIV = c_IntDef_ONats
| ~ spl0_792
| ~ spl0_796
| ~ spl0_1420
| ~ spl0_1671
| ~ spl0_2070 ),
inference(forward_demodulation,[],[f24639,f24637]) ).
fof(f24637,plain,
( ! [X0] : c_IntDef_ONats = c_union(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_796
| ~ spl0_1420
| ~ spl0_2070 ),
inference(forward_demodulation,[],[f24622,f7258]) ).
fof(f7258,plain,
( ! [X1,X5] : c_union(c_emptyset,X1,X5) = X1
| ~ spl0_796 ),
inference(avatar_component_clause,[],[f7257]) ).
fof(f24622,plain,
( ! [X0] : c_union(X0,c_IntDef_ONats,tc_nat) = c_union(c_emptyset,c_IntDef_ONats,tc_nat)
| ~ spl0_1420
| ~ spl0_2070 ),
inference(superposition,[],[f11615,f24495]) ).
fof(f24495,plain,
( ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_2070 ),
inference(avatar_component_clause,[],[f24494]) ).
fof(f11615,plain,
( ! [X24,X5,X20] : c_union(c_minus(X24,X20,tc_set(X5)),X20,X5) = c_union(X24,X20,X5)
| ~ spl0_1420 ),
inference(avatar_component_clause,[],[f11614]) ).
fof(f24639,plain,
( ! [X0] : c_UNIV = c_union(c_uminus(X0,tc_set(tc_nat)),c_IntDef_ONats,tc_nat)
| ~ spl0_792
| ~ spl0_1671
| ~ spl0_2070 ),
inference(forward_demodulation,[],[f24627,f7242]) ).
fof(f7242,plain,
( ! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5))
| ~ spl0_792 ),
inference(avatar_component_clause,[],[f7241]) ).
fof(f24627,plain,
( ! [X0] : c_union(c_uminus(X0,tc_set(tc_nat)),c_IntDef_ONats,tc_nat) = c_uminus(c_emptyset,tc_set(tc_nat))
| ~ spl0_1671
| ~ spl0_2070 ),
inference(superposition,[],[f15762,f24495]) ).
fof(f15762,plain,
( ! [X24,X5,X20] : c_uminus(c_minus(X20,X24,tc_set(X5)),tc_set(X5)) = c_union(c_uminus(X20,tc_set(X5)),X24,X5)
| ~ spl0_1671 ),
inference(avatar_component_clause,[],[f15761]) ).
fof(f24709,plain,
( spl0_2082
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2062 ),
inference(avatar_split_clause,[],[f24464,f24461,f11561,f8914,f24707]) ).
fof(f24707,plain,
( spl0_2082
<=> ! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f24461,plain,
( spl0_2062
<=> ! [X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f24464,plain,
( ! [X28] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1109
| ~ spl0_1407
| ~ spl0_2062 ),
inference(forward_demodulation,[],[f24462,f12533]) ).
fof(f24462,plain,
( ! [X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2062 ),
inference(avatar_component_clause,[],[f24461]) ).
fof(f24705,plain,
( spl0_2081
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2061 ),
inference(avatar_split_clause,[],[f24459,f24456,f11561,f8910,f24703]) ).
fof(f24703,plain,
( spl0_2081
<=> ! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f24456,plain,
( spl0_2061
<=> ! [X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f24459,plain,
( ! [X28] :
( c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1108
| ~ spl0_1407
| ~ spl0_2061 ),
inference(forward_demodulation,[],[f24457,f12534]) ).
fof(f24457,plain,
( ! [X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2061 ),
inference(avatar_component_clause,[],[f24456]) ).
fof(f24648,plain,
spl0_2080,
inference(avatar_split_clause,[],[f2933,f24646]) ).
fof(f2933,plain,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f700,f970,f970]) ).
fof(f700,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_4) ).
fof(f24644,plain,
spl0_2079,
inference(avatar_split_clause,[],[f2848,f24642]) ).
fof(f24642,plain,
( spl0_2079
<=> ! [X5,X19,X29,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X29,X5),c_minus(X19,c_Numeral_Onumber__of(X28,X5),X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),X5),X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f2848,plain,
! [X28,X29,X19,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X29,X5),c_minus(X19,c_Numeral_Onumber__of(X28,X5),X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),X5),X19,X5) ),
inference(definition_unfolding,[],[f948,f970]) ).
fof(f948,axiom,
! [X28,X29,X19,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X29,X5),c_minus(X19,c_Numeral_Onumber__of(X28,X5),X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X28)),X5),X19,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f24611,plain,
( spl0_2078
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2077 ),
inference(avatar_split_clause,[],[f24607,f24604,f10406,f10097,f6714,f3706,f24609]) ).
fof(f24609,plain,
( spl0_2078
<=> ! [X6,X2,X72] : c_Relation_Orel__comp(X72,c_Nat_Opower(X72,X2,tc_set(tc_prod(X6,X6))),X6,X6,X6) = c_Nat_Opower(X72,c_plus(c_1,X2,tc_nat),tc_set(tc_prod(X6,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f24604,plain,
( spl0_2077
<=> ! [X6,X2,X72] : c_Relation_Orel__comp(X72,c_Nat_Opower(X72,X2,tc_set(tc_prod(X6,X6))),X6,X6,X6) = c_Nat_Opower(X72,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_set(tc_prod(X6,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f24607,plain,
( ! [X2,X72,X6] : c_Relation_Orel__comp(X72,c_Nat_Opower(X72,X2,tc_set(tc_prod(X6,X6))),X6,X6,X6) = c_Nat_Opower(X72,c_plus(c_1,X2,tc_nat),tc_set(tc_prod(X6,X6)))
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2077 ),
inference(forward_demodulation,[],[f24605,f11227]) ).
fof(f24605,plain,
( ! [X2,X72,X6] : c_Relation_Orel__comp(X72,c_Nat_Opower(X72,X2,tc_set(tc_prod(X6,X6))),X6,X6,X6) = c_Nat_Opower(X72,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_set(tc_prod(X6,X6)))
| ~ spl0_2077 ),
inference(avatar_component_clause,[],[f24604]) ).
fof(f24606,plain,
spl0_2077,
inference(avatar_split_clause,[],[f2836,f24604]) ).
fof(f2836,plain,
! [X2,X72,X6] : c_Relation_Orel__comp(X72,c_Nat_Opower(X72,X2,tc_set(tc_prod(X6,X6))),X6,X6,X6) = c_Nat_Opower(X72,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_set(tc_prod(X6,X6))),
inference(definition_unfolding,[],[f1232,f1385]) ).
fof(f1232,axiom,
! [X2,X72,X6] : c_Nat_Opower(X72,c_Suc(X2),tc_set(tc_prod(X6,X6))) = c_Relation_Orel__comp(X72,c_Nat_Opower(X72,X2,tc_set(tc_prod(X6,X6))),X6,X6,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f24602,plain,
spl0_2076,
inference(avatar_split_clause,[],[f2831,f24600]) ).
fof(f24600,plain,
( spl0_2076
<=> ! [X24,X20,X5,X8] : c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),c_insert(X8,X24,X5),X5,X5) = c_insert(X8,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f2831,plain,
! [X8,X24,X5,X20] : c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),c_insert(X8,X24,X5),X5,X5) = c_insert(X8,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5),
inference(definition_unfolding,[],[f1527,f1214,f1214]) ).
fof(f1527,axiom,
! [X8,X24,X5,X20] : c_inter(c_insert(X8,X20,X5),c_insert(X8,X24,X5),X5) = c_insert(X8,c_inter(X20,X24,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__inter__insert_0) ).
fof(f24598,plain,
spl0_2075,
inference(avatar_split_clause,[],[f2825,f24596]) ).
fof(f24596,plain,
( spl0_2075
<=> ! [X20,X5,X24] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X20,X5),tc_List_Olist(X5)),c_List_Olists(X24,X5),tc_List_Olist(X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f2825,plain,
! [X24,X5,X20] : c_List_Olists(c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_List_Olists(X20,X5),tc_List_Olist(X5)),c_List_Olists(X24,X5),tc_List_Olist(X5),tc_List_Olist(X5)),
inference(definition_unfolding,[],[f478,f1214,f1214]) ).
fof(f478,axiom,
! [X24,X5,X20] : c_List_Olists(c_inter(X20,X24,X5),X5) = c_inter(c_List_Olists(X20,X5),c_List_Olists(X24,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__Int__eq_0) ).
fof(f24594,plain,
spl0_2074,
inference(avatar_split_clause,[],[f2824,f24592]) ).
fof(f24592,plain,
( spl0_2074
<=> ! [X20,X5,X24] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X20,X5),tc_set(X5)),c_Pow(X24,X5),tc_set(X5),tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f2824,plain,
! [X24,X5,X20] : c_Pow(c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) = c_Relation_OImage(c_Relation_Odiag(c_Pow(X20,X5),tc_set(X5)),c_Pow(X24,X5),tc_set(X5),tc_set(X5)),
inference(definition_unfolding,[],[f1465,f1214,f1214]) ).
fof(f1465,axiom,
! [X24,X5,X20] : c_Pow(c_inter(X20,X24,X5),X5) = c_inter(c_Pow(X20,X5),c_Pow(X24,X5),tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__Int__eq_0) ).
fof(f24512,plain,
( spl0_2073
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2072 ),
inference(avatar_split_clause,[],[f24508,f24504,f10406,f10097,f6714,f3706,f24510]) ).
fof(f24510,plain,
( spl0_2073
<=> ! [X2,X0] : c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_plus(c_1,X0,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X2,tc_nat),c_plus(c_1,X0,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f24504,plain,
( spl0_2072
<=> ! [X2,X0] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f24508,plain,
( ! [X2,X0] : c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_plus(c_1,X0,tc_nat)),tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X2,tc_nat),c_plus(c_1,X0,tc_nat))
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2072 ),
inference(forward_demodulation,[],[f24507,f11227]) ).
fof(f24507,plain,
( ! [X2,X0] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_plus(c_1,X0,tc_nat)) = c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_plus(c_1,X0,tc_nat)),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2072 ),
inference(forward_demodulation,[],[f24505,f11227]) ).
fof(f24505,plain,
( ! [X2,X0] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)),tc_nat)
| ~ spl0_2072 ),
inference(avatar_component_clause,[],[f24504]) ).
fof(f24506,plain,
spl0_2072,
inference(avatar_split_clause,[],[f2818,f24504]) ).
fof(f2818,plain,
! [X2,X0] : c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)) = c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)),tc_nat),
inference(definition_unfolding,[],[f3,f1385,f1385,f1385]) ).
fof(f3,axiom,
! [X2,X0] : c_Binomial_Obinomial(c_Suc(X2),c_Suc(X0)) = c_plus(c_Binomial_Obinomial(X2,X0),c_Binomial_Obinomial(X2,c_Suc(X0)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f24500,plain,
spl0_2071,
inference(avatar_split_clause,[],[f2782,f24498]) ).
fof(f24498,plain,
( spl0_2071
<=> ! [X13,X5] : c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f2782,plain,
! [X5,X13] : c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1551,f1557,f1557,f1557]) ).
fof(f1551,axiom,
! [X5,X13] : c_Transitive__Closure_Ortrancl(X13,X5) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X13,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f24496,plain,
( spl0_2070
| ~ spl0_1317
| ~ spl0_1348 ),
inference(avatar_split_clause,[],[f11337,f11295,f10322,f24494]) ).
fof(f10322,plain,
( spl0_1317
<=> ! [X20,X5,X24] :
( ~ c_lessequals(X20,X24,tc_set(X5))
| c_emptyset = c_minus(X20,X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f11295,plain,
( spl0_1348
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f11337,plain,
( ! [X0] : c_emptyset = c_minus(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1317
| ~ spl0_1348 ),
inference(resolution,[],[f11296,f10323]) ).
fof(f10323,plain,
( ! [X24,X5,X20] :
( ~ c_lessequals(X20,X24,tc_set(X5))
| c_emptyset = c_minus(X20,X24,tc_set(X5)) )
| ~ spl0_1317 ),
inference(avatar_component_clause,[],[f10322]) ).
fof(f11296,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1348 ),
inference(avatar_component_clause,[],[f11295]) ).
fof(f24492,plain,
spl0_2069,
inference(avatar_split_clause,[],[f1646,f24490]) ).
fof(f24490,plain,
( spl0_2069
<=> ! [X10,X13,X5,X76] :
( ~ c_in(X76,c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10))
| c_Pair(c_Main_OconverseE__2(X13,X76,X10,X5),c_Main_OconverseE__1(X13,X76,X10,X5),X5,X10) = X76 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f1646,axiom,
! [X10,X76,X5,X13] :
( ~ c_in(X76,c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10))
| c_Pair(c_Main_OconverseE__2(X13,X76,X10,X5),c_Main_OconverseE__1(X13,X76,X10,X5),X5,X10) = X76 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OconverseE_1) ).
fof(f24488,plain,
spl0_2068,
inference(avatar_split_clause,[],[f1157,f24486]) ).
fof(f24486,plain,
( spl0_2068
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X3,X5),c_Numeral_Onumber__of(X28,tc_nat),X5) = c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).
fof(f1157,axiom,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X3,X5),c_Numeral_Onumber__of(X28,tc_nat),X5) = c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f24484,plain,
spl0_2067,
inference(avatar_split_clause,[],[f667,f24482]) ).
fof(f24482,plain,
( spl0_2067
<=> ! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,X70),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f667,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,X70),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f24480,plain,
spl0_2066,
inference(avatar_split_clause,[],[f536,f24478]) ).
fof(f24478,plain,
( spl0_2066
<=> ! [X29,X34,X5,X3] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_Numeral_Onumber__of(X29,tc_nat),X5) = c_List_Onth(X34,c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f536,axiom,
! [X3,X29,X34,X5] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_Numeral_Onumber__of(X29,tc_nat),X5) = c_List_Onth(X34,c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__number__of_1) ).
fof(f24476,plain,
spl0_2065,
inference(avatar_split_clause,[],[f414,f24474]) ).
fof(f24474,plain,
( spl0_2065
<=> ! [X35,X34,X5,X2] : c_List_Odrop(X2,c_append(X34,X35,X5),X5) = c_append(c_List_Odrop(X2,X34,X5),c_List_Odrop(c_minus(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat),X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f414,axiom,
! [X2,X34,X35,X5] : c_List_Odrop(X2,c_append(X34,X35,X5),X5) = c_append(c_List_Odrop(X2,X34,X5),c_List_Odrop(c_minus(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat),X35,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__append_0) ).
fof(f24472,plain,
spl0_2064,
inference(avatar_split_clause,[],[f412,f24470]) ).
fof(f24470,plain,
( spl0_2064
<=> ! [X5,X34,X29,X3] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X29,tc_nat),c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f412,axiom,
! [X3,X29,X34,X5] :
( c_0 = c_Numeral_Onumber__of(X29,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X29,tc_nat),c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X29,tc_nat),c_1,tc_nat),X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Cons__number__of_1) ).
fof(f24468,plain,
spl0_2063,
inference(avatar_split_clause,[],[f367,f24466]) ).
fof(f24466,plain,
( spl0_2063
<=> ! [X35,X34,X20,X5] :
( ~ c_in(X35,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5))
| c_in(c_append(X34,X35,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f367,axiom,
! [X34,X35,X5,X20] :
( ~ c_in(X35,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5))
| c_in(c_append(X34,X35,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_2) ).
fof(f24463,plain,
spl0_2062,
inference(avatar_split_clause,[],[f288,f24461]) ).
fof(f288,axiom,
! [X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
fof(f24458,plain,
spl0_2061,
inference(avatar_split_clause,[],[f278,f24456]) ).
fof(f278,axiom,
! [X28] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
fof(f24454,plain,
spl0_2060,
inference(avatar_split_clause,[],[f222,f24452]) ).
fof(f24452,plain,
( spl0_2060
<=> ! [X1,X3] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X3,X1,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f222,axiom,
! [X3,X1] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X3,X1,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
fof(f24449,plain,
spl0_2059,
inference(avatar_split_clause,[],[f110,f24447]) ).
fof(f24447,plain,
( spl0_2059
<=> ! [X23,X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_less(X3,X23,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(X3,c_Finite__Set_OMin(X20,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f110,axiom,
! [X3,X5,X23,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_less(X3,X23,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(X3,c_Finite__Set_OMin(X20,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f24445,plain,
spl0_2058,
inference(avatar_split_clause,[],[f107,f24443]) ).
fof(f24443,plain,
( spl0_2058
<=> ! [X23,X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_lessequals(X3,X23,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(X3,c_Finite__Set_OMin(X20,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f107,axiom,
! [X3,X5,X23,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_lessequals(X3,X23,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(X3,c_Finite__Set_OMin(X20,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f24441,plain,
spl0_2057,
inference(avatar_split_clause,[],[f103,f24439]) ).
fof(f24439,plain,
( spl0_2057
<=> ! [X23,X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_less(X23,X3,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(c_Finite__Set_OMax(X20,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f103,axiom,
! [X3,X5,X23,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_less(X23,X3,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_less(c_Finite__Set_OMax(X20,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_0) ).
fof(f24437,plain,
spl0_2056,
inference(avatar_split_clause,[],[f100,f24435]) ).
fof(f24435,plain,
( spl0_2056
<=> ! [X23,X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_lessequals(X23,X3,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(c_Finite__Set_OMax(X20,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f100,axiom,
! [X3,X5,X23,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X23,X20,X5)
| c_lessequals(X23,X3,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_lessequals(c_Finite__Set_OMax(X20,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_0) ).
fof(f23712,plain,
( spl0_2055
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_2054 ),
inference(avatar_split_clause,[],[f23708,f23705,f19017,f7180,f7144,f23710]) ).
fof(f23710,plain,
( spl0_2055
<=> ! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_plus(c_1,c_1,tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f23705,plain,
( spl0_2054
<=> ! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f23708,plain,
( ! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_plus(c_1,c_1,tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) )
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_2054 ),
inference(forward_demodulation,[],[f23706,f19100]) ).
fof(f23706,plain,
( ! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) )
| ~ spl0_2054 ),
inference(avatar_component_clause,[],[f23705]) ).
fof(f23707,plain,
spl0_2054,
inference(avatar_split_clause,[],[f3112,f23705]) ).
fof(f3112,plain,
! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) ),
inference(forward_demodulation,[],[f3111,f997]) ).
fof(f3111,plain,
! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) ),
inference(forward_demodulation,[],[f3110,f995]) ).
fof(f3110,plain,
! [X28,X10] :
( c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) = c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X10)
| ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10) ),
inference(forward_demodulation,[],[f715,f997]) ).
fof(f715,axiom,
! [X28,X10] :
( ~ class_Power_Orecpower(X10)
| ~ class_Numeral_Onumber(X10)
| c_Nat_Opower(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X10) = c_times(c_Numeral_Onumber__of(X28,X10),c_Numeral_Onumber__of(X28,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f23703,plain,
spl0_2053,
inference(avatar_split_clause,[],[f3050,f23701]) ).
fof(f23701,plain,
( spl0_2053
<=> ! [X45,X18,X0] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X0,X18,tc_nat),X45,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X18,c_minus(X45,X0,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X0,X45,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f3050,plain,
! [X0,X18,X45] :
( c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X0,X18,tc_nat),X45,tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X18,c_minus(X45,X0,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X0,X45,tc_nat) ),
inference(forward_demodulation,[],[f3049,f2797]) ).
fof(f2797,plain,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X31,tc_nat),tc_nat),X67,tc_nat),
inference(definition_unfolding,[],[f1381,f1385]) ).
fof(f1381,axiom,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),tc_nat) = c_minus(c_Suc(X31),X67,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f3049,plain,
! [X0,X18,X45] :
( c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X45,X0,tc_nat),tc_nat),tc_nat),X18,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(c_plus(X0,X18,tc_nat),X45,tc_nat),tc_nat)
| ~ c_lessequals(X0,X45,tc_nat) ),
inference(forward_demodulation,[],[f2868,f2797]) ).
fof(f2868,plain,
! [X0,X18,X45] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X45,X0,tc_nat),tc_nat),tc_nat),X18,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat),c_plus(X0,X18,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f639,f1385,f1385]) ).
fof(f639,axiom,
! [X0,X18,X45] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_minus(c_Suc(c_minus(X45,X0,tc_nat)),X18,tc_nat) = c_minus(c_Suc(X45),c_plus(X0,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f23699,plain,
spl0_2052,
inference(avatar_split_clause,[],[f3048,f23697]) ).
fof(f23697,plain,
( spl0_2052
<=> ! [X45,X18,X0] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X45,c_plus(X18,X0,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X45,X0,tc_nat),X18,tc_nat),tc_nat)
| ~ c_lessequals(X0,X45,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).
fof(f3048,plain,
! [X0,X18,X45] :
( c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X45,c_plus(X18,X0,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_minus(X45,X0,tc_nat),X18,tc_nat),tc_nat)
| ~ c_lessequals(X0,X45,tc_nat) ),
inference(forward_demodulation,[],[f3047,f2796]) ).
fof(f2796,plain,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_Finite__Set_Ocard(c_SetInterval_OatMost(X67,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1388,f1385]) ).
fof(f1388,axiom,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_Suc(X67),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f3047,plain,
! [X0,X18,X45] :
( c_minus(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X45,X0,tc_nat),tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X45,c_plus(X18,X0,tc_nat),tc_nat),tc_nat)
| ~ c_lessequals(X0,X45,tc_nat) ),
inference(forward_demodulation,[],[f2867,f2796]) ).
fof(f2867,plain,
! [X0,X18,X45] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_minus(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X45,X0,tc_nat),tc_nat),tc_nat),tc_nat) = c_minus(c_plus(X18,X0,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f638,f1385,f1385]) ).
fof(f638,axiom,
! [X0,X18,X45] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_minus(X18,c_Suc(c_minus(X45,X0,tc_nat)),tc_nat) = c_minus(c_plus(X18,X0,tc_nat),c_Suc(X45),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f23649,plain,
( spl0_2051
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2050 ),
inference(avatar_split_clause,[],[f23645,f23642,f10406,f10097,f6714,f3706,f23647]) ).
fof(f23647,plain,
( spl0_2051
<=> ! [X20,X5,X3] :
( c_Finite__Set_Ocard(c_insert(X3,X20,X5),X5) = c_plus(c_1,c_Finite__Set_Ocard(X20,X5),tc_nat)
| c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f23642,plain,
( spl0_2050
<=> ! [X20,X5,X3] :
( c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X3,X20,X5),X5) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X20,X5),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f23645,plain,
( ! [X3,X5,X20] :
( c_Finite__Set_Ocard(c_insert(X3,X20,X5),X5) = c_plus(c_1,c_Finite__Set_Ocard(X20,X5),tc_nat)
| c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5)) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2050 ),
inference(forward_demodulation,[],[f23643,f11227]) ).
fof(f23643,plain,
( ! [X3,X5,X20] :
( c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X3,X20,X5),X5) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X20,X5),tc_nat),tc_nat) )
| ~ spl0_2050 ),
inference(avatar_component_clause,[],[f23642]) ).
fof(f23644,plain,
spl0_2050,
inference(avatar_split_clause,[],[f2923,f23642]) ).
fof(f2923,plain,
! [X3,X5,X20] :
( c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X3,X20,X5),X5) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(X20,X5),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f121,f1385]) ).
fof(f121,axiom,
! [X3,X5,X20] :
( c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_Finite__Set_Ocard(c_insert(X3,X20,X5),X5) = c_Suc(c_Finite__Set_Ocard(X20,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f23619,plain,
( spl0_2049
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2048 ),
inference(avatar_split_clause,[],[f23615,f23612,f10406,f10097,f6714,f3706,f23617]) ).
fof(f23617,plain,
( spl0_2049
<=> ! [X3,X34,X5,X2] : c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X5) = c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_plus(c_1,X2,tc_nat),tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f23612,plain,
( spl0_2048
<=> ! [X3,X34,X5,X2] : c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),X5) = c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f23615,plain,
( ! [X2,X3,X34,X5] : c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X5) = c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_plus(c_1,X2,tc_nat),tc_nat),X5)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_2048 ),
inference(forward_demodulation,[],[f23613,f11227]) ).
fof(f23613,plain,
( ! [X2,X3,X34,X5] : c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),X5) = c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X5)
| ~ spl0_2048 ),
inference(avatar_component_clause,[],[f23612]) ).
fof(f23614,plain,
spl0_2048,
inference(avatar_split_clause,[],[f2827,f23612]) ).
fof(f2827,plain,
! [X2,X3,X34,X5] : c_List_Osublist(c_List_Olist_OCons(X3,X34,X5),c_SetInterval_OlessThan(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),X5) = c_List_Olist_OCons(X3,c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X5),
inference(definition_unfolding,[],[f610,f607,f1385,f607]) ).
fof(f610,axiom,
! [X2,X3,X34,X5] : c_List_Otake(c_Suc(X2),c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Olist_OCons(X3,c_List_Otake(X2,X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__Suc__Cons_0) ).
fof(f23610,plain,
spl0_2047,
inference(avatar_split_clause,[],[f1641,f23608]) ).
fof(f23608,plain,
( spl0_2047
<=> ! [X10,X9,X13,X5,X20] :
( ~ c_in(X9,c_Relation_OImage(X13,X20,X10,X5),X5)
| c_in(c_Pair(c_Main_OImageE__1(X20,X9,X13,X10,X5),X9,X10,X5),X13,tc_prod(X10,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f1641,axiom,
! [X10,X9,X5,X13,X20] :
( ~ c_in(X9,c_Relation_OImage(X13,X20,X10,X5),X5)
| c_in(c_Pair(c_Main_OImageE__1(X20,X9,X13,X10,X5),X9,X10,X5),X13,tc_prod(X10,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_1) ).
fof(f23606,plain,
spl0_2046,
inference(avatar_split_clause,[],[f1583,f23604]) ).
fof(f23604,plain,
( spl0_2046
<=> ! [X24,X10,X20,X5,X19] :
( ~ c_in(X19,c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OuprodE__1(X20,X24,X19,X5,X10),X20,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f1583,axiom,
! [X10,X19,X24,X5,X20] :
( ~ c_in(X19,c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OuprodE__1(X20,X24,X19,X5,X10),X20,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_2) ).
fof(f23602,plain,
spl0_2045,
inference(avatar_split_clause,[],[f1582,f23600]) ).
fof(f23600,plain,
( spl0_2045
<=> ! [X24,X10,X20,X5,X19] :
( ~ c_in(X19,c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OuprodE__2(X20,X24,X19,X5,X10),X24,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f1582,axiom,
! [X10,X19,X24,X5,X20] :
( ~ c_in(X19,c_Datatype__Universe_Ouprod(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Main_OuprodE__2(X20,X24,X19,X5,X10),X24,tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OuprodE_1) ).
fof(f23598,plain,
spl0_2044,
inference(avatar_split_clause,[],[f1226,f23596]) ).
fof(f23596,plain,
( spl0_2044
<=> ! [X10,X9,X13,X5,X8] :
( ~ c_in(c_Pair(X9,X8,X10,X5),X13,tc_prod(X10,X5))
| c_in(c_Pair(X8,X9,X5,X10),c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f1226,axiom,
! [X10,X8,X9,X5,X13] :
( ~ c_in(c_Pair(X9,X8,X10,X5),X13,tc_prod(X10,X5))
| c_in(c_Pair(X8,X9,X5,X10),c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_1) ).
fof(f23594,plain,
( ~ spl0_56
| ~ spl0_2043
| ~ spl0_835
| ~ spl0_1716 ),
inference(avatar_split_clause,[],[f20489,f16537,f7416,f23591,f3432]) ).
fof(f23591,plain,
( spl0_2043
<=> c_IntDef_Oiszero(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f7416,plain,
( spl0_835
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f20489,plain,
( ~ c_IntDef_Oiszero(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_835
| ~ spl0_1716 ),
inference(superposition,[],[f7417,f16539]) ).
fof(f7417,plain,
( ! [X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_835 ),
inference(avatar_component_clause,[],[f7416]) ).
fof(f23589,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1225,f23587]) ).
fof(f23587,plain,
( spl0_2042
<=> ! [X10,X9,X13,X5,X8] :
( c_in(c_Pair(X9,X8,X10,X5),X13,tc_prod(X10,X5))
| ~ c_in(c_Pair(X8,X9,X5,X10),c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f1225,axiom,
! [X10,X8,X9,X5,X13] :
( c_in(c_Pair(X9,X8,X10,X5),X13,tc_prod(X10,X5))
| ~ c_in(c_Pair(X8,X9,X5,X10),c_Relation_Oconverse(X13,X10,X5),tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__iff_0) ).
fof(f23585,plain,
spl0_2041,
inference(avatar_split_clause,[],[f1173,f23583]) ).
fof(f23583,plain,
( spl0_2041
<=> ! [X5,X28] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f1173,axiom,
! [X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f23581,plain,
spl0_2040,
inference(avatar_split_clause,[],[f1163,f23579]) ).
fof(f23579,plain,
( spl0_2040
<=> ! [X5,X28] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f1163,axiom,
! [X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f23577,plain,
spl0_2039,
inference(avatar_split_clause,[],[f718,f23575]) ).
fof(f23575,plain,
( spl0_2039
<=> ! [X29,X28] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X28,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f718,axiom,
! [X28,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X28,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f23573,plain,
spl0_2038,
inference(avatar_split_clause,[],[f669,f23571]) ).
fof(f23571,plain,
( spl0_2038
<=> ! [X29,X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f669,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f23569,plain,
spl0_2037,
inference(avatar_split_clause,[],[f114,f23567]) ).
fof(f23567,plain,
( spl0_2037
<=> ! [X20,X3,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Finite__Set_OMin(c_insert(X3,X20,X10),X10) = c_Orderings_Omin(X3,c_Finite__Set_OMin(X20,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f114,axiom,
! [X3,X10,X20] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Finite__Set_OMin(c_insert(X3,X20,X10),X10) = c_Orderings_Omin(X3,c_Finite__Set_OMin(X20,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__insert_0) ).
fof(f23565,plain,
spl0_2036,
inference(avatar_split_clause,[],[f112,f23563]) ).
fof(f23563,plain,
( spl0_2036
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X3,c_Finite__Set_OMin(X20,X5),X5)
| ~ c_less(X3,c_Main_OMin__gr__iff__1(X20,X3,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f112,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X3,c_Finite__Set_OMin(X20,X5),X5)
| ~ c_less(X3,c_Main_OMin__gr__iff__1(X20,X3,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f23561,plain,
spl0_2035,
inference(avatar_split_clause,[],[f111,f23559]) ).
fof(f23559,plain,
( spl0_2035
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X3,c_Finite__Set_OMin(X20,X5),X5)
| c_in(c_Main_OMin__gr__iff__1(X20,X3,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f111,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(X3,c_Finite__Set_OMin(X20,X5),X5)
| c_in(c_Main_OMin__gr__iff__1(X20,X3,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f23557,plain,
spl0_2034,
inference(avatar_split_clause,[],[f109,f23555]) ).
fof(f23555,plain,
( spl0_2034
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X3,c_Finite__Set_OMin(X20,X5),X5)
| ~ c_lessequals(X3,c_Main_OMin__ge__iff__1(X20,X3,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f109,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X3,c_Finite__Set_OMin(X20,X5),X5)
| ~ c_lessequals(X3,c_Main_OMin__ge__iff__1(X20,X3,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f23553,plain,
spl0_2033,
inference(avatar_split_clause,[],[f108,f23551]) ).
fof(f23551,plain,
( spl0_2033
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X3,c_Finite__Set_OMin(X20,X5),X5)
| c_in(c_Main_OMin__ge__iff__1(X20,X3,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).
fof(f108,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X3,c_Finite__Set_OMin(X20,X5),X5)
| c_in(c_Main_OMin__ge__iff__1(X20,X3,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f23549,plain,
( spl0_2032
| ~ spl0_1037
| ~ spl0_1620
| ~ spl0_1701 ),
inference(avatar_split_clause,[],[f17348,f16205,f15542,f8423,f23547]) ).
fof(f23547,plain,
( spl0_2032
<=> ! [X2,X0,X1] :
( c_emptyset != X2
| ~ c_in(X0,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f8423,plain,
( spl0_1037
<=> ! [X5,X1] : c_Relation_OImage(c_Relation_Odiag(X1,X5),c_UNIV,X5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f16205,plain,
( spl0_1701
<=> ! [X24,X9,X20,X5] :
( ~ c_in(X9,X20,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f17348,plain,
( ! [X2,X0,X1] :
( c_emptyset != X2
| ~ c_in(X0,X2,X1) )
| ~ spl0_1037
| ~ spl0_1620
| ~ spl0_1701 ),
inference(forward_demodulation,[],[f17339,f8424]) ).
fof(f8424,plain,
( ! [X1,X5] : c_Relation_OImage(c_Relation_Odiag(X1,X5),c_UNIV,X5,X5) = X1
| ~ spl0_1037 ),
inference(avatar_component_clause,[],[f8423]) ).
fof(f17339,plain,
( ! [X2,X0,X1] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X2,X1),c_UNIV,X1,X1)
| ~ c_in(X0,X2,X1) )
| ~ spl0_1620
| ~ spl0_1701 ),
inference(superposition,[],[f16206,f15543]) ).
fof(f16206,plain,
( ! [X9,X24,X5,X20] :
( c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5)
| ~ c_in(X9,X20,X5) )
| ~ spl0_1701 ),
inference(avatar_component_clause,[],[f16205]) ).
fof(f23545,plain,
spl0_2031,
inference(avatar_split_clause,[],[f105,f23543]) ).
fof(f23543,plain,
( spl0_2031
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X20,X5),X3,X5)
| ~ c_less(c_Main_OMax__less__iff__1(X20,X3,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f105,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X20,X5),X3,X5)
| ~ c_less(c_Main_OMax__less__iff__1(X20,X3,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_2) ).
fof(f23541,plain,
spl0_2030,
inference(avatar_split_clause,[],[f104,f23539]) ).
fof(f23539,plain,
( spl0_2030
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X20,X5),X3,X5)
| c_in(c_Main_OMax__less__iff__1(X20,X3,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f104,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_less(c_Finite__Set_OMax(X20,X5),X3,X5)
| c_in(c_Main_OMax__less__iff__1(X20,X3,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__less__iff_1) ).
fof(f23537,plain,
spl0_2029,
inference(avatar_split_clause,[],[f102,f23535]) ).
fof(f23535,plain,
( spl0_2029
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X20,X5),X3,X5)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X20,X3,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f102,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X20,X5),X3,X5)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X20,X3,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_2) ).
fof(f23533,plain,
spl0_2028,
inference(avatar_split_clause,[],[f101,f23531]) ).
fof(f23531,plain,
( spl0_2028
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X20,X5),X3,X5)
| c_in(c_Main_OMax__le__iff__1(X20,X3,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f101,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMax(X20,X5),X3,X5)
| c_in(c_Main_OMax__le__iff__1(X20,X3,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__le__iff_1) ).
fof(f23529,plain,
spl0_2027,
inference(avatar_split_clause,[],[f99,f23527]) ).
fof(f23527,plain,
( spl0_2027
<=> ! [X20,X3,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Finite__Set_OMax(c_insert(X3,X20,X10),X10) = c_Orderings_Omax(X3,c_Finite__Set_OMax(X20,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f99,axiom,
! [X3,X10,X20] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Finite__Set_OMax(c_insert(X3,X20,X10),X10) = c_Orderings_Omax(X3,c_Finite__Set_OMax(X20,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__insert_0) ).
fof(f23405,plain,
( spl0_2026
| ~ spl0_1046
| ~ spl0_1522 ),
inference(avatar_split_clause,[],[f14011,f13136,f8493,f23403]) ).
fof(f23403,plain,
( spl0_2026
<=> ! [X0] : c_in(X0,c_List_Olists(c_IntDef_ONats,tc_nat),tc_List_Olist(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f8493,plain,
( spl0_1046
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f13136,plain,
( spl0_1522
<=> ! [X34,X20,X5] :
( ~ c_in(c_Main_Oin__listsI__1(X20,X34,X5),X20,X5)
| c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f14011,plain,
( ! [X0] : c_in(X0,c_List_Olists(c_IntDef_ONats,tc_nat),tc_List_Olist(tc_nat))
| ~ spl0_1046
| ~ spl0_1522 ),
inference(resolution,[],[f13137,f8494]) ).
fof(f8494,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1046 ),
inference(avatar_component_clause,[],[f8493]) ).
fof(f13137,plain,
( ! [X34,X5,X20] :
( ~ c_in(c_Main_Oin__listsI__1(X20,X34,X5),X20,X5)
| c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5)) )
| ~ spl0_1522 ),
inference(avatar_component_clause,[],[f13136]) ).
fof(f22954,plain,
( spl0_2025
| ~ spl0_44
| ~ spl0_732
| ~ spl0_1189 ),
inference(avatar_split_clause,[],[f9818,f9435,f6996,f3372,f22951]) ).
fof(f22951,plain,
( spl0_2025
<=> c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f3372,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f6996,plain,
( spl0_732
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f9435,plain,
( spl0_1189
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X1,X5)
| c_OrderedGroup_Opprt(X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f9818,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_1 = c_OrderedGroup_Opprt(c_1,tc_IntDef_Oint)
| ~ spl0_732
| ~ spl0_1189 ),
inference(resolution,[],[f9436,f6998]) ).
fof(f6998,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_732 ),
inference(avatar_component_clause,[],[f6996]) ).
fof(f9436,plain,
( ! [X1,X5] :
( ~ c_lessequals(c_0,X1,X5)
| ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_OrderedGroup_Opprt(X1,X5) = X1 )
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9435]) ).
fof(f22815,plain,
spl0_2024,
inference(avatar_split_clause,[],[f2932,f22813]) ).
fof(f22813,plain,
( spl0_2024
<=> ! [X29,X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f2932,plain,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f697,f970]) ).
fof(f697,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_1) ).
fof(f22811,plain,
spl0_2023,
inference(avatar_split_clause,[],[f2931,f22809]) ).
fof(f22809,plain,
( spl0_2023
<=> ! [X29,X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f2931,plain,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f698,f970]) ).
fof(f698,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X70)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_2) ).
fof(f22807,plain,
spl0_2022,
inference(avatar_split_clause,[],[f2904,f22805]) ).
fof(f22805,plain,
( spl0_2022
<=> ! [X2,X17,X18] :
( ~ c_lessequals(c_plus(X17,X18,tc_nat),X2,tc_nat)
| c_List_Oupt(X17,c_plus(X17,X18,tc_nat)) = c_List_Osublist(c_List_Oupt(X17,X2),c_SetInterval_OlessThan(X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f2904,plain,
! [X2,X18,X17] :
( ~ c_lessequals(c_plus(X17,X18,tc_nat),X2,tc_nat)
| c_List_Oupt(X17,c_plus(X17,X18,tc_nat)) = c_List_Osublist(c_List_Oupt(X17,X2),c_SetInterval_OlessThan(X18,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f618,f607]) ).
fof(f618,axiom,
! [X2,X18,X17] :
( ~ c_lessequals(c_plus(X17,X18,tc_nat),X2,tc_nat)
| c_List_Otake(X18,c_List_Oupt(X17,X2),tc_nat) = c_List_Oupt(X17,c_plus(X17,X18,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__upt_0) ).
fof(f22803,plain,
spl0_2021,
inference(avatar_split_clause,[],[f2794,f22801]) ).
fof(f22801,plain,
( spl0_2021
<=> ! [X5,X72] : c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f2794,plain,
! [X72,X5] : c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5) = c_Transitive__Closure_Otrancl(c_union(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1553,f1557,f1557]) ).
fof(f1553,axiom,
! [X72,X5] : c_Transitive__Closure_Ortrancl(X72,X5) = c_Transitive__Closure_Ortrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f22799,plain,
spl0_2020,
inference(avatar_split_clause,[],[f1689,f22797]) ).
fof(f22797,plain,
( spl0_2020
<=> ! [X5,X13,X9,X8] :
( ~ c_in(c_Pair(X8,X9,X5,X5),X13,tc_prod(X5,X5))
| c_in(c_Pair(X8,X9,X5,X5),c_Transitive__Closure_Otrancl(X13,X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f1689,axiom,
! [X8,X9,X5,X13] :
( ~ c_in(c_Pair(X8,X9,X5,X5),X13,tc_prod(X5,X5))
| c_in(c_Pair(X8,X9,X5,X5),c_Transitive__Closure_Otrancl(X13,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f22795,plain,
spl0_2019,
inference(avatar_split_clause,[],[f1642,f22793]) ).
fof(f22793,plain,
( spl0_2019
<=> ! [X10,X9,X20,X13,X5,X8] :
( ~ c_in(X8,X20,X5)
| c_in(X9,c_Relation_OImage(X13,X20,X5,X10),X10)
| ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f1642,axiom,
! [X10,X8,X9,X5,X13,X20] :
( ~ c_in(X8,X20,X5)
| c_in(X9,c_Relation_OImage(X13,X20,X5,X10),X10)
| ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageI_0) ).
fof(f22788,plain,
spl0_2018,
inference(avatar_split_clause,[],[f1403,f22786]) ).
fof(f22786,plain,
( spl0_2018
<=> ! [X17,X18,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X17,X2,X5)
| c_minus(c_SetInterval_OatLeastLessThan(X17,X18,X5),c_SetInterval_OatLeastLessThan(X17,X2,X5),tc_set(X5)) = c_SetInterval_OatLeastLessThan(X2,X18,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f1403,axiom,
! [X2,X18,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X17,X2,X5)
| c_minus(c_SetInterval_OatLeastLessThan(X17,X18,X5),c_SetInterval_OatLeastLessThan(X17,X2,X5),tc_set(X5)) = c_SetInterval_OatLeastLessThan(X2,X18,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__diff_0) ).
fof(f22784,plain,
spl0_2017,
inference(avatar_split_clause,[],[f1197,f22782]) ).
fof(f22782,plain,
( spl0_2017
<=> ! [X5,X3,X9,X1] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X3,X1,tc_nat)
| ~ c_less(c_1,X9,X5)
| c_less(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f1197,axiom,
! [X3,X1,X9,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X3,X1,tc_nat)
| ~ c_less(c_1,X9,X5)
| c_less(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f22780,plain,
spl0_2016,
inference(avatar_split_clause,[],[f1196,f22778]) ).
fof(f22778,plain,
( spl0_2016
<=> ! [X5,X3,X9,X1] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X9,X5)
| c_less(X3,X1,tc_nat)
| ~ c_less(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f1196,axiom,
! [X3,X1,X9,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X9,X5)
| c_less(X3,X1,tc_nat)
| ~ c_less(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f22776,plain,
spl0_2015,
inference(avatar_split_clause,[],[f1192,f22774]) ).
fof(f22774,plain,
( spl0_2015
<=> ! [X5,X3,X9,X1] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_less(c_1,X9,X5)
| c_lessequals(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f1192,axiom,
! [X3,X1,X9,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X3,X1,tc_nat)
| ~ c_less(c_1,X9,X5)
| c_lessequals(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_1) ).
fof(f22772,plain,
spl0_2014,
inference(avatar_split_clause,[],[f1191,f22770]) ).
fof(f22770,plain,
( spl0_2014
<=> ! [X5,X3,X9,X1] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X9,X5)
| c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f1191,axiom,
! [X3,X1,X9,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,X9,X5)
| c_lessequals(X3,X1,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X9,X3,X5),c_Nat_Opower(X9,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__increasing__iff_0) ).
fof(f22768,plain,
spl0_2013,
inference(avatar_split_clause,[],[f1177,f22766]) ).
fof(f22766,plain,
( spl0_2013
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X3,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f1177,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X3,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f22764,plain,
spl0_2012,
inference(avatar_split_clause,[],[f1174,f22762]) ).
fof(f22762,plain,
( spl0_2012
<=> ! [X5,X28] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f1174,axiom,
! [X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_0,X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f22760,plain,
spl0_2011,
inference(avatar_split_clause,[],[f1171,f22758]) ).
fof(f22758,plain,
( spl0_2011
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X3,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f1171,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X3,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f22756,plain,
spl0_2010,
inference(avatar_split_clause,[],[f1169,f22754]) ).
fof(f22754,plain,
( spl0_2010
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X3,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f1169,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X3,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f22752,plain,
spl0_2009,
inference(avatar_split_clause,[],[f1166,f22750]) ).
fof(f22750,plain,
( spl0_2009
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X3,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f1166,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X3,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f22748,plain,
( spl0_2008
| ~ spl0_44
| ~ spl0_732
| ~ spl0_1186 ),
inference(avatar_split_clause,[],[f9767,f9423,f6996,f3372,f22745]) ).
fof(f22745,plain,
( spl0_2008
<=> c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f9423,plain,
( spl0_1186
<=> ! [X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X3,X5)
| c_0 = c_OrderedGroup_Onprt(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f9767,plain,
( ~ class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| c_0 = c_OrderedGroup_Onprt(c_1,tc_IntDef_Oint)
| ~ spl0_732
| ~ spl0_1186 ),
inference(resolution,[],[f9424,f6998]) ).
fof(f9424,plain,
( ! [X3,X5] :
( ~ c_lessequals(c_0,X3,X5)
| ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(X3,X5) )
| ~ spl0_1186 ),
inference(avatar_component_clause,[],[f9423]) ).
fof(f22743,plain,
spl0_2007,
inference(avatar_split_clause,[],[f1160,f22741]) ).
fof(f22741,plain,
( spl0_2007
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X3,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f1160,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X3,c_0,X5)
| c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f22739,plain,
spl0_2006,
inference(avatar_split_clause,[],[f1009,f22737]) ).
fof(f22737,plain,
( spl0_2006
<=> ! [X5,X29,X28,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X29,X5),c_times(c_Numeral_Onumber__of(X28,X5),X30,X5),X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X29,X28),X5),X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f1009,axiom,
! [X28,X29,X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X29,X5),c_times(c_Numeral_Onumber__of(X28,X5),X30,X5),X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X29,X28),X5),X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__number__of__left_0) ).
fof(f22735,plain,
spl0_2005,
inference(avatar_split_clause,[],[f949,f22733]) ).
fof(f22733,plain,
( spl0_2005
<=> ! [X5,X29,X28,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X29,X5),c_plus(c_Numeral_Onumber__of(X28,X5),X30,X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,X28),X5),X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f949,axiom,
! [X28,X29,X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X29,X5),c_plus(c_Numeral_Onumber__of(X28,X5),X30,X5),X5) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,X28),X5),X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Oadd__number__of__left_0) ).
fof(f22731,plain,
spl0_2004,
inference(avatar_split_clause,[],[f702,f22729]) ).
fof(f22729,plain,
( spl0_2004
<=> ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f702,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_1) ).
fof(f22727,plain,
spl0_2003,
inference(avatar_split_clause,[],[f676,f22725]) ).
fof(f22725,plain,
( spl0_2003
<=> ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) != c_Numeral_Onumber__of(X70,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f676,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) != c_Numeral_Onumber__of(X70,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_1) ).
fof(f22723,plain,
spl0_2002,
inference(avatar_split_clause,[],[f666,f22721]) ).
fof(f22721,plain,
( spl0_2002
<=> ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_plus(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f666,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_plus(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f22719,plain,
spl0_2001,
inference(avatar_split_clause,[],[f476,f22717]) ).
fof(f22717,plain,
( spl0_2001
<=> ! [X17,X34,X3,X5,X1] :
( ~ c_less(X17,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X34,X17,X3,X5),X17,X1,X5) = c_List_Olist__update(X34,X17,X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f476,axiom,
! [X3,X1,X17,X34,X5] :
( ~ c_less(X17,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X34,X17,X3,X5),X17,X1,X5) = c_List_Olist__update(X34,X17,X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__overwrite_0) ).
fof(f22715,plain,
spl0_2000,
inference(avatar_split_clause,[],[f475,f22713]) ).
fof(f22713,plain,
( spl0_2000
<=> ! [X35,X34,X3,X5,X1] : c_List_Olist__update(c_append(X34,c_List_Olist_OCons(X3,X35,X5),X5),c_Nat_Osize(X34,tc_List_Olist(X5)),X1,X5) = c_append(X34,c_List_Olist_OCons(X1,X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f475,axiom,
! [X3,X1,X34,X35,X5] : c_List_Olist__update(c_append(X34,c_List_Olist_OCons(X3,X35,X5),X5),c_Nat_Osize(X34,tc_List_Olist(X5)),X1,X5) = c_append(X34,c_List_Olist_OCons(X1,X35,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__length_0) ).
fof(f22711,plain,
spl0_1999,
inference(avatar_split_clause,[],[f196,f22709]) ).
fof(f22709,plain,
( spl0_1999
<=> ! [X1,X3] :
( X1 = X3
| c_IntDef_OAbs__Integ(X3) != c_IntDef_OAbs__Integ(X1)
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f196,axiom,
! [X3,X1] :
( X1 = X3
| c_IntDef_OAbs__Integ(X3) != c_IntDef_OAbs__Integ(X1)
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
fof(f22707,plain,
spl0_1998,
inference(avatar_split_clause,[],[f135,f22705]) ).
fof(f22705,plain,
( spl0_1998
<=> ! [X20,X1,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X1,X20,X10)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Orderings_Omax(X1,c_Finite__Set_OMin(X20,X10),X10) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f135,axiom,
! [X10,X1,X20] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X1,X20,X10)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Orderings_Omax(X1,c_Finite__Set_OMin(X20,X10),X10) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f22703,plain,
( spl0_1997
| ~ spl0_872
| ~ spl0_977 ),
inference(avatar_split_clause,[],[f8527,f8180,f7612,f22701]) ).
fof(f22701,plain,
( spl0_1997
<=> ! [X0] : c_lessequals(c_0,c_Nat_Opower(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f7612,plain,
( spl0_872
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f8180,plain,
( spl0_977
<=> ! [X2,X3] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f8527,plain,
( ! [X0] : c_lessequals(c_0,c_Nat_Opower(c_0,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_872
| ~ spl0_977 ),
inference(superposition,[],[f8181,f7614]) ).
fof(f7614,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_872 ),
inference(avatar_component_clause,[],[f7612]) ).
fof(f8181,plain,
( ! [X2,X3] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_977 ),
inference(avatar_component_clause,[],[f8180]) ).
fof(f22699,plain,
spl0_1996,
inference(avatar_split_clause,[],[f134,f22697]) ).
fof(f22697,plain,
( spl0_1996
<=> ! [X20,X1,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X1,X20,X10)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Orderings_Omin(X1,c_Finite__Set_OMax(X20,X10),X10) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f134,axiom,
! [X10,X1,X20] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X1,X20,X10)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_Orderings_Omin(X1,c_Finite__Set_OMax(X20,X10),X10) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f22695,plain,
spl0_1995,
inference(avatar_split_clause,[],[f63,f22693]) ).
fof(f22693,plain,
( spl0_1995
<=> ! [X2,X0,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_plus(X0,c_div(X18,X2,tc_nat),tc_nat) = c_div(c_plus(X18,c_times(X2,X0,tc_nat),tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f63,axiom,
! [X2,X0,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_plus(X0,c_div(X18,X2,tc_nat),tc_nat) = c_div(c_plus(X18,c_times(X2,X0,tc_nat),tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self2_0) ).
fof(f22691,plain,
spl0_1994,
inference(avatar_split_clause,[],[f61,f22689]) ).
fof(f22689,plain,
( spl0_1994
<=> ! [X2,X0,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_div(c_plus(X18,c_times(X0,X2,tc_nat),tc_nat),X2,tc_nat) = c_plus(X0,c_div(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f61,axiom,
! [X2,X0,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_div(c_plus(X18,c_times(X0,X2,tc_nat),tc_nat),X2,tc_nat) = c_plus(X0,c_div(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1_0) ).
fof(f22254,plain,
( spl0_98
| ~ spl0_1993
| ~ spl0_871
| ~ spl0_968 ),
inference(avatar_split_clause,[],[f8478,f8143,f7602,f22251,f3642]) ).
fof(f3642,plain,
( spl0_98
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f22251,plain,
( spl0_1993
<=> c_less(c_1,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f7602,plain,
( spl0_871
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f8143,plain,
( spl0_968
<=> ! [X30] :
( c_0 = X30
| ~ c_less(c_HOL_Oabs(X30,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f8478,plain,
( ~ c_less(c_1,c_1,tc_IntDef_Oint)
| c_0 = c_1
| ~ spl0_871
| ~ spl0_968 ),
inference(superposition,[],[f8144,f7604]) ).
fof(f7604,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_871 ),
inference(avatar_component_clause,[],[f7602]) ).
fof(f8144,plain,
( ! [X30] :
( ~ c_less(c_HOL_Oabs(X30,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| c_0 = X30 )
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8143]) ).
fof(f22066,plain,
( spl0_1992
| ~ spl0_127
| ~ spl0_1772 ),
inference(avatar_split_clause,[],[f18567,f17629,f3771,f22064]) ).
fof(f22064,plain,
( spl0_1992
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f17629,plain,
( spl0_1772
<=> ! [X5,X10,X13,X9,X8] :
( c_in(X9,c_Relation_ORange(X13,X5,X10),X10)
| ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f18567,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ORange(c_UNIV,X1,X2),X2)
| ~ spl0_127
| ~ spl0_1772 ),
inference(resolution,[],[f17630,f3772]) ).
fof(f17630,plain,
( ! [X10,X8,X9,X5,X13] :
( ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10))
| c_in(X9,c_Relation_ORange(X13,X5,X10),X10) )
| ~ spl0_1772 ),
inference(avatar_component_clause,[],[f17629]) ).
fof(f22062,plain,
( spl0_1991
| ~ spl0_127
| ~ spl0_1769 ),
inference(avatar_split_clause,[],[f18505,f17617,f3771,f22060]) ).
fof(f22060,plain,
( spl0_1991
<=> ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f17617,plain,
( spl0_1769
<=> ! [X10,X9,X13,X5,X8] :
( c_in(X8,c_Relation_ODomain(X13,X5,X10),X5)
| ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f18505,plain,
( ! [X2,X0,X1] : c_in(X0,c_Relation_ODomain(c_UNIV,X1,X2),X1)
| ~ spl0_127
| ~ spl0_1769 ),
inference(resolution,[],[f17618,f3772]) ).
fof(f17618,plain,
( ! [X10,X8,X9,X5,X13] :
( ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10))
| c_in(X8,c_Relation_ODomain(X13,X5,X10),X5) )
| ~ spl0_1769 ),
inference(avatar_component_clause,[],[f17617]) ).
fof(f21825,plain,
( spl0_1990
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_1989 ),
inference(avatar_split_clause,[],[f21821,f21817,f19017,f7180,f7144,f21823]) ).
fof(f21823,plain,
( spl0_1990
<=> ! [X18] :
( c_1 = c_Divides_Oop_Amod(X18,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f21817,plain,
( spl0_1989
<=> ! [X18] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X18,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_1989])]) ).
fof(f21821,plain,
( ! [X18] :
( c_1 = c_Divides_Oop_Amod(X18,c_plus(c_1,c_1,tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat) )
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_1989 ),
inference(forward_demodulation,[],[f21820,f19100]) ).
fof(f21820,plain,
( ! [X18] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_plus(c_1,c_1,tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_768
| ~ spl0_777
| ~ spl0_1852
| ~ spl0_1989 ),
inference(forward_demodulation,[],[f21818,f19100]) ).
fof(f21818,plain,
( ! [X18] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_1989 ),
inference(avatar_component_clause,[],[f21817]) ).
fof(f21819,plain,
spl0_1989,
inference(avatar_split_clause,[],[f3098,f21817]) ).
fof(f3098,plain,
! [X18] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3097,f997]) ).
fof(f3097,plain,
! [X18] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3096,f995]) ).
fof(f3096,plain,
! [X18] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3095,f997]) ).
fof(f3095,plain,
! [X18] :
( c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3094,f997]) ).
fof(f3094,plain,
! [X18] :
( c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f3093,f995]) ).
fof(f3093,plain,
! [X18] :
( c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f816,f997]) ).
fof(f816,axiom,
! [X18] :
( c_1 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Omod2__gr__0_0) ).
fof(f21792,plain,
( spl0_1988
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1987 ),
inference(avatar_split_clause,[],[f21788,f21785,f10406,f10097,f6714,f3706,f21790]) ).
fof(f21790,plain,
( spl0_1988
<=> ! [X18,X0,X2] : c_minus(X18,c_plus(X2,X0,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X2,X18,tc_nat),tc_nat),c_plus(c_1,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f21785,plain,
( spl0_1987
<=> ! [X2,X0,X18] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X2,X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = c_minus(X18,c_plus(X2,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f21788,plain,
( ! [X2,X0,X18] : c_minus(X18,c_plus(X2,X0,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X2,X18,tc_nat),tc_nat),c_plus(c_1,X0,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1987 ),
inference(forward_demodulation,[],[f21786,f11227]) ).
fof(f21786,plain,
( ! [X2,X0,X18] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X2,X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = c_minus(X18,c_plus(X2,X0,tc_nat),tc_nat)
| ~ spl0_1987 ),
inference(avatar_component_clause,[],[f21785]) ).
fof(f21787,plain,
spl0_1987,
inference(avatar_split_clause,[],[f3004,f21785]) ).
fof(f3004,plain,
! [X2,X0,X18] : c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X2,X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) = c_minus(X18,c_plus(X2,X0,tc_nat),tc_nat),
inference(forward_demodulation,[],[f3003,f878]) ).
fof(f878,axiom,
! [X0,X45,X17] : c_minus(c_minus(X17,X45,tc_nat),X0,tc_nat) = c_minus(X17,c_plus(X45,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__left_0) ).
fof(f3003,plain,
! [X2,X0,X18] : c_minus(c_minus(X18,X2,tc_nat),X0,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X2,X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2828,f2797]) ).
fof(f2828,plain,
! [X2,X0,X18] : c_minus(c_minus(X18,X2,tc_nat),X0,tc_nat) = c_minus(c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f859,f1385,f1385]) ).
fof(f859,axiom,
! [X2,X0,X18] : c_minus(c_minus(c_Suc(X18),X2,tc_nat),c_Suc(X0),tc_nat) = c_minus(c_minus(X18,X2,tc_nat),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__diff__diff_0) ).
fof(f21783,plain,
spl0_1986,
inference(avatar_split_clause,[],[f2953,f21781]) ).
fof(f21781,plain,
( spl0_1986
<=> ! [X5,X1,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f2953,plain,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ),
inference(definition_unfolding,[],[f981,f970]) ).
fof(f981,axiom,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X5),X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f21779,plain,
spl0_1985,
inference(avatar_split_clause,[],[f2952,f21777]) ).
fof(f21777,plain,
( spl0_1985
<=> ! [X5,X1,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f2952,plain,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f989,f970]) ).
fof(f989,axiom,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f21775,plain,
spl0_1984,
inference(avatar_split_clause,[],[f2951,f21773]) ).
fof(f21773,plain,
( spl0_1984
<=> ! [X5,X1,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f2951,plain,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ),
inference(definition_unfolding,[],[f990,f970]) ).
fof(f990,axiom,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X5),X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f21771,plain,
spl0_1983,
inference(avatar_split_clause,[],[f2950,f21769]) ).
fof(f21769,plain,
( spl0_1983
<=> ! [X5,X1,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f2950,plain,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ),
inference(definition_unfolding,[],[f980,f970]) ).
fof(f980,axiom,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(X3)),X5),X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_Numeral_Onumber__of(X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f21731,plain,
spl0_1982,
inference(avatar_split_clause,[],[f2930,f21729]) ).
fof(f21729,plain,
( spl0_1982
<=> ! [X24,X20,X5,X73] :
( ~ c_lessequals(X73,X24,tc_set(X5))
| ~ c_lessequals(X73,X20,tc_set(X5))
| c_lessequals(X73,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f2930,plain,
! [X73,X24,X5,X20] :
( ~ c_lessequals(X73,X24,tc_set(X5))
| ~ c_lessequals(X73,X20,tc_set(X5))
| c_lessequals(X73,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ),
inference(definition_unfolding,[],[f1452,f1214]) ).
fof(f1452,axiom,
! [X73,X24,X5,X20] :
( ~ c_lessequals(X73,X24,tc_set(X5))
| ~ c_lessequals(X73,X20,tc_set(X5))
| c_lessequals(X73,c_inter(X20,X24,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_2) ).
fof(f21727,plain,
spl0_1981,
inference(avatar_split_clause,[],[f2901,f21725]) ).
fof(f21725,plain,
( spl0_1981
<=> ! [X20,X5,X24,X8] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),X24,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f2901,plain,
! [X8,X24,X5,X20] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),X24,X5,X5) ),
inference(definition_unfolding,[],[f1519,f1214,f1214]) ).
fof(f1519,axiom,
! [X8,X24,X5,X20] :
( c_emptyset = c_inter(X20,X24,X5)
| c_emptyset != c_inter(c_insert(X8,X20,X5),X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__1_1) ).
fof(f21723,plain,
spl0_1980,
inference(avatar_split_clause,[],[f2899,f21721]) ).
fof(f21721,plain,
( spl0_1980
<=> ! [X24,X9,X20,X5] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f2899,plain,
! [X9,X24,X5,X20] :
( c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5) ),
inference(definition_unfolding,[],[f1506,f1214,f1214]) ).
fof(f1506,axiom,
! [X9,X24,X5,X20] :
( c_emptyset = c_inter(X20,X24,X5)
| c_emptyset != c_inter(X20,c_insert(X9,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_1) ).
fof(f21662,plain,
( spl0_1979
| ~ spl0_112
| ~ spl0_670
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1690
| ~ spl0_1978 ),
inference(avatar_split_clause,[],[f21658,f21654,f16107,f10406,f10097,f7144,f7120,f6714,f3706,f21660]) ).
fof(f21660,plain,
( spl0_1979
<=> ! [X45,X17] :
( c_List_Oupt(X17,c_plus(c_1,X45,tc_nat)) = c_append(c_List_Oupt(X17,X45),c_List_Oreplicate(c_1,X45,tc_nat),tc_nat)
| ~ c_lessequals(X17,X45,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f7120,plain,
( spl0_762
<=> ! [X6,X3] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X3,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f16107,plain,
( spl0_1690
<=> ! [X6,X2,X3] : c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6) = c_List_Oreplicate(c_plus(c_1,X2,tc_nat),X3,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f21654,plain,
( spl0_1978
<=> ! [X45,X17] :
( ~ c_lessequals(X17,X45,tc_nat)
| c_append(c_List_Oupt(X17,X45),c_List_Olist_OCons(X45,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X17,c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f21658,plain,
( ! [X45,X17] :
( c_List_Oupt(X17,c_plus(c_1,X45,tc_nat)) = c_append(c_List_Oupt(X17,X45),c_List_Oreplicate(c_1,X45,tc_nat),tc_nat)
| ~ c_lessequals(X17,X45,tc_nat) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1690
| ~ spl0_1978 ),
inference(forward_demodulation,[],[f21657,f16133]) ).
fof(f16133,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690 ),
inference(forward_demodulation,[],[f16110,f7145]) ).
fof(f16110,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_762
| ~ spl0_1690 ),
inference(superposition,[],[f16108,f7121]) ).
fof(f7121,plain,
( ! [X3,X6] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X3,X6)
| ~ spl0_762 ),
inference(avatar_component_clause,[],[f7120]) ).
fof(f16108,plain,
( ! [X2,X3,X6] : c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6) = c_List_Oreplicate(c_plus(c_1,X2,tc_nat),X3,X6)
| ~ spl0_1690 ),
inference(avatar_component_clause,[],[f16107]) ).
fof(f21657,plain,
( ! [X45,X17] :
( c_append(c_List_Oupt(X17,X45),c_List_Olist_OCons(X45,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X17,c_plus(c_1,X45,tc_nat))
| ~ c_lessequals(X17,X45,tc_nat) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1978 ),
inference(forward_demodulation,[],[f21655,f11227]) ).
fof(f21655,plain,
( ! [X45,X17] :
( ~ c_lessequals(X17,X45,tc_nat)
| c_append(c_List_Oupt(X17,X45),c_List_Olist_OCons(X45,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X17,c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat)) )
| ~ spl0_1978 ),
inference(avatar_component_clause,[],[f21654]) ).
fof(f21656,plain,
spl0_1978,
inference(avatar_split_clause,[],[f2866,f21654]) ).
fof(f2866,plain,
! [X45,X17] :
( ~ c_lessequals(X17,X45,tc_nat)
| c_append(c_List_Oupt(X17,X45),c_List_Olist_OCons(X45,c_List_Olist_ONil,tc_nat),tc_nat) = c_List_Oupt(X17,c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f623,f1385]) ).
fof(f623,axiom,
! [X45,X17] :
( ~ c_lessequals(X17,X45,tc_nat)
| c_List_Oupt(X17,c_Suc(X45)) = c_append(c_List_Oupt(X17,X45),c_List_Olist_OCons(X45,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_0) ).
fof(f21652,plain,
spl0_1977,
inference(avatar_split_clause,[],[f2830,f21650]) ).
fof(f21650,plain,
( spl0_1977
<=> ! [X20,X5,X24] : c_union(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),X5) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f2830,plain,
! [X24,X5,X20] : c_union(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),X5) = c_uminus(c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)),
inference(definition_unfolding,[],[f1416,f1214]) ).
fof(f1416,axiom,
! [X24,X5,X20] : c_uminus(c_inter(X20,X24,X5),tc_set(X5)) = c_union(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Int_0) ).
fof(f21648,plain,
spl0_1976,
inference(avatar_split_clause,[],[f2829,f21646]) ).
fof(f21646,plain,
( spl0_1976
<=> ! [X20,X5,X24] : c_uminus(c_union(X20,X24,X5),tc_set(X5)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X20,tc_set(X5)),X5),c_uminus(X24,tc_set(X5)),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f2829,plain,
! [X24,X5,X20] : c_uminus(c_union(X20,X24,X5),tc_set(X5)) = c_Relation_OImage(c_Relation_Odiag(c_uminus(X20,tc_set(X5)),X5),c_uminus(X24,tc_set(X5)),X5,X5),
inference(definition_unfolding,[],[f1418,f1214]) ).
fof(f1418,axiom,
! [X24,X5,X20] : c_uminus(c_union(X20,X24,X5),tc_set(X5)) = c_inter(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Un_0) ).
fof(f21644,plain,
spl0_1975,
inference(avatar_split_clause,[],[f2823,f21642]) ).
fof(f21642,plain,
( spl0_1975
<=> ! [X18,X34,X5,X2] : c_List_Osublist(c_List_Osublist(X34,c_SetInterval_OlessThan(X18,tc_nat),X5),c_SetInterval_OlessThan(X2,tc_nat),X5) = c_List_Osublist(X34,c_SetInterval_OlessThan(c_Orderings_Omin(X2,X18,tc_nat),tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f2823,plain,
! [X2,X18,X34,X5] : c_List_Osublist(c_List_Osublist(X34,c_SetInterval_OlessThan(X18,tc_nat),X5),c_SetInterval_OlessThan(X2,tc_nat),X5) = c_List_Osublist(X34,c_SetInterval_OlessThan(c_Orderings_Omin(X2,X18,tc_nat),tc_nat),X5),
inference(definition_unfolding,[],[f617,f607,f607,f607]) ).
fof(f617,axiom,
! [X2,X18,X34,X5] : c_List_Otake(X2,c_List_Otake(X18,X34,X5),X5) = c_List_Otake(c_Orderings_Omin(X2,X18,tc_nat),X34,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__take_0) ).
fof(f21621,plain,
( spl0_1974
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1973 ),
inference(avatar_split_clause,[],[f21617,f21612,f10406,f10097,f6714,f3706,f21619]) ).
fof(f21619,plain,
( spl0_1974
<=> ! [X2,X18] : c_plus(c_1,c_Orderings_Omin(X18,X2,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X18,tc_nat),c_plus(c_1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f21612,plain,
( spl0_1973
<=> ! [X2,X18] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X18,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f21617,plain,
( ! [X2,X18] : c_plus(c_1,c_Orderings_Omin(X18,X2,tc_nat),tc_nat) = c_Orderings_Omin(c_plus(c_1,X18,tc_nat),c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1973 ),
inference(forward_demodulation,[],[f21616,f11227]) ).
fof(f21616,plain,
( ! [X2,X18] : c_plus(c_1,c_Orderings_Omin(X18,X2,tc_nat),tc_nat) = c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1973 ),
inference(forward_demodulation,[],[f21615,f11227]) ).
fof(f21615,plain,
( ! [X2,X18] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omin(X18,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1973 ),
inference(forward_demodulation,[],[f21613,f11227]) ).
fof(f21613,plain,
( ! [X2,X18] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X18,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_1973 ),
inference(avatar_component_clause,[],[f21612]) ).
fof(f21614,plain,
spl0_1973,
inference(avatar_split_clause,[],[f2799,f21612]) ).
fof(f2799,plain,
! [X2,X18] : c_Orderings_Omin(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omin(X18,X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f896,f1385,f1385,f1385]) ).
fof(f896,axiom,
! [X2,X18] : c_Orderings_Omin(c_Suc(X18),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omin(X18,X2,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__Suc__Suc_0) ).
fof(f21594,plain,
( spl0_1972
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1971 ),
inference(avatar_split_clause,[],[f21590,f21585,f10406,f10097,f6714,f3706,f21592]) ).
fof(f21592,plain,
( spl0_1972
<=> ! [X2,X18] : c_plus(c_1,c_Orderings_Omax(X18,X2,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X18,tc_nat),c_plus(c_1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f21585,plain,
( spl0_1971
<=> ! [X2,X18] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X18,X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f21590,plain,
( ! [X2,X18] : c_plus(c_1,c_Orderings_Omax(X18,X2,tc_nat),tc_nat) = c_Orderings_Omax(c_plus(c_1,X18,tc_nat),c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1971 ),
inference(forward_demodulation,[],[f21589,f11227]) ).
fof(f21589,plain,
( ! [X2,X18] : c_plus(c_1,c_Orderings_Omax(X18,X2,tc_nat),tc_nat) = c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1971 ),
inference(forward_demodulation,[],[f21588,f11227]) ).
fof(f21588,plain,
( ! [X2,X18] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_plus(c_1,c_Orderings_Omax(X18,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1971 ),
inference(forward_demodulation,[],[f21586,f11227]) ).
fof(f21586,plain,
( ! [X2,X18] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X18,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_1971 ),
inference(avatar_component_clause,[],[f21585]) ).
fof(f21587,plain,
spl0_1971,
inference(avatar_split_clause,[],[f2798,f21585]) ).
fof(f2798,plain,
! [X2,X18] : c_Orderings_Omax(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Orderings_Omax(X18,X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f893,f1385,f1385,f1385]) ).
fof(f893,axiom,
! [X2,X18] : c_Orderings_Omax(c_Suc(X18),c_Suc(X2),tc_nat) = c_Suc(c_Orderings_Omax(X18,X2,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__Suc__Suc_0) ).
fof(f21583,plain,
spl0_1970,
inference(avatar_split_clause,[],[f1647,f21581]) ).
fof(f21581,plain,
( spl0_1970
<=> ! [X20,X5,X19] :
( ~ c_in(X19,c_Relation_Odiag(X20,X5),tc_prod(X5,X5))
| c_Pair(c_Main_OdiagE__1(X20,X19,X5),c_Main_OdiagE__1(X20,X19,X5),X5,X5) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f1647,axiom,
! [X19,X5,X20] :
( ~ c_in(X19,c_Relation_Odiag(X20,X5),tc_prod(X5,X5))
| c_Pair(c_Main_OdiagE__1(X20,X19,X5),c_Main_OdiagE__1(X20,X19,X5),X5,X5) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_0) ).
fof(f21579,plain,
spl0_1969,
inference(avatar_split_clause,[],[f1643,f21577]) ).
fof(f21577,plain,
( spl0_1969
<=> ! [X5,X10,X13,X9] :
( ~ c_in(X9,c_Relation_ORange(X13,X10,X5),X5)
| c_in(c_Pair(c_Main_ORangeE__1(X9,X13,X5,X10),X9,X10,X5),X13,tc_prod(X10,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f1643,axiom,
! [X10,X9,X5,X13] :
( ~ c_in(X9,c_Relation_ORange(X13,X10,X5),X5)
| c_in(c_Pair(c_Main_ORangeE__1(X9,X13,X5,X10),X9,X10,X5),X13,tc_prod(X10,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeE_0) ).
fof(f21575,plain,
spl0_1968,
inference(avatar_split_clause,[],[f1637,f21573]) ).
fof(f21573,plain,
( spl0_1968
<=> ! [X10,X13,X5,X8] :
( ~ c_in(X8,c_Relation_ODomain(X13,X5,X10),X5)
| c_in(c_Pair(X8,c_Main_ODomainE__1(X8,X13,X5,X10),X5,X10),X13,tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f1637,axiom,
! [X10,X8,X5,X13] :
( ~ c_in(X8,c_Relation_ODomain(X13,X5,X10),X5)
| c_in(c_Pair(X8,c_Main_ODomainE__1(X8,X13,X5,X10),X5,X10),X13,tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainE_0) ).
fof(f21571,plain,
spl0_1967,
inference(avatar_split_clause,[],[f1628,f21569]) ).
fof(f21569,plain,
( spl0_1967
<=> ! [X20,X5,X67,X8] :
( ~ c_in(X8,X20,X5)
| ~ c_in(X67,c_List_Olists(X20,X5),tc_List_Olist(X5))
| c_in(c_List_Olist_OCons(X8,X67,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f1628,axiom,
! [X8,X5,X67,X20] :
( ~ c_in(X8,X20,X5)
| ~ c_in(X67,c_List_Olists(X20,X5),tc_List_Olist(X5))
| c_in(c_List_Olist_OCons(X8,X67,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_OCons_0) ).
fof(f21567,plain,
spl0_1966,
inference(avatar_split_clause,[],[f1590,f21565]) ).
fof(f21565,plain,
( spl0_1966
<=> ! [X24,X10,X12,X5,X20] :
( ~ c_in(X12,X24,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Datatype__Universe_OIn1(X12,X5,X10),c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f1590,axiom,
! [X10,X24,X5,X12,X20] :
( ~ c_in(X12,X24,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Datatype__Universe_OIn1(X12,X5,X10),c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f21559,plain,
spl0_1965,
inference(avatar_split_clause,[],[f1589,f21557]) ).
fof(f21557,plain,
( spl0_1965
<=> ! [X24,X10,X11,X20,X5] :
( ~ c_in(X11,X20,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Datatype__Universe_OIn0(X11,X5,X10),c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f1589,axiom,
! [X10,X11,X24,X5,X20] :
( ~ c_in(X11,X20,tc_set(tc_Datatype__Universe_Onode(X5,X10)))
| c_in(c_Datatype__Universe_OIn0(X11,X5,X10),c_Datatype__Universe_Ousum(X20,X24,X5,X10),tc_set(tc_Datatype__Universe_Onode(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f21555,plain,
spl0_1964,
inference(avatar_split_clause,[],[f1407,f21553]) ).
fof(f21553,plain,
( spl0_1964
<=> ! [X18,X45,X17,X5,X2] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X18,X17,X5)
| ~ c_lessequals(X45,X2,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f1407,axiom,
! [X2,X18,X45,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X18,X17,X5)
| ~ c_lessequals(X45,X2,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_3) ).
fof(f21551,plain,
spl0_1963,
inference(avatar_split_clause,[],[f1405,f21549]) ).
fof(f21549,plain,
( spl0_1963
<=> ! [X2,X17,X18,X5,X45] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X45,X17,X5)
| c_lessequals(X45,X2,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f1405,axiom,
! [X2,X18,X45,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X45,X17,X5)
| c_lessequals(X45,X2,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_1) ).
fof(f21547,plain,
spl0_1962,
inference(avatar_split_clause,[],[f1404,f21545]) ).
fof(f21545,plain,
( spl0_1962
<=> ! [X2,X18,X17,X5,X45] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X45,X17,X5)
| c_lessequals(X18,X17,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f1404,axiom,
! [X2,X18,X45,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X45,X17,X5)
| c_lessequals(X18,X17,X5)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_0) ).
fof(f21543,plain,
spl0_1961,
inference(avatar_split_clause,[],[f1217,f21541]) ).
fof(f21541,plain,
( spl0_1961
<=> ! [X5,X10,X13,X9,X8] :
( ~ c_in(c_Pair(X8,X9,X10,X5),X13,tc_prod(X10,X5))
| c_in(X9,c_Relation_OImage(X13,c_insert(X8,c_emptyset,X10),X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f1217,axiom,
! [X10,X8,X9,X5,X13] :
( ~ c_in(c_Pair(X8,X9,X10,X5),X13,tc_prod(X10,X5))
| c_in(X9,c_Relation_OImage(X13,c_insert(X8,c_emptyset,X10),X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_1) ).
fof(f21539,plain,
spl0_1960,
inference(avatar_split_clause,[],[f1216,f21537]) ).
fof(f21537,plain,
( spl0_1960
<=> ! [X5,X10,X13,X9,X8] :
( c_in(c_Pair(X8,X9,X10,X5),X13,tc_prod(X10,X5))
| ~ c_in(X9,c_Relation_OImage(X13,c_insert(X8,c_emptyset,X10),X10,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f1216,axiom,
! [X10,X8,X9,X5,X13] :
( c_in(c_Pair(X8,X9,X10,X5),X13,tc_prod(X10,X5))
| ~ c_in(X9,c_Relation_OImage(X13,c_insert(X8,c_emptyset,X10),X10,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__singleton__iff_0) ).
fof(f21535,plain,
spl0_1959,
inference(avatar_split_clause,[],[f1176,f21533]) ).
fof(f21533,plain,
( spl0_1959
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X3
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f1176,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X3
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f21531,plain,
spl0_1958,
inference(avatar_split_clause,[],[f1159,f21529]) ).
fof(f21529,plain,
( spl0_1958
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X3
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f1159,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X3
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f21527,plain,
spl0_1957,
inference(avatar_split_clause,[],[f1015,f21525]) ).
fof(f21525,plain,
( spl0_1957
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_plus(c_HOL_Oabs(X8,X5),c_HOL_Oabs(X9,X5),X5) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X8,X5),c_HOL_Oabs(X9,X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f1015,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_plus(c_HOL_Oabs(X8,X5),c_HOL_Oabs(X9,X5),X5) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X8,X5),c_HOL_Oabs(X9,X5),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f21523,plain,
spl0_1956,
inference(avatar_split_clause,[],[f962,f21521]) ).
fof(f21521,plain,
( spl0_1956
<=> ! [X5,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_HOL_Oabs(c_Numeral_Onumber__of(X3,X5),X5) = c_uminus(c_Numeral_Onumber__of(X3,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f962,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_HOL_Oabs(c_Numeral_Onumber__of(X3,X5),X5) = c_uminus(c_Numeral_Onumber__of(X3,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f21516,plain,
spl0_1955,
inference(avatar_split_clause,[],[f651,f21514]) ).
fof(f21514,plain,
( spl0_1955
<=> ! [X18,X5,X2] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_lessequals(X2,X18,tc_nat)
| c_NatArith_Oof__nat(c_minus(X18,X2,tc_nat),X5) = c_minus(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f651,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_lessequals(X2,X18,tc_nat)
| c_NatArith_Oof__nat(c_minus(X18,X2,tc_nat),X5) = c_minus(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__diff_0) ).
fof(f21512,plain,
spl0_1954,
inference(avatar_split_clause,[],[f513,f21510]) ).
fof(f21510,plain,
( spl0_1954
<=> ! [X65,X58,X53,X56,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X1,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble8,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f513,axiom,
! [X21,X58,X65,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X1,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble8,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__9_0) ).
fof(f21508,plain,
spl0_1953,
inference(avatar_split_clause,[],[f512,f21506]) ).
fof(f21506,plain,
( spl0_1953
<=> ! [X56,X65,X21,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X1,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble7,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f512,axiom,
! [X21,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X1,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble7,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__8_0) ).
fof(f21504,plain,
spl0_1952,
inference(avatar_split_clause,[],[f511,f21502]) ).
fof(f21502,plain,
( spl0_1952
<=> ! [X56,X65,X58,X59,X1,X54,X53,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X1,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble6,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f511,axiom,
! [X21,X58,X65,X59,X56,X54,X1,X55,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X1,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble6,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__7_0) ).
fof(f21500,plain,
spl0_1951,
inference(avatar_split_clause,[],[f510,f21498]) ).
fof(f21498,plain,
( spl0_1951
<=> ! [X65,X58,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X1,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f510,axiom,
! [X21,X58,X65,X59,X1,X54,X57,X55,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X1,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble5,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__6_0) ).
fof(f21496,plain,
spl0_1950,
inference(avatar_split_clause,[],[f509,f21494]) ).
fof(f21494,plain,
( spl0_1950
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X22,X62,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X1,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble4,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f509,axiom,
! [X21,X58,X65,X59,X1,X54,X56,X57,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X1,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble4,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__5_0) ).
fof(f21492,plain,
spl0_1949,
inference(avatar_split_clause,[],[f508,f21490]) ).
fof(f21490,plain,
( spl0_1949
<=> ! [X56,X65,X58,X53,X59,X1,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X1,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble3,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f508,axiom,
! [X21,X58,X65,X59,X1,X56,X57,X55,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X1,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble3,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__4_0) ).
fof(f21488,plain,
spl0_1948,
inference(avatar_split_clause,[],[f507,f21486]) ).
fof(f21486,plain,
( spl0_1948
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X1,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble2,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f507,axiom,
! [X21,X58,X65,X59,X1,X54,X56,X55,X57,X62,X63,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X1,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble2,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__3_0) ).
fof(f21484,plain,
spl0_1947,
inference(avatar_split_clause,[],[f506,f21482]) ).
fof(f21482,plain,
( spl0_1947
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X1,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f506,axiom,
! [X65,X58,X59,X1,X54,X56,X55,X57,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X1,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__2_0) ).
fof(f21480,plain,
spl0_1946,
inference(avatar_split_clause,[],[f505,f21478]) ).
fof(f21478,plain,
( spl0_1946
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X1,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble0,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f505,axiom,
! [X21,X58,X65,X59,X1,X54,X56,X55,X57,X62,X63,X53,X66,X60,X61,X5,X64] : c_List_Onibble_Onibble__rec(X1,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble0,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__1_0) ).
fof(f21476,plain,
( spl0_1945
| ~ spl0_113
| ~ spl0_1756 ),
inference(avatar_split_clause,[],[f21384,f17565,f3711,f21473]) ).
fof(f21473,plain,
( spl0_1945
<=> c_less(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f3711,plain,
( spl0_113
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f17565,plain,
( spl0_1756
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f21384,plain,
( c_less(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1756 ),
inference(superposition,[],[f17566,f3713]) ).
fof(f3713,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f3711]) ).
fof(f17566,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1756 ),
inference(avatar_component_clause,[],[f17565]) ).
fof(f21471,plain,
spl0_1944,
inference(avatar_split_clause,[],[f504,f21469]) ).
fof(f21469,plain,
( spl0_1944
<=> ! [X56,X66,X21,X58,X59,X1,X54,X57,X55,X62,X22,X63,X53,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X1,c_List_Onibble_ONibbleF,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f504,axiom,
! [X21,X58,X59,X56,X54,X57,X55,X62,X1,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X1,c_List_Onibble_ONibbleF,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__16_0) ).
fof(f21467,plain,
spl0_1943,
inference(avatar_split_clause,[],[f503,f21465]) ).
fof(f21465,plain,
( spl0_1943
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X60,X63,X66,X21,X61,X22,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X1,X65,c_List_Onibble_ONibbleE,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f503,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X62,X1,X63,X53,X22,X66,X60,X61,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X1,X65,c_List_Onibble_ONibbleE,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__15_0) ).
fof(f21463,plain,
spl0_1942,
inference(avatar_split_clause,[],[f502,f21461]) ).
fof(f21461,plain,
( spl0_1942
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X60,X53,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X1,X64,X65,c_List_Onibble_ONibbleD,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f502,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X62,X1,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X1,X64,X65,c_List_Onibble_ONibbleD,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__14_0) ).
fof(f21459,plain,
spl0_1941,
inference(avatar_split_clause,[],[f501,f21457]) ).
fof(f21457,plain,
( spl0_1941
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X1,X63,X64,X65,c_List_Onibble_ONibbleC,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f501,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X1,X63,X64,X65,c_List_Onibble_ONibbleC,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__13_0) ).
fof(f21455,plain,
spl0_1940,
inference(avatar_split_clause,[],[f500,f21453]) ).
fof(f21453,plain,
( spl0_1940
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X1,X62,X63,X64,X65,c_List_Onibble_ONibbleB,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f500,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X60,X5,X64] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X1,X62,X63,X64,X65,c_List_Onibble_ONibbleB,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__12_0) ).
fof(f21451,plain,
spl0_1939,
inference(avatar_split_clause,[],[f499,f21449]) ).
fof(f21449,plain,
( spl0_1939
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X63,X53,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X1,X61,X62,X63,X64,X65,c_List_Onibble_ONibbleA,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f499,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X61,X5,X64] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X1,X61,X62,X63,X64,X65,c_List_Onibble_ONibbleA,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__11_0) ).
fof(f21447,plain,
spl0_1938,
inference(avatar_split_clause,[],[f498,f21445]) ).
fof(f21445,plain,
( spl0_1938
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X63,X53,X60,X21,X61,X64,X5] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X1,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble9,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f498,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X60,X61,X5,X64] : c_List_Onibble_Onibble__rec(X22,X21,X53,X54,X55,X56,X57,X58,X59,X1,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble9,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Orecs__10_0) ).
fof(f21443,plain,
spl0_1937,
inference(avatar_split_clause,[],[f497,f21441]) ).
fof(f21441,plain,
( spl0_1937
<=> ! [X65,X58,X53,X56,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X1,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble8,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f497,axiom,
! [X21,X58,X65,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X1,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble8,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__9_0) ).
fof(f21439,plain,
spl0_1936,
inference(avatar_split_clause,[],[f496,f21437]) ).
fof(f21437,plain,
( spl0_1936
<=> ! [X56,X65,X21,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X1,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble7,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f496,axiom,
! [X21,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X1,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble7,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__8_0) ).
fof(f21435,plain,
spl0_1935,
inference(avatar_split_clause,[],[f495,f21433]) ).
fof(f21433,plain,
( spl0_1935
<=> ! [X56,X65,X58,X59,X1,X54,X53,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X1,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble6,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f495,axiom,
! [X21,X58,X65,X59,X56,X54,X1,X55,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X1,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble6,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__7_0) ).
fof(f21431,plain,
( spl0_1934
| ~ spl0_112
| ~ spl0_1756 ),
inference(avatar_split_clause,[],[f21383,f17565,f3706,f21428]) ).
fof(f21428,plain,
( spl0_1934
<=> c_less(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f21383,plain,
( c_less(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_1756 ),
inference(superposition,[],[f17566,f3708]) ).
fof(f21426,plain,
spl0_1933,
inference(avatar_split_clause,[],[f494,f21424]) ).
fof(f21424,plain,
( spl0_1933
<=> ! [X65,X58,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X1,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f494,axiom,
! [X21,X58,X65,X59,X1,X54,X57,X55,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X1,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble5,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__6_0) ).
fof(f21422,plain,
spl0_1932,
inference(avatar_split_clause,[],[f493,f21420]) ).
fof(f21420,plain,
( spl0_1932
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X22,X62,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X1,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble4,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f493,axiom,
! [X21,X58,X65,X59,X1,X54,X56,X57,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X1,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble4,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__5_0) ).
fof(f21418,plain,
spl0_1931,
inference(avatar_split_clause,[],[f492,f21416]) ).
fof(f21416,plain,
( spl0_1931
<=> ! [X56,X65,X58,X53,X59,X1,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X1,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble3,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f492,axiom,
! [X21,X58,X65,X59,X1,X56,X57,X55,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X1,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble3,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__4_0) ).
fof(f21414,plain,
spl0_1930,
inference(avatar_split_clause,[],[f491,f21412]) ).
fof(f21412,plain,
( spl0_1930
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X1,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble2,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f491,axiom,
! [X21,X58,X65,X59,X1,X54,X56,X55,X57,X62,X63,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X1,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble2,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__3_0) ).
fof(f21410,plain,
spl0_1929,
inference(avatar_split_clause,[],[f490,f21408]) ).
fof(f21408,plain,
( spl0_1929
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X1,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f490,axiom,
! [X65,X58,X59,X1,X54,X56,X55,X57,X62,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X1,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__2_0) ).
fof(f21406,plain,
spl0_1928,
inference(avatar_split_clause,[],[f489,f21404]) ).
fof(f21404,plain,
( spl0_1928
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X1,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble0,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f489,axiom,
! [X21,X58,X65,X59,X1,X54,X56,X55,X57,X62,X63,X53,X66,X60,X61,X5,X64] : c_List_Onibble_Onibble__case(X1,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble0,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__1_0) ).
fof(f21402,plain,
spl0_1927,
inference(avatar_split_clause,[],[f488,f21400]) ).
fof(f21400,plain,
( spl0_1927
<=> ! [X56,X66,X21,X58,X59,X1,X54,X57,X55,X62,X22,X63,X53,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X1,c_List_Onibble_ONibbleF,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f488,axiom,
! [X21,X58,X59,X56,X54,X57,X55,X62,X1,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X64,X1,c_List_Onibble_ONibbleF,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__16_0) ).
fof(f21398,plain,
spl0_1926,
inference(avatar_split_clause,[],[f487,f21396]) ).
fof(f21396,plain,
( spl0_1926
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X60,X63,X66,X21,X61,X22,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X1,X65,c_List_Onibble_ONibbleE,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f487,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X62,X1,X63,X53,X22,X66,X60,X61,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X63,X1,X65,c_List_Onibble_ONibbleE,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__15_0) ).
fof(f21394,plain,
spl0_1925,
inference(avatar_split_clause,[],[f486,f21392]) ).
fof(f21392,plain,
( spl0_1925
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X60,X53,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X1,X64,X65,c_List_Onibble_ONibbleD,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f486,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X62,X1,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X62,X1,X64,X65,c_List_Onibble_ONibbleD,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__14_0) ).
fof(f21390,plain,
spl0_1924,
inference(avatar_split_clause,[],[f485,f21388]) ).
fof(f21388,plain,
( spl0_1924
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X22,X60,X63,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X1,X63,X64,X65,c_List_Onibble_ONibbleC,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f485,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X63,X53,X22,X66,X60,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X61,X1,X63,X64,X65,c_List_Onibble_ONibbleC,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__13_0) ).
fof(f21380,plain,
spl0_1923,
inference(avatar_split_clause,[],[f484,f21378]) ).
fof(f21378,plain,
( spl0_1923
<=> ! [X56,X65,X58,X53,X59,X1,X54,X57,X55,X62,X22,X60,X63,X66,X21,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X1,X62,X63,X64,X65,c_List_Onibble_ONibbleB,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f484,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X60,X5,X64] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X60,X1,X62,X63,X64,X65,c_List_Onibble_ONibbleB,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__12_0) ).
fof(f21376,plain,
spl0_1922,
inference(avatar_split_clause,[],[f483,f21374]) ).
fof(f21374,plain,
( spl0_1922
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X63,X53,X66,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X1,X61,X62,X63,X64,X65,c_List_Onibble_ONibbleA,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f483,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X66,X61,X5,X64] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X66,X1,X61,X62,X63,X64,X65,c_List_Onibble_ONibbleA,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__11_0) ).
fof(f21372,plain,
spl0_1921,
inference(avatar_split_clause,[],[f482,f21370]) ).
fof(f21370,plain,
( spl0_1921
<=> ! [X56,X65,X58,X59,X1,X54,X57,X55,X62,X22,X63,X53,X60,X21,X61,X64,X5] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X1,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble9,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f482,axiom,
! [X21,X58,X65,X59,X56,X54,X57,X55,X1,X62,X63,X53,X22,X60,X61,X5,X64] : c_List_Onibble_Onibble__case(X22,X21,X53,X54,X55,X56,X57,X58,X59,X1,X60,X61,X62,X63,X64,X65,c_List_Onibble_ONibble9,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Ocases__10_0) ).
fof(f21368,plain,
spl0_1920,
inference(avatar_split_clause,[],[f470,f21366]) ).
fof(f21366,plain,
( spl0_1920
<=> ! [X51,X8,X6,X46] :
( ~ c_in(X8,c_List_Oset(X51,X6),X6)
| c_List_Olist__inter(c_List_Olist_OCons(X8,X46,X6),X51,X6) = c_List_Olist_OCons(X8,c_List_Olist__inter(X46,X51,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f470,axiom,
! [X51,X46,X8,X6] :
( ~ c_in(X8,c_List_Oset(X51,X6),X6)
| c_List_Olist__inter(c_List_Olist_OCons(X8,X46,X6),X51,X6) = c_List_Olist_OCons(X8,c_List_Olist__inter(X46,X51,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_0) ).
fof(f21364,plain,
spl0_1919,
inference(avatar_split_clause,[],[f455,f21362]) ).
fof(f21362,plain,
( spl0_1919
<=> ! [X35,X34,X10,X5] : c_Nat_Osize(c_List_Ozip(X34,X35,X5,X10),tc_List_Olist(tc_prod(X5,X10))) = c_Orderings_Omin(c_Nat_Osize(X34,tc_List_Olist(X5)),c_Nat_Osize(X35,tc_List_Olist(X10)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f455,axiom,
! [X10,X34,X35,X5] : c_Nat_Osize(c_List_Ozip(X34,X35,X5,X10),tc_List_Olist(tc_prod(X5,X10))) = c_Orderings_Omin(c_Nat_Osize(X34,tc_List_Olist(X5)),c_Nat_Osize(X35,tc_List_Olist(X10)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__zip_0) ).
fof(f21360,plain,
spl0_1918,
inference(avatar_split_clause,[],[f364,f21358]) ).
fof(f21358,plain,
( spl0_1918
<=> ! [X38,X34,X5,X35,X39] :
( X38 = X39
| c_Nat_Osize(X38,tc_List_Olist(X5)) != c_Nat_Osize(X39,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f364,axiom,
! [X38,X39,X34,X5,X35] :
( X38 = X39
| c_Nat_Osize(X38,tc_List_Olist(X5)) != c_Nat_Osize(X39,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_3) ).
fof(f21356,plain,
spl0_1917,
inference(avatar_split_clause,[],[f363,f21354]) ).
fof(f21354,plain,
( spl0_1917
<=> ! [X38,X35,X34,X5,X39] :
( X34 = X35
| c_Nat_Osize(X38,tc_List_Olist(X5)) != c_Nat_Osize(X39,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f363,axiom,
! [X38,X39,X34,X35,X5] :
( X34 = X35
| c_Nat_Osize(X38,tc_List_Olist(X5)) != c_Nat_Osize(X39,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_2) ).
fof(f21352,plain,
spl0_1916,
inference(avatar_split_clause,[],[f362,f21350]) ).
fof(f21350,plain,
( spl0_1916
<=> ! [X38,X34,X5,X35,X39] :
( X38 = X39
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f362,axiom,
! [X38,X39,X34,X5,X35] :
( X38 = X39
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_1) ).
fof(f21348,plain,
spl0_1915,
inference(avatar_split_clause,[],[f361,f21346]) ).
fof(f21346,plain,
( spl0_1915
<=> ! [X38,X35,X34,X5,X39] :
( X34 = X35
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f361,axiom,
! [X38,X39,X34,X35,X5] :
( X34 = X35
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(X35,tc_List_Olist(X5))
| c_append(X34,X38,X5) != c_append(X35,X39,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__eq__append__conv_0) ).
fof(f21344,plain,
spl0_1914,
inference(avatar_split_clause,[],[f309,f21342]) ).
fof(f21342,plain,
( spl0_1914
<=> ! [X29,X28] : c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f309,axiom,
! [X28,X29] : c_div(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_Numeral_Onumber__of(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
fof(f21338,plain,
spl0_1913,
inference(avatar_split_clause,[],[f124,f21336]) ).
fof(f21336,plain,
( spl0_1913
<=> ! [X24,X20,X5,X8] :
( ~ c_in(c_minus(X20,X24,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X20,c_insert(X8,X24,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f124,axiom,
! [X8,X24,X5,X20] :
( ~ c_in(c_minus(X20,X24,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X20,c_insert(X8,X24,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f21334,plain,
spl0_1912,
inference(avatar_split_clause,[],[f123,f21332]) ).
fof(f21332,plain,
( spl0_1912
<=> ! [X24,X20,X5,X8] :
( c_in(c_minus(X20,X24,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_minus(X20,c_insert(X8,X24,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f123,axiom,
! [X8,X24,X5,X20] :
( c_in(c_minus(X20,X24,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_minus(X20,c_insert(X8,X24,X5),tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f21225,plain,
( spl0_1911
| ~ spl0_56
| ~ spl0_1443
| ~ spl0_1895 ),
inference(avatar_split_clause,[],[f20735,f20732,f11721,f3432,f21223]) ).
fof(f21223,plain,
( spl0_1911
<=> ! [X70,X29] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f20732,plain,
( spl0_1895
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f20735,plain,
( ! [X70,X29] :
( c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) )
| ~ spl0_56
| ~ spl0_1443
| ~ spl0_1895 ),
inference(forward_demodulation,[],[f20733,f12807]) ).
fof(f20733,plain,
( ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) )
| ~ spl0_1895 ),
inference(avatar_component_clause,[],[f20732]) ).
fof(f21221,plain,
( spl0_1910
| ~ spl0_56
| ~ spl0_1443
| ~ spl0_1894 ),
inference(avatar_split_clause,[],[f20730,f20727,f11721,f3432,f21219]) ).
fof(f21219,plain,
( spl0_1910
<=> ! [X70,X29] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f20727,plain,
( spl0_1894
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f20730,plain,
( ! [X70,X29] :
( ~ c_IntDef_Oneg(c_uminus(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) )
| ~ spl0_56
| ~ spl0_1443
| ~ spl0_1894 ),
inference(forward_demodulation,[],[f20728,f12807]) ).
fof(f20728,plain,
( ! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) )
| ~ spl0_1894 ),
inference(avatar_component_clause,[],[f20727]) ).
fof(f20904,plain,
( spl0_1909
| ~ spl0_1537
| ~ spl0_1908 ),
inference(avatar_split_clause,[],[f20900,f20897,f13560,f20902]) ).
fof(f20902,plain,
( spl0_1909
<=> ! [X5,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f13560,plain,
( spl0_1537
<=> c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f20897,plain,
( spl0_1908
<=> ! [X5,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f20900,plain,
( ! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) )
| ~ spl0_1537
| ~ spl0_1908 ),
inference(forward_demodulation,[],[f20898,f13562]) ).
fof(f13562,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1537 ),
inference(avatar_component_clause,[],[f13560]) ).
fof(f20898,plain,
( ! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) )
| ~ spl0_1908 ),
inference(avatar_component_clause,[],[f20897]) ).
fof(f20899,plain,
spl0_1908,
inference(avatar_split_clause,[],[f3151,f20897]) ).
fof(f3151,plain,
! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2948,f997]) ).
fof(f2948,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f160,f970]) ).
fof(f160,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_1) ).
fof(f20892,plain,
spl0_1907,
inference(avatar_split_clause,[],[f3149,f20890]) ).
fof(f20890,plain,
( spl0_1907
<=> ! [X5,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f3149,plain,
! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2946,f997]) ).
fof(f2946,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f156,f970]) ).
fof(f156,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_1) ).
fof(f20888,plain,
spl0_1906,
inference(avatar_split_clause,[],[f3147,f20886]) ).
fof(f20886,plain,
( spl0_1906
<=> ! [X5,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f3147,plain,
! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2944,f997]) ).
fof(f2944,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5) ),
inference(definition_unfolding,[],[f168,f970]) ).
fof(f168,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_1) ).
fof(f20867,plain,
( spl0_1905
| ~ spl0_1537
| ~ spl0_1904 ),
inference(avatar_split_clause,[],[f20863,f20860,f13560,f20865]) ).
fof(f20865,plain,
( spl0_1905
<=> ! [X5,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f20860,plain,
( spl0_1904
<=> ! [X5,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f20863,plain,
( ! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) )
| ~ spl0_1537
| ~ spl0_1904 ),
inference(forward_demodulation,[],[f20861,f13562]) ).
fof(f20861,plain,
( ! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) )
| ~ spl0_1904 ),
inference(avatar_component_clause,[],[f20860]) ).
fof(f20862,plain,
spl0_1904,
inference(avatar_split_clause,[],[f3144,f20860]) ).
fof(f3144,plain,
! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2942,f997]) ).
fof(f2942,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f164,f970]) ).
fof(f164,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_1) ).
fof(f20841,plain,
( spl0_1903
| ~ spl0_1537
| ~ spl0_1902 ),
inference(avatar_split_clause,[],[f20837,f20834,f13560,f20839]) ).
fof(f20839,plain,
( spl0_1903
<=> ! [X5,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f20834,plain,
( spl0_1902
<=> ! [X5,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f20837,plain,
( ! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) )
| ~ spl0_1537
| ~ spl0_1902 ),
inference(forward_demodulation,[],[f20835,f13562]) ).
fof(f20835,plain,
( ! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) )
| ~ spl0_1902 ),
inference(avatar_component_clause,[],[f20834]) ).
fof(f20836,plain,
spl0_1902,
inference(avatar_split_clause,[],[f3141,f20834]) ).
fof(f3141,plain,
! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2940,f997]) ).
fof(f2940,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f159,f970]) ).
fof(f159,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__13_0) ).
fof(f20832,plain,
spl0_1901,
inference(avatar_split_clause,[],[f3139,f20830]) ).
fof(f20830,plain,
( spl0_1901
<=> ! [X5,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f3139,plain,
! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2938,f997]) ).
fof(f2938,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f155,f970]) ).
fof(f155,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__11_0) ).
fof(f20828,plain,
spl0_1900,
inference(avatar_split_clause,[],[f3137,f20826]) ).
fof(f20826,plain,
( spl0_1900
<=> ! [X5,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f3137,plain,
! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5) ),
inference(forward_demodulation,[],[f2936,f997]) ).
fof(f2936,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5) ),
inference(definition_unfolding,[],[f167,f970]) ).
fof(f167,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_1,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__17_0) ).
fof(f20771,plain,
( spl0_1899
| ~ spl0_1537
| ~ spl0_1898 ),
inference(avatar_split_clause,[],[f20767,f20764,f13560,f20769]) ).
fof(f20769,plain,
( spl0_1899
<=> ! [X5,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f20764,plain,
( spl0_1898
<=> ! [X5,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f20767,plain,
( ! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) )
| ~ spl0_1537
| ~ spl0_1898 ),
inference(forward_demodulation,[],[f20765,f13562]) ).
fof(f20765,plain,
( ! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) )
| ~ spl0_1898 ),
inference(avatar_component_clause,[],[f20764]) ).
fof(f20766,plain,
spl0_1898,
inference(avatar_split_clause,[],[f3134,f20764]) ).
fof(f3134,plain,
! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2934,f997]) ).
fof(f2934,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f163,f970]) ).
fof(f163,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__15_0) ).
fof(f20745,plain,
( spl0_1897
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1896 ),
inference(avatar_split_clause,[],[f20741,f20737,f10422,f3432,f20743]) ).
fof(f20743,plain,
( spl0_1897
<=> ! [X3] :
( c_1 = c_Divides_Oop_Amod(X3,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X3,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f10422,plain,
( spl0_1342
<=> ! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f20737,plain,
( spl0_1896
<=> ! [X3] :
( c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f20741,plain,
( ! [X3] :
( c_1 = c_Divides_Oop_Amod(X3,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X3,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1896 ),
inference(forward_demodulation,[],[f20740,f11298]) ).
fof(f11298,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_56
| ~ spl0_1342 ),
inference(resolution,[],[f10423,f3434]) ).
fof(f10423,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X5) )
| ~ spl0_1342 ),
inference(avatar_component_clause,[],[f10422]) ).
fof(f20740,plain,
( ! [X3] :
( c_0 = c_Divides_Oop_Amod(X3,c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1896 ),
inference(forward_demodulation,[],[f20738,f11298]) ).
fof(f20738,plain,
( ! [X3] :
( c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1896 ),
inference(avatar_component_clause,[],[f20737]) ).
fof(f20739,plain,
spl0_1896,
inference(avatar_split_clause,[],[f3092,f20737]) ).
fof(f3092,plain,
! [X3] :
( c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3091,f997]) ).
fof(f3091,plain,
! [X3] :
( c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3090,f995]) ).
fof(f3090,plain,
! [X3] :
( c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3089,f997]) ).
fof(f3089,plain,
! [X3] :
( c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3088,f997]) ).
fof(f3088,plain,
! [X3] :
( c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3087,f995]) ).
fof(f3087,plain,
! [X3] :
( c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1149,f997]) ).
fof(f1149,axiom,
! [X3] :
( c_1 = c_Divides_Oop_Amod(X3,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X3,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneq__one__mod__two_0) ).
fof(f20734,plain,
spl0_1895,
inference(avatar_split_clause,[],[f2929,f20732]) ).
fof(f2929,plain,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f696,f970]) ).
fof(f696,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X70),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_0) ).
fof(f20729,plain,
spl0_1894,
inference(avatar_split_clause,[],[f2928,f20727]) ).
fof(f2928,plain,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X70),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f699,f970]) ).
fof(f699,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X70),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__nat__number__of_3) ).
fof(f20725,plain,
spl0_1893,
inference(avatar_split_clause,[],[f1601,f20723]) ).
fof(f20723,plain,
( spl0_1893
<=> ! [X20,X5] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| ~ c_in(c_Main_Ofinite__Union__1(X20,X5),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Union(X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f1601,axiom,
! [X5,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| ~ c_in(c_Main_Ofinite__Union__1(X20,X5),c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Union(X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_1) ).
fof(f20721,plain,
spl0_1892,
inference(avatar_split_clause,[],[f1600,f20719]) ).
fof(f20719,plain,
( spl0_1892
<=> ! [X20,X5] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| c_in(c_Main_Ofinite__Union__1(X20,X5),X20,tc_set(X5))
| c_in(c_Union(X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f1600,axiom,
! [X5,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(tc_set(X5)))
| c_in(c_Main_Ofinite__Union__1(X20,X5),X20,tc_set(X5))
| c_in(c_Union(X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Union_0) ).
fof(f20680,plain,
spl0_1891,
inference(avatar_split_clause,[],[f1193,f20678]) ).
fof(f20678,plain,
( spl0_1891
<=> ! [X18,X8,X5,X2] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| X2 = X18
| ~ c_less(c_1,X8,X5)
| c_Nat_Opower(X8,X2,X5) != c_Nat_Opower(X8,X18,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f1193,axiom,
! [X2,X18,X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__semidom(X5)
| X2 = X18
| ~ c_less(c_1,X8,X5)
| c_Nat_Opower(X8,X2,X5) != c_Nat_Opower(X8,X18,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__inject__exp_0) ).
fof(f20676,plain,
spl0_1890,
inference(avatar_split_clause,[],[f1168,f20674]) ).
fof(f20674,plain,
( spl0_1890
<=> ! [X2,X5,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X2,tc_nat)
| c_Nat_Opower(c_uminus(X3,X5),X2,X5) = c_uminus(c_Nat_Opower(X3,X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f1168,axiom,
! [X2,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X2,tc_nat)
| c_Nat_Opower(c_uminus(X3,X5),X2,X5) = c_uminus(c_Nat_Opower(X3,X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__odd_0) ).
fof(f20672,plain,
spl0_1889,
inference(avatar_split_clause,[],[f1161,f20670]) ).
fof(f20670,plain,
( spl0_1889
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X3
| c_lessequals(X3,c_0,X5)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f1161,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X3
| c_lessequals(X3,c_0,X5)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f20668,plain,
spl0_1888,
inference(avatar_split_clause,[],[f814,f20666]) ).
fof(f20666,plain,
( spl0_1888
<=> ! [X29,X8,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10)
| c_less(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f814,axiom,
! [X10,X29,X8] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10)
| c_less(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f20664,plain,
spl0_1887,
inference(avatar_split_clause,[],[f813,f20662]) ).
fof(f20662,plain,
( spl0_1887
<=> ! [X29,X8,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f813,axiom,
! [X10,X29,X8] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10)
| c_less(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f20660,plain,
spl0_1886,
inference(avatar_split_clause,[],[f810,f20658]) ).
fof(f20658,plain,
( spl0_1886
<=> ! [X29,X8,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10)
| c_lessequals(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f810,axiom,
! [X10,X29,X8] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10)
| c_lessequals(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f20656,plain,
spl0_1885,
inference(avatar_split_clause,[],[f809,f20654]) ).
fof(f20654,plain,
( spl0_1885
<=> ! [X29,X8,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f809,axiom,
! [X10,X29,X8] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(c_uminus(X8,X10),c_Numeral_Onumber__of(X29,X10),X10)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f20652,plain,
spl0_1884,
inference(avatar_split_clause,[],[f803,f20650]) ).
fof(f20650,plain,
( spl0_1884
<=> ! [X29,X9,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f803,axiom,
! [X10,X29,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10)
| c_less(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f20648,plain,
spl0_1883,
inference(avatar_split_clause,[],[f802,f20646]) ).
fof(f20646,plain,
( spl0_1883
<=> ! [X29,X9,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10)
| c_less(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f802,axiom,
! [X10,X29,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_less(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10)
| c_less(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f20644,plain,
spl0_1882,
inference(avatar_split_clause,[],[f787,f20642]) ).
fof(f20642,plain,
( spl0_1882
<=> ! [X29,X9,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f787,axiom,
! [X10,X29,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10)
| c_lessequals(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f20640,plain,
( spl0_1881
| ~ spl0_908
| ~ spl0_1021
| ~ spl0_1716 ),
inference(avatar_split_clause,[],[f20503,f16537,f8358,f7784,f20637]) ).
fof(f20637,plain,
( spl0_1881
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f7784,plain,
( spl0_908
<=> ! [X28] : c_IntDef_Onat(c_Numeral_Onumber__of(X28,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X28,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f8358,plain,
( spl0_1021
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f20503,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)
| ~ spl0_908
| ~ spl0_1021
| ~ spl0_1716 ),
inference(forward_demodulation,[],[f20463,f8360]) ).
fof(f8360,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_1021 ),
inference(avatar_component_clause,[],[f8358]) ).
fof(f20463,plain,
( c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) = c_Numeral_Onumber__of(c_Numeral_OMin,tc_nat)
| ~ spl0_908
| ~ spl0_1716 ),
inference(superposition,[],[f7785,f16539]) ).
fof(f7785,plain,
( ! [X28] : c_IntDef_Onat(c_Numeral_Onumber__of(X28,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X28,tc_nat)
| ~ spl0_908 ),
inference(avatar_component_clause,[],[f7784]) ).
fof(f20635,plain,
spl0_1880,
inference(avatar_split_clause,[],[f786,f20633]) ).
fof(f20633,plain,
( spl0_1880
<=> ! [X29,X9,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10)
| c_lessequals(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f786,axiom,
! [X10,X29,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ c_lessequals(c_Numeral_Onumber__of(X29,X10),c_uminus(X9,X10),X10)
| c_lessequals(X9,c_uminus(c_Numeral_Onumber__of(X29,X10),X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f20631,plain,
spl0_1879,
inference(avatar_split_clause,[],[f717,f20629]) ).
fof(f20629,plain,
( spl0_1879
<=> ! [X29,X28] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X28,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f717,axiom,
! [X28,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X28,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f20627,plain,
spl0_1878,
inference(avatar_split_clause,[],[f596,f20625]) ).
fof(f20625,plain,
( spl0_1878
<=> ! [X34,X5,X3] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Oset(c_List_Oremove1(X3,X34,X5),X5) = c_minus(c_List_Oset(X34,X5),c_insert(X3,c_emptyset,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f596,axiom,
! [X3,X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Oset(c_List_Oremove1(X3,X34,X5),X5) = c_minus(c_List_Oset(X34,X5),c_insert(X3,c_emptyset,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remove1__eq_0) ).
fof(f20623,plain,
spl0_1877,
inference(avatar_split_clause,[],[f115,f20621]) ).
fof(f20621,plain,
( spl0_1877
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMin(X20,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f115,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(c_Finite__Set_OMin(X20,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__le_0) ).
fof(f20619,plain,
spl0_1876,
inference(avatar_split_clause,[],[f97,f20617]) ).
fof(f20617,plain,
( spl0_1876
<=> ! [X20,X5,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X3,c_Finite__Set_OMax(X20,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f97,axiom,
! [X3,X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X3,X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_lessequals(X3,c_Finite__Set_OMax(X20,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__ge_0) ).
fof(f20195,plain,
( spl0_1875
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1861 ),
inference(avatar_split_clause,[],[f20044,f20041,f16107,f7144,f7120,f20193]) ).
fof(f20193,plain,
( spl0_1875
<=> ! [X35,X34,X5,X1] :
( c_append(c_List_Orev(X35,X5),c_List_Oreplicate(c_1,X1,X5),X5) = X34
| c_List_Olist_OCons(X1,X35,X5) != c_List_Orev(X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f20041,plain,
( spl0_1861
<=> ! [X35,X34,X5,X1] :
( c_List_Olist_OCons(X1,X35,X5) != c_List_Orev(X34,X5)
| c_append(c_List_Orev(X35,X5),c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) = X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f20044,plain,
( ! [X1,X34,X35,X5] :
( c_append(c_List_Orev(X35,X5),c_List_Oreplicate(c_1,X1,X5),X5) = X34
| c_List_Olist_OCons(X1,X35,X5) != c_List_Orev(X34,X5) )
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1861 ),
inference(forward_demodulation,[],[f20042,f16133]) ).
fof(f20042,plain,
( ! [X1,X34,X35,X5] :
( c_List_Olist_OCons(X1,X35,X5) != c_List_Orev(X34,X5)
| c_append(c_List_Orev(X35,X5),c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) = X34 )
| ~ spl0_1861 ),
inference(avatar_component_clause,[],[f20041]) ).
fof(f20162,plain,
( spl0_1874
| ~ spl0_1716
| ~ spl0_1858 ),
inference(avatar_split_clause,[],[f20023,f20020,f16537,f20160]) ).
fof(f20160,plain,
( spl0_1874
<=> ! [X9] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X9,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f20020,plain,
( spl0_1858
<=> ! [X9] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X9,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f20023,plain,
( ! [X9] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X9,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1716
| ~ spl0_1858 ),
inference(forward_demodulation,[],[f20021,f16539]) ).
fof(f20021,plain,
( ! [X9] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X9,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_1858 ),
inference(avatar_component_clause,[],[f20020]) ).
fof(f20106,plain,
spl0_1873,
inference(avatar_split_clause,[],[f3067,f20104]) ).
fof(f20104,plain,
( spl0_1873
<=> ! [X70] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f3067,plain,
! [X70] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2892,f2745]) ).
fof(f2745,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f857,f1385]) ).
fof(f857,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2892,plain,
! [X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,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(X70,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f713,f1385]) ).
fof(f713,axiom,
! [X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f20102,plain,
spl0_1872,
inference(avatar_split_clause,[],[f2898,f20100]) ).
fof(f20100,plain,
( spl0_1872
<=> ! [X13,X5,X33] :
( ~ c_in(X33,X13,tc_prod(X5,X5))
| c_in(X33,c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f2898,plain,
! [X5,X13,X33] :
( ~ c_in(X33,X13,tc_prod(X5,X5))
| c_in(X33,c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
inference(definition_unfolding,[],[f1687,f1557]) ).
fof(f1687,axiom,
! [X5,X13,X33] :
( ~ c_in(X33,X13,tc_prod(X5,X5))
| c_in(X33,c_Transitive__Closure_Ortrancl(X13,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f20098,plain,
spl0_1871,
inference(avatar_split_clause,[],[f2896,f20096]) ).
fof(f20096,plain,
( spl0_1871
<=> ! [X34,X5,X35] :
( ~ c_List_Odistinct(c_append(X34,X35,X5),X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X34,X5),X5),c_List_Oset(X35,X5),X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f2896,plain,
! [X34,X35,X5] :
( ~ c_List_Odistinct(c_append(X34,X35,X5),X5)
| c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_List_Oset(X34,X5),X5),c_List_Oset(X35,X5),X5,X5) ),
inference(definition_unfolding,[],[f398,f1214]) ).
fof(f398,axiom,
! [X34,X35,X5] :
( ~ c_List_Odistinct(c_append(X34,X35,X5),X5)
| c_emptyset = c_inter(c_List_Oset(X34,X5),c_List_Oset(X35,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_2) ).
fof(f20094,plain,
spl0_1870,
inference(avatar_split_clause,[],[f2847,f20092]) ).
fof(f20092,plain,
( spl0_1870
<=> ! [X5,X28,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_uminus(c_Numeral_Onumber__of(X28,X5),X5),X30,X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X28),X5),X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f2847,plain,
! [X28,X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_uminus(c_Numeral_Onumber__of(X28,X5),X5),X30,X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X28),X5),X30,X5) ),
inference(definition_unfolding,[],[f1006,f970]) ).
fof(f1006,axiom,
! [X28,X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_uminus(c_Numeral_Onumber__of(X28,X5),X5),X30,X5) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X28),X5),X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f20090,plain,
spl0_1869,
inference(avatar_split_clause,[],[f2821,f20088]) ).
fof(f20088,plain,
( spl0_1869
<=> ! [X35,X34,X6,X3] : c_append(c_List_Orev(c_List_Olist_OCons(X3,X34,X6),X6),X35,X6) = c_append(c_List_Orev(X34,X6),c_List_Olist_OCons(X3,X35,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f2821,plain,
! [X3,X6,X34,X35] : c_append(c_List_Orev(c_List_Olist_OCons(X3,X34,X6),X6),X35,X6) = c_append(c_List_Orev(X34,X6),c_List_Olist_OCons(X3,X35,X6),X6),
inference(definition_unfolding,[],[f428,f426,f426]) ).
fof(f426,axiom,
! [X3,X34,X5] : c_List_Oitrev(X34,X3,X5) = c_append(c_List_Orev(X34,X5),X3,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f428,axiom,
! [X3,X6,X34,X35] : c_List_Oitrev(c_List_Olist_OCons(X3,X34,X6),X35,X6) = c_List_Oitrev(X34,c_List_Olist_OCons(X3,X35,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__2_0) ).
fof(f20072,plain,
spl0_1868,
inference(avatar_split_clause,[],[f1625,f20070]) ).
fof(f20070,plain,
( spl0_1868
<=> ! [X13,X34,X5] :
( c_List_Olist_ONil = X34
| ~ c_in(c_Pair(X34,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f1625,axiom,
! [X34,X5,X13] :
( c_List_Olist_ONil = X34
| ~ c_in(c_Pair(X34,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil2_0) ).
fof(f20068,plain,
spl0_1867,
inference(avatar_split_clause,[],[f1624,f20066]) ).
fof(f20066,plain,
( spl0_1867
<=> ! [X13,X34,X5] :
( c_List_Olist_ONil = X34
| ~ c_in(c_Pair(c_List_Olist_ONil,X34,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f1624,axiom,
! [X34,X5,X13] :
( c_List_Olist_ONil = X34
| ~ c_in(c_Pair(c_List_Olist_ONil,X34,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olistrel(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil1_0) ).
fof(f20064,plain,
spl0_1866,
inference(avatar_split_clause,[],[f963,f20062]) ).
fof(f20062,plain,
( spl0_1866
<=> ! [X5,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_Numeral_Onumber__of(X3,X5) = c_HOL_Oabs(c_Numeral_Onumber__of(X3,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f963,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_Numeral_Onumber__of(X3,X5) = c_HOL_Oabs(c_Numeral_Onumber__of(X3,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f20060,plain,
spl0_1865,
inference(avatar_split_clause,[],[f705,f20058]) ).
fof(f20058,plain,
( spl0_1865
<=> ! [X29,X70] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X29,X70),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f705,axiom,
! [X70,X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X29,X70),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_1) ).
fof(f20056,plain,
spl0_1864,
inference(avatar_split_clause,[],[f641,f20054]) ).
fof(f20054,plain,
( spl0_1864
<=> ! [X45,X0,X17] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_minus(X17,c_minus(X45,X0,tc_nat),tc_nat) = c_minus(c_plus(X17,X0,tc_nat),X45,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f641,axiom,
! [X0,X45,X17] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_minus(X17,c_minus(X45,X0,tc_nat),tc_nat) = c_minus(c_plus(X17,X0,tc_nat),X45,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__right_0) ).
fof(f20052,plain,
spl0_1863,
inference(avatar_split_clause,[],[f637,f20050]) ).
fof(f20050,plain,
( spl0_1863
<=> ! [X45,X0,X17] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_plus(X17,c_minus(X45,X0,tc_nat),tc_nat) = c_minus(c_plus(X17,X45,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f637,axiom,
! [X0,X45,X17] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_plus(X17,c_minus(X45,X0,tc_nat),tc_nat) = c_minus(c_plus(X17,X45,tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f20048,plain,
spl0_1862,
inference(avatar_split_clause,[],[f636,f20046]) ).
fof(f20046,plain,
( spl0_1862
<=> ! [X45,X0,X17] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_plus(c_minus(X45,X0,tc_nat),X17,tc_nat) = c_minus(c_plus(X45,X17,tc_nat),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f636,axiom,
! [X0,X45,X17] :
( ~ c_lessequals(X0,X45,tc_nat)
| c_plus(c_minus(X45,X0,tc_nat),X17,tc_nat) = c_minus(c_plus(X45,X17,tc_nat),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f20043,plain,
spl0_1861,
inference(avatar_split_clause,[],[f567,f20041]) ).
fof(f567,axiom,
! [X1,X34,X35,X5] :
( c_List_Olist_OCons(X1,X35,X5) != c_List_Orev(X34,X5)
| c_append(c_List_Orev(X35,X5),c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) = X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_0) ).
fof(f20039,plain,
spl0_1860,
inference(avatar_split_clause,[],[f555,f20037]) ).
fof(f20037,plain,
( spl0_1860
<=> ! [X6,X34,X3] :
( c_in(X3,c_List_Oset(X34,X6),X6)
| c_List_Oremdups(c_List_Olist_OCons(X3,X34,X6),X6) = c_List_Olist_OCons(X3,c_List_Oremdups(X34,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f555,axiom,
! [X3,X6,X34] :
( c_in(X3,c_List_Oset(X34,X6),X6)
| c_List_Oremdups(c_List_Olist_OCons(X3,X34,X6),X6) = c_List_Olist_OCons(X3,c_List_Oremdups(X34,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_1) ).
fof(f20035,plain,
spl0_1859,
inference(avatar_split_clause,[],[f458,f20033]) ).
fof(f20033,plain,
( spl0_1859
<=> ! [X13,X5,X23,X47] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X23,X47,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f458,axiom,
! [X47,X5,X23,X13] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X23,X47,X5),tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__left_1) ).
fof(f20022,plain,
spl0_1858,
inference(avatar_split_clause,[],[f294,f20020]) ).
fof(f294,axiom,
! [X9] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X9,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X9,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f20018,plain,
spl0_1857,
inference(avatar_split_clause,[],[f60,f20016]) ).
fof(f20016,plain,
( spl0_1857
<=> ! [X9,X8,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(X8,X9,tc_nat) = c_div(c_times(X8,X19,tc_nat),c_times(X9,X19,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f60,axiom,
! [X8,X19,X9] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(X8,X9,tc_nat) = c_div(c_times(X8,X19,tc_nat),c_times(X9,X19,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult2_0) ).
fof(f20014,plain,
spl0_1856,
inference(avatar_split_clause,[],[f59,f20012]) ).
fof(f20012,plain,
( spl0_1856
<=> ! [X9,X8,X19] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_times(X19,X8,tc_nat),c_times(X19,X9,tc_nat),tc_nat) = c_div(X8,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f59,axiom,
! [X8,X19,X9] :
( ~ c_less(c_0,X19,tc_nat)
| c_div(c_times(X19,X8,tc_nat),c_times(X19,X9,tc_nat),tc_nat) = c_div(X8,X9,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__mult1_0) ).
fof(f19344,plain,
( spl0_1855
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1825 ),
inference(avatar_split_clause,[],[f18901,f18897,f16107,f7144,f7120,f19342]) ).
fof(f19342,plain,
( spl0_1855
<=> ! [X3,X34,X5,X35,X1] :
( c_append(X35,c_List_Oreplicate(c_1,X1,X5),X5) != c_append(X34,c_List_Oreplicate(c_1,X3,X5),X5)
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f18897,plain,
( spl0_1825
<=> ! [X3,X34,X5,X35,X1] :
( X1 = X3
| c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f18901,plain,
( ! [X3,X1,X34,X35,X5] :
( c_append(X35,c_List_Oreplicate(c_1,X1,X5),X5) != c_append(X34,c_List_Oreplicate(c_1,X3,X5),X5)
| X1 = X3 )
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f18900,f16133]) ).
fof(f18900,plain,
( ! [X3,X1,X34,X5,X35] :
( c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Oreplicate(c_1,X1,X5),X5)
| X1 = X3 )
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1825 ),
inference(forward_demodulation,[],[f18898,f16133]) ).
fof(f18898,plain,
( ! [X3,X1,X34,X5,X35] :
( X1 = X3
| c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) )
| ~ spl0_1825 ),
inference(avatar_component_clause,[],[f18897]) ).
fof(f19340,plain,
( spl0_1854
| ~ spl0_113
| ~ spl0_1691 ),
inference(avatar_split_clause,[],[f18962,f16137,f3711,f19337]) ).
fof(f19337,plain,
( spl0_1854
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f16137,plain,
( spl0_1691
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f18962,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1691 ),
inference(superposition,[],[f16138,f3713]) ).
fof(f16138,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1691 ),
inference(avatar_component_clause,[],[f16137]) ).
fof(f19335,plain,
( spl0_1853
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1824 ),
inference(avatar_split_clause,[],[f18895,f18891,f16107,f7144,f7120,f19333]) ).
fof(f19333,plain,
( spl0_1853
<=> ! [X3,X34,X5,X35,X1] :
( c_append(X35,c_List_Oreplicate(c_1,X1,X5),X5) != c_append(X34,c_List_Oreplicate(c_1,X3,X5),X5)
| X34 = X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f18891,plain,
( spl0_1824
<=> ! [X35,X34,X3,X5,X1] :
( X34 = X35
| c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f18895,plain,
( ! [X3,X1,X34,X35,X5] :
( c_append(X35,c_List_Oreplicate(c_1,X1,X5),X5) != c_append(X34,c_List_Oreplicate(c_1,X3,X5),X5)
| X34 = X35 )
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1824 ),
inference(forward_demodulation,[],[f18894,f16133]) ).
fof(f18894,plain,
( ! [X3,X1,X34,X5,X35] :
( c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Oreplicate(c_1,X1,X5),X5)
| X34 = X35 )
| ~ spl0_762
| ~ spl0_768
| ~ spl0_1690
| ~ spl0_1824 ),
inference(forward_demodulation,[],[f18892,f16133]) ).
fof(f18892,plain,
( ! [X3,X1,X34,X35,X5] :
( X34 = X35
| c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) )
| ~ spl0_1824 ),
inference(avatar_component_clause,[],[f18891]) ).
fof(f19019,plain,
( spl0_1852
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1851 ),
inference(avatar_split_clause,[],[f19015,f19011,f10406,f10097,f6714,f3706,f19017]) ).
fof(f19011,plain,
( spl0_1851
<=> ! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X2,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_1851])]) ).
fof(f19015,plain,
( ! [X2] : c_plus(X2,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,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f19014,f11227]) ).
fof(f19014,plain,
( ! [X2] : c_plus(X2,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,X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1851 ),
inference(forward_demodulation,[],[f19012,f11227]) ).
fof(f19012,plain,
( ! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat) = c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1851 ),
inference(avatar_component_clause,[],[f19011]) ).
fof(f19013,plain,
spl0_1851,
inference(avatar_split_clause,[],[f2992,f19011]) ).
fof(f19009,plain,
( spl0_1850
| ~ spl0_112
| ~ spl0_1691 ),
inference(avatar_split_clause,[],[f18961,f16137,f3706,f19006]) ).
fof(f19006,plain,
( spl0_1850
<=> c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f18961,plain,
( c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_1691 ),
inference(superposition,[],[f16138,f3708]) ).
fof(f19004,plain,
spl0_1849,
inference(avatar_split_clause,[],[f2922,f19002]) ).
fof(f19002,plain,
( spl0_1849
<=> ! [X24,X20,X5,X19] :
( ~ c_in(X19,X24,X5)
| ~ c_in(X19,X20,X5)
| c_in(X19,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f2922,plain,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X24,X5)
| ~ c_in(X19,X20,X5)
| c_in(X19,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ),
inference(definition_unfolding,[],[f1449,f1214]) ).
fof(f1449,axiom,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X24,X5)
| ~ c_in(X19,X20,X5)
| c_in(X19,c_inter(X20,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).
fof(f19000,plain,
spl0_1848,
inference(avatar_split_clause,[],[f2917,f18998]) ).
fof(f18998,plain,
( spl0_1848
<=> ! [X5,X1,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X1,X5) = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f2917,plain,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X1,X5) = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f983,f970]) ).
fof(f983,axiom,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X1,X5) = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f18996,plain,
spl0_1847,
inference(avatar_split_clause,[],[f2916,f18994]) ).
fof(f18994,plain,
( spl0_1847
<=> ! [X5,X1,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X1,X5) != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f2916,plain,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X1,X5) != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f982,f970]) ).
fof(f982,axiom,
! [X3,X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(X1,X5) != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f18992,plain,
spl0_1846,
inference(avatar_split_clause,[],[f2871,f18990]) ).
fof(f18990,plain,
( spl0_1846
<=> ! [X17,X34,X5,X2] :
( ~ c_less(X17,X2,tc_nat)
| c_List_Onth(X34,X17,X5) = c_List_Onth(c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X17,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f2871,plain,
! [X2,X17,X34,X5] :
( ~ c_less(X17,X2,tc_nat)
| c_List_Onth(X34,X17,X5) = c_List_Onth(c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),X17,X5) ),
inference(definition_unfolding,[],[f544,f607]) ).
fof(f544,axiom,
! [X2,X17,X34,X5] :
( ~ c_less(X17,X2,tc_nat)
| c_List_Onth(c_List_Otake(X2,X34,X5),X17,X5) = c_List_Onth(X34,X17,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__take_0) ).
fof(f18988,plain,
spl0_1845,
inference(avatar_split_clause,[],[f2844,f18986]) ).
fof(f18986,plain,
( spl0_1845
<=> ! [X29,X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f2844,plain,
! [X28,X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),X5) ),
inference(definition_unfolding,[],[f961,f970]) ).
fof(f961,axiom,
! [X28,X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(X28)),X5) = c_minus(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f18984,plain,
spl0_1844,
inference(avatar_split_clause,[],[f1515,f18982]) ).
fof(f18982,plain,
( spl0_1844
<=> ! [X24,X20,X5,X3] :
( ~ c_in(X3,X24,X5)
| c_minus(X20,X24,tc_set(X5)) = c_minus(c_insert(X3,X20,X5),X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f1515,axiom,
! [X3,X24,X5,X20] :
( ~ c_in(X3,X24,X5)
| c_minus(X20,X24,tc_set(X5)) = c_minus(c_insert(X3,X20,X5),X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff1_0) ).
fof(f18980,plain,
spl0_1843,
inference(avatar_split_clause,[],[f1488,f18978]) ).
fof(f18978,plain,
( spl0_1843
<=> ! [X24,X20,X5,X73] :
( ~ c_lessequals(X24,X73,tc_set(X5))
| ~ c_lessequals(X20,X73,tc_set(X5))
| c_lessequals(c_union(X20,X24,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f1488,axiom,
! [X73,X24,X5,X20] :
( ~ c_lessequals(X24,X73,tc_set(X5))
| ~ c_lessequals(X20,X73,tc_set(X5))
| c_lessequals(c_union(X20,X24,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_2) ).
fof(f18976,plain,
spl0_1842,
inference(avatar_split_clause,[],[f1438,f18974]) ).
fof(f18974,plain,
( spl0_1842
<=> ! [X24,X20,X5,X3] :
( c_in(X3,X20,X5)
| c_minus(X20,X24,tc_set(X5)) = c_minus(X20,c_insert(X3,X24,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f1438,axiom,
! [X3,X24,X5,X20] :
( c_in(X3,X20,X5)
| c_minus(X20,X24,tc_set(X5)) = c_minus(X20,c_insert(X3,X24,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__insert0_0) ).
fof(f18972,plain,
spl0_1841,
inference(avatar_split_clause,[],[f1178,f18970]) ).
fof(f18970,plain,
( spl0_1841
<=> ! [X28,X3] :
( c_less(c_0,X3,tc_nat)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f1178,axiom,
! [X3,X28] :
( c_less(c_0,X3,tc_nat)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f18968,plain,
spl0_1840,
inference(avatar_split_clause,[],[f1170,f18966]) ).
fof(f18966,plain,
( spl0_1840
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f1170,axiom,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f18957,plain,
spl0_1839,
inference(avatar_split_clause,[],[f1167,f18955]) ).
fof(f18955,plain,
( spl0_1839
<=> ! [X2,X5,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X2,tc_nat)
| c_Nat_Opower(c_uminus(X3,X5),X2,X5) = c_Nat_Opower(X3,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f1167,axiom,
! [X2,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X2,tc_nat)
| c_Nat_Opower(c_uminus(X3,X5),X2,X5) = c_Nat_Opower(X3,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__minus__even_0) ).
fof(f18953,plain,
spl0_1838,
inference(avatar_split_clause,[],[f1164,f18951]) ).
fof(f18951,plain,
( spl0_1838
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f1164,axiom,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X28,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f18949,plain,
spl0_1837,
inference(avatar_split_clause,[],[f918,f18947]) ).
fof(f18947,plain,
( spl0_1837
<=> ! [X2,X0,X18] :
( ~ c_less(X18,X2,tc_nat)
| ~ c_less(c_0,X0,tc_nat)
| c_less(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f918,axiom,
! [X2,X0,X18] :
( ~ c_less(X18,X2,tc_nat)
| ~ c_less(c_0,X0,tc_nat)
| c_less(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_2) ).
fof(f18945,plain,
spl0_1836,
inference(avatar_split_clause,[],[f915,f18943]) ).
fof(f18943,plain,
( spl0_1836
<=> ! [X2,X0,X18] :
( ~ c_less(X18,X2,tc_nat)
| ~ c_less(c_0,X0,tc_nat)
| c_less(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f915,axiom,
! [X2,X0,X18] :
( ~ c_less(X18,X2,tc_nat)
| ~ c_less(c_0,X0,tc_nat)
| c_less(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_2) ).
fof(f18941,plain,
spl0_1835,
inference(avatar_split_clause,[],[f910,f18939]) ).
fof(f18939,plain,
( spl0_1835
<=> ! [X2,X0,X18] :
( ~ c_less(c_0,X0,tc_nat)
| c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f910,axiom,
! [X2,X0,X18] :
( ~ c_less(c_0,X0,tc_nat)
| c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_0) ).
fof(f18937,plain,
spl0_1834,
inference(avatar_split_clause,[],[f907,f18935]) ).
fof(f18935,plain,
( spl0_1834
<=> ! [X2,X0,X18] :
( ~ c_less(c_0,X0,tc_nat)
| c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f907,axiom,
! [X2,X0,X18] :
( ~ c_less(c_0,X0,tc_nat)
| c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_0) ).
fof(f18933,plain,
spl0_1833,
inference(avatar_split_clause,[],[f770,f18931]) ).
fof(f18931,plain,
( spl0_1833
<=> ! [X29,X9,X10] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Oab__group__add(X10)
| c_uminus(X9,X10) != c_Numeral_Onumber__of(X29,X10)
| c_uminus(c_Numeral_Onumber__of(X29,X10),X10) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f770,axiom,
! [X10,X29,X9] :
( ~ class_Numeral_Onumber(X10)
| ~ class_OrderedGroup_Oab__group__add(X10)
| c_uminus(X9,X10) != c_Numeral_Onumber__of(X29,X10)
| c_uminus(c_Numeral_Onumber__of(X29,X10),X10) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f18929,plain,
spl0_1832,
inference(avatar_split_clause,[],[f671,f18927]) ).
fof(f18927,plain,
( spl0_1832
<=> ! [X1,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f671,axiom,
! [X3,X1] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f18925,plain,
spl0_1831,
inference(avatar_split_clause,[],[f670,f18923]) ).
fof(f18923,plain,
( spl0_1831
<=> ! [X1,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f670,axiom,
! [X3,X1] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X1,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f18921,plain,
spl0_1830,
inference(avatar_split_clause,[],[f562,f18919]) ).
fof(f18919,plain,
( spl0_1830
<=> ! [X3,X34,X6,X1] :
( X1 = X3
| c_List_Oremove1(X3,c_List_Olist_OCons(X1,X34,X6),X6) = c_List_Olist_OCons(X1,c_List_Oremove1(X3,X34,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f562,axiom,
! [X3,X1,X6,X34] :
( X1 = X3
| c_List_Oremove1(X3,c_List_Olist_OCons(X1,X34,X6),X6) = c_List_Olist_OCons(X1,c_List_Oremove1(X3,X34,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_1) ).
fof(f18917,plain,
spl0_1829,
inference(avatar_split_clause,[],[f545,f18915]) ).
fof(f18915,plain,
( spl0_1829
<=> ! [X45,X0,X17] :
( ~ c_less(c_plus(X17,X0,tc_nat),X45,tc_nat)
| c_plus(X17,X0,tc_nat) = c_List_Onth(c_List_Oupt(X17,X45),X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f545,axiom,
! [X0,X45,X17] :
( ~ c_less(c_plus(X17,X0,tc_nat),X45,tc_nat)
| c_plus(X17,X0,tc_nat) = c_List_Onth(c_List_Oupt(X17,X45),X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__upt_0) ).
fof(f18913,plain,
spl0_1828,
inference(avatar_split_clause,[],[f538,f18911]) ).
fof(f18911,plain,
( spl0_1828
<=> ! [X35,X34,X5,X2] : c_List_Onth(c_append(X34,X35,X5),c_plus(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat),X5) = c_List_Onth(X35,X2,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f538,axiom,
! [X2,X34,X35,X5] : c_List_Onth(c_append(X34,X35,X5),c_plus(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat),X5) = c_List_Onth(X35,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__append__length__plus_0) ).
fof(f18909,plain,
spl0_1827,
inference(avatar_split_clause,[],[f471,f18907]) ).
fof(f18907,plain,
( spl0_1827
<=> ! [X51,X8,X6,X46] :
( c_in(X8,c_List_Oset(X51,X6),X6)
| c_List_Olist__inter(c_List_Olist_OCons(X8,X46,X6),X51,X6) = c_List_Olist__inter(X46,X51,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f471,axiom,
! [X51,X46,X8,X6] :
( c_in(X8,c_List_Oset(X51,X6),X6)
| c_List_Olist__inter(c_List_Olist_OCons(X8,X46,X6),X51,X6) = c_List_Olist__inter(X46,X51,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__2_1) ).
fof(f18905,plain,
spl0_1826,
inference(avatar_split_clause,[],[f440,f18903]) ).
fof(f18903,plain,
( spl0_1826
<=> ! [X34,X5,X35] : c_Nat_Osize(c_append(X34,X35,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X34,tc_List_Olist(X5)),c_Nat_Osize(X35,tc_List_Olist(X5)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f440,axiom,
! [X34,X35,X5] : c_Nat_Osize(c_append(X34,X35,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X34,tc_List_Olist(X5)),c_Nat_Osize(X35,tc_List_Olist(X5)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__append_0) ).
fof(f18899,plain,
spl0_1825,
inference(avatar_split_clause,[],[f358,f18897]) ).
fof(f358,axiom,
! [X3,X1,X34,X5,X35] :
( X1 = X3
| c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_1) ).
fof(f18893,plain,
spl0_1824,
inference(avatar_split_clause,[],[f357,f18891]) ).
fof(f357,axiom,
! [X3,X1,X34,X35,X5] :
( X34 = X35
| c_append(X34,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) != c_append(X35,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend1__eq__conv_0) ).
fof(f18889,plain,
spl0_1823,
inference(avatar_split_clause,[],[f322,f18887]) ).
fof(f18887,plain,
( spl0_1823
<=> ! [X1,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f322,axiom,
! [X3,X1] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f18885,plain,
spl0_1822,
inference(avatar_split_clause,[],[f321,f18883]) ).
fof(f18883,plain,
( spl0_1822
<=> ! [X1,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f321,axiom,
! [X3,X1] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X1,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f18881,plain,
spl0_1821,
inference(avatar_split_clause,[],[f314,f18879]) ).
fof(f18879,plain,
( spl0_1821
<=> ! [X9,X8] :
( c_0 = X8
| c_plus(c_div(X9,X8,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X9,X8,tc_IntDef_Oint),X8,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f314,axiom,
! [X8,X9] :
( c_0 = X8
| c_plus(c_div(X9,X8,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X9,X8,tc_IntDef_Oint),X8,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f18877,plain,
spl0_1820,
inference(avatar_split_clause,[],[f313,f18875]) ).
fof(f18875,plain,
( spl0_1820
<=> ! [X9,X8] :
( c_0 = X8
| c_div(c_plus(X8,X9,tc_IntDef_Oint),X8,tc_IntDef_Oint) = c_plus(c_div(X9,X8,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f313,axiom,
! [X8,X9] :
( c_0 = X8
| c_div(c_plus(X8,X9,tc_IntDef_Oint),X8,tc_IntDef_Oint) = c_plus(c_div(X9,X8,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f18869,plain,
spl0_1819,
inference(avatar_split_clause,[],[f133,f18867]) ).
fof(f18867,plain,
( spl0_1819
<=> ! [X20,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_lessequals(c_Finite__Set_OMin(X20,X10),c_Finite__Set_OMax(X20,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f133,axiom,
! [X10,X20] :
( ~ class_Orderings_Olinorder(X10)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X10))
| c_lessequals(c_Finite__Set_OMin(X20,X10),c_Finite__Set_OMax(X20,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f18865,plain,
spl0_1818,
inference(avatar_split_clause,[],[f129,f18863]) ).
fof(f18863,plain,
( spl0_1818
<=> ! [X5,X27,X26] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_union(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f129,axiom,
! [X26,X27,X5] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_union(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_2) ).
fof(f18528,plain,
( ~ spl0_1817
| ~ spl0_112
| ~ spl0_1641 ),
inference(avatar_split_clause,[],[f18400,f15641,f3706,f18525]) ).
fof(f18525,plain,
( spl0_1817
<=> c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f15641,plain,
( spl0_1641
<=> ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f18400,plain,
( ~ c_less(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_1641 ),
inference(superposition,[],[f15642,f3708]) ).
fof(f15642,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1641 ),
inference(avatar_component_clause,[],[f15641]) ).
fof(f18137,plain,
( ~ spl0_1816
| ~ spl0_112
| ~ spl0_1618 ),
inference(avatar_split_clause,[],[f18023,f15091,f3706,f18134]) ).
fof(f18134,plain,
( spl0_1816
<=> c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f15091,plain,
( spl0_1618
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f18023,plain,
( ~ c_less(c_1,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_1618 ),
inference(superposition,[],[f15092,f3708]) ).
fof(f15092,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1618 ),
inference(avatar_component_clause,[],[f15091]) ).
fof(f17983,plain,
spl0_1815,
inference(avatar_split_clause,[],[f3150,f17981]) ).
fof(f17981,plain,
( spl0_1815
<=> ! [X5,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f3150,plain,
! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2947,f955]) ).
fof(f955,axiom,
! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f2947,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f154,f970]) ).
fof(f154,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_1) ).
fof(f17979,plain,
spl0_1814,
inference(avatar_split_clause,[],[f3148,f17977]) ).
fof(f17977,plain,
( spl0_1814
<=> ! [X5,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f3148,plain,
! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2945,f955]) ).
fof(f2945,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5) ),
inference(definition_unfolding,[],[f166,f970]) ).
fof(f166,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_1) ).
fof(f17975,plain,
spl0_1813,
inference(avatar_split_clause,[],[f3140,f17973]) ).
fof(f17973,plain,
( spl0_1813
<=> ! [X5,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f3140,plain,
! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2939,f955]) ).
fof(f2939,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f153,f970]) ).
fof(f153,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__10_0) ).
fof(f17971,plain,
spl0_1812,
inference(avatar_split_clause,[],[f3138,f17969]) ).
fof(f17969,plain,
( spl0_1812
<=> ! [X5,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f3138,plain,
! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X3),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2937,f955]) ).
fof(f2937,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X3)),X5),X5) ),
inference(definition_unfolding,[],[f165,f970]) ).
fof(f165,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__16_0) ).
fof(f17967,plain,
spl0_1811,
inference(avatar_split_clause,[],[f3106,f17965]) ).
fof(f17965,plain,
( spl0_1811
<=> ! [X5,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,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f3106,plain,
! [X1,X5] :
( ~ 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,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X1,X5) ),
inference(forward_demodulation,[],[f2913,f997]) ).
fof(f2913,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X1,X5)
| ~ 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,X1)),X5),X5) ),
inference(definition_unfolding,[],[f177,f970]) ).
fof(f177,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X1,X5)
| ~ 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(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_1) ).
fof(f17954,plain,
( spl0_1810
| ~ spl0_1537
| ~ spl0_1809 ),
inference(avatar_split_clause,[],[f17950,f17947,f13560,f17952]) ).
fof(f17952,plain,
( spl0_1810
<=> ! [X5,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f17947,plain,
( spl0_1809
<=> ! [X5,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f17950,plain,
( ! [X3,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5) )
| ~ spl0_1537
| ~ spl0_1809 ),
inference(forward_demodulation,[],[f17948,f13562]) ).
fof(f17948,plain,
( ! [X3,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5) )
| ~ spl0_1809 ),
inference(avatar_component_clause,[],[f17947]) ).
fof(f17949,plain,
spl0_1809,
inference(avatar_split_clause,[],[f3105,f17947]) ).
fof(f3105,plain,
! [X3,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5) ),
inference(forward_demodulation,[],[f2912,f997]) ).
fof(f2912,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f181,f970]) ).
fof(f181,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_1) ).
fof(f17945,plain,
spl0_1808,
inference(avatar_split_clause,[],[f3100,f17943]) ).
fof(f17943,plain,
( spl0_1808
<=> ! [X5,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,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f3100,plain,
! [X1,X5] :
( 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,X1)),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X1,X5) ),
inference(forward_demodulation,[],[f2909,f997]) ).
fof(f2909,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X1,X5)
| 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,X1)),X5),X5) ),
inference(definition_unfolding,[],[f176,f970]) ).
fof(f176,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X1,X5)
| 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(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__7_0) ).
fof(f17932,plain,
( spl0_1807
| ~ spl0_1537
| ~ spl0_1806 ),
inference(avatar_split_clause,[],[f17928,f17925,f13560,f17930]) ).
fof(f17930,plain,
( spl0_1807
<=> ! [X5,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f17925,plain,
( spl0_1806
<=> ! [X5,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f17928,plain,
( ! [X3,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5) )
| ~ spl0_1537
| ~ spl0_1806 ),
inference(forward_demodulation,[],[f17926,f13562]) ).
fof(f17926,plain,
( ! [X3,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5) )
| ~ spl0_1806 ),
inference(avatar_component_clause,[],[f17925]) ).
fof(f17927,plain,
spl0_1806,
inference(avatar_split_clause,[],[f3099,f17925]) ).
fof(f3099,plain,
! [X3,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5) ),
inference(forward_demodulation,[],[f2908,f997]) ).
fof(f2908,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
inference(definition_unfolding,[],[f180,f970]) ).
fof(f180,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__9_0) ).
fof(f17921,plain,
( spl0_1805
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1804 ),
inference(avatar_split_clause,[],[f17917,f17914,f10422,f3432,f17919]) ).
fof(f17919,plain,
( spl0_1805
<=> ! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f17914,plain,
( spl0_1804
<=> ! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f17917,plain,
( ! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1804 ),
inference(forward_demodulation,[],[f17915,f11298]) ).
fof(f17915,plain,
( ! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1804 ),
inference(avatar_component_clause,[],[f17914]) ).
fof(f17916,plain,
spl0_1804,
inference(avatar_split_clause,[],[f3070,f17914]) ).
fof(f3070,plain,
! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3069,f997]) ).
fof(f3069,plain,
! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3068,f995]) ).
fof(f3068,plain,
! [X29] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1114,f997]) ).
fof(f1114,axiom,
! [X29] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
fof(f17910,plain,
( spl0_1803
| ~ spl0_118
| ~ spl0_770
| ~ spl0_1467 ),
inference(avatar_split_clause,[],[f13312,f12915,f7152,f3733,f17907]) ).
fof(f17907,plain,
( spl0_1803
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f3733,plain,
( spl0_118
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f7152,plain,
( spl0_770
<=> ! [X18] : c_0 = c_minus(X18,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f12915,plain,
( spl0_1467
<=> ! [X45,X17] :
( ~ c_less(X17,X45,tc_nat)
| c_List_Olast(c_List_Oupt(X17,X45),tc_nat) = c_minus(X45,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f13312,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_118
| ~ spl0_770
| ~ spl0_1467 ),
inference(forward_demodulation,[],[f13295,f7153]) ).
fof(f7153,plain,
( ! [X18] : c_0 = c_minus(X18,X18,tc_nat)
| ~ spl0_770 ),
inference(avatar_component_clause,[],[f7152]) ).
fof(f13295,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_118
| ~ spl0_1467 ),
inference(resolution,[],[f12916,f3735]) ).
fof(f3735,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f3733]) ).
fof(f12916,plain,
( ! [X45,X17] :
( ~ c_less(X17,X45,tc_nat)
| c_List_Olast(c_List_Oupt(X17,X45),tc_nat) = c_minus(X45,c_1,tc_nat) )
| ~ spl0_1467 ),
inference(avatar_component_clause,[],[f12915]) ).
fof(f17905,plain,
( spl0_1802
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1801 ),
inference(avatar_split_clause,[],[f17901,f17898,f10422,f3432,f17903]) ).
fof(f17903,plain,
( spl0_1802
<=> ! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f17898,plain,
( spl0_1801
<=> ! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f17901,plain,
( ! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),c_plus(c_1,c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_56
| ~ spl0_1342
| ~ spl0_1801 ),
inference(forward_demodulation,[],[f17899,f11298]) ).
fof(f17899,plain,
( ! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1801 ),
inference(avatar_component_clause,[],[f17898]) ).
fof(f17900,plain,
spl0_1801,
inference(avatar_split_clause,[],[f3066,f17898]) ).
fof(f3066,plain,
! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3065,f997]) ).
fof(f3065,plain,
! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f3064,f995]) ).
fof(f3064,plain,
! [X29] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1113,f997]) ).
fof(f1113,axiom,
! [X29] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,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/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
fof(f17895,plain,
( spl0_1800
| ~ spl0_1537
| ~ spl0_1799 ),
inference(avatar_split_clause,[],[f17891,f17888,f13560,f17893]) ).
fof(f17893,plain,
( spl0_1800
<=> ! [X29,X5] :
( c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_OMin),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f17888,plain,
( spl0_1799
<=> ! [X29,X5] :
( c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f17891,plain,
( ! [X29,X5] :
( c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_OMin),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_1537
| ~ spl0_1799 ),
inference(forward_demodulation,[],[f17889,f13562]) ).
fof(f17889,plain,
( ! [X29,X5] :
( c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_1799 ),
inference(avatar_component_clause,[],[f17888]) ).
fof(f17890,plain,
spl0_1799,
inference(avatar_split_clause,[],[f3035,f17888]) ).
fof(f3035,plain,
! [X29,X5] :
( c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f2846,f997]) ).
fof(f2846,plain,
! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5) ),
inference(definition_unfolding,[],[f173,f970]) ).
fof(f173,axiom,
! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__5_0) ).
fof(f17886,plain,
spl0_1798,
inference(avatar_split_clause,[],[f3034,f17884]) ).
fof(f17884,plain,
( spl0_1798
<=> ! [X5,X28] :
( c_minus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X28)),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f3034,plain,
! [X28,X5] :
( c_minus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__mult(c_Numeral_OMin,X28)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f2845,f997]) ).
fof(f2845,plain,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = 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,X28)),X5) ),
inference(definition_unfolding,[],[f172,f970]) ).
fof(f172,axiom,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_minus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X28)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__4_0) ).
fof(f17882,plain,
spl0_1797,
inference(avatar_split_clause,[],[f2996,f17880]) ).
fof(f17880,plain,
( spl0_1797
<=> ! [X2] : c_plus(X2,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),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f2996,plain,
! [X2] : c_plus(X2,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),X2,tc_nat),
inference(forward_demodulation,[],[f2995,f997]) ).
fof(f2995,plain,
! [X2] : c_plus(X2,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),X2,tc_nat),
inference(forward_demodulation,[],[f2994,f995]) ).
fof(f2994,plain,
! [X2] : c_plus(X2,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),X2,tc_nat),
inference(forward_demodulation,[],[f2993,f997]) ).
fof(f2993,plain,
! [X2] : 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),X2,tc_nat) = c_plus(X2,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2817,f2992]) ).
fof(f2817,plain,
! [X2] : 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),X2,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f722,f1385,f1385]) ).
fof(f722,axiom,
! [X2] : 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),X2,tc_nat) = c_Suc(c_Suc(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f17860,plain,
( spl0_1796
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1795 ),
inference(avatar_split_clause,[],[f17856,f17853,f10406,f10097,f6714,f3706,f17858]) ).
fof(f17858,plain,
( spl0_1796
<=> ! [X29] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X29),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f17853,plain,
( spl0_1795
<=> ! [X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X29),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f17856,plain,
( ! [X29] :
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(X29),tc_nat) = c_plus(c_1,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1795 ),
inference(forward_demodulation,[],[f17854,f11227]) ).
fof(f17854,plain,
( ! [X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X29),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1795 ),
inference(avatar_component_clause,[],[f17853]) ).
fof(f17855,plain,
spl0_1795,
inference(avatar_split_clause,[],[f2891,f17853]) ).
fof(f2891,plain,
! [X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(c_Numeral_Obin__succ(X29),tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f664,f1385]) ).
fof(f664,axiom,
! [X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X29,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X29),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f17851,plain,
spl0_1794,
inference(avatar_split_clause,[],[f2822,f17849]) ).
fof(f17849,plain,
( spl0_1794
<=> ! [X17,X0,X5,X3] : c_List_Oreplicate(c_Orderings_Omin(X17,X0,tc_nat),X3,X5) = c_List_Osublist(c_List_Oreplicate(X0,X3,X5),c_SetInterval_OlessThan(X17,tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f2822,plain,
! [X3,X0,X17,X5] : c_List_Oreplicate(c_Orderings_Omin(X17,X0,tc_nat),X3,X5) = c_List_Osublist(c_List_Oreplicate(X0,X3,X5),c_SetInterval_OlessThan(X17,tc_nat),X5),
inference(definition_unfolding,[],[f616,f607]) ).
fof(f616,axiom,
! [X3,X0,X17,X5] : c_List_Otake(X17,c_List_Oreplicate(X0,X3,X5),X5) = c_List_Oreplicate(c_Orderings_Omin(X17,X0,tc_nat),X3,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__replicate_0) ).
fof(f17847,plain,
spl0_1793,
inference(avatar_split_clause,[],[f2820,f17845]) ).
fof(f17845,plain,
( spl0_1793
<=> ! [X34,X2,X5] : c_Orderings_Omin(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) = c_Nat_Osize(c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f2820,plain,
! [X2,X34,X5] : c_Orderings_Omin(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) = c_Nat_Osize(c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5),tc_List_Olist(X5)),
inference(definition_unfolding,[],[f452,f607]) ).
fof(f452,axiom,
! [X2,X34,X5] : c_Nat_Osize(c_List_Otake(X2,X34,X5),tc_List_Olist(X5)) = c_Orderings_Omin(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__take_0) ).
fof(f17843,plain,
spl0_1792,
inference(avatar_split_clause,[],[f2816,f17841]) ).
fof(f17841,plain,
( spl0_1792
<=> ! [X5,X24,X8] : c_Inter(c_insert(X8,X24,tc_set(X5)),X5) = c_Relation_OImage(c_Relation_Odiag(X8,X5),c_Inter(X24,X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f2816,plain,
! [X8,X24,X5] : c_Inter(c_insert(X8,X24,tc_set(X5)),X5) = c_Relation_OImage(c_Relation_Odiag(X8,X5),c_Inter(X24,X5),X5,X5),
inference(definition_unfolding,[],[f1464,f1214]) ).
fof(f1464,axiom,
! [X8,X24,X5] : c_Inter(c_insert(X8,X24,tc_set(X5)),X5) = c_inter(X8,c_Inter(X24,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__insert_0) ).
fof(f17838,plain,
( spl0_1791
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1790 ),
inference(avatar_split_clause,[],[f17834,f17831,f10406,f10097,f6714,f3706,f17836]) ).
fof(f17836,plain,
( spl0_1791
<=> ! [X17,X10,X0,X5] : c_Datatype__Universe_ONumb(X17,X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_ONumb(X17,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f17831,plain,
( spl0_1790
<=> ! [X17,X10,X0,X5] : c_Datatype__Universe_ONumb(X17,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X17,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f17834,plain,
( ! [X10,X0,X17,X5] : c_Datatype__Universe_ONumb(X17,X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_ONumb(X17,X5,X10),X5,X10)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1790 ),
inference(forward_demodulation,[],[f17832,f11227]) ).
fof(f17832,plain,
( ! [X10,X0,X17,X5] : c_Datatype__Universe_ONumb(X17,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X17,X5,X10),X5,X10)
| ~ spl0_1790 ),
inference(avatar_component_clause,[],[f17831]) ).
fof(f17833,plain,
spl0_1790,
inference(avatar_split_clause,[],[f2815,f17831]) ).
fof(f2815,plain,
! [X10,X0,X17,X5] : c_Datatype__Universe_ONumb(X17,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_ONumb(X17,X5,X10),X5,X10),
inference(definition_unfolding,[],[f48,f1385]) ).
fof(f48,axiom,
! [X10,X0,X17,X5] : c_Datatype__Universe_ONumb(X17,X5,X10) = c_Datatype__Universe_Ontrunc(c_Suc(X0),c_Datatype__Universe_ONumb(X17,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f17828,plain,
( spl0_1789
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1788 ),
inference(avatar_split_clause,[],[f17824,f17821,f10406,f10097,f6714,f3706,f17826]) ).
fof(f17826,plain,
( spl0_1789
<=> ! [X10,X0,X5,X8] : c_Datatype__Universe_OLeaf(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_OLeaf(X8,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f17821,plain,
( spl0_1788
<=> ! [X10,X0,X5,X8] : c_Datatype__Universe_OLeaf(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X8,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f17824,plain,
( ! [X10,X0,X8,X5] : c_Datatype__Universe_OLeaf(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_OLeaf(X8,X5,X10),X5,X10)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1788 ),
inference(forward_demodulation,[],[f17822,f11227]) ).
fof(f17822,plain,
( ! [X10,X0,X8,X5] : c_Datatype__Universe_OLeaf(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X8,X5,X10),X5,X10)
| ~ spl0_1788 ),
inference(avatar_component_clause,[],[f17821]) ).
fof(f17823,plain,
spl0_1788,
inference(avatar_split_clause,[],[f2814,f17821]) ).
fof(f2814,plain,
! [X10,X0,X8,X5] : c_Datatype__Universe_OLeaf(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OLeaf(X8,X5,X10),X5,X10),
inference(definition_unfolding,[],[f47,f1385]) ).
fof(f47,axiom,
! [X10,X0,X8,X5] : c_Datatype__Universe_OLeaf(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Suc(X0),c_Datatype__Universe_OLeaf(X8,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f17818,plain,
( spl0_1786
| spl0_1787
| ~ spl0_723
| ~ spl0_1460 ),
inference(avatar_split_clause,[],[f13214,f12887,f6949,f17816,f17813]) ).
fof(f17813,plain,
( spl0_1786
<=> ! [X1] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f17816,plain,
( spl0_1787
<=> ! [X0] : c_lessequals(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f6949,plain,
( spl0_723
<=> ! [X20,X5] : c_lessequals(X20,X20,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f12887,plain,
( spl0_1460
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X28,X30,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f13214,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X1)) )
| ~ spl0_723
| ~ spl0_1460 ),
inference(resolution,[],[f12888,f6950]) ).
fof(f6950,plain,
( ! [X5,X20] : c_lessequals(X20,X20,tc_set(X5))
| ~ spl0_723 ),
inference(avatar_component_clause,[],[f6949]) ).
fof(f12888,plain,
( ! [X28,X5,X30] :
( ~ c_lessequals(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5)
| c_lessequals(X28,X30,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X5) )
| ~ spl0_1460 ),
inference(avatar_component_clause,[],[f12887]) ).
fof(f17811,plain,
( spl0_1785
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1784 ),
inference(avatar_split_clause,[],[f17807,f17804,f10406,f10097,f6714,f3706,f17809]) ).
fof(f17809,plain,
( spl0_1785
<=> ! [X10,X0,X5,X8] : c_Datatype__Universe_OAtom(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_OAtom(X8,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f17804,plain,
( spl0_1784
<=> ! [X10,X0,X5,X8] : c_Datatype__Universe_OAtom(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X8,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f17807,plain,
( ! [X10,X0,X8,X5] : c_Datatype__Universe_OAtom(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_plus(c_1,X0,tc_nat),c_Datatype__Universe_OAtom(X8,X5,X10),X5,X10)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1784 ),
inference(forward_demodulation,[],[f17805,f11227]) ).
fof(f17805,plain,
( ! [X10,X0,X8,X5] : c_Datatype__Universe_OAtom(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X8,X5,X10),X5,X10)
| ~ spl0_1784 ),
inference(avatar_component_clause,[],[f17804]) ).
fof(f17806,plain,
spl0_1784,
inference(avatar_split_clause,[],[f2813,f17804]) ).
fof(f2813,plain,
! [X10,X0,X8,X5] : c_Datatype__Universe_OAtom(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),c_Datatype__Universe_OAtom(X8,X5,X10),X5,X10),
inference(definition_unfolding,[],[f44,f1385]) ).
fof(f44,axiom,
! [X10,X0,X8,X5] : c_Datatype__Universe_OAtom(X8,X5,X10) = c_Datatype__Universe_Ontrunc(c_Suc(X0),c_Datatype__Universe_OAtom(X8,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f17802,plain,
spl0_1783,
inference(avatar_split_clause,[],[f2802,f17800]) ).
fof(f17800,plain,
( spl0_1783
<=> ! [X13,X5,X8] : c_in(c_Pair(X8,X8,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f2802,plain,
! [X8,X5,X13] : c_in(c_Pair(X8,X8,X5,X5),c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),tc_prod(X5,X5)),
inference(definition_unfolding,[],[f1688,f1557]) ).
fof(f1688,axiom,
! [X8,X5,X13] : c_in(c_Pair(X8,X8,X5,X5),c_Transitive__Closure_Ortrancl(X13,X5),tc_prod(X5,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f17798,plain,
spl0_1782,
inference(avatar_split_clause,[],[f2800,f17796]) ).
fof(f17796,plain,
( spl0_1782
<=> ! [X13,X5] : c_union(c_Transitive__Closure_Otrancl(X13,X5),c_Relation_OId,tc_prod(X5,X5)) = c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f2800,plain,
! [X5,X13] : c_union(c_Transitive__Closure_Otrancl(X13,X5),c_Relation_OId,tc_prod(X5,X5)) = c_Transitive__Closure_Otrancl(c_union(X13,c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1549,f1557]) ).
fof(f1549,axiom,
! [X5,X13] : c_union(c_Transitive__Closure_Otrancl(X13,X5),c_Relation_OId,tc_prod(X5,X5)) = c_Transitive__Closure_Ortrancl(X13,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f17775,plain,
( spl0_1781
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1780 ),
inference(avatar_split_clause,[],[f17771,f17768,f10406,f10097,f6714,f3706,f17773]) ).
fof(f17773,plain,
( spl0_1781
<=> ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(X18,c_plus(c_1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f17768,plain,
( spl0_1780
<=> ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f17771,plain,
( ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(X18,c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1780 ),
inference(forward_demodulation,[],[f17769,f11227]) ).
fof(f17769,plain,
( ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_1780 ),
inference(avatar_component_clause,[],[f17768]) ).
fof(f17770,plain,
spl0_1780,
inference(avatar_split_clause,[],[f2793,f17768]) ).
fof(f2793,plain,
! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f868,f1385,f1385]) ).
fof(f868,axiom,
! [X2,X18] : c_plus(X18,c_Suc(X2),tc_nat) = c_Suc(c_plus(X18,X2,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__Suc__right_0) ).
fof(f17685,plain,
( spl0_1779
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1778 ),
inference(avatar_split_clause,[],[f17681,f17677,f10406,f10097,f6714,f3706,f17683]) ).
fof(f17683,plain,
( spl0_1779
<=> ! [X2,X18] : c_plus(c_plus(c_1,X18,tc_nat),X2,tc_nat) = c_plus(c_1,c_plus(X18,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f17677,plain,
( spl0_1778
<=> ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f17681,plain,
( ! [X2,X18] : c_plus(c_plus(c_1,X18,tc_nat),X2,tc_nat) = c_plus(c_1,c_plus(X18,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1778 ),
inference(forward_demodulation,[],[f17680,f11227]) ).
fof(f17680,plain,
( ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(c_plus(c_1,X18,tc_nat),X2,tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1778 ),
inference(forward_demodulation,[],[f17678,f11227]) ).
fof(f17678,plain,
( ! [X2,X18] : c_Finite__Set_Ocard(c_SetInterval_OatMost(c_plus(X18,X2,tc_nat),tc_nat),tc_nat) = c_plus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_1778 ),
inference(avatar_component_clause,[],[f17677]) ).
fof(f17679,plain,
spl0_1778,
inference(avatar_split_clause,[],[f2792,f17677]) ).
fof(f17675,plain,
( spl0_1777
| ~ spl0_808
| ~ spl0_1450 ),
inference(avatar_split_clause,[],[f12859,f11783,f7308,f17673]) ).
fof(f17673,plain,
( spl0_1777
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f7308,plain,
( spl0_808
<=> ! [X18,X2] : c_lessequals(c_div(X18,X2,tc_nat),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f11783,plain,
( spl0_1450
<=> ! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f12859,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_808
| ~ spl0_1450 ),
inference(superposition,[],[f7309,f11784]) ).
fof(f11784,plain,
( ! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X1
| ~ spl0_1450 ),
inference(avatar_component_clause,[],[f11783]) ).
fof(f7309,plain,
( ! [X2,X18] : c_lessequals(c_div(X18,X2,tc_nat),X18,tc_nat)
| ~ spl0_808 ),
inference(avatar_component_clause,[],[f7308]) ).
fof(f17649,plain,
( spl0_1776
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1775 ),
inference(avatar_split_clause,[],[f17645,f17641,f10406,f10097,f6714,f3706,f17647]) ).
fof(f17647,plain,
( spl0_1776
<=> ! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_plus(c_1,X18,tc_nat),c_plus(c_1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f17641,plain,
( spl0_1775
<=> ! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f17645,plain,
( ! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_plus(c_1,X18,tc_nat),c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1775 ),
inference(forward_demodulation,[],[f17644,f11227]) ).
fof(f17644,plain,
( ! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1775 ),
inference(forward_demodulation,[],[f17642,f11227]) ).
fof(f17642,plain,
( ! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_1775 ),
inference(avatar_component_clause,[],[f17641]) ).
fof(f17643,plain,
spl0_1775,
inference(avatar_split_clause,[],[f2791,f17641]) ).
fof(f2791,plain,
! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f876,f1385,f1385]) ).
fof(f876,axiom,
! [X2,X18] : c_minus(X18,X2,tc_nat) = c_minus(c_Suc(X18),c_Suc(X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f17639,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1682,f17637]) ).
fof(f17637,plain,
( spl0_1774
<=> ! [X5,X24,X10,X9,X20] :
( ~ c_in(X9,X24,X5)
| c_in(c_Sum__Type_OInr(X9,X5,X10),c_Sum__Type_OPlus(X20,X24,X10,X5),tc_sum(X10,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f1682,axiom,
! [X10,X9,X24,X5,X20] :
( ~ c_in(X9,X24,X5)
| c_in(c_Sum__Type_OInr(X9,X5,X10),c_Sum__Type_OPlus(X20,X24,X10,X5),tc_sum(X10,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInrI_0) ).
fof(f17635,plain,
spl0_1773,
inference(avatar_split_clause,[],[f1681,f17633]) ).
fof(f17633,plain,
( spl0_1773
<=> ! [X24,X10,X20,X5,X8] :
( ~ c_in(X8,X20,X5)
| c_in(c_Sum__Type_OInl(X8,X5,X10),c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f1681,axiom,
! [X10,X8,X24,X5,X20] :
( ~ c_in(X8,X20,X5)
| c_in(c_Sum__Type_OInl(X8,X5,X10),c_Sum__Type_OPlus(X20,X24,X5,X10),tc_sum(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInlI_0) ).
fof(f17631,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1644,f17629]) ).
fof(f1644,axiom,
! [X10,X8,X9,X5,X13] :
( c_in(X9,c_Relation_ORange(X13,X5,X10),X10)
| ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORangeI_0) ).
fof(f17627,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1640,f17625]) ).
fof(f17625,plain,
( spl0_1771
<=> ! [X10,X9,X13,X5,X20] :
( ~ c_in(X9,c_Relation_OImage(X13,X20,X10,X5),X5)
| c_in(c_Main_OImageE__1(X20,X9,X13,X10,X5),X20,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f1640,axiom,
! [X10,X9,X5,X13,X20] :
( ~ c_in(X9,c_Relation_OImage(X13,X20,X10,X5),X5)
| c_in(c_Main_OImageE__1(X20,X9,X13,X10,X5),X20,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImageE_0) ).
fof(f17623,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1639,f17621]) ).
fof(f17621,plain,
( spl0_1770
<=> ! [X5,X33] :
( ~ c_in(X33,c_Relation_OId,tc_prod(X5,X5))
| c_Pair(c_Main_OIdE__1(X33,X5),c_Main_OIdE__1(X33,X5),X5,X5) = X33 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f1639,axiom,
! [X5,X33] :
( ~ c_in(X33,c_Relation_OId,tc_prod(X5,X5))
| c_Pair(c_Main_OIdE__1(X33,X5),c_Main_OIdE__1(X33,X5),X5,X5) = X33 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OIdE_0) ).
fof(f17619,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1638,f17617]) ).
fof(f1638,axiom,
! [X10,X8,X9,X5,X13] :
( c_in(X8,c_Relation_ODomain(X13,X5,X10),X5)
| ~ c_in(c_Pair(X8,X9,X5,X10),X13,tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomainI_0) ).
fof(f17615,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1626,f17613]) ).
fof(f17613,plain,
( spl0_1768
<=> ! [X20,X5,X3,X67] :
( c_in(X67,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(c_List_Olist_OCons(X3,X67,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f1626,axiom,
! [X3,X5,X67,X20] :
( c_in(X67,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(c_List_Olist_OCons(X3,X67,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_0) ).
fof(f17611,plain,
( spl0_1767
| ~ spl0_1137
| ~ spl0_1406 ),
inference(avatar_split_clause,[],[f12528,f11557,f9226,f17609]) ).
fof(f17609,plain,
( spl0_1767
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f9226,plain,
( spl0_1137
<=> ! [X9,X5,X8,X10] : c_0 = c_Nat_Osize(c_Pair(X8,X9,X5,X10),tc_prod(X5,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f11557,plain,
( spl0_1406
<=> ! [X5,X1,X10] : c_Pair(c_fst(X1,X5,X10),c_snd(X1,X5,X10),X5,X10) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f12528,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1137
| ~ spl0_1406 ),
inference(superposition,[],[f9227,f11558]) ).
fof(f11558,plain,
( ! [X10,X1,X5] : c_Pair(c_fst(X1,X5,X10),c_snd(X1,X5,X10),X5,X10) = X1
| ~ spl0_1406 ),
inference(avatar_component_clause,[],[f11557]) ).
fof(f9227,plain,
( ! [X10,X8,X9,X5] : c_0 = c_Nat_Osize(c_Pair(X8,X9,X5,X10),tc_prod(X5,X10))
| ~ spl0_1137 ),
inference(avatar_component_clause,[],[f9226]) ).
fof(f17607,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1614,f17605]) ).
fof(f17605,plain,
( spl0_1766
<=> ! [X23,X34,X20,X5] :
( c_in(X23,X20,X5)
| ~ c_in(X23,c_List_Oset(X34,X5),X5)
| ~ c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f1614,axiom,
! [X34,X5,X23,X20] :
( c_in(X23,X20,X5)
| ~ c_in(X23,c_List_Oset(X34,X5),X5)
| ~ c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsD__dest_0) ).
fof(f17603,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1538,f17601]) ).
fof(f17601,plain,
( spl0_1765
<=> ! [X20,X5,X3] :
( ~ c_lessequals(X20,c_insert(X3,c_emptyset,X5),tc_set(X5))
| c_insert(X3,X20,X5) = c_insert(X3,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f1538,axiom,
! [X3,X5,X20] :
( ~ c_lessequals(X20,c_insert(X3,c_emptyset,X5),tc_set(X5))
| c_insert(X3,X20,X5) = c_insert(X3,c_emptyset,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_2) ).
fof(f17599,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1534,f17597]) ).
fof(f17597,plain,
( spl0_1764
<=> ! [X20,X9,X5,X8] :
( c_lessequals(X20,c_insert(X9,c_emptyset,X5),tc_set(X5))
| c_insert(X8,X20,X5) != c_insert(X9,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f1534,axiom,
! [X8,X9,X5,X20] :
( c_lessequals(X20,c_insert(X9,c_emptyset,X5),tc_set(X5))
| c_insert(X8,X20,X5) != c_insert(X9,c_emptyset,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_1) ).
fof(f17595,plain,
spl0_1763,
inference(avatar_split_clause,[],[f1531,f17593]) ).
fof(f17593,plain,
( spl0_1763
<=> ! [X24,X20,X5,X3] :
( ~ c_in(X3,X24,X5)
| ~ c_lessequals(X20,X24,tc_set(X5))
| c_lessequals(c_insert(X3,X20,X5),X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f1531,axiom,
! [X3,X24,X5,X20] :
( ~ c_in(X3,X24,X5)
| ~ c_lessequals(X20,X24,tc_set(X5))
| c_lessequals(c_insert(X3,X20,X5),X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_2) ).
fof(f17591,plain,
spl0_1762,
inference(avatar_split_clause,[],[f1414,f17589]) ).
fof(f17589,plain,
( spl0_1762
<=> ! [X5,X0] :
( ~ class_Orderings_Oorder(X5)
| c_insert(X0,c_emptyset,X5) = c_minus(c_insert(X0,c_emptyset,X5),c_SetInterval_OlessThan(X0,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f1414,axiom,
! [X0,X5] :
( ~ class_Orderings_Oorder(X5)
| c_insert(X0,c_emptyset,X5) = c_minus(c_insert(X0,c_emptyset,X5),c_SetInterval_OlessThan(X0,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f17587,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1406,f17585]) ).
fof(f17585,plain,
( spl0_1761
<=> ! [X2,X17,X18,X5,X45] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X45,X17,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f1406,axiom,
! [X2,X18,X45,X17,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X45,X17,X5)
| c_lessequals(c_SetInterval_OatLeastLessThan(X17,X45,X5),c_SetInterval_OatLeastLessThan(X18,X2,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Oivl__subset_2) ).
fof(f17583,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1397,f17581]) ).
fof(f17581,plain,
( spl0_1760
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X67,X17,X5)
| ~ c_less(X17,X31,X5)
| c_in(X17,c_SetInterval_OgreaterThanLessThan(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f1397,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X67,X17,X5)
| ~ c_less(X17,X31,X5)
| c_in(X17,c_SetInterval_OgreaterThanLessThan(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f17579,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1394,f17577]) ).
fof(f17577,plain,
( spl0_1759
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X17,X31,X5)
| ~ c_less(X67,X17,X5)
| c_in(X17,c_SetInterval_OgreaterThanAtMost(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f1394,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X17,X31,X5)
| ~ c_less(X67,X17,X5)
| c_in(X17,c_SetInterval_OgreaterThanAtMost(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f17575,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1367,f17573]) ).
fof(f17573,plain,
( spl0_1758
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X67,X17,X5)
| ~ c_less(X17,X31,X5)
| c_in(X17,c_SetInterval_OatLeastLessThan(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1367,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X67,X17,X5)
| ~ c_less(X17,X31,X5)
| c_in(X17,c_SetInterval_OatLeastLessThan(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f17571,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1362,f17569]) ).
fof(f17569,plain,
( spl0_1757
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X67,X17,X5)
| ~ c_lessequals(X17,X31,X5)
| c_in(X17,c_SetInterval_OatLeastAtMost(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1362,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X67,X17,X5)
| ~ c_lessequals(X17,X31,X5)
| c_in(X17,c_SetInterval_OatLeastAtMost(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f17567,plain,
( spl0_1756
| ~ spl0_113
| ~ spl0_1114
| ~ spl0_1209 ),
inference(avatar_split_clause,[],[f9906,f9520,f8934,f3711,f17565]) ).
fof(f8934,plain,
( spl0_1114
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f9520,plain,
( spl0_1209
<=> ! [X18,X2] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f9906,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1114
| ~ spl0_1209 ),
inference(forward_demodulation,[],[f9903,f8935]) ).
fof(f8935,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1114 ),
inference(avatar_component_clause,[],[f8934]) ).
fof(f9903,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_113
| ~ spl0_1209 ),
inference(superposition,[],[f9521,f3713]) ).
fof(f9521,plain,
( ! [X2,X18] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint)
| ~ spl0_1209 ),
inference(avatar_component_clause,[],[f9520]) ).
fof(f17563,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1165,f17561]) ).
fof(f17561,plain,
( spl0_1755
<=> ! [X5,X28,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X3,c_0,X5)
| ~ c_less(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f1165,axiom,
! [X3,X28,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X3,c_0,X5)
| ~ c_less(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f17559,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1148,f17557]) ).
fof(f17557,plain,
( spl0_1754
<=> ! [X5,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| c_Parity_Oeven(X3,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f1148,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| c_Parity_Oeven(X3,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneg__one__odd__power_0) ).
fof(f17555,plain,
spl0_1753,
inference(avatar_split_clause,[],[f1146,f17553]) ).
fof(f17553,plain,
( spl0_1753
<=> ! [X5,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X3,tc_nat)
| c_uminus(c_1,X5) = c_Nat_Opower(c_uminus(c_1,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f1146,axiom,
! [X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_Parity_Oeven(X3,tc_nat)
| c_uminus(c_1,X5) = c_Nat_Opower(c_uminus(c_1,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__odd__power_0) ).
fof(f17551,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1107,f17549]) ).
fof(f17549,plain,
( spl0_1752
<=> ! [X10,X3,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_lessequals(X3,X30,X10)
| ~ c_lessequals(X1,X30,X10)
| c_lessequals(c_Orderings_Omax(X3,X1,X10),X30,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f1107,axiom,
! [X3,X10,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_lessequals(X3,X30,X10)
| ~ c_lessequals(X1,X30,X10)
| c_lessequals(c_Orderings_Omax(X3,X1,X10),X30,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f17547,plain,
spl0_1751,
inference(avatar_split_clause,[],[f1102,f17545]) ).
fof(f17545,plain,
( spl0_1751
<=> ! [X3,X10,X30,X1] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_lessequals(X3,X1,X10)
| ~ c_lessequals(X3,X30,X10)
| c_lessequals(X3,c_Orderings_Omin(X1,X30,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f1102,axiom,
! [X3,X10,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| ~ c_lessequals(X3,X1,X10)
| ~ c_lessequals(X3,X30,X10)
| c_lessequals(X3,c_Orderings_Omin(X1,X30,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f17543,plain,
spl0_1750,
inference(avatar_split_clause,[],[f1099,f17541]) ).
fof(f17541,plain,
( spl0_1750
<=> ! [X5,X3,X30,X1] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X30,X3,X5)
| ~ c_less(X30,X1,X5)
| c_less(X30,c_Orderings_Omin(X3,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f1099,axiom,
! [X3,X1,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X30,X3,X5)
| ~ c_less(X30,X1,X5)
| c_less(X30,c_Orderings_Omin(X3,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f17539,plain,
spl0_1749,
inference(avatar_split_clause,[],[f1096,f17537]) ).
fof(f17537,plain,
( spl0_1749
<=> ! [X5,X3,X1,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X3,X30,X5)
| ~ c_less(X1,X30,X5)
| c_less(c_Orderings_Omax(X3,X1,X5),X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f1096,axiom,
! [X3,X1,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_less(X3,X30,X5)
| ~ c_less(X1,X30,X5)
| c_less(c_Orderings_Omax(X3,X1,X5),X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f17535,plain,
spl0_1748,
inference(avatar_split_clause,[],[f1078,f17533]) ).
fof(f17533,plain,
( spl0_1748
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Omeet(X8,X9,X5),X5) = c_LOrder_Ojoin(c_uminus(X8,X5),c_uminus(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f1078,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Omeet(X8,X9,X5),X5) = c_LOrder_Ojoin(c_uminus(X8,X5),c_uminus(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f17531,plain,
spl0_1747,
inference(avatar_split_clause,[],[f1069,f17529]) ).
fof(f17529,plain,
( spl0_1747
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Ojoin(X8,X9,X5),X5) = c_LOrder_Omeet(c_uminus(X8,X5),c_uminus(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f1069,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_uminus(c_LOrder_Ojoin(X8,X9,X5),X5) = c_LOrder_Omeet(c_uminus(X8,X5),c_uminus(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f17527,plain,
spl0_1746,
inference(avatar_split_clause,[],[f1055,f17525]) ).
fof(f17525,plain,
( spl0_1746
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_plus(X8,X9,X5),X5) = c_plus(c_uminus(X8,X5),c_uminus(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f1055,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_plus(X8,X9,X5),X5) = c_plus(c_uminus(X8,X5),c_uminus(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f17523,plain,
spl0_1745,
inference(avatar_split_clause,[],[f684,f17521]) ).
fof(f17521,plain,
( spl0_1745
<=> ! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f684,axiom,
! [X70,X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f17519,plain,
spl0_1744,
inference(avatar_split_clause,[],[f677,f17517]) ).
fof(f17517,plain,
( spl0_1744
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f677,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_nat) = c_Numeral_Onumber__of(X70,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f17515,plain,
spl0_1743,
inference(avatar_split_clause,[],[f665,f17513]) ).
fof(f17513,plain,
( spl0_1743
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X70,tc_nat) = c_plus(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f665,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X70,tc_nat) = c_plus(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f17511,plain,
spl0_1742,
inference(avatar_split_clause,[],[f662,f17509]) ).
fof(f17509,plain,
( spl0_1742
<=> ! [X2,X5,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_times(X18,X2,tc_nat),X5) = c_times(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f662,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_times(X18,X2,tc_nat),X5) = c_times(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__mult_0) ).
fof(f17507,plain,
spl0_1741,
inference(avatar_split_clause,[],[f650,f17505]) ).
fof(f17505,plain,
( spl0_1741
<=> ! [X2,X5,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_plus(X18,X2,tc_nat),X5) = c_plus(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f650,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_NatArith_Oof__nat(c_plus(X18,X2,tc_nat),X5) = c_plus(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__add_0) ).
fof(f17503,plain,
spl0_1740,
inference(avatar_split_clause,[],[f622,f17501]) ).
fof(f17501,plain,
( spl0_1740
<=> ! [X2,X5,X3] :
( c_0 = X2
| c_List_Otl(c_List_Oreplicate(X2,X3,X5),X5) = c_List_Oreplicate(c_minus(X2,c_1,tc_nat),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f622,axiom,
! [X2,X3,X5] :
( c_0 = X2
| c_List_Otl(c_List_Oreplicate(X2,X3,X5),X5) = c_List_Oreplicate(c_minus(X2,c_1,tc_nat),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl__replicate_0) ).
fof(f17499,plain,
spl0_1739,
inference(avatar_split_clause,[],[f540,f17497]) ).
fof(f17497,plain,
( spl0_1739
<=> ! [X17,X34,X5,X1] :
( ~ c_less(X17,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Olist__update(X34,X17,X1,X5),X17,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f540,axiom,
! [X1,X17,X34,X5] :
( ~ c_less(X17,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Onth(c_List_Olist__update(X34,X17,X1,X5),X17,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__list__update__eq_0) ).
fof(f17495,plain,
spl0_1738,
inference(avatar_split_clause,[],[f474,f17493]) ).
fof(f17493,plain,
( spl0_1738
<=> ! [X5,X1,X17] :
( ~ c_less(X17,c_Nat_Osize(X1,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(X1,X17,c_List_Onth(X1,X17,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f474,axiom,
! [X1,X17,X5] :
( ~ c_less(X17,c_Nat_Osize(X1,tc_List_Olist(X5)),tc_nat)
| c_List_Olist__update(X1,X17,c_List_Onth(X1,X17,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__id_0) ).
fof(f17491,plain,
spl0_1737,
inference(avatar_split_clause,[],[f433,f17489]) ).
fof(f17489,plain,
( spl0_1737
<=> ! [X34,X5,X2] :
( ~ c_less(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Olast(X34,X5) = c_List_Olast(c_List_Odrop(X2,X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f433,axiom,
! [X2,X34,X5] :
( ~ c_less(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_List_Olast(X34,X5) = c_List_Olast(c_List_Odrop(X2,X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__drop_0) ).
fof(f17487,plain,
spl0_1736,
inference(avatar_split_clause,[],[f366,f17485]) ).
fof(f17485,plain,
( spl0_1736
<=> ! [X34,X20,X5,X35] :
( c_in(X35,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X34,X35,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f366,axiom,
! [X34,X35,X5,X20] :
( c_in(X35,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X34,X35,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_1) ).
fof(f17483,plain,
( spl0_1734
| ~ spl0_1735
| ~ spl0_125
| ~ spl0_1183 ),
inference(avatar_split_clause,[],[f9739,f9411,f3763,f17480,f17477]) ).
fof(f17477,plain,
( spl0_1734
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f17480,plain,
( spl0_1735
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f3763,plain,
( spl0_125
<=> ! [X2] : c_lessequals(c_0,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f9411,plain,
( spl0_1183
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(c_0,X1,X5)
| c_HOL_Oabs(X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f9739,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_125
| ~ spl0_1183 ),
inference(resolution,[],[f9412,f3764]) ).
fof(f3764,plain,
( ! [X2] : c_lessequals(c_0,X2,tc_nat)
| ~ spl0_125 ),
inference(avatar_component_clause,[],[f3763]) ).
fof(f9412,plain,
( ! [X1,X5] :
( ~ c_lessequals(c_0,X1,X5)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X1,X5) = X1 )
| ~ spl0_1183 ),
inference(avatar_component_clause,[],[f9411]) ).
fof(f17475,plain,
spl0_1733,
inference(avatar_split_clause,[],[f365,f17473]) ).
fof(f17473,plain,
( spl0_1733
<=> ! [X35,X34,X20,X5] :
( c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X34,X35,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f365,axiom,
! [X34,X5,X35,X20] :
( c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5))
| ~ c_in(c_append(X34,X35,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__in__lists__conv_0) ).
fof(f17471,plain,
spl0_1732,
inference(avatar_split_clause,[],[f258,f17469]) ).
fof(f17469,plain,
( spl0_1732
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_times(X28,X30,tc_IntDef_Oint),X5) = c_times(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f258,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_times(X28,X30,tc_IntDef_Oint),X5) = c_times(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__mult_0) ).
fof(f17467,plain,
spl0_1731,
inference(avatar_split_clause,[],[f244,f17465]) ).
fof(f17465,plain,
( spl0_1731
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_minus(X28,X30,tc_IntDef_Oint),X5) = c_minus(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f244,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_minus(X28,X30,tc_IntDef_Oint),X5) = c_minus(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__diff_0) ).
fof(f17463,plain,
spl0_1730,
inference(avatar_split_clause,[],[f243,f17461]) ).
fof(f17461,plain,
( spl0_1730
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_plus(X28,X30,tc_IntDef_Oint),X5) = c_plus(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f243,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_plus(X28,X30,tc_IntDef_Oint),X5) = c_plus(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__add_0) ).
fof(f17459,plain,
spl0_1729,
inference(avatar_split_clause,[],[f207,f17457]) ).
fof(f17457,plain,
( spl0_1729
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X8,c_IntDef_ONats,X5)
| ~ c_in(X9,c_IntDef_ONats,X5)
| c_in(c_times(X8,X9,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f207,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X8,c_IntDef_ONats,X5)
| ~ c_in(X9,c_IntDef_ONats,X5)
| c_in(c_times(X8,X9,X5),c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__mult_0) ).
fof(f17455,plain,
spl0_1728,
inference(avatar_split_clause,[],[f206,f17453]) ).
fof(f17453,plain,
( spl0_1728
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X8,c_IntDef_ONats,X5)
| ~ c_in(X9,c_IntDef_ONats,X5)
| c_in(c_plus(X8,X9,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f206,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_in(X8,c_IntDef_ONats,X5)
| ~ c_in(X9,c_IntDef_ONats,X5)
| c_in(c_plus(X8,X9,X5),c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__add_0) ).
fof(f17451,plain,
spl0_1727,
inference(avatar_split_clause,[],[f203,f17449]) ).
fof(f17449,plain,
( spl0_1727
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| ~ c_in(X9,c_IntDef_OInts,X5)
| c_in(c_times(X8,X9,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f203,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| ~ c_in(X9,c_IntDef_OInts,X5)
| c_in(c_times(X8,X9,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__mult_0) ).
fof(f17447,plain,
spl0_1726,
inference(avatar_split_clause,[],[f201,f17445]) ).
fof(f17445,plain,
( spl0_1726
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| ~ c_in(X9,c_IntDef_OInts,X5)
| c_in(c_minus(X8,X9,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f201,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| ~ c_in(X9,c_IntDef_OInts,X5)
| c_in(c_minus(X8,X9,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__diff_0) ).
fof(f17443,plain,
spl0_1725,
inference(avatar_split_clause,[],[f200,f17441]) ).
fof(f17441,plain,
( spl0_1725
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| ~ c_in(X9,c_IntDef_OInts,X5)
| c_in(c_plus(X8,X9,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f200,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| ~ c_in(X9,c_IntDef_OInts,X5)
| c_in(c_plus(X8,X9,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__add_0) ).
fof(f17439,plain,
spl0_1724,
inference(avatar_split_clause,[],[f147,f17437]) ).
fof(f17437,plain,
( spl0_1724
<=> ! [X2,X0,X18] :
( ~ c_Divides_Oop_Advd(X0,X2,tc_nat)
| ~ c_Divides_Oop_Advd(X0,X18,tc_nat)
| c_Divides_Oop_Advd(X0,c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f147,axiom,
! [X2,X0,X18] :
( ~ c_Divides_Oop_Advd(X0,X2,tc_nat)
| ~ c_Divides_Oop_Advd(X0,X18,tc_nat)
| c_Divides_Oop_Advd(X0,c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f17435,plain,
( spl0_1723
| ~ spl0_700
| ~ spl0_727
| ~ spl0_866
| ~ spl0_1178 ),
inference(avatar_split_clause,[],[f9721,f9391,f7541,f6965,f6852,f17432]) ).
fof(f17432,plain,
( spl0_1723
<=> 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_1723])]) ).
fof(f6852,plain,
( spl0_700
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f6965,plain,
( spl0_727
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f7541,plain,
( spl0_866
<=> 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_866])]) ).
fof(f9391,plain,
( spl0_1178
<=> ! [X29,X28] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),X28) = c_Numeral_OBit(c_Numeral_Obin__mult(X29,X28),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f9721,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),c_Numeral_OPls)
| ~ spl0_700
| ~ spl0_727
| ~ spl0_866
| ~ spl0_1178 ),
inference(forward_demodulation,[],[f9720,f6854]) ).
fof(f6854,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f6852]) ).
fof(f9720,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_727
| ~ spl0_866
| ~ spl0_1178 ),
inference(forward_demodulation,[],[f9716,f7543]) ).
fof(f7543,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_866 ),
inference(avatar_component_clause,[],[f7541]) ).
fof(f9716,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_727
| ~ spl0_1178 ),
inference(superposition,[],[f9392,f6967]) ).
fof(f6967,plain,
( c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)
| ~ spl0_727 ),
inference(avatar_component_clause,[],[f6965]) ).
fof(f9392,plain,
( ! [X28,X29] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),X28) = c_Numeral_OBit(c_Numeral_Obin__mult(X29,X28),c_Numeral_Obit_OB0)
| ~ spl0_1178 ),
inference(avatar_component_clause,[],[f9391]) ).
fof(f17430,plain,
spl0_1722,
inference(avatar_split_clause,[],[f131,f17428]) ).
fof(f17428,plain,
( spl0_1722
<=> ! [X13,X5,X10] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(tc_prod(X10,X5)))
| c_in(c_Relation_Oconverse(X13,X10,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f131,axiom,
! [X10,X5,X13] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(tc_prod(X10,X5)))
| c_in(c_Relation_Oconverse(X13,X10,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_1) ).
fof(f17426,plain,
spl0_1721,
inference(avatar_split_clause,[],[f130,f17424]) ).
fof(f17424,plain,
( spl0_1721
<=> ! [X13,X5,X10] :
( c_in(X13,c_Finite__Set_OFinites,tc_set(tc_prod(X10,X5)))
| ~ c_in(c_Relation_Oconverse(X13,X10,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X10))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f130,axiom,
! [X10,X5,X13] :
( c_in(X13,c_Finite__Set_OFinites,tc_set(tc_prod(X10,X5)))
| ~ c_in(c_Relation_Oconverse(X13,X10,X5),c_Finite__Set_OFinites,tc_set(tc_prod(X5,X10))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__converse_0) ).
fof(f17270,plain,
( spl0_1720
| ~ spl0_118
| ~ spl0_1158 ),
inference(avatar_split_clause,[],[f9628,f9311,f3733,f17267]) ).
fof(f17267,plain,
( spl0_1720
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f9311,plain,
( spl0_1158
<=> ! [X45,X1] :
( ~ c_less(X1,X45,tc_nat)
| c_List_Ohd(c_List_Oupt(X1,X45),tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f9628,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_118
| ~ spl0_1158 ),
inference(resolution,[],[f9312,f3735]) ).
fof(f9312,plain,
( ! [X1,X45] :
( ~ c_less(X1,X45,tc_nat)
| c_List_Ohd(c_List_Oupt(X1,X45),tc_nat) = X1 )
| ~ spl0_1158 ),
inference(avatar_component_clause,[],[f9311]) ).
fof(f17040,plain,
( spl0_1719
| ~ spl0_778
| ~ spl0_1094 ),
inference(avatar_split_clause,[],[f9141,f8853,f7184,f17038]) ).
fof(f17038,plain,
( spl0_1719
<=> ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f7184,plain,
( spl0_778
<=> ! [X1] : c_minus(X1,c_0,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f8853,plain,
( spl0_1094
<=> ! [X2,X18] :
( c_lessequals(X18,X2,tc_nat)
| c_0 != c_minus(X18,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f9141,plain,
( ! [X0] :
( c_0 != X0
| c_lessequals(X0,c_0,tc_nat) )
| ~ spl0_778
| ~ spl0_1094 ),
inference(superposition,[],[f8854,f7185]) ).
fof(f7185,plain,
( ! [X1] : c_minus(X1,c_0,tc_nat) = X1
| ~ spl0_778 ),
inference(avatar_component_clause,[],[f7184]) ).
fof(f8854,plain,
( ! [X2,X18] :
( c_0 != c_minus(X18,X2,tc_nat)
| c_lessequals(X18,X2,tc_nat) )
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f8853]) ).
fof(f16777,plain,
( spl0_1718
| ~ spl0_854
| ~ spl0_1020 ),
inference(avatar_split_clause,[],[f8613,f8354,f7492,f16775]) ).
fof(f16775,plain,
( spl0_1718
<=> ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f7492,plain,
( spl0_854
<=> ! [X20,X5,X3] : c_in(X3,c_insert(X3,X20,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f8354,plain,
( spl0_1020
<=> ! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f8613,plain,
( ! [X0] : c_in(c_emptyset,c_Pow(c_emptyset,X0),tc_set(X0))
| ~ spl0_854
| ~ spl0_1020 ),
inference(superposition,[],[f7493,f8355]) ).
fof(f8355,plain,
( ! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5))
| ~ spl0_1020 ),
inference(avatar_component_clause,[],[f8354]) ).
fof(f7493,plain,
( ! [X3,X5,X20] : c_in(X3,c_insert(X3,X20,X5),X5)
| ~ spl0_854 ),
inference(avatar_component_clause,[],[f7492]) ).
fof(f16696,plain,
( spl0_1717
| ~ spl0_13
| ~ spl0_1010 ),
inference(avatar_split_clause,[],[f8604,f8314,f3217,f16694]) ).
fof(f16694,plain,
( spl0_1717
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f3217,plain,
( spl0_13
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f8314,plain,
( spl0_1010
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_uminus(X1,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f8604,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_13
| ~ spl0_1010 ),
inference(resolution,[],[f8315,f3219]) ).
fof(f3219,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f3217]) ).
fof(f8315,plain,
( ! [X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_uminus(X1,X5),X5) = X1 )
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f8314]) ).
fof(f16540,plain,
( spl0_1716
| ~ spl0_56
| ~ spl0_1006 ),
inference(avatar_split_clause,[],[f8596,f8298,f3432,f16537]) ).
fof(f8298,plain,
( spl0_1006
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f8596,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_1006 ),
inference(resolution,[],[f8299,f3434]) ).
fof(f8299,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) )
| ~ spl0_1006 ),
inference(avatar_component_clause,[],[f8298]) ).
fof(f16386,plain,
( spl0_1715
| ~ spl0_854
| ~ spl0_994 ),
inference(avatar_split_clause,[],[f8562,f8249,f7492,f16384]) ).
fof(f16384,plain,
( spl0_1715
<=> ! [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_1715])]) ).
fof(f8249,plain,
( spl0_994
<=> ! [X6] : c_List_Olistset(c_List_Olist_ONil,X6) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f8562,plain,
( ! [X0] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X0),tc_List_Olist(X0))
| ~ spl0_854
| ~ spl0_994 ),
inference(superposition,[],[f7493,f8250]) ).
fof(f8250,plain,
( ! [X6] : c_List_Olistset(c_List_Olist_ONil,X6) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X6))
| ~ spl0_994 ),
inference(avatar_component_clause,[],[f8249]) ).
fof(f16304,plain,
( spl0_1712
| spl0_1714 ),
inference(avatar_split_clause,[],[f3155,f16302,f16281]) ).
fof(f16281,plain,
( spl0_1712
<=> ! [X28] : c_0 != c_Numeral_Onumber__of(X28,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f16302,plain,
( spl0_1714
<=> ! [X5,X3] :
( ~ class_Power_Orecpower(X5)
| c_less(c_0,c_Nat_Opower(X3,c_0,X5),X5)
| ~ class_Ring__and__Field_Oordered__idom(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f3155,plain,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X28,tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_0,X5),X5) ),
inference(inner_rewriting,[],[f1175]) ).
fof(f1175,axiom,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X28,tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f16290,plain,
( ~ spl0_698
| ~ spl0_1712 ),
inference(avatar_contradiction_clause,[],[f16289]) ).
fof(f16289,plain,
( $false
| ~ spl0_698
| ~ spl0_1712 ),
inference(trivial_inequality_removal,[],[f16287]) ).
fof(f16287,plain,
( c_0 != c_0
| ~ spl0_698
| ~ spl0_1712 ),
inference(superposition,[],[f16282,f6844]) ).
fof(f6844,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_698 ),
inference(avatar_component_clause,[],[f6842]) ).
fof(f6842,plain,
( spl0_698
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f16282,plain,
( ! [X28] : c_0 != c_Numeral_Onumber__of(X28,tc_nat)
| ~ spl0_1712 ),
inference(avatar_component_clause,[],[f16281]) ).
fof(f16286,plain,
( spl0_1712
| spl0_1713 ),
inference(avatar_split_clause,[],[f3154,f16284,f16281]) ).
fof(f16284,plain,
( spl0_1713
<=> ! [X5,X3] :
( ~ class_Power_Orecpower(X5)
| ~ c_lessequals(c_Nat_Opower(X3,c_0,X5),c_0,X5)
| ~ class_Ring__and__Field_Oordered__idom(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f3154,plain,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X3,c_0,X5),c_0,X5) ),
inference(inner_rewriting,[],[f1158]) ).
fof(f1158,axiom,
! [X28,X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 != c_Numeral_Onumber__of(X28,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f16253,plain,
( spl0_1711
| ~ spl0_112
| ~ spl0_670
| ~ spl0_768
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1602
| ~ spl0_1709 ),
inference(avatar_split_clause,[],[f16245,f16241,f14444,f10406,f10097,f7144,f6714,f3706,f16251]) ).
fof(f16251,plain,
( spl0_1711
<=> ! [X1] :
( c_plus(c_1,c_minus(X1,c_1,tc_nat),tc_nat) = X1
| ~ c_less(c_0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f14444,plain,
( spl0_1602
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_plus(c_1,X67,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f16241,plain,
( spl0_1709
<=> ! [X1] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X1,tc_nat),tc_nat),tc_nat),tc_nat) = X1
| ~ c_less(c_0,X1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f16245,plain,
( ! [X1] :
( c_plus(c_1,c_minus(X1,c_1,tc_nat),tc_nat) = X1
| ~ c_less(c_0,X1,tc_nat) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_768
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1602
| ~ spl0_1709 ),
inference(forward_demodulation,[],[f16244,f14447]) ).
fof(f14447,plain,
( ! [X0] : c_minus(X0,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X0,tc_nat),tc_nat)
| ~ spl0_768
| ~ spl0_1602 ),
inference(superposition,[],[f14445,f7145]) ).
fof(f14445,plain,
( ! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_plus(c_1,X67,tc_nat),tc_nat)
| ~ spl0_1602 ),
inference(avatar_component_clause,[],[f14444]) ).
fof(f16244,plain,
( ! [X1] :
( c_plus(c_1,c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X1,tc_nat),tc_nat),tc_nat) = X1
| ~ c_less(c_0,X1,tc_nat) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1709 ),
inference(forward_demodulation,[],[f16242,f11227]) ).
fof(f16242,plain,
( ! [X1] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X1,tc_nat),tc_nat),tc_nat),tc_nat) = X1
| ~ c_less(c_0,X1,tc_nat) )
| ~ spl0_1709 ),
inference(avatar_component_clause,[],[f16241]) ).
fof(f16249,plain,
( spl0_1710
| ~ spl0_113
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8109,f7921,f3711,f16247]) ).
fof(f16247,plain,
( spl0_1710
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f7921,plain,
( spl0_942
<=> ! [X18,X2] : c_lessequals(c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8109,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_942 ),
inference(superposition,[],[f7922,f3713]) ).
fof(f7922,plain,
( ! [X2,X18] : c_lessequals(c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint)
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f7921]) ).
fof(f16243,plain,
spl0_1709,
inference(avatar_split_clause,[],[f3045,f16241]) ).
fof(f3045,plain,
! [X1] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(c_0,X1,tc_nat),tc_nat),tc_nat),tc_nat) = X1
| ~ c_less(c_0,X1,tc_nat) ),
inference(forward_demodulation,[],[f2863,f2796]) ).
fof(f2863,plain,
! [X1] :
( ~ c_less(c_0,X1,tc_nat)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_minus(X1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),tc_nat),tc_nat) = X1 ),
inference(definition_unfolding,[],[f865,f1385,f1385]) ).
fof(f865,axiom,
! [X1] :
( ~ c_less(c_0,X1,tc_nat)
| c_Suc(c_minus(X1,c_Suc(c_0),tc_nat)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__pred_0) ).
fof(f16239,plain,
spl0_1708,
inference(avatar_split_clause,[],[f2894,f16237]) ).
fof(f16237,plain,
( spl0_1708
<=> ! [X24,X20,X5,X73] :
( c_lessequals(X73,X20,tc_set(X5))
| ~ c_lessequals(X73,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f2894,plain,
! [X73,X24,X5,X20] :
( c_lessequals(X73,X20,tc_set(X5))
| ~ c_lessequals(X73,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ),
inference(definition_unfolding,[],[f1450,f1214]) ).
fof(f1450,axiom,
! [X73,X24,X5,X20] :
( c_lessequals(X73,X20,tc_set(X5))
| ~ c_lessequals(X73,c_inter(X20,X24,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_0) ).
fof(f16235,plain,
spl0_1707,
inference(avatar_split_clause,[],[f2893,f16233]) ).
fof(f16233,plain,
( spl0_1707
<=> ! [X24,X20,X5,X73] :
( c_lessequals(X73,X24,tc_set(X5))
| ~ c_lessequals(X73,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f2893,plain,
! [X73,X24,X5,X20] :
( c_lessequals(X73,X24,tc_set(X5))
| ~ c_lessequals(X73,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),tc_set(X5)) ),
inference(definition_unfolding,[],[f1451,f1214]) ).
fof(f1451,axiom,
! [X73,X24,X5,X20] :
( c_lessequals(X73,X24,tc_set(X5))
| ~ c_lessequals(X73,c_inter(X20,X24,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__subset__iff_1) ).
fof(f16231,plain,
spl0_1706,
inference(avatar_split_clause,[],[f2889,f16229]) ).
fof(f16229,plain,
( spl0_1706
<=> ! [X5,X27,X26] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X26,X5),X27,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f2889,plain,
! [X26,X27,X5] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X26,X5),X27,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
inference(definition_unfolding,[],[f1598,f1214]) ).
fof(f1598,axiom,
! [X26,X27,X5] :
( ~ c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_inter(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_0) ).
fof(f16227,plain,
spl0_1705,
inference(avatar_split_clause,[],[f2888,f16225]) ).
fof(f16225,plain,
( spl0_1705
<=> ! [X5,X27,X26] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X26,X5),X27,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f2888,plain,
! [X26,X27,X5] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Relation_OImage(c_Relation_Odiag(X26,X5),X27,X5,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
inference(definition_unfolding,[],[f1599,f1214]) ).
fof(f1599,axiom,
! [X26,X27,X5] :
( ~ c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_inter(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).
fof(f16221,plain,
spl0_1704,
inference(avatar_split_clause,[],[f2881,f16219]) ).
fof(f16219,plain,
( spl0_1704
<=> ! [X18,X2] :
( c_lessequals(X2,X18,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f2881,plain,
! [X2,X18] :
( c_lessequals(X2,X18,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f860,f1385,f1385]) ).
fof(f860,axiom,
! [X2,X18] :
( c_lessequals(X2,X18,tc_nat)
| ~ c_lessequals(c_Suc(X2),c_Suc(X18),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_0) ).
fof(f16215,plain,
spl0_1703,
inference(avatar_split_clause,[],[f2879,f16213]) ).
fof(f16213,plain,
( spl0_1703
<=> ! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f2879,plain,
! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f862,f1385,f1385]) ).
fof(f862,axiom,
! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_Suc(X18),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_0) ).
fof(f16211,plain,
spl0_1702,
inference(avatar_split_clause,[],[f2874,f16209]) ).
fof(f16209,plain,
( spl0_1702
<=> ! [X24,X20,X5,X8] :
( ~ c_in(X8,X24,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),X24,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f2874,plain,
! [X8,X24,X5,X20] :
( ~ c_in(X8,X24,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(c_insert(X8,X20,X5),X5),X24,X5,X5) ),
inference(definition_unfolding,[],[f1521,f1214]) ).
fof(f1521,axiom,
! [X8,X24,X5,X20] :
( ~ c_in(X8,X24,X5)
| c_emptyset != c_inter(c_insert(X8,X20,X5),X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__disjoint__2_0) ).
fof(f16207,plain,
spl0_1701,
inference(avatar_split_clause,[],[f2872,f16205]) ).
fof(f2872,plain,
! [X9,X24,X5,X20] :
( ~ c_in(X9,X20,X5)
| c_emptyset != c_Relation_OImage(c_Relation_Odiag(X20,X5),c_insert(X9,X24,X5),X5,X5) ),
inference(definition_unfolding,[],[f1505,f1214]) ).
fof(f1505,axiom,
! [X9,X24,X5,X20] :
( ~ c_in(X9,X20,X5)
| c_emptyset != c_inter(X20,c_insert(X9,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odisjoint__insert__2_0) ).
fof(f16201,plain,
spl0_1700,
inference(avatar_split_clause,[],[f2870,f16199]) ).
fof(f16199,plain,
( spl0_1700
<=> ! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f2870,plain,
! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f863,f1385,f1385]) ).
fof(f863,axiom,
! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_Suc(X18),c_Suc(X2),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__less__eq_1) ).
fof(f16197,plain,
( spl0_1699
| ~ spl0_112
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8108,f7921,f3706,f16195]) ).
fof(f16195,plain,
( spl0_1699
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f8108,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_942 ),
inference(superposition,[],[f7922,f3708]) ).
fof(f16191,plain,
spl0_1698,
inference(avatar_split_clause,[],[f2865,f16189]) ).
fof(f16189,plain,
( spl0_1698
<=> ! [X18,X2] :
( ~ c_lessequals(X2,X18,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f2865,plain,
! [X2,X18] :
( ~ c_lessequals(X2,X18,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f861,f1385,f1385]) ).
fof(f861,axiom,
! [X2,X18] :
( ~ c_lessequals(X2,X18,tc_nat)
| c_lessequals(c_Suc(X2),c_Suc(X18),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__le__mono_1) ).
fof(f16183,plain,
( spl0_1697
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1696 ),
inference(avatar_split_clause,[],[f16179,f16176,f10406,f10097,f6714,f3706,f16181]) ).
fof(f16181,plain,
( spl0_1697
<=> ! [X6,X18] :
( c_plus(c_NatArith_Oof__nat(X18,X6),c_1,X6) = c_NatArith_Oof__nat(c_plus(c_1,X18,tc_nat),X6)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f16176,plain,
( spl0_1696
<=> ! [X6,X18] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X6)
| c_plus(c_NatArith_Oof__nat(X18,X6),c_1,X6) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f16179,plain,
( ! [X18,X6] :
( c_plus(c_NatArith_Oof__nat(X18,X6),c_1,X6) = c_NatArith_Oof__nat(c_plus(c_1,X18,tc_nat),X6)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X6) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1696 ),
inference(forward_demodulation,[],[f16177,f11227]) ).
fof(f16177,plain,
( ! [X18,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X6)
| c_plus(c_NatArith_Oof__nat(X18,X6),c_1,X6) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X6) )
| ~ spl0_1696 ),
inference(avatar_component_clause,[],[f16176]) ).
fof(f16178,plain,
spl0_1696,
inference(avatar_split_clause,[],[f2850,f16176]) ).
fof(f2850,plain,
! [X18,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X6)
| c_plus(c_NatArith_Oof__nat(X18,X6),c_1,X6) = c_NatArith_Oof__nat(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X6) ),
inference(definition_unfolding,[],[f643,f1385]) ).
fof(f643,axiom,
! [X18,X6] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X6)
| c_NatArith_Oof__nat(c_Suc(X18),X6) = c_plus(c_NatArith_Oof__nat(X18,X6),c_1,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f16170,plain,
( spl0_1695
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1694 ),
inference(avatar_split_clause,[],[f16166,f16163,f10406,f10097,f6714,f3706,f16168]) ).
fof(f16168,plain,
( spl0_1695
<=> ! [X3,X34,X5,X2] : c_List_Onth(X34,X2,X5) = c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_plus(c_1,X2,tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f16163,plain,
( spl0_1694
<=> ! [X3,X34,X5,X2] : c_List_Onth(X34,X2,X5) = c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f16166,plain,
( ! [X2,X3,X34,X5] : c_List_Onth(X34,X2,X5) = c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_plus(c_1,X2,tc_nat),X5)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1694 ),
inference(forward_demodulation,[],[f16164,f11227]) ).
fof(f16164,plain,
( ! [X2,X3,X34,X5] : c_List_Onth(X34,X2,X5) = c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X5)
| ~ spl0_1694 ),
inference(avatar_component_clause,[],[f16163]) ).
fof(f16165,plain,
spl0_1694,
inference(avatar_split_clause,[],[f2810,f16163]) ).
fof(f2810,plain,
! [X2,X3,X34,X5] : c_List_Onth(X34,X2,X5) = c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X5),
inference(definition_unfolding,[],[f534,f1385]) ).
fof(f534,axiom,
! [X2,X3,X34,X5] : c_List_Onth(c_List_Olist_OCons(X3,X34,X5),c_Suc(X2),X5) = c_List_Onth(X34,X2,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__Suc_0) ).
fof(f16148,plain,
( spl0_1693
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1692 ),
inference(avatar_split_clause,[],[f16144,f16141,f10406,f10097,f6714,f3706,f16146]) ).
fof(f16146,plain,
( spl0_1693
<=> ! [X3,X34,X5,X2] : c_List_Odrop(X2,X34,X5) = c_List_Odrop(c_plus(c_1,X2,tc_nat),c_List_Olist_OCons(X3,X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f16141,plain,
( spl0_1692
<=> ! [X3,X34,X5,X2] : c_List_Odrop(X2,X34,X5) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_List_Olist_OCons(X3,X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f16144,plain,
( ! [X2,X3,X34,X5] : c_List_Odrop(X2,X34,X5) = c_List_Odrop(c_plus(c_1,X2,tc_nat),c_List_Olist_OCons(X3,X34,X5),X5)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1692 ),
inference(forward_demodulation,[],[f16142,f11227]) ).
fof(f16142,plain,
( ! [X2,X3,X34,X5] : c_List_Odrop(X2,X34,X5) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_List_Olist_OCons(X3,X34,X5),X5)
| ~ spl0_1692 ),
inference(avatar_component_clause,[],[f16141]) ).
fof(f16143,plain,
spl0_1692,
inference(avatar_split_clause,[],[f2809,f16141]) ).
fof(f2809,plain,
! [X2,X3,X34,X5] : c_List_Odrop(X2,X34,X5) = c_List_Odrop(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),c_List_Olist_OCons(X3,X34,X5),X5),
inference(definition_unfolding,[],[f413,f1385]) ).
fof(f413,axiom,
! [X2,X3,X34,X5] : c_List_Odrop(c_Suc(X2),c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Odrop(X2,X34,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__Suc__Cons_0) ).
fof(f16139,plain,
( spl0_1691
| ~ spl0_112
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8106,f7921,f3706,f16137]) ).
fof(f8106,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_942 ),
inference(superposition,[],[f7922,f3708]) ).
fof(f16109,plain,
( spl0_1690
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1689 ),
inference(avatar_split_clause,[],[f16105,f16102,f10406,f10097,f6714,f3706,f16107]) ).
fof(f16102,plain,
( spl0_1689
<=> ! [X6,X2,X3] : c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X3,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f16105,plain,
( ! [X2,X3,X6] : c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6) = c_List_Oreplicate(c_plus(c_1,X2,tc_nat),X3,X6)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1689 ),
inference(forward_demodulation,[],[f16103,f11227]) ).
fof(f16103,plain,
( ! [X2,X3,X6] : c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X3,X6)
| ~ spl0_1689 ),
inference(avatar_component_clause,[],[f16102]) ).
fof(f16104,plain,
spl0_1689,
inference(avatar_split_clause,[],[f2808,f16102]) ).
fof(f2808,plain,
! [X2,X3,X6] : c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6) = c_List_Oreplicate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X3,X6),
inference(definition_unfolding,[],[f564,f1385]) ).
fof(f564,axiom,
! [X2,X3,X6] : c_List_Oreplicate(c_Suc(X2),X3,X6) = c_List_Olist_OCons(X3,c_List_Oreplicate(X2,X3,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f16005,plain,
( spl0_1688
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1687 ),
inference(avatar_split_clause,[],[f16001,f15998,f10406,f10097,f6714,f3706,f16003]) ).
fof(f16003,plain,
( spl0_1688
<=> ! [X2,X18] : c_plus(X2,c_times(X18,X2,tc_nat),tc_nat) = c_times(c_plus(c_1,X18,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f15998,plain,
( spl0_1687
<=> ! [X2,X18] : c_plus(X2,c_times(X18,X2,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f16001,plain,
( ! [X2,X18] : c_plus(X2,c_times(X18,X2,tc_nat),tc_nat) = c_times(c_plus(c_1,X18,tc_nat),X2,tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1687 ),
inference(forward_demodulation,[],[f15999,f11227]) ).
fof(f15999,plain,
( ! [X2,X18] : c_plus(X2,c_times(X18,X2,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat)
| ~ spl0_1687 ),
inference(avatar_component_clause,[],[f15998]) ).
fof(f16000,plain,
spl0_1687,
inference(avatar_split_clause,[],[f2807,f15998]) ).
fof(f2807,plain,
! [X2,X18] : c_plus(X2,c_times(X18,X2,tc_nat),tc_nat) = c_times(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),X2,tc_nat),
inference(definition_unfolding,[],[f940,f1385]) ).
fof(f940,axiom,
! [X2,X18] : c_times(c_Suc(X18),X2,tc_nat) = c_plus(X2,c_times(X18,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f15905,plain,
( spl0_1686
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1685 ),
inference(avatar_split_clause,[],[f15901,f15898,f10406,f10097,f6714,f3706,f15903]) ).
fof(f15903,plain,
( spl0_1686
<=> ! [X2,X18] : c_plus(X18,c_times(X18,X2,tc_nat),tc_nat) = c_times(X18,c_plus(c_1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f15898,plain,
( spl0_1685
<=> ! [X2,X18] : c_plus(X18,c_times(X18,X2,tc_nat),tc_nat) = c_times(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f15901,plain,
( ! [X2,X18] : c_plus(X18,c_times(X18,X2,tc_nat),tc_nat) = c_times(X18,c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1685 ),
inference(forward_demodulation,[],[f15899,f11227]) ).
fof(f15899,plain,
( ! [X2,X18] : c_plus(X18,c_times(X18,X2,tc_nat),tc_nat) = c_times(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_1685 ),
inference(avatar_component_clause,[],[f15898]) ).
fof(f15900,plain,
spl0_1685,
inference(avatar_split_clause,[],[f2806,f15898]) ).
fof(f2806,plain,
! [X2,X18] : c_plus(X18,c_times(X18,X2,tc_nat),tc_nat) = c_times(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f898,f1385]) ).
fof(f898,axiom,
! [X2,X18] : c_times(X18,c_Suc(X2),tc_nat) = c_plus(X18,c_times(X18,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__Suc__right_0) ).
fof(f15842,plain,
( spl0_1684
| ~ spl0_939
| ~ spl0_940 ),
inference(avatar_split_clause,[],[f8102,f7913,f7908,f15839]) ).
fof(f15839,plain,
( spl0_1684
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f7908,plain,
( spl0_939
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f7913,plain,
( spl0_940
<=> ! [X5,X1] : c_Set_Ocontents(c_insert(X1,c_emptyset,X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f8102,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_939
| ~ spl0_940 ),
inference(superposition,[],[f7914,f7910]) ).
fof(f7910,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_939 ),
inference(avatar_component_clause,[],[f7908]) ).
fof(f7914,plain,
( ! [X1,X5] : c_Set_Ocontents(c_insert(X1,c_emptyset,X5),X5) = X1
| ~ spl0_940 ),
inference(avatar_component_clause,[],[f7913]) ).
fof(f15837,plain,
( spl0_1683
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1682 ),
inference(avatar_split_clause,[],[f15833,f15830,f10406,f10097,f6714,f3706,f15835]) ).
fof(f15835,plain,
( spl0_1683
<=> ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_nat),tc_nat) = c_Nat_Opower(X33,c_plus(c_1,X2,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f15830,plain,
( spl0_1682
<=> ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_nat),tc_nat) = c_Nat_Opower(X33,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f15833,plain,
( ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_nat),tc_nat) = c_Nat_Opower(X33,c_plus(c_1,X2,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1682 ),
inference(forward_demodulation,[],[f15831,f11227]) ).
fof(f15831,plain,
( ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_nat),tc_nat) = c_Nat_Opower(X33,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat)
| ~ spl0_1682 ),
inference(avatar_component_clause,[],[f15830]) ).
fof(f15832,plain,
spl0_1682,
inference(avatar_split_clause,[],[f2805,f15830]) ).
fof(f2805,plain,
! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_nat),tc_nat) = c_Nat_Opower(X33,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1186,f1385]) ).
fof(f1186,axiom,
! [X2,X33] : c_Nat_Opower(X33,c_Suc(X2),tc_nat) = c_times(X33,c_Nat_Opower(X33,X2,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__2_0) ).
fof(f15804,plain,
( spl0_1681
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1680 ),
inference(avatar_split_clause,[],[f15800,f15797,f10406,f10097,f6714,f3706,f15802]) ).
fof(f15802,plain,
( spl0_1681
<=> ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X33,c_plus(c_1,X2,tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f15797,plain,
( spl0_1680
<=> ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X33,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f15800,plain,
( ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X33,c_plus(c_1,X2,tc_nat),tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1680 ),
inference(forward_demodulation,[],[f15798,f11227]) ).
fof(f15798,plain,
( ! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X33,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_IntDef_Oint)
| ~ spl0_1680 ),
inference(avatar_component_clause,[],[f15797]) ).
fof(f15799,plain,
spl0_1680,
inference(avatar_split_clause,[],[f2804,f15797]) ).
fof(f2804,plain,
! [X2,X33] : c_times(X33,c_Nat_Opower(X33,X2,tc_IntDef_Oint),tc_IntDef_Oint) = c_Nat_Opower(X33,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_IntDef_Oint),
inference(definition_unfolding,[],[f306,f1385]) ).
fof(f306,axiom,
! [X2,X33] : c_Nat_Opower(X33,c_Suc(X2),tc_IntDef_Oint) = c_times(X33,c_Nat_Opower(X33,X2,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f15795,plain,
spl0_1679,
inference(avatar_split_clause,[],[f2803,f15793]) ).
fof(f15793,plain,
( spl0_1679
<=> ! [X20,X5,X24] : c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5) = c_minus(X20,c_uminus(X24,tc_set(X5)),tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f2803,plain,
! [X24,X5,X20] : c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5) = c_minus(X20,c_uminus(X24,tc_set(X5)),tc_set(X5)),
inference(definition_unfolding,[],[f1427,f1214]) ).
fof(f1427,axiom,
! [X24,X5,X20] : c_inter(X20,X24,X5) = c_minus(X20,c_uminus(X24,tc_set(X5)),tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__Compl_0) ).
fof(f15791,plain,
spl0_1678,
inference(avatar_split_clause,[],[f1649,f15789]) ).
fof(f15789,plain,
( spl0_1678
<=> ! [X20,X5,X8] :
( ~ c_in(X8,X20,X5)
| c_in(c_Pair(X8,X8,X5,X5),c_Relation_Odiag(X20,X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f1649,axiom,
! [X8,X5,X20] :
( ~ c_in(X8,X20,X5)
| c_in(c_Pair(X8,X8,X5,X5),c_Relation_Odiag(X20,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagI_0) ).
fof(f15787,plain,
spl0_1677,
inference(avatar_split_clause,[],[f1615,f15785]) ).
fof(f15785,plain,
( spl0_1677
<=> ! [X34,X20,X5] :
( c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5))
| c_in(c_Main_Oin__listsI__1(X20,X34,X5),c_List_Oset(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f1615,axiom,
! [X34,X5,X20] :
( c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5))
| c_in(c_Main_Oin__listsI__1(X20,X34,X5),c_List_Oset(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_0) ).
fof(f15783,plain,
spl0_1676,
inference(avatar_split_clause,[],[f1516,f15781]) ).
fof(f15781,plain,
( spl0_1676
<=> ! [X20,X5,X8] : c_insert(X8,X20,X5) = c_insert(X8,c_minus(X20,c_insert(X8,c_emptyset,X5),tc_set(X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f1516,axiom,
! [X8,X5,X20] : c_insert(X8,X20,X5) = c_insert(X8,c_minus(X20,c_insert(X8,c_emptyset,X5),tc_set(X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__Diff__single_0) ).
fof(f15779,plain,
spl0_1675,
inference(avatar_split_clause,[],[f1491,f15777]) ).
fof(f15777,plain,
( spl0_1675
<=> ! [X20,X5,X24] : c_Union(c_union(X20,X24,tc_set(X5)),X5) = c_union(c_Union(X20,X5),c_Union(X24,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f1491,axiom,
! [X24,X5,X20] : c_Union(c_union(X20,X24,tc_set(X5)),X5) = c_union(c_Union(X20,X5),c_Union(X24,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Un__distrib_0) ).
fof(f15775,plain,
spl0_1674,
inference(avatar_split_clause,[],[f1437,f15773]) ).
fof(f15773,plain,
( spl0_1674
<=> ! [X24,X20,X5,X19] :
( ~ c_in(X19,X20,X5)
| c_in(X19,X24,X5)
| c_in(X19,c_minus(X20,X24,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f1437,axiom,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X20,X5)
| c_in(X19,X24,X5)
| c_in(X19,c_minus(X20,X24,tc_set(X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_2) ).
fof(f15771,plain,
spl0_1673,
inference(avatar_split_clause,[],[f1426,f15769]) ).
fof(f15769,plain,
( spl0_1673
<=> ! [X20,X5,X24] :
( ~ c_lessequals(X24,X20,tc_set(X5))
| c_lessequals(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f1426,axiom,
! [X24,X5,X20] :
( ~ c_lessequals(X24,X20,tc_set(X5))
| c_lessequals(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f15767,plain,
spl0_1672,
inference(avatar_split_clause,[],[f1425,f15765]) ).
fof(f15765,plain,
( spl0_1672
<=> ! [X20,X5,X24] :
( c_lessequals(X24,X20,tc_set(X5))
| ~ c_lessequals(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f1425,axiom,
! [X24,X5,X20] :
( c_lessequals(X24,X20,tc_set(X5))
| ~ c_lessequals(c_uminus(X20,tc_set(X5)),c_uminus(X24,tc_set(X5)),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f15763,plain,
spl0_1671,
inference(avatar_split_clause,[],[f1415,f15761]) ).
fof(f1415,axiom,
! [X24,X5,X20] : c_uminus(c_minus(X20,X24,tc_set(X5)),tc_set(X5)) = c_union(c_uminus(X20,tc_set(X5)),X24,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__Diff__eq_0) ).
fof(f15759,plain,
spl0_1670,
inference(avatar_split_clause,[],[f1201,f15757]) ).
fof(f15757,plain,
( spl0_1670
<=> ! [X2,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X8
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X8,X5),X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f1201,axiom,
! [X2,X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X8
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X8,X5),X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f15755,plain,
spl0_1669,
inference(avatar_split_clause,[],[f1200,f15753]) ).
fof(f15753,plain,
( spl0_1669
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X5),X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f1200,axiom,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X5),X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f15751,plain,
spl0_1668,
inference(avatar_split_clause,[],[f1035,f15749]) ).
fof(f15749,plain,
( spl0_1668
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f1035,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f15747,plain,
spl0_1667,
inference(avatar_split_clause,[],[f1034,f15745]) ).
fof(f15745,plain,
( spl0_1667
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f1034,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f15743,plain,
spl0_1666,
inference(avatar_split_clause,[],[f1033,f15741]) ).
fof(f15741,plain,
( spl0_1666
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f1033,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f15739,plain,
spl0_1665,
inference(avatar_split_clause,[],[f1032,f15737]) ).
fof(f15737,plain,
( spl0_1665
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f1032,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f15735,plain,
( spl0_1663
| ~ spl0_1664
| ~ spl0_829
| ~ spl0_919 ),
inference(avatar_split_clause,[],[f8066,f7828,f7392,f15732,f15729]) ).
fof(f15729,plain,
( spl0_1663
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f15732,plain,
( spl0_1664
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f7392,plain,
( spl0_829
<=> ! [X17] :
( c_0 = X17
| ~ c_lessequals(X17,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f7828,plain,
( spl0_919
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_OrderedGroup_Onprt(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f8066,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_829
| ~ spl0_919 ),
inference(resolution,[],[f7829,f7393]) ).
fof(f7393,plain,
( ! [X17] :
( ~ c_lessequals(X17,c_0,tc_nat)
| c_0 = X17 )
| ~ spl0_829 ),
inference(avatar_component_clause,[],[f7392]) ).
fof(f7829,plain,
( ! [X8,X5] :
( c_lessequals(c_OrderedGroup_Onprt(X8,X5),c_0,X5)
| ~ class_OrderedGroup_Olordered__ab__group(X5) )
| ~ spl0_919 ),
inference(avatar_component_clause,[],[f7828]) ).
fof(f15727,plain,
spl0_1662,
inference(avatar_split_clause,[],[f1030,f15725]) ).
fof(f15725,plain,
( spl0_1662
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f1030,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f15723,plain,
spl0_1661,
inference(avatar_split_clause,[],[f1029,f15721]) ).
fof(f15721,plain,
( spl0_1661
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f1029,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_plus(X8,X19,X5),c_plus(X9,X19,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f15719,plain,
spl0_1660,
inference(avatar_split_clause,[],[f1028,f15717]) ).
fof(f15717,plain,
( spl0_1660
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f1028,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f15715,plain,
spl0_1659,
inference(avatar_split_clause,[],[f1027,f15713]) ).
fof(f15713,plain,
( spl0_1659
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f1027,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_plus(X19,X8,X5),c_plus(X19,X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f15711,plain,
spl0_1658,
inference(avatar_split_clause,[],[f987,f15709]) ).
fof(f15709,plain,
( spl0_1658
<=> ! [X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X28,X5),X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f987,axiom,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X28,X5),X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f15707,plain,
spl0_1657,
inference(avatar_split_clause,[],[f986,f15705]) ).
fof(f15705,plain,
( spl0_1657
<=> ! [X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X28,X5),X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f986,axiom,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X28,X5),X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f15703,plain,
spl0_1656,
inference(avatar_split_clause,[],[f979,f15701]) ).
fof(f15701,plain,
( spl0_1656
<=> ! [X5,X28,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X28,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X28,X3),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f979,axiom,
! [X28,X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X28,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X28,X3),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f15699,plain,
spl0_1655,
inference(avatar_split_clause,[],[f978,f15697]) ).
fof(f15697,plain,
( spl0_1655
<=> ! [X5,X28,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X28,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X28,X3),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f978,axiom,
! [X28,X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X28,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X28,X3),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f15695,plain,
spl0_1654,
inference(avatar_split_clause,[],[f960,f15693]) ).
fof(f15693,plain,
( spl0_1654
<=> ! [X29,X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X29,X28),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f960,axiom,
! [X28,X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X29,X28),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f15691,plain,
spl0_1653,
inference(avatar_split_clause,[],[f957,f15689]) ).
fof(f15689,plain,
( spl0_1653
<=> ! [X29,X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,X28),X5) = c_plus(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f957,axiom,
! [X28,X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,X28),X5) = c_plus(c_Numeral_Onumber__of(X29,X5),c_Numeral_Onumber__of(X28,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f15687,plain,
( spl0_1652
| ~ spl0_112
| ~ spl0_885 ),
inference(avatar_split_clause,[],[f8015,f7690,f3706,f15685]) ).
fof(f15685,plain,
( spl0_1652
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f7690,plain,
( spl0_885
<=> ! [X18,X2] : ~ c_less(c_IntDef_Oint(X2),c_uminus(c_IntDef_Oint(X18),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f8015,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_885 ),
inference(superposition,[],[f7691,f3708]) ).
fof(f7691,plain,
( ! [X2,X18] : ~ c_less(c_IntDef_Oint(X2),c_uminus(c_IntDef_Oint(X18),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_885 ),
inference(avatar_component_clause,[],[f7690]) ).
fof(f15683,plain,
spl0_1651,
inference(avatar_split_clause,[],[f812,f15681]) ).
fof(f15681,plain,
( spl0_1651
<=> ! [X8,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(c_uminus(c_1,X10),X8,X10)
| c_less(c_uminus(X8,X10),c_1,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f812,axiom,
! [X10,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(c_uminus(c_1,X10),X8,X10)
| c_less(c_uminus(X8,X10),c_1,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f15679,plain,
spl0_1650,
inference(avatar_split_clause,[],[f811,f15677]) ).
fof(f15677,plain,
( spl0_1650
<=> ! [X8,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(c_uminus(X8,X10),c_1,X10)
| c_less(c_uminus(c_1,X10),X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f811,axiom,
! [X10,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(c_uminus(X8,X10),c_1,X10)
| c_less(c_uminus(c_1,X10),X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f15675,plain,
spl0_1649,
inference(avatar_split_clause,[],[f808,f15673]) ).
fof(f15673,plain,
( spl0_1649
<=> ! [X8,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(c_uminus(c_1,X10),X8,X10)
| c_lessequals(c_uminus(X8,X10),c_1,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f808,axiom,
! [X10,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(c_uminus(c_1,X10),X8,X10)
| c_lessequals(c_uminus(X8,X10),c_1,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f15671,plain,
spl0_1648,
inference(avatar_split_clause,[],[f807,f15669]) ).
fof(f15669,plain,
( spl0_1648
<=> ! [X8,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(c_uminus(X8,X10),c_1,X10)
| c_lessequals(c_uminus(c_1,X10),X8,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f807,axiom,
! [X10,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(c_uminus(X8,X10),c_1,X10)
| c_lessequals(c_uminus(c_1,X10),X8,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f15667,plain,
spl0_1647,
inference(avatar_split_clause,[],[f801,f15665]) ).
fof(f15665,plain,
( spl0_1647
<=> ! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(X9,c_uminus(c_1,X10),X10)
| c_less(c_1,c_uminus(X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f801,axiom,
! [X10,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(X9,c_uminus(c_1,X10),X10)
| c_less(c_1,c_uminus(X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f15663,plain,
spl0_1646,
inference(avatar_split_clause,[],[f800,f15661]) ).
fof(f15661,plain,
( spl0_1646
<=> ! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(c_1,c_uminus(X9,X10),X10)
| c_less(X9,c_uminus(c_1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f800,axiom,
! [X10,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_less(c_1,c_uminus(X9,X10),X10)
| c_less(X9,c_uminus(c_1,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f15659,plain,
spl0_1645,
inference(avatar_split_clause,[],[f785,f15657]) ).
fof(f15657,plain,
( spl0_1645
<=> ! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(X9,c_uminus(c_1,X10),X10)
| c_lessequals(c_1,c_uminus(X9,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f785,axiom,
! [X10,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(X9,c_uminus(c_1,X10),X10)
| c_lessequals(c_1,c_uminus(X9,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f15655,plain,
spl0_1644,
inference(avatar_split_clause,[],[f784,f15653]) ).
fof(f15653,plain,
( spl0_1644
<=> ! [X9,X10] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(c_1,c_uminus(X9,X10),X10)
| c_lessequals(X9,c_uminus(c_1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f784,axiom,
! [X10,X9] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X10)
| ~ class_HOL_Oone(X10)
| ~ c_lessequals(c_1,c_uminus(X9,X10),X10)
| c_lessequals(X9,c_uminus(c_1,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f15651,plain,
spl0_1643,
inference(avatar_split_clause,[],[f710,f15649]) ).
fof(f15649,plain,
( spl0_1643
<=> ! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,X5) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X29,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f710,axiom,
! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,X5) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X29,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f15647,plain,
spl0_1642,
inference(avatar_split_clause,[],[f621,f15645]) ).
fof(f15645,plain,
( spl0_1642
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X34
| c_List_Otl(c_append(X34,X35,X5),X5) = c_append(c_List_Otl(X34,X5),X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f621,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X34
| c_List_Otl(c_append(X34,X35,X5),X5) = c_append(c_List_Otl(X34,X5),X35,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl__append2_0) ).
fof(f15643,plain,
( spl0_1641
| ~ spl0_113
| ~ spl0_885 ),
inference(avatar_split_clause,[],[f8014,f7690,f3711,f15641]) ).
fof(f8014,plain,
( ! [X0] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_885 ),
inference(superposition,[],[f7691,f3713]) ).
fof(f15639,plain,
spl0_1640,
inference(avatar_split_clause,[],[f605,f15637]) ).
fof(f15637,plain,
( spl0_1640
<=> ! [X20,X5,X3] :
( ~ c_in(c_0,X20,tc_nat)
| c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) = c_List_Osublist(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f605,axiom,
! [X3,X5,X20] :
( ~ c_in(c_0,X20,tc_nat)
| c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) = c_List_Osublist(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_0) ).
fof(f15634,plain,
spl0_1639,
inference(avatar_split_clause,[],[f568,f15632]) ).
fof(f15632,plain,
( spl0_1639
<=> ! [X5,X1,X35] : c_List_Olist_OCons(X1,X35,X5) = c_List_Orev(c_append(c_List_Orev(X35,X5),c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f568,axiom,
! [X1,X35,X5] : c_List_Olist_OCons(X1,X35,X5) = c_List_Orev(c_append(c_List_Orev(X35,X5),c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__eq__Cons__iff_1) ).
fof(f15630,plain,
spl0_1638,
inference(avatar_split_clause,[],[f565,f15628]) ).
fof(f15628,plain,
( spl0_1638
<=> ! [X6,X34,X3] : c_List_Orev(c_List_Olist_OCons(X3,X34,X6),X6) = c_append(c_List_Orev(X34,X6),c_List_Olist_OCons(X3,c_List_Olist_ONil,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f565,axiom,
! [X3,X6,X34] : c_List_Orev(c_List_Olist_OCons(X3,X34,X6),X6) = c_append(c_List_Orev(X34,X6),c_List_Olist_OCons(X3,c_List_Olist_ONil,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev_Osimps__2_0) ).
fof(f15626,plain,
spl0_1637,
inference(avatar_split_clause,[],[f554,f15624]) ).
fof(f15624,plain,
( spl0_1637
<=> ! [X6,X34,X3] :
( ~ c_in(X3,c_List_Oset(X34,X6),X6)
| c_List_Oremdups(c_List_Olist_OCons(X3,X34,X6),X6) = c_List_Oremdups(X34,X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f554,axiom,
! [X3,X6,X34] :
( ~ c_in(X3,c_List_Oset(X34,X6),X6)
| c_List_Oremdups(c_List_Olist_OCons(X3,X34,X6),X6) = c_List_Oremdups(X34,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups_Osimps__2_0) ).
fof(f15622,plain,
spl0_1636,
inference(avatar_split_clause,[],[f542,f15620]) ).
fof(f15620,plain,
( spl0_1636
<=> ! [X34,X5,X2] :
( ~ c_less(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_in(c_List_Onth(X34,X2,X5),c_List_Oset(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f542,axiom,
! [X2,X34,X5] :
( ~ c_less(X2,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat)
| c_in(c_List_Onth(X34,X2,X5),c_List_Oset(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__mem_0) ).
fof(f15618,plain,
spl0_1635,
inference(avatar_split_clause,[],[f541,f15616]) ).
fof(f15616,plain,
( spl0_1635
<=> ! [X17,X34,X3,X5,X45] :
( X17 = X45
| c_List_Onth(c_List_Olist__update(X34,X17,X3,X5),X45,X5) = c_List_Onth(X34,X45,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f541,axiom,
! [X3,X45,X17,X34,X5] :
( X17 = X45
| c_List_Onth(c_List_Olist__update(X34,X17,X3,X5),X45,X5) = c_List_Onth(X34,X45,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__list__update__neq_0) ).
fof(f15614,plain,
spl0_1634,
inference(avatar_split_clause,[],[f459,f15612]) ).
fof(f15612,plain,
( spl0_1634
<=> ! [X13,X5,X3] : ~ c_in(c_Pair(X3,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f459,axiom,
! [X3,X5,X13] : ~ c_in(c_Pair(X3,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olexord(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexord__Nil__right_0) ).
fof(f15610,plain,
spl0_1633,
inference(avatar_split_clause,[],[f446,f15608]) ).
fof(f15608,plain,
( spl0_1633
<=> ! [X34,X5] :
( c_List_Oremdups(X34,X5) = X34
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(c_List_Oremdups(X34,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f446,axiom,
! [X34,X5] :
( c_List_Oremdups(X34,X5) = X34
| c_Nat_Osize(X34,tc_List_Olist(X5)) != c_Nat_Osize(c_List_Oremdups(X34,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__eq_0) ).
fof(f15606,plain,
spl0_1632,
inference(avatar_split_clause,[],[f386,f15604]) ).
fof(f15604,plain,
( spl0_1632
<=> ! [X34,X5,X35] : c_List_Oconcat(c_append(X34,X35,tc_List_Olist(X5)),X5) = c_append(c_List_Oconcat(X34,X5),c_List_Oconcat(X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f386,axiom,
! [X34,X35,X5] : c_List_Oconcat(c_append(X34,X35,tc_List_Olist(X5)),X5) = c_append(c_List_Oconcat(X34,X5),c_List_Oconcat(X35,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__append_0) ).
fof(f15602,plain,
spl0_1631,
inference(avatar_split_clause,[],[f379,f15600]) ).
fof(f15600,plain,
( spl0_1631
<=> ! [X6,X34,X3] :
( c_List_Olist_ONil = X34
| c_List_Obutlast(c_List_Olist_OCons(X3,X34,X6),X6) = c_List_Olist_OCons(X3,c_List_Obutlast(X34,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f379,axiom,
! [X3,X6,X34] :
( c_List_Olist_ONil = X34
| c_List_Obutlast(c_List_Olist_OCons(X3,X34,X6),X6) = c_List_Olist_OCons(X3,c_List_Obutlast(X34,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_1) ).
fof(f15584,plain,
spl0_1630,
inference(avatar_split_clause,[],[f360,f15582]) ).
fof(f15582,plain,
( spl0_1630
<=> ! [X5,X1] :
( c_List_Olist_ONil = X1
| c_append(c_List_Obutlast(X1,X5),c_List_Olist_OCons(c_List_Olast(X1,X5),c_List_Olist_ONil,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f360,axiom,
! [X1,X5] :
( c_List_Olist_ONil = X1
| c_append(c_List_Obutlast(X1,X5),c_List_Olist_OCons(c_List_Olast(X1,X5),c_List_Olist_ONil,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__butlast__last__id_0) ).
fof(f15580,plain,
spl0_1629,
inference(avatar_split_clause,[],[f356,f15578]) ).
fof(f15578,plain,
( spl0_1629
<=> ! [X13,X5,X35] : ~ c_in(c_Pair(c_List_Olist_ONil,X35,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f356,axiom,
! [X35,X5,X13] : ~ c_in(c_Pair(c_List_Olist_ONil,X35,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__notin__lex_0) ).
fof(f15576,plain,
spl0_1628,
inference(avatar_split_clause,[],[f348,f15574]) ).
fof(f15574,plain,
( spl0_1628
<=> ! [X36,X5,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Oconcat(X36,X5)
| ~ c_in(X23,c_List_Oset(X36,tc_List_Olist(X5)),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f348,axiom,
! [X36,X5,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Oconcat(X36,X5)
| ~ c_in(X23,c_List_Oset(X36,tc_List_Olist(X5)),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_0) ).
fof(f15572,plain,
spl0_1627,
inference(avatar_split_clause,[],[f347,f15570]) ).
fof(f15570,plain,
( spl0_1627
<=> ! [X13,X34,X5] : ~ c_in(c_Pair(X34,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f347,axiom,
! [X34,X5,X13] : ~ c_in(c_Pair(X34,c_List_Olist_ONil,tc_List_Olist(X5),tc_List_Olist(X5)),c_List_Olex(X13,X5),tc_prod(tc_List_Olist(X5),tc_List_Olist(X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil2__notin__lex_0) ).
fof(f15568,plain,
spl0_1626,
inference(avatar_split_clause,[],[f152,f15566]) ).
fof(f15566,plain,
( spl0_1626
<=> ! [X2,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f152,axiom,
! [X2,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f15564,plain,
spl0_1625,
inference(avatar_split_clause,[],[f144,f15562]) ).
fof(f15562,plain,
( spl0_1625
<=> ! [X18,X2] : c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X18,c_plus(X2,X18,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f144,axiom,
! [X2,X18] : c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X18,c_plus(X2,X18,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_H_0) ).
fof(f15560,plain,
spl0_1624,
inference(avatar_split_clause,[],[f143,f15558]) ).
fof(f15558,plain,
( spl0_1624
<=> ! [X2,X18] : c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X18,c_plus(X18,X2,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f143,axiom,
! [X2,X18] : c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X18,c_plus(X18,X2,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__add2_0) ).
fof(f15556,plain,
spl0_1623,
inference(avatar_split_clause,[],[f142,f15554]) ).
fof(f15554,plain,
( spl0_1623
<=> ! [X2,X18] : c_GCD_Ogcd(c_Pair(c_plus(X18,X2,tc_nat),X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f142,axiom,
! [X2,X18] : c_GCD_Ogcd(c_Pair(c_plus(X18,X2,tc_nat),X2,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__add1_0) ).
fof(f15552,plain,
spl0_1622,
inference(avatar_split_clause,[],[f113,f15550]) ).
fof(f15550,plain,
( spl0_1622
<=> ! [X20,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMin(X20,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f113,axiom,
! [X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMin(X20,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__in_0) ).
fof(f15548,plain,
spl0_1621,
inference(avatar_split_clause,[],[f98,f15546]) ).
fof(f15546,plain,
( spl0_1621
<=> ! [X20,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMax(X20,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f98,axiom,
! [X5,X20] :
( ~ class_Orderings_Olinorder(X5)
| c_emptyset = X20
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Finite__Set_OMax(X20,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__in_0) ).
fof(f15544,plain,
( spl0_1620
| ~ spl0_793
| ~ spl0_1592 ),
inference(avatar_split_clause,[],[f15236,f14382,f7245,f15542]) ).
fof(f14382,plain,
( spl0_1592
<=> ! [X24,X20,X5,X8] : c_union(X20,c_insert(X8,X24,X5),X5) = c_insert(X8,c_union(X20,X24,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f15236,plain,
( ! [X2,X1] : c_UNIV = c_insert(X2,c_UNIV,X1)
| ~ spl0_793
| ~ spl0_1592 ),
inference(forward_demodulation,[],[f15221,f7246]) ).
fof(f15221,plain,
( ! [X2,X0,X1] : c_insert(X2,c_UNIV,X1) = c_union(c_UNIV,c_insert(X2,X0,X1),X1)
| ~ spl0_793
| ~ spl0_1592 ),
inference(superposition,[],[f14383,f7246]) ).
fof(f14383,plain,
( ! [X8,X24,X5,X20] : c_union(X20,c_insert(X8,X24,X5),X5) = c_insert(X8,c_union(X20,X24,X5),X5)
| ~ spl0_1592 ),
inference(avatar_component_clause,[],[f14382]) ).
fof(f15181,plain,
( spl0_1619
| ~ spl0_723
| ~ spl0_1584 ),
inference(avatar_split_clause,[],[f15135,f14349,f6949,f15179]) ).
fof(f15179,plain,
( spl0_1619
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f14349,plain,
( spl0_1584
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X1,X3,X5)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X3,X5),c_SetInterval_OgreaterThan(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f15135,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_723
| ~ spl0_1584 ),
inference(resolution,[],[f14350,f6950]) ).
fof(f14350,plain,
( ! [X3,X1,X5] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X3,X5),c_SetInterval_OgreaterThan(X1,X5),tc_set(X5))
| c_lessequals(X1,X3,X5)
| ~ class_Orderings_Olinorder(X5) )
| ~ spl0_1584 ),
inference(avatar_component_clause,[],[f14349]) ).
fof(f15093,plain,
( spl0_1618
| ~ spl0_112
| ~ spl0_885 ),
inference(avatar_split_clause,[],[f8013,f7690,f3706,f15091]) ).
fof(f8013,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_885 ),
inference(superposition,[],[f7691,f3708]) ).
fof(f14893,plain,
( spl0_1617
| ~ spl0_739
| ~ spl0_1557 ),
inference(avatar_split_clause,[],[f14887,f14240,f7027,f14891]) ).
fof(f14891,plain,
( spl0_1617
<=> ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f7027,plain,
( spl0_739
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(c_0,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f14240,plain,
( spl0_1557
<=> ! [X2,X5,X1] :
( c_List_Orotate(X2,X1,X5) = X1
| c_0 != c_Divides_Oop_Amod(X2,c_Nat_Osize(X1,tc_List_Olist(X5)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f14887,plain,
( ! [X0,X1] : c_List_Orotate(c_0,X0,X1) = X0
| ~ spl0_739
| ~ spl0_1557 ),
inference(trivial_inequality_removal,[],[f14877]) ).
fof(f14877,plain,
( ! [X0,X1] :
( c_0 != c_0
| c_List_Orotate(c_0,X0,X1) = X0 )
| ~ spl0_739
| ~ spl0_1557 ),
inference(superposition,[],[f14241,f7028]) ).
fof(f7028,plain,
( ! [X18] : c_0 = c_Divides_Oop_Amod(c_0,X18,tc_nat)
| ~ spl0_739 ),
inference(avatar_component_clause,[],[f7027]) ).
fof(f14241,plain,
( ! [X2,X1,X5] :
( c_0 != c_Divides_Oop_Amod(X2,c_Nat_Osize(X1,tc_List_Olist(X5)),tc_nat)
| c_List_Orotate(X2,X1,X5) = X1 )
| ~ spl0_1557 ),
inference(avatar_component_clause,[],[f14240]) ).
fof(f14655,plain,
( spl0_1616
| ~ spl0_112
| ~ spl0_882 ),
inference(avatar_split_clause,[],[f7999,f7678,f3706,f14653]) ).
fof(f14653,plain,
( spl0_1616
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f7678,plain,
( spl0_882
<=> ! [X18,X2] :
( X2 = X18
| c_IntDef_Oint(X18) != c_IntDef_Oint(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f7999,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_112
| ~ spl0_882 ),
inference(superposition,[],[f7679,f3708]) ).
fof(f7679,plain,
( ! [X2,X18] :
( c_IntDef_Oint(X18) != c_IntDef_Oint(X2)
| X2 = X18 )
| ~ spl0_882 ),
inference(avatar_component_clause,[],[f7678]) ).
fof(f14538,plain,
spl0_1615,
inference(avatar_split_clause,[],[f3153,f14536]) ).
fof(f14536,plain,
( spl0_1615
<=> ! [X5,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f3153,plain,
! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5) ),
inference(forward_demodulation,[],[f3152,f956]) ).
fof(f956,axiom,
! [X1] : c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3152,plain,
! [X3,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2949,f2744]) ).
fof(f2744,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f967,f970]) ).
fof(f967,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f2949,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f158,f970]) ).
fof(f158,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_1) ).
fof(f14534,plain,
spl0_1614,
inference(avatar_split_clause,[],[f3146,f14532]) ).
fof(f14532,plain,
( spl0_1614
<=> ! [X5,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f3146,plain,
! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f3145,f956]) ).
fof(f3145,plain,
! [X1,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2943,f2744]) ).
fof(f2943,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f162,f970]) ).
fof(f162,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_1) ).
fof(f14530,plain,
spl0_1613,
inference(avatar_split_clause,[],[f3143,f14528]) ).
fof(f14528,plain,
( spl0_1613
<=> ! [X5,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f3143,plain,
! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5) ),
inference(forward_demodulation,[],[f3142,f956]) ).
fof(f3142,plain,
! [X3,X5] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5) ),
inference(forward_demodulation,[],[f2941,f2744]) ).
fof(f2941,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f157,f970]) ).
fof(f157,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_Numeral_Onumber__of(X3,X5),c_0,X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__12_0) ).
fof(f14526,plain,
spl0_1612,
inference(avatar_split_clause,[],[f3136,f14524]) ).
fof(f14524,plain,
( spl0_1612
<=> ! [X5,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f3136,plain,
! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X1,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f3135,f956]) ).
fof(f3135,plain,
! [X1,X5] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5) ),
inference(forward_demodulation,[],[f2935,f2744]) ).
fof(f2935,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f161,f970]) ).
fof(f161,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X1,X5),X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X1,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__14_0) ).
fof(f14522,plain,
spl0_1611,
inference(avatar_split_clause,[],[f3117,f14520]) ).
fof(f14520,plain,
( spl0_1611
<=> ! [X2,X18] :
( c_lessequals(c_1,c_times(X18,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X2,tc_nat)
| ~ c_lessequals(c_1,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f3117,plain,
! [X2,X18] :
( c_lessequals(c_1,c_times(X18,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X2,tc_nat)
| ~ c_lessequals(c_1,X18,tc_nat) ),
inference(forward_demodulation,[],[f2921,f2745]) ).
fof(f2921,plain,
! [X2,X18] :
( ~ c_lessequals(c_1,X2,tc_nat)
| ~ c_lessequals(c_1,X18,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X18,X2,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f938,f1385]) ).
fof(f938,axiom,
! [X2,X18] :
( ~ c_lessequals(c_1,X2,tc_nat)
| ~ c_lessequals(c_1,X18,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_2) ).
fof(f14518,plain,
spl0_1610,
inference(avatar_split_clause,[],[f3033,f14516]) ).
fof(f14516,plain,
( spl0_1610
<=> ! [X29,X5] :
( c_plus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f3033,plain,
! [X29,X5] :
( c_plus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f171,f997]) ).
fof(f171,axiom,
! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_Numeral_Onumber__of(X29,X5),c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X29,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__3_0) ).
fof(f14514,plain,
spl0_1609,
inference(avatar_split_clause,[],[f3032,f14512]) ).
fof(f14512,plain,
( spl0_1609
<=> ! [X5,X28] :
( c_plus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X28),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f3032,plain,
! [X28,X5] :
( c_plus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X28),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f170,f997]) ).
fof(f170,axiom,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_1,c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X28),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__2_0) ).
fof(f14510,plain,
spl0_1608,
inference(avatar_split_clause,[],[f3005,f14508]) ).
fof(f14508,plain,
( spl0_1608
<=> ! [X13,X5] : c_List_Olistset(c_List_Olist_ONil,X5) = c_Relation_OImage(c_List_Olistrel(X13,X5),c_List_Olistset(c_List_Olist_ONil,X5),tc_List_Olist(X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f3005,plain,
! [X5,X13] : c_List_Olistset(c_List_Olist_ONil,X5) = c_Relation_OImage(c_List_Olistrel(X13,X5),c_List_Olistset(c_List_Olist_ONil,X5),tc_List_Olist(X5),tc_List_Olist(X5)),
inference(forward_demodulation,[],[f477,f480]) ).
fof(f480,axiom,
! [X6] : c_List_Olistset(c_List_Olist_ONil,X6) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X6)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f477,axiom,
! [X5,X13] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X5)) = c_Relation_OImage(c_List_Olistrel(X13,X5),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X5)),tc_List_Olist(X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistrel__Nil_0) ).
fof(f14506,plain,
spl0_1607,
inference(avatar_split_clause,[],[f3002,f14504]) ).
fof(f14504,plain,
( spl0_1607
<=> ! [X50,X5,X8] : c_Nat_Osize(c_List_Olist_OCons(X8,X50,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X50,tc_List_Olist(X5)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f3002,plain,
! [X50,X8,X5] : c_Nat_Osize(c_List_Olist_OCons(X8,X50,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X50,tc_List_Olist(X5)),c_1,tc_nat),
inference(forward_demodulation,[],[f2826,f2745]) ).
fof(f2826,plain,
! [X50,X8,X5] : c_Nat_Osize(c_List_Olist_OCons(X8,X50,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X50,tc_List_Olist(X5)),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f468,f1385]) ).
fof(f468,axiom,
! [X50,X8,X5] : c_Nat_Osize(c_List_Olist_OCons(X8,X50,X5),tc_List_Olist(X5)) = c_plus(c_Nat_Osize(X50,tc_List_Olist(X5)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Osize__2_0) ).
fof(f14502,plain,
spl0_1606,
inference(avatar_split_clause,[],[f2998,f14500]) ).
fof(f14500,plain,
( spl0_1606
<=> ! [X24,X5,X73,X8] : c_union(c_insert(X8,X24,X5),X73,X5) = c_union(X24,c_insert(X8,X73,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f2998,plain,
! [X73,X8,X24,X5] : c_union(c_insert(X8,X24,X5),X73,X5) = c_union(X24,c_insert(X8,X73,X5),X5),
inference(forward_demodulation,[],[f1484,f1485]) ).
fof(f1485,axiom,
! [X8,X24,X5,X20] : c_union(X20,c_insert(X8,X24,X5),X5) = c_insert(X8,c_union(X20,X24,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__right_0) ).
fof(f1484,axiom,
! [X73,X8,X24,X5] : c_union(c_insert(X8,X24,X5),X73,X5) = c_insert(X8,c_union(X24,X73,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__insert__left_0) ).
fof(f14498,plain,
spl0_1605,
inference(avatar_split_clause,[],[f2903,f14496]) ).
fof(f14496,plain,
( spl0_1605
<=> ! [X2,X5,X1] :
( c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f2903,plain,
! [X2,X1,X5] :
( c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),X2,tc_nat) ),
inference(definition_unfolding,[],[f611,f607]) ).
fof(f611,axiom,
! [X2,X1,X5] :
( c_List_Otake(X2,X1,X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__all_0) ).
fof(f14478,plain,
( spl0_1604
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1603 ),
inference(avatar_split_clause,[],[f14465,f14462,f10406,f10097,f6714,f3706,f14476]) ).
fof(f14476,plain,
( spl0_1604
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),tc_nat) = c_minus(c_plus(c_1,X31,tc_nat),X67,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f14462,plain,
( spl0_1603
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X31,tc_nat),tc_nat),X67,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f14465,plain,
( ! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),tc_nat) = c_minus(c_plus(c_1,X31,tc_nat),X67,tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1603 ),
inference(forward_demodulation,[],[f14463,f11227]) ).
fof(f14463,plain,
( ! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),tc_nat) = c_minus(c_Finite__Set_Ocard(c_SetInterval_OatMost(X31,tc_nat),tc_nat),X67,tc_nat)
| ~ spl0_1603 ),
inference(avatar_component_clause,[],[f14462]) ).
fof(f14464,plain,
spl0_1603,
inference(avatar_split_clause,[],[f2797,f14462]) ).
fof(f14446,plain,
( spl0_1602
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1601 ),
inference(avatar_split_clause,[],[f14442,f14439,f10406,f10097,f6714,f3706,f14444]) ).
fof(f14439,plain,
( spl0_1601
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_Finite__Set_Ocard(c_SetInterval_OatMost(X67,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f14442,plain,
( ! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_plus(c_1,X67,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1601 ),
inference(forward_demodulation,[],[f14440,f11227]) ).
fof(f14440,plain,
( ! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,c_Finite__Set_Ocard(c_SetInterval_OatMost(X67,tc_nat),tc_nat),tc_nat)
| ~ spl0_1601 ),
inference(avatar_component_clause,[],[f14439]) ).
fof(f14441,plain,
spl0_1601,
inference(avatar_split_clause,[],[f2796,f14439]) ).
fof(f14417,plain,
( spl0_1600
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1599 ),
inference(avatar_split_clause,[],[f14413,f14410,f10406,f10097,f6714,f3706,f14415]) ).
fof(f14415,plain,
( spl0_1600
<=> ! [X34,X5,X2] : c_List_Orotate1(c_List_Orotate(X2,X34,X5),X5) = c_List_Orotate(c_plus(c_1,X2,tc_nat),X34,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f14410,plain,
( spl0_1599
<=> ! [X34,X5,X2] : c_List_Orotate1(c_List_Orotate(X2,X34,X5),X5) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X34,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f14413,plain,
( ! [X2,X34,X5] : c_List_Orotate1(c_List_Orotate(X2,X34,X5),X5) = c_List_Orotate(c_plus(c_1,X2,tc_nat),X34,X5)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1599 ),
inference(forward_demodulation,[],[f14411,f11227]) ).
fof(f14411,plain,
( ! [X2,X34,X5] : c_List_Orotate1(c_List_Orotate(X2,X34,X5),X5) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X34,X5)
| ~ spl0_1599 ),
inference(avatar_component_clause,[],[f14410]) ).
fof(f14412,plain,
spl0_1599,
inference(avatar_split_clause,[],[f2795,f14410]) ).
fof(f2795,plain,
! [X2,X34,X5] : c_List_Orotate1(c_List_Orotate(X2,X34,X5),X5) = c_List_Orotate(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X34,X5),
inference(definition_unfolding,[],[f579,f1385]) ).
fof(f579,axiom,
! [X2,X34,X5] : c_List_Orotate(c_Suc(X2),X34,X5) = c_List_Orotate1(c_List_Orotate(X2,X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__Suc_0) ).
fof(f14408,plain,
spl0_1598,
inference(avatar_split_clause,[],[f1695,f14406]) ).
fof(f14406,plain,
( spl0_1598
<=> ! [X82,X81,X5,X10] :
( ~ c_Wellfounded__Recursion_Owf(X81,X10)
| ~ c_Wellfounded__Recursion_Owf(X82,X5)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X82,X81,X5,X10),tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f1695,axiom,
! [X82,X10,X81,X5] :
( ~ c_Wellfounded__Recursion_Owf(X81,X10)
| ~ c_Wellfounded__Recursion_Owf(X82,X5)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X82,X81,X5,X10),tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f14404,plain,
spl0_1597,
inference(avatar_split_clause,[],[f1693,f14402]) ).
fof(f14402,plain,
( spl0_1597
<=> ! [X10,X5,X80,X79] :
( ~ c_Relation_Otrans(X79,X10)
| ~ c_Relation_Otrans(X80,X5)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X80,X79,X5,X10),tc_prod(X5,X10)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f1693,axiom,
! [X10,X80,X79,X5] :
( ~ c_Relation_Otrans(X79,X10)
| ~ c_Relation_Otrans(X80,X5)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X80,X79,X5,X10),tc_prod(X5,X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f14400,plain,
spl0_1596,
inference(avatar_split_clause,[],[f1648,f14398]) ).
fof(f14398,plain,
( spl0_1596
<=> ! [X20,X5,X19] :
( c_in(c_Main_OdiagE__1(X20,X19,X5),X20,X5)
| ~ c_in(X19,c_Relation_Odiag(X20,X5),tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f1648,axiom,
! [X19,X5,X20] :
( c_in(c_Main_OdiagE__1(X20,X19,X5),X20,X5)
| ~ c_in(X19,c_Relation_Odiag(X20,X5),tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OdiagE_1) ).
fof(f14396,plain,
spl0_1595,
inference(avatar_split_clause,[],[f1563,f14394]) ).
fof(f14394,plain,
( spl0_1595
<=> ! [X13,X5,X1,X3] :
( c_Wellfounded__Recursion_Owf(X13,X5)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f1563,axiom,
! [X3,X1,X5,X13] :
( c_Wellfounded__Recursion_Owf(X13,X5)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f14392,plain,
spl0_1594,
inference(avatar_split_clause,[],[f1560,f14390]) ).
fof(f14390,plain,
( spl0_1594
<=> ! [X13,X5,X1,X3] :
( c_Wellfounded__Recursion_Oacyclic(X13,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f1560,axiom,
! [X3,X1,X5,X13] :
( c_Wellfounded__Recursion_Oacyclic(X13,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X1,X3,X5,X5),X13,tc_prod(X5,X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f14388,plain,
spl0_1593,
inference(avatar_split_clause,[],[f1498,f14386]) ).
fof(f14386,plain,
( spl0_1593
<=> ! [X23,X20,X5,X73] :
( ~ c_in(X20,X23,X5)
| ~ c_in(X23,X73,tc_set(X5))
| c_in(X20,c_Union(X73,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f1498,axiom,
! [X73,X5,X23,X20] :
( ~ c_in(X20,X23,X5)
| ~ c_in(X23,X73,tc_set(X5))
| c_in(X20,c_Union(X73,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_2) ).
fof(f14384,plain,
spl0_1592,
inference(avatar_split_clause,[],[f1485,f14382]) ).
fof(f14380,plain,
spl0_1591,
inference(avatar_split_clause,[],[f1481,f14378]) ).
fof(f14378,plain,
( spl0_1591
<=> ! [X24,X20,X5,X19] :
( c_in(X19,X20,X5)
| c_in(X19,X24,X5)
| ~ c_in(X19,c_union(X20,X24,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f1481,axiom,
! [X19,X24,X5,X20] :
( c_in(X19,X20,X5)
| c_in(X19,X24,X5)
| ~ c_in(X19,c_union(X20,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
fof(f14376,plain,
spl0_1590,
inference(avatar_split_clause,[],[f1461,f14374]) ).
fof(f14374,plain,
( spl0_1590
<=> ! [X23,X20,X5,X73] :
( c_in(X20,X23,X5)
| ~ c_in(X23,X73,tc_set(X5))
| ~ c_in(X20,c_Inter(X73,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f1461,axiom,
! [X73,X5,X23,X20] :
( c_in(X20,X23,X5)
| ~ c_in(X23,X73,tc_set(X5))
| ~ c_in(X20,c_Inter(X73,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_0) ).
fof(f14372,plain,
spl0_1589,
inference(avatar_split_clause,[],[f1434,f14370]) ).
fof(f14370,plain,
( spl0_1589
<=> ! [X20,X5,X24] : c_minus(X20,X24,tc_set(X5)) = c_minus(c_minus(X20,X24,tc_set(X5)),X24,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f1434,axiom,
! [X24,X5,X20] : c_minus(X20,X24,tc_set(X5)) = c_minus(c_minus(X20,X24,tc_set(X5)),X24,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__idemp_0) ).
fof(f14368,plain,
spl0_1588,
inference(avatar_split_clause,[],[f1413,f14366]) ).
fof(f14366,plain,
( spl0_1588
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X3,X1,X5)
| c_lessequals(c_SetInterval_OlessThan(X3,X5),c_SetInterval_OlessThan(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f1413,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X3,X1,X5)
| c_lessequals(c_SetInterval_OlessThan(X3,X5),c_SetInterval_OlessThan(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f14364,plain,
spl0_1587,
inference(avatar_split_clause,[],[f1412,f14362]) ).
fof(f14362,plain,
( spl0_1587
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X3,X1,X5)
| ~ c_lessequals(c_SetInterval_OlessThan(X3,X5),c_SetInterval_OlessThan(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f1412,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X3,X1,X5)
| ~ c_lessequals(c_SetInterval_OlessThan(X3,X5),c_SetInterval_OlessThan(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f14360,plain,
spl0_1586,
inference(avatar_split_clause,[],[f1402,f14358]) ).
fof(f14358,plain,
( spl0_1586
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X1,X3,X5)
| c_lessequals(c_SetInterval_OgreaterThan(X3,X5),c_SetInterval_OgreaterThan(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f1402,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| ~ c_lessequals(X1,X3,X5)
| c_lessequals(c_SetInterval_OgreaterThan(X3,X5),c_SetInterval_OgreaterThan(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f14356,plain,
( ~ spl0_43
| ~ spl0_1585
| ~ spl0_1269
| spl0_1416 ),
inference(avatar_split_clause,[],[f13255,f11597,f10129,f14353,f3367]) ).
fof(f3367,plain,
( spl0_43
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f14353,plain,
( spl0_1585
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f10129,plain,
( spl0_1269
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_lessequals(c_0,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f11597,plain,
( spl0_1416
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f13255,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint)
| ~ spl0_1269
| spl0_1416 ),
inference(resolution,[],[f11599,f10130]) ).
fof(f10130,plain,
( ! [X8,X5] :
( c_lessequals(c_0,c_uminus(X8,X5),X5)
| ~ c_lessequals(X8,c_0,X5)
| ~ class_OrderedGroup_Opordered__ab__group__add(X5) )
| ~ spl0_1269 ),
inference(avatar_component_clause,[],[f10129]) ).
fof(f11599,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| spl0_1416 ),
inference(avatar_component_clause,[],[f11597]) ).
fof(f14351,plain,
spl0_1584,
inference(avatar_split_clause,[],[f1401,f14349]) ).
fof(f1401,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_lessequals(X1,X3,X5)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X3,X5),c_SetInterval_OgreaterThan(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f14347,plain,
spl0_1583,
inference(avatar_split_clause,[],[f1389,f14345]) ).
fof(f14345,plain,
( spl0_1583
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X31,c_plus(X67,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f1389,axiom,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X31,c_plus(X67,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f14343,plain,
spl0_1582,
inference(avatar_split_clause,[],[f1382,f14341]) ).
fof(f14341,plain,
( spl0_1582
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X31,X67,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f1382,axiom,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X31,X67,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f14339,plain,
spl0_1581,
inference(avatar_split_clause,[],[f1380,f14337]) ).
fof(f14337,plain,
( spl0_1581
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X3,X1,X5)
| c_lessequals(c_SetInterval_OatMost(X3,X5),c_SetInterval_OatMost(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f1380,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X3,X1,X5)
| c_lessequals(c_SetInterval_OatMost(X3,X5),c_SetInterval_OatMost(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f14335,plain,
spl0_1580,
inference(avatar_split_clause,[],[f1379,f14333]) ).
fof(f14333,plain,
( spl0_1580
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X3,X1,X5)
| ~ c_lessequals(c_SetInterval_OatMost(X3,X5),c_SetInterval_OatMost(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f1379,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X3,X1,X5)
| ~ c_lessequals(c_SetInterval_OatMost(X3,X5),c_SetInterval_OatMost(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f14331,plain,
spl0_1579,
inference(avatar_split_clause,[],[f1374,f14329]) ).
fof(f14329,plain,
( spl0_1579
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X1,X3,X5)
| c_lessequals(c_SetInterval_OatLeast(X3,X5),c_SetInterval_OatLeast(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f1374,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X1,X3,X5)
| c_lessequals(c_SetInterval_OatLeast(X3,X5),c_SetInterval_OatLeast(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f14327,plain,
spl0_1578,
inference(avatar_split_clause,[],[f1373,f14325]) ).
fof(f14325,plain,
( spl0_1578
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X1,X3,X5)
| ~ c_lessequals(c_SetInterval_OatLeast(X3,X5),c_SetInterval_OatLeast(X1,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f1373,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X1,X3,X5)
| ~ c_lessequals(c_SetInterval_OatLeast(X3,X5),c_SetInterval_OatLeast(X1,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f14323,plain,
spl0_1577,
inference(avatar_split_clause,[],[f1331,f14321]) ).
fof(f14321,plain,
( spl0_1577
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Oring(X5)
| c_uminus(c_times(X8,X9,X5),X5) = c_times(X8,c_uminus(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f1331,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_uminus(c_times(X8,X9,X5),X5) = c_times(X8,c_uminus(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f14319,plain,
spl0_1576,
inference(avatar_split_clause,[],[f1330,f14317]) ).
fof(f14317,plain,
( spl0_1576
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(c_uminus(X8,X5),X9,X5) = c_uminus(c_times(X8,X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f1330,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(c_uminus(X8,X5),X9,X5) = c_uminus(c_times(X8,X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f14315,plain,
spl0_1575,
inference(avatar_split_clause,[],[f1308,f14313]) ).
fof(f14313,plain,
( spl0_1575
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(X8,X9,X5) = c_times(c_uminus(X8,X5),c_uminus(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f1308,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Oring(X5)
| c_times(X8,X9,X5) = c_times(c_uminus(X8,X5),c_uminus(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f14311,plain,
( spl0_1574
| ~ spl0_867
| ~ spl0_1308 ),
inference(avatar_split_clause,[],[f12325,f10285,f7546,f14308]) ).
fof(f14308,plain,
( spl0_1574
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f7546,plain,
( spl0_867
<=> ! [X28] : c_Numeral_Obin__add(c_Numeral_OMin,X28) = c_Numeral_Obin__add(X28,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f10285,plain,
( spl0_1308
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f12325,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_867
| ~ spl0_1308 ),
inference(superposition,[],[f10287,f7547]) ).
fof(f7547,plain,
( ! [X28] : c_Numeral_Obin__add(c_Numeral_OMin,X28) = c_Numeral_Obin__add(X28,c_Numeral_OMin)
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f7546]) ).
fof(f10287,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_1308 ),
inference(avatar_component_clause,[],[f10285]) ).
fof(f14306,plain,
spl0_1573,
inference(avatar_split_clause,[],[f1153,f14304]) ).
fof(f14304,plain,
( spl0_1573
<=> ! [X5,X28] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f1153,axiom,
! [X28,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Numeral_Onumber__of(X28,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X28,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Opower__0__left__number__of_1) ).
fof(f14302,plain,
spl0_1572,
inference(avatar_split_clause,[],[f1147,f14300]) ).
fof(f14300,plain,
( spl0_1572
<=> ! [X5,X3] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ c_Parity_Oeven(X3,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f1147,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Power_Orecpower(X5)
| ~ c_Parity_Oeven(X3,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oneg__one__even__power_0) ).
fof(f14298,plain,
spl0_1571,
inference(avatar_split_clause,[],[f1145,f14296]) ).
fof(f14296,plain,
( spl0_1571
<=> ! [X5,X3] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X3,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X5),X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f1145,axiom,
! [X3,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_Parity_Oeven(X3,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X5),X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ominus__one__even__power_0) ).
fof(f14294,plain,
spl0_1570,
inference(avatar_split_clause,[],[f1050,f14292]) ).
fof(f14292,plain,
( spl0_1570
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| ~ c_less(X8,c_0,X5)
| c_less(c_plus(X8,X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f1050,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| ~ c_less(X8,c_0,X5)
| c_less(c_plus(X8,X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f14290,plain,
spl0_1569,
inference(avatar_split_clause,[],[f1049,f14288]) ).
fof(f14288,plain,
( spl0_1569
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| c_less(X8,c_0,X5)
| ~ c_less(c_plus(X8,X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f1049,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ class_Orderings_Olinorder(X5)
| c_less(X8,c_0,X5)
| ~ c_less(c_plus(X8,X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f14286,plain,
spl0_1568,
inference(avatar_split_clause,[],[f921,f14284]) ).
fof(f14284,plain,
( spl0_1568
<=> ! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_times(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f921,axiom,
! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_times(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f14282,plain,
spl0_1567,
inference(avatar_split_clause,[],[f901,f14280]) ).
fof(f14280,plain,
( spl0_1567
<=> ! [X18,X0,X2] :
( X2 = X18
| c_0 = X0
| c_times(X2,X0,tc_nat) != c_times(X18,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f901,axiom,
! [X2,X0,X18] :
( X2 = X18
| c_0 = X0
| c_times(X2,X0,tc_nat) != c_times(X18,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel2_0) ).
fof(f14278,plain,
spl0_1566,
inference(avatar_split_clause,[],[f899,f14276]) ).
fof(f14276,plain,
( spl0_1566
<=> ! [X18,X0,X2] :
( X2 = X18
| c_0 = X0
| c_times(X0,X2,tc_nat) != c_times(X0,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f899,axiom,
! [X2,X0,X18] :
( X2 = X18
| c_0 = X0
| c_times(X0,X2,tc_nat) != c_times(X0,X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__cancel1_0) ).
fof(f14274,plain,
spl0_1565,
inference(avatar_split_clause,[],[f878,f14272]) ).
fof(f14272,plain,
( spl0_1565
<=> ! [X45,X0,X17] : c_minus(c_minus(X17,X45,tc_nat),X0,tc_nat) = c_minus(X17,c_plus(X45,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f14270,plain,
spl0_1564,
inference(avatar_split_clause,[],[f869,f14268]) ).
fof(f14268,plain,
( spl0_1564
<=> ! [X18,X2] :
( c_less(c_0,X18,tc_nat)
| c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_plus(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f869,axiom,
! [X2,X18] :
( c_less(c_0,X18,tc_nat)
| c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_plus(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_0) ).
fof(f14266,plain,
spl0_1563,
inference(avatar_split_clause,[],[f704,f14264]) ).
fof(f14264,plain,
( spl0_1563
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f704,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omult__nat__number__of_0) ).
fof(f14262,plain,
spl0_1562,
inference(avatar_split_clause,[],[f701,f14260]) ).
fof(f14260,plain,
( spl0_1562
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f701,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Omod__nat__number__of_0) ).
fof(f14258,plain,
spl0_1561,
inference(avatar_split_clause,[],[f688,f14256]) ).
fof(f14256,plain,
( spl0_1561
<=> ! [X29] :
( c_0 != c_Numeral_Onumber__of(X29,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f688,axiom,
! [X29] :
( c_0 != c_Numeral_Onumber__of(X29,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_0) ).
fof(f14254,plain,
spl0_1560,
inference(avatar_split_clause,[],[f668,f14252]) ).
fof(f14252,plain,
( spl0_1560
<=> ! [X29,X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f668,axiom,
! [X70,X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X29,tc_nat),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f14250,plain,
spl0_1559,
inference(avatar_split_clause,[],[f642,f14248]) ).
fof(f14248,plain,
( spl0_1559
<=> ! [X18,X2] :
( ~ c_less(c_0,X18,tc_nat)
| ~ c_less(c_0,X2,tc_nat)
| c_less(c_minus(X18,X2,tc_nat),X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f642,axiom,
! [X2,X18] :
( ~ c_less(c_0,X18,tc_nat)
| ~ c_less(c_0,X2,tc_nat)
| c_less(c_minus(X18,X2,tc_nat),X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__less_0) ).
fof(f14246,plain,
spl0_1558,
inference(avatar_split_clause,[],[f590,f14244]) ).
fof(f14244,plain,
( spl0_1558
<=> ! [X34,X5,X35] : c_List_Oset(c_append(X34,X35,X5),X5) = c_union(c_List_Oset(X34,X5),c_List_Oset(X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f590,axiom,
! [X34,X35,X5] : c_List_Oset(c_append(X34,X35,X5),X5) = c_union(c_List_Oset(X34,X5),c_List_Oset(X35,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__append_0) ).
fof(f14242,plain,
spl0_1557,
inference(avatar_split_clause,[],[f580,f14240]) ).
fof(f580,axiom,
! [X2,X1,X5] :
( c_List_Orotate(X2,X1,X5) = X1
| c_0 != c_Divides_Oop_Amod(X2,c_Nat_Osize(X1,tc_List_Olist(X5)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__id_0) ).
fof(f14238,plain,
spl0_1556,
inference(avatar_split_clause,[],[f566,f14236]) ).
fof(f14236,plain,
( spl0_1556
<=> ! [X34,X5,X35] : c_List_Orev(c_append(X34,X35,X5),X5) = c_append(c_List_Orev(X35,X5),c_List_Orev(X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f566,axiom,
! [X34,X35,X5] : c_List_Orev(c_append(X34,X35,X5),X5) = c_append(c_List_Orev(X35,X5),c_List_Orev(X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__append_0) ).
fof(f14234,plain,
spl0_1555,
inference(avatar_split_clause,[],[f549,f14232]) ).
fof(f14232,plain,
( spl0_1555
<=> ! [X35,X34,X6,X3] : c_append(c_List_Olist_OCons(X3,X34,X6),X35,X6) = c_List_Olist_OCons(X3,c_append(X34,X35,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f549,axiom,
! [X3,X6,X34,X35] : c_append(c_List_Olist_OCons(X3,X34,X6),X35,X6) = c_List_Olist_OCons(X3,c_append(X34,X35,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f14230,plain,
spl0_1554,
inference(avatar_split_clause,[],[f537,f14228]) ).
fof(f14228,plain,
( spl0_1554
<=> ! [X35,X34,X5,X1] : c_List_Onth(c_append(X34,c_List_Olist_OCons(X1,X35,X5),X5),c_Nat_Osize(X34,tc_List_Olist(X5)),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f537,axiom,
! [X1,X34,X35,X5] : c_List_Onth(c_append(X34,c_List_Olist_OCons(X1,X35,X5),X5),c_Nat_Osize(X34,tc_List_Olist(X5)),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__append__length_0) ).
fof(f14226,plain,
( ~ spl0_1553
| spl0_98
| ~ spl0_802
| ~ spl0_1093
| ~ spl0_1225 ),
inference(avatar_split_clause,[],[f11992,f9933,f8849,f7282,f3642,f14223]) ).
fof(f14223,plain,
( spl0_1553
<=> c_IntDef_Oiszero(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f7282,plain,
( spl0_802
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f8849,plain,
( spl0_1093
<=> ! [X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X29,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f9933,plain,
( spl0_1225
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f11992,plain,
( c_0 = c_1
| ~ c_IntDef_Oiszero(c_1,tc_IntDef_Oint)
| ~ spl0_802
| ~ spl0_1093
| ~ spl0_1225 ),
inference(forward_demodulation,[],[f11986,f7284]) ).
fof(f7284,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat)
| ~ spl0_802 ),
inference(avatar_component_clause,[],[f7282]) ).
fof(f11986,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_1093
| ~ spl0_1225 ),
inference(superposition,[],[f8850,f9935]) ).
fof(f9935,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f9933]) ).
fof(f8850,plain,
( ! [X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X29,tc_nat) )
| ~ spl0_1093 ),
inference(avatar_component_clause,[],[f8849]) ).
fof(f14221,plain,
spl0_1552,
inference(avatar_split_clause,[],[f532,f14219]) ).
fof(f14219,plain,
( spl0_1552
<=> ! [X44,X34,X5,X3] :
( c_in(X3,c_List_Oset(X34,X5),X5)
| ~ c_in(X3,c_List_Oset(c_List_Osublist(X34,X44,X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f532,axiom,
! [X3,X44,X34,X5] :
( c_in(X3,c_List_Oset(X34,X5),X5)
| ~ c_in(X3,c_List_Oset(c_List_Osublist(X34,X44,X5),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onotin__set__sublistI_0) ).
fof(f14217,plain,
spl0_1551,
inference(avatar_split_clause,[],[f531,f14215]) ).
fof(f14215,plain,
( spl0_1551
<=> ! [X3,X34,X5,X1] :
( c_in(X3,c_List_Oset(X34,X5),X5)
| ~ c_in(X3,c_List_Oset(c_List_Oremove1(X1,X34,X5),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f531,axiom,
! [X3,X1,X34,X5] :
( c_in(X3,c_List_Oset(X34,X5),X5)
| ~ c_in(X3,c_List_Oset(c_List_Oremove1(X1,X34,X5),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onotin__set__remove1_0) ).
fof(f14213,plain,
spl0_1550,
inference(avatar_split_clause,[],[f442,f14211]) ).
fof(f14211,plain,
( spl0_1550
<=> ! [X34,X2,X5] : c_Nat_Osize(c_List_Odrop(X2,X34,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f442,axiom,
! [X2,X34,X5] : c_Nat_Osize(c_List_Odrop(X2,X34,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__drop_0) ).
fof(f14209,plain,
spl0_1549,
inference(avatar_split_clause,[],[f418,f14207]) ).
fof(f14207,plain,
( spl0_1549
<=> ! [X17,X0,X5,X3] : c_List_Odrop(X17,c_List_Oreplicate(X0,X3,X5),X5) = c_List_Oreplicate(c_minus(X0,X17,tc_nat),X3,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f418,axiom,
! [X3,X0,X17,X5] : c_List_Odrop(X17,c_List_Oreplicate(X0,X3,X5),X5) = c_List_Oreplicate(c_minus(X0,X17,tc_nat),X3,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__replicate_0) ).
fof(f14205,plain,
spl0_1548,
inference(avatar_split_clause,[],[f415,f14203]) ).
fof(f14203,plain,
( spl0_1548
<=> ! [X18,X34,X5,X2] : c_List_Odrop(X2,c_List_Odrop(X18,X34,X5),X5) = c_List_Odrop(c_plus(X2,X18,tc_nat),X34,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f415,axiom,
! [X2,X18,X34,X5] : c_List_Odrop(X2,c_List_Odrop(X18,X34,X5),X5) = c_List_Odrop(c_plus(X2,X18,tc_nat),X34,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__drop_0) ).
fof(f14201,plain,
spl0_1547,
inference(avatar_split_clause,[],[f395,f14199]) ).
fof(f14199,plain,
( spl0_1547
<=> ! [X6,X34,X3] :
( ~ c_List_Odistinct(X34,X6)
| c_List_Odistinct(c_List_Olist_OCons(X3,X34,X6),X6)
| c_in(X3,c_List_Oset(X34,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f395,axiom,
! [X3,X6,X34] :
( ~ c_List_Odistinct(X34,X6)
| c_List_Odistinct(c_List_Olist_OCons(X3,X34,X6),X6)
| c_in(X3,c_List_Oset(X34,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_2) ).
fof(f14197,plain,
spl0_1546,
inference(avatar_split_clause,[],[f388,f14195]) ).
fof(f14195,plain,
( spl0_1546
<=> ! [X36,X5] :
( c_List_Olist_ONil = c_List_Oconcat(X36,X5)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X36,X5),c_List_Oset(X36,tc_List_Olist(X5)),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f388,axiom,
! [X36,X5] :
( c_List_Olist_ONil = c_List_Oconcat(X36,X5)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X36,X5),c_List_Oset(X36,tc_List_Olist(X5)),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f14193,plain,
spl0_1545,
inference(avatar_split_clause,[],[f359,f14191]) ).
fof(f14191,plain,
( spl0_1545
<=> ! [X37,X34,X5,X35] : c_append(c_append(X34,X35,X5),X37,X5) = c_append(X34,c_append(X35,X37,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f359,axiom,
! [X37,X34,X35,X5] : c_append(c_append(X34,X35,X5),X37,X5) = c_append(X34,c_append(X35,X37,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__assoc_0) ).
fof(f14189,plain,
spl0_1544,
inference(avatar_split_clause,[],[f349,f14187]) ).
fof(f14187,plain,
( spl0_1544
<=> ! [X36,X5] :
( c_List_Olist_ONil = c_List_Oconcat(X36,X5)
| c_in(c_Main_ONil__eq__concat__conv__1(X36,X5),c_List_Oset(X36,tc_List_Olist(X5)),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f349,axiom,
! [X36,X5] :
( c_List_Olist_ONil = c_List_Oconcat(X36,X5)
| c_in(c_Main_ONil__eq__concat__conv__1(X36,X5),c_List_Oset(X36,tc_List_Olist(X5)),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_1) ).
fof(f14185,plain,
spl0_1543,
inference(avatar_split_clause,[],[f336,f14183]) ).
fof(f14183,plain,
( spl0_1543
<=> ! [X9,X8] : c_Divides_Oop_Amod(c_uminus(X8,tc_IntDef_Oint),c_uminus(X9,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f336,axiom,
! [X8,X9] : c_Divides_Oop_Amod(c_uminus(X8,tc_IntDef_Oint),c_uminus(X9,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f14181,plain,
( spl0_1542
| ~ spl0_977
| ~ spl0_1216 ),
inference(avatar_split_clause,[],[f11733,f9645,f8180,f14179]) ).
fof(f14179,plain,
( spl0_1542
<=> ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f9645,plain,
( spl0_1216
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f11733,plain,
( ! [X0] : c_lessequals(c_0,c_HOL_Oabs(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_977
| ~ spl0_1216 ),
inference(superposition,[],[f8181,f9646]) ).
fof(f9646,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_1216 ),
inference(avatar_component_clause,[],[f9645]) ).
fof(f14177,plain,
spl0_1541,
inference(avatar_split_clause,[],[f80,f14175]) ).
fof(f14175,plain,
( spl0_1541
<=> ! [X2,X0,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_plus(X18,c_times(X2,X0,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f80,axiom,
! [X2,X0,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_plus(X18,c_times(X2,X0,tc_nat),tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self2_0) ).
fof(f14173,plain,
spl0_1540,
inference(avatar_split_clause,[],[f78,f14171]) ).
fof(f14171,plain,
( spl0_1540
<=> ! [X2,X0,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_plus(X18,c_times(X0,X2,tc_nat),tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f78,axiom,
! [X2,X0,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_plus(X18,c_times(X0,X2,tc_nat),tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1_0) ).
fof(f14169,plain,
spl0_1539,
inference(avatar_split_clause,[],[f58,f14167]) ).
fof(f14167,plain,
( spl0_1539
<=> ! [X2,X18] :
( ~ c_less(c_1,X2,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_div(X18,X2,tc_nat),X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f58,axiom,
! [X2,X18] :
( ~ c_less(c_1,X2,tc_nat)
| ~ c_less(c_0,X18,tc_nat)
| c_less(c_div(X18,X2,tc_nat),X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less__dividend_0) ).
fof(f13681,plain,
( spl0_1538
| ~ spl0_700
| ~ spl0_701
| ~ spl0_703
| ~ spl0_779
| ~ spl0_1449 ),
inference(avatar_split_clause,[],[f12854,f11779,f7188,f6865,f6857,f6852,f13679]) ).
fof(f13679,plain,
( spl0_1538
<=> ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f6857,plain,
( spl0_701
<=> ! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f6865,plain,
( spl0_703
<=> ! [X28] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X28) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f7188,plain,
( spl0_779
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f11779,plain,
( spl0_1449
<=> ! [X29,X28] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),X28) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),X28),X28) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f12854,plain,
( ! [X0] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0) = X0
| ~ spl0_700
| ~ spl0_701
| ~ spl0_703
| ~ spl0_779
| ~ spl0_1449 ),
inference(forward_demodulation,[],[f12853,f6858]) ).
fof(f6858,plain,
( ! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = X1
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f6857]) ).
fof(f12853,plain,
( ! [X0] : c_Numeral_Obin__add(c_Numeral_OPls,X0) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X0)
| ~ spl0_700
| ~ spl0_703
| ~ spl0_779
| ~ spl0_1449 ),
inference(forward_demodulation,[],[f12852,f7190]) ).
fof(f7190,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_779 ),
inference(avatar_component_clause,[],[f7188]) ).
fof(f12852,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_700
| ~ spl0_703
| ~ spl0_1449 ),
inference(forward_demodulation,[],[f12841,f6866]) ).
fof(f6866,plain,
( ! [X28] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X28)
| ~ spl0_703 ),
inference(avatar_component_clause,[],[f6865]) ).
fof(f12841,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_700
| ~ spl0_1449 ),
inference(superposition,[],[f11780,f6854]) ).
fof(f11780,plain,
( ! [X28,X29] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),X28) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),X28),X28)
| ~ spl0_1449 ),
inference(avatar_component_clause,[],[f11779]) ).
fof(f13563,plain,
( spl0_1537
| ~ spl0_699
| ~ spl0_701
| ~ spl0_727
| ~ spl0_779
| ~ spl0_867
| ~ spl0_1448 ),
inference(avatar_split_clause,[],[f12835,f11775,f7546,f7188,f6965,f6857,f6847,f13560]) ).
fof(f6847,plain,
( spl0_699
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f11775,plain,
( spl0_1448
<=> ! [X28] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f12835,plain,
( c_Numeral_OMin = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_699
| ~ spl0_701
| ~ spl0_727
| ~ spl0_779
| ~ spl0_867
| ~ spl0_1448 ),
inference(forward_demodulation,[],[f12834,f6849]) ).
fof(f6849,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_699 ),
inference(avatar_component_clause,[],[f6847]) ).
fof(f12834,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_701
| ~ spl0_727
| ~ spl0_779
| ~ spl0_867
| ~ spl0_1448 ),
inference(forward_demodulation,[],[f12833,f7190]) ).
fof(f12833,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_701
| ~ spl0_727
| ~ spl0_867
| ~ spl0_1448 ),
inference(forward_demodulation,[],[f12832,f6858]) ).
fof(f12832,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_727
| ~ spl0_867
| ~ spl0_1448 ),
inference(forward_demodulation,[],[f12826,f7547]) ).
fof(f12826,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_727
| ~ spl0_1448 ),
inference(superposition,[],[f11776,f6967]) ).
fof(f11776,plain,
( ! [X28] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),c_Numeral_Obit_OB1)
| ~ spl0_1448 ),
inference(avatar_component_clause,[],[f11775]) ).
fof(f13410,plain,
( spl0_1536
| ~ spl0_760
| ~ spl0_1364 ),
inference(avatar_split_clause,[],[f11933,f11374,f7112,f13408]) ).
fof(f13408,plain,
( spl0_1536
<=> ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f7112,plain,
( spl0_760
<=> ! [X6,X34,X3] : ~ c_List_Onull(c_List_Olist_OCons(X3,X34,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f11374,plain,
( spl0_1364
<=> ! [X5,X1] :
( c_List_Olist_ONil = X1
| c_List_Olist_OCons(c_List_Ohd(X1,X5),c_List_Otl(X1,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f11933,plain,
( ! [X0,X1] :
( ~ c_List_Onull(X0,X1)
| c_List_Olist_ONil = X0 )
| ~ spl0_760
| ~ spl0_1364 ),
inference(superposition,[],[f7113,f11375]) ).
fof(f11375,plain,
( ! [X1,X5] :
( c_List_Olist_OCons(c_List_Ohd(X1,X5),c_List_Otl(X1,X5),X5) = X1
| c_List_Olist_ONil = X1 )
| ~ spl0_1364 ),
inference(avatar_component_clause,[],[f11374]) ).
fof(f7113,plain,
( ! [X3,X6,X34] : ~ c_List_Onull(c_List_Olist_OCons(X3,X34,X6),X6)
| ~ spl0_760 ),
inference(avatar_component_clause,[],[f7112]) ).
fof(f13204,plain,
spl0_1535,
inference(avatar_split_clause,[],[f3109,f13202]) ).
fof(f13202,plain,
( spl0_1535
<=> ! [X5,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f3109,plain,
! [X1,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X1,X5) ),
inference(forward_demodulation,[],[f2915,f955]) ).
fof(f2915,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X1,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f175,f970]) ).
fof(f175,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X1,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_1) ).
fof(f13200,plain,
spl0_1534,
inference(avatar_split_clause,[],[f3104,f13198]) ).
fof(f13198,plain,
( spl0_1534
<=> ! [X5,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f3104,plain,
! [X1,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X1),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X1,X5) ),
inference(forward_demodulation,[],[f2911,f955]) ).
fof(f2911,plain,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X1,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__mult(c_Numeral_OMin,X1)),X5),X5) ),
inference(definition_unfolding,[],[f174,f970]) ).
fof(f174,axiom,
! [X1,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X1,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X1)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__6_0) ).
fof(f13196,plain,
spl0_1533,
inference(avatar_split_clause,[],[f2997,f13194]) ).
fof(f13194,plain,
( spl0_1533
<=> ! [X70] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f2997,plain,
! [X70] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X70,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2819,f2745]) ).
fof(f2819,plain,
! [X70] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X70,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(X70,tc_nat),tc_nat),
inference(definition_unfolding,[],[f711,f1385]) ).
fof(f711,axiom,
! [X70] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f13189,plain,
spl0_1532,
inference(avatar_split_clause,[],[f2920,f13187]) ).
fof(f13187,plain,
( spl0_1532
<=> ! [X34,X5,X2] :
( c_List_Olist_ONil = X34
| c_0 = X2
| c_List_Olist_ONil != c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f2920,plain,
! [X2,X34,X5] :
( c_List_Olist_ONil = X34
| c_0 = X2
| c_List_Olist_ONil != c_List_Osublist(X34,c_SetInterval_OlessThan(X2,tc_nat),X5) ),
inference(definition_unfolding,[],[f613,f607]) ).
fof(f613,axiom,
! [X2,X34,X5] :
( c_List_Olist_ONil = X34
| c_0 = X2
| c_List_Olist_ONil != c_List_Otake(X2,X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otake__eq__Nil_0) ).
fof(f13180,plain,
( spl0_1531
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1530 ),
inference(avatar_split_clause,[],[f13176,f13173,f10406,f10097,f6714,f3706,f13178]) ).
fof(f13178,plain,
( spl0_1531
<=> ! [X29] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f13173,plain,
( spl0_1530
<=> ! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f13176,plain,
( ! [X29] :
( c_1 = c_plus(c_1,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1530 ),
inference(forward_demodulation,[],[f13174,f11227]) ).
fof(f13174,plain,
( ! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),tc_nat) )
| ~ spl0_1530 ),
inference(avatar_component_clause,[],[f13173]) ).
fof(f13175,plain,
spl0_1530,
inference(avatar_split_clause,[],[f2886,f13173]) ).
fof(f2886,plain,
! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_Numeral_Onumber__of(X29,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f663,f1385]) ).
fof(f663,axiom,
! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X29,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f13171,plain,
spl0_1529,
inference(avatar_split_clause,[],[f2884,f13169]) ).
fof(f13169,plain,
( spl0_1529
<=> ! [X24,X20,X5,X19] :
( c_in(X19,X20,X5)
| ~ c_in(X19,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f2884,plain,
! [X19,X24,X5,X20] :
( c_in(X19,X20,X5)
| ~ c_in(X19,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ),
inference(definition_unfolding,[],[f1447,f1214]) ).
fof(f1447,axiom,
! [X19,X24,X5,X20] :
( c_in(X19,X20,X5)
| ~ c_in(X19,c_inter(X20,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_0) ).
fof(f13167,plain,
spl0_1528,
inference(avatar_split_clause,[],[f2883,f13165]) ).
fof(f13165,plain,
( spl0_1528
<=> ! [X24,X20,X5,X19] :
( c_in(X19,X24,X5)
| ~ c_in(X19,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f2883,plain,
! [X19,X24,X5,X20] :
( c_in(X19,X24,X5)
| ~ c_in(X19,c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5),X5) ),
inference(definition_unfolding,[],[f1448,f1214]) ).
fof(f1448,axiom,
! [X19,X24,X5,X20] :
( c_in(X19,X24,X5)
| ~ c_in(X19,c_inter(X20,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).
fof(f13163,plain,
spl0_1527,
inference(avatar_split_clause,[],[f2853,f13161]) ).
fof(f13161,plain,
( spl0_1527
<=> ! [X18,X2] :
( X2 = X18
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f2853,plain,
! [X2,X18] :
( X2 = X18
| c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f858,f1385,f1385]) ).
fof(f858,axiom,
! [X2,X18] :
( X2 = X18
| c_Suc(X2) != c_Suc(X18) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__Suc__eq_0) ).
fof(f13159,plain,
spl0_1526,
inference(avatar_split_clause,[],[f2801,f13157]) ).
fof(f13157,plain,
( spl0_1526
<=> ! [X2,X5,X1] : c_append(c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X5),c_List_Odrop(X2,X1,X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f2801,plain,
! [X2,X1,X5] : c_append(c_List_Osublist(X1,c_SetInterval_OlessThan(X2,tc_nat),X5),c_List_Odrop(X2,X1,X5),X5) = X1,
inference(definition_unfolding,[],[f376,f607]) ).
fof(f376,axiom,
! [X2,X1,X5] : c_append(c_List_Otake(X2,X1,X5),c_List_Odrop(X2,X1,X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__take__drop__id_0) ).
fof(f13155,plain,
spl0_1525,
inference(avatar_split_clause,[],[f1667,f13153]) ).
fof(f13153,plain,
( spl0_1525
<=> ! [X20,X73,X5] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(c_Main_OUnionE__1(X20,X73,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f1667,axiom,
! [X73,X5,X20] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(c_Main_OUnionE__1(X20,X73,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_0) ).
fof(f13151,plain,
spl0_1524,
inference(avatar_split_clause,[],[f1664,f13149]) ).
fof(f13149,plain,
( spl0_1524
<=> ! [X20,X73,X5] :
( c_in(X20,c_Inter(X73,X5),X5)
| c_in(c_Main_OInterI__1(X20,X73,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f1664,axiom,
! [X73,X5,X20] :
( c_in(X20,c_Inter(X73,X5),X5)
| c_in(c_Main_OInterI__1(X20,X73,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f13142,plain,
spl0_1523,
inference(avatar_split_clause,[],[f1627,f13140]) ).
fof(f13140,plain,
( spl0_1523
<=> ! [X20,X5,X67,X3] :
( c_in(X3,X20,X5)
| ~ c_in(c_List_Olist_OCons(X3,X67,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f1627,axiom,
! [X3,X5,X67,X20] :
( c_in(X3,X20,X5)
| ~ c_in(c_List_Olist_OCons(X3,X67,X5),c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f13138,plain,
spl0_1522,
inference(avatar_split_clause,[],[f1616,f13136]) ).
fof(f1616,axiom,
! [X34,X5,X20] :
( ~ c_in(c_Main_Oin__listsI__1(X20,X34,X5),X20,X5)
| c_in(X34,c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f13134,plain,
spl0_1521,
inference(avatar_split_clause,[],[f1611,f13132]) ).
fof(f13132,plain,
( spl0_1521
<=> ! [X18,X74] :
( c_0 != c_Divides_Oop_Amod(X18,X74,tc_IntDef_Oint)
| c_times(X74,c_Main_Ozmod__eq__0D__dest__1(X74,X18),tc_IntDef_Oint) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f1611,axiom,
! [X18,X74] :
( c_0 != c_Divides_Oop_Amod(X18,X74,tc_IntDef_Oint)
| c_times(X74,c_Main_Ozmod__eq__0D__dest__1(X74,X18),tc_IntDef_Oint) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f13130,plain,
spl0_1520,
inference(avatar_split_clause,[],[f1595,f13128]) ).
fof(f13128,plain,
( spl0_1520
<=> ! [X18,X74] :
( c_0 != c_Divides_Oop_Amod(X18,X74,tc_nat)
| c_times(X74,c_Main_Omod__eq__0D__dest__1(X74,X18),tc_nat) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f1595,axiom,
! [X18,X74] :
( c_0 != c_Divides_Oop_Amod(X18,X74,tc_nat)
| c_times(X74,c_Main_Omod__eq__0D__dest__1(X74,X18),tc_nat) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f13126,plain,
spl0_1519,
inference(avatar_split_clause,[],[f1568,f13124]) ).
fof(f13124,plain,
( spl0_1519
<=> ! [X1,X3] :
( ~ c_less(X3,X1,tc_nat)
| c_in(c_Pair(X3,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f1568,axiom,
! [X3,X1] :
( ~ c_less(X3,X1,tc_nat)
| c_in(c_Pair(X3,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f13122,plain,
spl0_1518,
inference(avatar_split_clause,[],[f1567,f13120]) ).
fof(f13120,plain,
( spl0_1518
<=> ! [X1,X3] :
( c_less(X3,X1,tc_nat)
| ~ c_in(c_Pair(X3,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f1567,axiom,
! [X3,X1] :
( c_less(X3,X1,tc_nat)
| ~ c_in(c_Pair(X3,X1,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f13118,plain,
spl0_1517,
inference(avatar_split_clause,[],[f1524,f13116]) ).
fof(f13116,plain,
( spl0_1517
<=> ! [X5,X20,X9,X8] :
( X8 = X9
| c_in(X8,X20,X5)
| ~ c_in(X8,c_insert(X9,X20,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f1524,axiom,
! [X8,X9,X5,X20] :
( X8 = X9
| c_in(X8,X20,X5)
| ~ c_in(X8,c_insert(X9,X20,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_0) ).
fof(f13114,plain,
spl0_1516,
inference(avatar_split_clause,[],[f1499,f13112]) ).
fof(f13112,plain,
( spl0_1516
<=> ! [X5,X24,X8] : c_Union(c_insert(X8,X24,tc_set(X5)),X5) = c_union(X8,c_Union(X24,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f1499,axiom,
! [X8,X24,X5] : c_Union(c_insert(X8,X24,tc_set(X5)),X5) = c_union(X8,c_Union(X24,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__insert_0) ).
fof(f13110,plain,
spl0_1515,
inference(avatar_split_clause,[],[f1496,f13108]) ).
fof(f13108,plain,
( spl0_1515
<=> ! [X20,X73,X5] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(c_Main_OUnion__iff__1(X20,X73,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f1496,axiom,
! [X73,X5,X20] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(c_Main_OUnion__iff__1(X20,X73,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_0) ).
fof(f13106,plain,
spl0_1514,
inference(avatar_split_clause,[],[f1462,f13104]) ).
fof(f13104,plain,
( spl0_1514
<=> ! [X20,X73,X5] :
( c_in(X20,c_Inter(X73,X5),X5)
| c_in(c_Main_OInter__iff__1(X20,X73,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f1462,axiom,
! [X73,X5,X20] :
( c_in(X20,c_Inter(X73,X5),X5)
| c_in(c_Main_OInter__iff__1(X20,X73,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_1) ).
fof(f13102,plain,
spl0_1513,
inference(avatar_split_clause,[],[f1329,f13100]) ).
fof(f13100,plain,
( spl0_1513
<=> ! [X9,X5,X8] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_0 = X8
| c_0 = X9
| c_0 != c_times(X8,X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f1329,axiom,
! [X8,X9,X5] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X5)
| c_0 = X8
| c_0 = X9
| c_0 != c_times(X8,X9,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f13098,plain,
spl0_1512,
inference(avatar_split_clause,[],[f1313,f13096]) ).
fof(f13096,plain,
( spl0_1512
<=> ! [X9,X5,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X9
| c_0 = X19
| c_times(X9,X19,X5) != X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f1313,axiom,
! [X19,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X9
| c_0 = X19
| c_times(X9,X19,X5) != X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_0) ).
fof(f13094,plain,
spl0_1511,
inference(avatar_split_clause,[],[f1309,f13092]) ).
fof(f13092,plain,
( spl0_1511
<=> ! [X9,X5,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X9
| c_0 = X19
| c_times(X19,X9,X5) != X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f1309,axiom,
! [X19,X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = X9
| c_0 = X19
| c_times(X19,X9,X5) != X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_0) ).
fof(f13090,plain,
spl0_1510,
inference(avatar_split_clause,[],[f1204,f13088]) ).
fof(f13088,plain,
( spl0_1510
<=> ! [X5,X10,X71,X9,X8,X7] :
( X9 = X71
| c_Pair(X8,X9,X5,X10) != c_Pair(X7,X71,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f1204,axiom,
! [X10,X71,X8,X9,X7,X5] :
( X9 = X71
| c_Pair(X8,X9,X5,X10) != c_Pair(X7,X71,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_1) ).
fof(f13086,plain,
spl0_1509,
inference(avatar_split_clause,[],[f1203,f13084]) ).
fof(f13084,plain,
( spl0_1509
<=> ! [X10,X9,X7,X71,X5,X8] :
( X7 = X8
| c_Pair(X8,X9,X5,X10) != c_Pair(X7,X71,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f1203,axiom,
! [X10,X71,X8,X9,X7,X5] :
( X7 = X8
| c_Pair(X8,X9,X5,X10) != c_Pair(X7,X71,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_OPair__eq_0) ).
fof(f13082,plain,
spl0_1508,
inference(avatar_split_clause,[],[f1190,f13080]) ).
fof(f13080,plain,
( spl0_1508
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X2,tc_nat)
| c_0 = c_Nat_Opower(c_0,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f1190,axiom,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X2,tc_nat)
| c_0 = c_Nat_Opower(c_0,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_2) ).
fof(f13078,plain,
spl0_1507,
inference(avatar_split_clause,[],[f1189,f13076]) ).
fof(f13076,plain,
( spl0_1507
<=> ! [X2,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X2,tc_nat)
| c_0 != c_Nat_Opower(X8,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f1189,axiom,
! [X2,X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X2,tc_nat)
| c_0 != c_Nat_Opower(X8,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_1) ).
fof(f13074,plain,
spl0_1506,
inference(avatar_split_clause,[],[f1109,f13072]) ).
fof(f13072,plain,
( spl0_1506
<=> ! [X1,X3,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omax(X3,X1,X10) = c_Orderings_Omax(X3,c_Orderings_Omax(X3,X1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f1109,axiom,
! [X3,X10,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omax(X3,X1,X10) = c_Orderings_Omax(X3,c_Orderings_Omax(X3,X1,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f13070,plain,
spl0_1505,
inference(avatar_split_clause,[],[f1104,f13068]) ).
fof(f13068,plain,
( spl0_1505
<=> ! [X1,X3,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omin(X3,X1,X10) = c_Orderings_Omin(X3,c_Orderings_Omin(X3,X1,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f1104,axiom,
! [X3,X10,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omin(X3,X1,X10) = c_Orderings_Omin(X3,c_Orderings_Omin(X3,X1,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f13066,plain,
spl0_1504,
inference(avatar_split_clause,[],[f1087,f13064]) ).
fof(f13064,plain,
( spl0_1504
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_OrderedGroup_Opprt(X8,X5),c_OrderedGroup_Opprt(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f1087,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_OrderedGroup_Opprt(X8,X5),c_OrderedGroup_Opprt(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__mono_0) ).
fof(f13062,plain,
( ~ spl0_1502
| spl0_1503
| ~ spl0_125
| ~ spl0_1268 ),
inference(avatar_split_clause,[],[f10690,f10125,f3763,f13060,f13056]) ).
fof(f13056,plain,
( spl0_1502
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f13060,plain,
( spl0_1503
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f10125,plain,
( spl0_1268
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X8,c_0,X5)
| ~ c_lessequals(c_0,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f10690,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_125
| ~ spl0_1268 ),
inference(resolution,[],[f10126,f3764]) ).
fof(f10126,plain,
( ! [X8,X5] :
( ~ c_lessequals(c_0,c_uminus(X8,X5),X5)
| c_lessequals(X8,c_0,X5)
| ~ class_OrderedGroup_Opordered__ab__group__add(X5) )
| ~ spl0_1268 ),
inference(avatar_component_clause,[],[f10125]) ).
fof(f13054,plain,
spl0_1501,
inference(avatar_split_clause,[],[f1083,f13052]) ).
fof(f13052,plain,
( spl0_1501
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_OrderedGroup_Onprt(X8,X5),c_OrderedGroup_Onprt(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f1083,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_OrderedGroup_Onprt(X8,X5),c_OrderedGroup_Onprt(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__mono_0) ).
fof(f13050,plain,
spl0_1500,
inference(avatar_split_clause,[],[f1077,f13048]) ).
fof(f13048,plain,
( spl0_1500
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_uminus(X9,X5),c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f1077,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_uminus(X9,X5),c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f13046,plain,
spl0_1499,
inference(avatar_split_clause,[],[f1076,f13044]) ).
fof(f13044,plain,
( spl0_1499
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_uminus(X9,X5),c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f1076,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_uminus(X9,X5),c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f13042,plain,
spl0_1498,
inference(avatar_split_clause,[],[f1073,f13040]) ).
fof(f13040,plain,
( spl0_1498
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_uminus(X9,X5),c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f1073,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_uminus(X9,X5),c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f13038,plain,
spl0_1497,
inference(avatar_split_clause,[],[f1072,f13036]) ).
fof(f13036,plain,
( spl0_1497
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_uminus(X9,X5),c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f1072,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_uminus(X9,X5),c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f13034,plain,
spl0_1496,
inference(avatar_split_clause,[],[f1036,f13032]) ).
fof(f13032,plain,
( spl0_1496
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X9 = X19
| c_plus(X19,X8,X5) != c_plus(X9,X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f1036,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X9 = X19
| c_plus(X19,X8,X5) != c_plus(X9,X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f13030,plain,
spl0_1495,
inference(avatar_split_clause,[],[f1031,f13028]) ).
fof(f13028,plain,
( spl0_1495
<=> ! [X5,X19,X9,X8] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X9 = X19
| c_plus(X8,X9,X5) != c_plus(X8,X19,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f1031,axiom,
! [X8,X19,X9,X5] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X5)
| X9 = X19
| c_plus(X8,X9,X5) != c_plus(X8,X19,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f13026,plain,
spl0_1494,
inference(avatar_split_clause,[],[f952,f13024]) ).
fof(f13024,plain,
( spl0_1494
<=> ! [X29,X28] : c_Numeral_Obin__add(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X29,c_Numeral_Obin__succ(X28)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f952,axiom,
! [X28,X29] : c_Numeral_Obin__add(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X29,c_Numeral_Obin__succ(X28)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f13022,plain,
spl0_1493,
inference(avatar_split_clause,[],[f926,f13020]) ).
fof(f13020,plain,
( spl0_1493
<=> ! [X2,X0,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f926,axiom,
! [X2,X0,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f13018,plain,
spl0_1492,
inference(avatar_split_clause,[],[f925,f13016]) ).
fof(f13016,plain,
( spl0_1492
<=> ! [X2,X0,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f925,axiom,
! [X2,X0,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f13013,plain,
spl0_1491,
inference(avatar_split_clause,[],[f924,f13011]) ).
fof(f13011,plain,
( spl0_1491
<=> ! [X2,X0,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f924,axiom,
! [X2,X0,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f13009,plain,
spl0_1490,
inference(avatar_split_clause,[],[f923,f13007]) ).
fof(f13007,plain,
( spl0_1490
<=> ! [X2,X0,X18] :
( c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f923,axiom,
! [X2,X0,X18] :
( c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_plus(X0,X18,tc_nat),c_plus(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f13005,plain,
spl0_1489,
inference(avatar_split_clause,[],[f917,f13003]) ).
fof(f13003,plain,
( spl0_1489
<=> ! [X2,X0,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f917,axiom,
! [X2,X0,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_1) ).
fof(f13001,plain,
spl0_1488,
inference(avatar_split_clause,[],[f916,f12999]) ).
fof(f12999,plain,
( spl0_1488
<=> ! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| ~ c_less(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f916,axiom,
! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| ~ c_less(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel2_0) ).
fof(f12997,plain,
spl0_1487,
inference(avatar_split_clause,[],[f914,f12995]) ).
fof(f12995,plain,
( spl0_1487
<=> ! [X2,X0,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f914,axiom,
! [X2,X0,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_1) ).
fof(f12993,plain,
spl0_1486,
inference(avatar_split_clause,[],[f913,f12991]) ).
fof(f12991,plain,
( spl0_1486
<=> ! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| ~ c_less(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f913,axiom,
! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| ~ c_less(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__less__cancel1_0) ).
fof(f12989,plain,
spl0_1485,
inference(avatar_split_clause,[],[f912,f12987]) ).
fof(f12987,plain,
( spl0_1485
<=> ! [X2,X0,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f912,axiom,
! [X2,X0,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_2) ).
fof(f12985,plain,
spl0_1484,
inference(avatar_split_clause,[],[f911,f12983]) ).
fof(f12983,plain,
( spl0_1484
<=> ! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| c_lessequals(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f911,axiom,
! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| c_lessequals(c_times(X18,X0,tc_nat),c_times(X2,X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel2_1) ).
fof(f12981,plain,
spl0_1483,
inference(avatar_split_clause,[],[f909,f12979]) ).
fof(f12979,plain,
( spl0_1483
<=> ! [X2,X0,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f909,axiom,
! [X2,X0,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_2) ).
fof(f12977,plain,
spl0_1482,
inference(avatar_split_clause,[],[f908,f12975]) ).
fof(f12975,plain,
( spl0_1482
<=> ! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| c_lessequals(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f908,axiom,
! [X2,X0,X18] :
( c_less(c_0,X0,tc_nat)
| c_lessequals(c_times(X0,X18,tc_nat),c_times(X0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__le__cancel1_1) ).
fof(f12973,plain,
( spl0_1481
| ~ spl0_798
| ~ spl0_1435 ),
inference(avatar_split_clause,[],[f12772,f11676,f7265,f12971]) ).
fof(f12971,plain,
( spl0_1481
<=> ! [X0,X1] : c_emptyset != c_UNITY_OAllowedActs(X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f7265,plain,
( spl0_798
<=> ! [X20,X5,X8] : c_emptyset != c_insert(X8,X20,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f11676,plain,
( spl0_1435
<=> ! [X5,X26] : c_UNITY_OAllowedActs(X26,X5) = c_insert(c_Relation_OId,c_UNITY_OAllowedActs(X26,X5),tc_set(tc_prod(X5,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f12772,plain,
( ! [X0,X1] : c_emptyset != c_UNITY_OAllowedActs(X0,X1)
| ~ spl0_798
| ~ spl0_1435 ),
inference(superposition,[],[f7266,f11677]) ).
fof(f11677,plain,
( ! [X26,X5] : c_UNITY_OAllowedActs(X26,X5) = c_insert(c_Relation_OId,c_UNITY_OAllowedActs(X26,X5),tc_set(tc_prod(X5,X5)))
| ~ spl0_1435 ),
inference(avatar_component_clause,[],[f11676]) ).
fof(f7266,plain,
( ! [X8,X5,X20] : c_emptyset != c_insert(X8,X20,X5)
| ~ spl0_798 ),
inference(avatar_component_clause,[],[f7265]) ).
fof(f12969,plain,
spl0_1480,
inference(avatar_split_clause,[],[f768,f12967]) ).
fof(f12967,plain,
( spl0_1480
<=> ! [X9,X10] :
( ~ class_HOL_Oone(X10)
| ~ class_OrderedGroup_Oab__group__add(X10)
| c_1 != c_uminus(X9,X10)
| c_uminus(c_1,X10) = X9 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f768,axiom,
! [X10,X9] :
( ~ class_HOL_Oone(X10)
| ~ class_OrderedGroup_Oab__group__add(X10)
| c_1 != c_uminus(X9,X10)
| c_uminus(c_1,X10) = X9 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f12965,plain,
spl0_1479,
inference(avatar_split_clause,[],[f709,f12963]) ).
fof(f12963,plain,
( spl0_1479
<=> ! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X29,tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f709,axiom,
! [X29,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X29,tc_nat),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f12961,plain,
spl0_1478,
inference(avatar_split_clause,[],[f661,f12959]) ).
fof(f12959,plain,
( spl0_1478
<=> ! [X2,X5,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X18,X2,tc_nat)
| c_less(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f661,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(X18,X2,tc_nat)
| c_less(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f12957,plain,
spl0_1477,
inference(avatar_split_clause,[],[f660,f12955]) ).
fof(f12955,plain,
( spl0_1477
<=> ! [X2,X5,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(X18,X2,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f660,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(X18,X2,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f12953,plain,
spl0_1476,
inference(avatar_split_clause,[],[f658,f12951]) ).
fof(f12951,plain,
( spl0_1476
<=> ! [X2,X5,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f658,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f12949,plain,
spl0_1475,
inference(avatar_split_clause,[],[f657,f12947]) ).
fof(f12947,plain,
( spl0_1475
<=> ! [X2,X5,X18] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f657,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X18,X5),c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f12945,plain,
spl0_1474,
inference(avatar_split_clause,[],[f597,f12943]) ).
fof(f12943,plain,
( spl0_1474
<=> ! [X2,X5,X3] :
( c_0 = X2
| c_insert(X3,c_emptyset,X5) = c_List_Oset(c_List_Oreplicate(X2,X3,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f597,axiom,
! [X2,X3,X5] :
( c_0 = X2
| c_insert(X3,c_emptyset,X5) = c_List_Oset(c_List_Oreplicate(X2,X3,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__replicate_0) ).
fof(f12941,plain,
spl0_1473,
inference(avatar_split_clause,[],[f574,f12939]) ).
fof(f12939,plain,
( spl0_1473
<=> ! [X34,X5,X3] :
( c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) = X34
| c_List_Orev(X34,X5) != c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f574,axiom,
! [X3,X34,X5] :
( c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) = X34
| c_List_Orev(X34,X5) != c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_0) ).
fof(f12937,plain,
spl0_1472,
inference(avatar_split_clause,[],[f551,f12935]) ).
fof(f12935,plain,
( spl0_1472
<=> ! [X3,X6,X35,X1] :
( X1 = X3
| c_List_Oop_Amem(X3,X35,X6)
| ~ c_List_Oop_Amem(X3,c_List_Olist_OCons(X1,X35,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f551,axiom,
! [X3,X1,X6,X35] :
( X1 = X3
| c_List_Oop_Amem(X3,X35,X6)
| ~ c_List_Oop_Amem(X3,c_List_Olist_OCons(X1,X35,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f12933,plain,
spl0_1471,
inference(avatar_split_clause,[],[f481,f12931]) ).
fof(f12931,plain,
( spl0_1471
<=> ! [X6,X52,X20] : c_List_Olistset(c_List_Olist_OCons(X20,X52,tc_set(X6)),X6) = c_List_Oset__Cons(X20,c_List_Olistset(X52,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f481,axiom,
! [X6,X52,X20] : c_List_Olistset(c_List_Olist_OCons(X20,X52,tc_set(X6)),X6) = c_List_Oset__Cons(X20,c_List_Olistset(X52,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__2_0) ).
fof(f12929,plain,
spl0_1470,
inference(avatar_split_clause,[],[f473,f12927]) ).
fof(f12927,plain,
( spl0_1470
<=> ! [X17,X3,X5,X1] :
( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),X17,tc_nat)
| c_List_Olist__update(X1,X17,X3,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f473,axiom,
! [X3,X1,X17,X5] :
( ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),X17,tc_nat)
| c_List_Olist__update(X1,X17,X3,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update__beyond_0) ).
fof(f12925,plain,
spl0_1469,
inference(avatar_split_clause,[],[f453,f12923]) ).
fof(f12923,plain,
( spl0_1469
<=> ! [X34,X5] : c_minus(c_Nat_Osize(X34,tc_List_Olist(X5)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X34,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f453,axiom,
! [X34,X5] : c_minus(c_Nat_Osize(X34,tc_List_Olist(X5)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X34,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__tl_0) ).
fof(f12921,plain,
spl0_1468,
inference(avatar_split_clause,[],[f441,f12919]) ).
fof(f12919,plain,
( spl0_1468
<=> ! [X34,X5] : c_Nat_Osize(c_List_Obutlast(X34,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X34,tc_List_Olist(X5)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f441,axiom,
! [X34,X5] : c_Nat_Osize(c_List_Obutlast(X34,X5),tc_List_Olist(X5)) = c_minus(c_Nat_Osize(X34,tc_List_Olist(X5)),c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__butlast_0) ).
fof(f12917,plain,
spl0_1467,
inference(avatar_split_clause,[],[f437,f12915]) ).
fof(f437,axiom,
! [X45,X17] :
( ~ c_less(X17,X45,tc_nat)
| c_List_Olast(c_List_Oupt(X17,X45),tc_nat) = c_minus(X45,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__upt_0) ).
fof(f12913,plain,
spl0_1466,
inference(avatar_split_clause,[],[f385,f12911]) ).
fof(f12911,plain,
( spl0_1466
<=> ! [X6,X34,X3] : c_List_Oconcat(c_List_Olist_OCons(X3,X34,tc_List_Olist(X6)),X6) = c_append(X3,c_List_Oconcat(X34,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f385,axiom,
! [X3,X6,X34] : c_List_Oconcat(c_List_Olist_OCons(X3,X34,tc_List_Olist(X6)),X6) = c_append(X3,c_List_Oconcat(X34,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__2_0) ).
fof(f12909,plain,
spl0_1465,
inference(avatar_split_clause,[],[f297,f12907]) ).
fof(f12907,plain,
( spl0_1465
<=> ! [X13,X32] : c_IntDiv_OnegateSnd(c_Pair(X32,X13,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X32,c_uminus(X13,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f12905,plain,
spl0_1464,
inference(avatar_split_clause,[],[f272,f12903]) ).
fof(f12903,plain,
( spl0_1464
<=> ! [X28,X30] :
( ~ c_less(X28,X30,tc_IntDef_Oint)
| ~ c_less(c_0,X30,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X28),c_IntDef_Onat(X30),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f272,axiom,
! [X28,X30] :
( ~ c_less(X28,X30,tc_IntDef_Oint)
| ~ c_less(c_0,X30,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X28),c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_2) ).
fof(f12901,plain,
spl0_1463,
inference(avatar_split_clause,[],[f256,f12899]) ).
fof(f12899,plain,
( spl0_1463
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X28,X30,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f256,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X28,X30,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_1) ).
fof(f12897,plain,
spl0_1462,
inference(avatar_split_clause,[],[f255,f12895]) ).
fof(f12895,plain,
( spl0_1462
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X28,X30,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f255,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X28,X30,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__iff_0) ).
fof(f12893,plain,
spl0_1461,
inference(avatar_split_clause,[],[f252,f12891]) ).
fof(f12891,plain,
( spl0_1461
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X28,X30,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f252,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X28,X30,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_1) ).
fof(f12889,plain,
spl0_1460,
inference(avatar_split_clause,[],[f251,f12887]) ).
fof(f251,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X28,X30,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X28,X5),c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__iff_0) ).
fof(f12885,plain,
spl0_1459,
inference(avatar_split_clause,[],[f122,f12883]) ).
fof(f12883,plain,
( spl0_1459
<=> ! [X25,X5,X24] :
( ~ c_in(X24,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X24,X25,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f122,axiom,
! [X24,X5,X25] :
( ~ c_in(X24,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_minus(X24,X25,tc_set(X5)),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f12881,plain,
spl0_1458,
inference(avatar_split_clause,[],[f39,f12879]) ).
fof(f12879,plain,
( spl0_1458
<=> ! [X15,X11,X10,X12,X5,X16] :
( X12 = X16
| c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_OScons(X15,X16,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f39,axiom,
! [X10,X11,X16,X15,X5,X12] :
( X12 = X16
| c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_OScons(X15,X16,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f12877,plain,
spl0_1457,
inference(avatar_split_clause,[],[f38,f12875]) ).
fof(f12875,plain,
( spl0_1457
<=> ! [X16,X11,X10,X12,X5,X15] :
( X11 = X15
| c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_OScons(X15,X16,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f38,axiom,
! [X10,X11,X16,X15,X5,X12] :
( X11 = X15
| c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_OScons(X15,X16,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f12817,plain,
( spl0_1456
| ~ spl0_127
| ~ spl0_1427 ),
inference(avatar_split_clause,[],[f12682,f11644,f3771,f12815]) ).
fof(f11644,plain,
( spl0_1427
<=> ! [X13,X5,X8] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| ~ c_in(c_Pair(X8,X8,X5,X5),X13,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f12682,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X0)
| ~ spl0_127
| ~ spl0_1427 ),
inference(resolution,[],[f11645,f3772]) ).
fof(f11645,plain,
( ! [X8,X5,X13] :
( ~ c_in(c_Pair(X8,X8,X5,X5),X13,tc_prod(X5,X5))
| ~ c_Wellfounded__Recursion_Owf(X13,X5) )
| ~ spl0_1427 ),
inference(avatar_component_clause,[],[f11644]) ).
fof(f12700,plain,
( spl0_1455
| ~ spl0_1111
| ~ spl0_1427 ),
inference(avatar_split_clause,[],[f12677,f11644,f8922,f12698]) ).
fof(f12698,plain,
( spl0_1455
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f8922,plain,
( spl0_1111
<=> ! [X5,X3] : c_in(c_Pair(X3,X3,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f12677,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1111
| ~ spl0_1427 ),
inference(resolution,[],[f11645,f8923]) ).
fof(f8923,plain,
( ! [X3,X5] : c_in(c_Pair(X3,X3,X5,X5),c_Relation_OId,tc_prod(X5,X5))
| ~ spl0_1111 ),
inference(avatar_component_clause,[],[f8922]) ).
fof(f12451,plain,
( ~ spl0_1453
| spl0_1454
| ~ spl0_125
| ~ spl0_1232 ),
inference(avatar_split_clause,[],[f10483,f9962,f3763,f12449,f12445]) ).
fof(f12445,plain,
( spl0_1453
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f12449,plain,
( spl0_1454
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f9962,plain,
( spl0_1232
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X30,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f10483,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_125
| ~ spl0_1232 ),
inference(resolution,[],[f9963,f3764]) ).
fof(f9963,plain,
( ! [X5,X30] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(X30,X5),X5)
| c_lessequals(c_0,X30,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X5) )
| ~ spl0_1232 ),
inference(avatar_component_clause,[],[f9962]) ).
fof(f11793,plain,
spl0_1452,
inference(avatar_split_clause,[],[f3063,f11791]) ).
fof(f11791,plain,
( spl0_1452
<=> ! [X70] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f3063,plain,
! [X70] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X70,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2887,f2745]) ).
fof(f2887,plain,
! [X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,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(X70,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f712,f1385,f1385]) ).
fof(f712,axiom,
! [X70] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X70,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X70,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f11789,plain,
spl0_1451,
inference(avatar_split_clause,[],[f3046,f11787]) ).
fof(f11787,plain,
( spl0_1451
<=> ! [X2,X17] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X17,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ c_less(c_0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f3046,plain,
! [X2,X17] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X17,X2,tc_nat),tc_nat),X2,tc_nat)
| ~ c_less(c_0,X2,tc_nat) ),
inference(forward_demodulation,[],[f2864,f2796]) ).
fof(f2864,plain,
! [X2,X17] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_minus(X2,c_Finite__Set_Ocard(c_SetInterval_OatMost(X17,tc_nat),tc_nat),tc_nat),X2,tc_nat) ),
inference(definition_unfolding,[],[f877,f1385]) ).
fof(f877,axiom,
! [X2,X17] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_minus(X2,c_Suc(X17),tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f11785,plain,
spl0_1450,
inference(avatar_split_clause,[],[f3001,f11783]) ).
fof(f3001,plain,
! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X1,
inference(forward_demodulation,[],[f3000,f997]) ).
fof(f3000,plain,
! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X1,
inference(forward_demodulation,[],[f2999,f995]) ).
fof(f2999,plain,
! [X1] : c_div(c_plus(X1,X1,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X1,
inference(forward_demodulation,[],[f724,f997]) ).
fof(f724,axiom,
! [X1] : c_div(c_plus(X1,X1,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) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f11781,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2989,f11779]) ).
fof(f2989,plain,
! [X28,X29] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),X28) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),X28),X28),
inference(forward_demodulation,[],[f969,f968]) ).
fof(f968,axiom,
! [X28,X29] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),X28) = c_Numeral_OBit(c_Numeral_Obin__mult(X29,X28),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f969,axiom,
! [X28,X29] : c_Numeral_Obin__mult(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),X28) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X29,X28),c_Numeral_Obit_OB0),X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f11777,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2986,f11775]) ).
fof(f2986,plain,
! [X28] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X28)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2787,f2760]) ).
fof(f2760,plain,
! [X28] : c_Numeral_Obin__add(c_Numeral_OMin,X28) = c_Numeral_Obin__add(X28,c_Numeral_OMin),
inference(definition_unfolding,[],[f953,f954]) ).
fof(f954,axiom,
! [X28] : c_Numeral_Obin__pred(X28) = c_Numeral_Obin__add(X28,c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f953,axiom,
! [X28] : c_Numeral_Obin__add(c_Numeral_OMin,X28) = c_Numeral_Obin__pred(X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2787,plain,
! [X28] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X28),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f965,f970,f954,f970]) ).
fof(f965,axiom,
! [X28] : c_Numeral_Obin__minus(c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X28)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f11773,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2897,f11771]) ).
fof(f11771,plain,
( spl0_1447
<=> ! [X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X29),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2897,plain,
! [X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X29),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f694,f970]) ).
fof(f694,axiom,
! [X29] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X29),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f11769,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2895,f11767]) ).
fof(f11767,plain,
( spl0_1446
<=> ! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X29),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X29,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f2895,plain,
! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X29),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X29,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f695,f970]) ).
fof(f695,axiom,
! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X29),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X29,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f11737,plain,
( spl0_1445
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1444 ),
inference(avatar_split_clause,[],[f11728,f11725,f10406,f10097,f6714,f3706,f11735]) ).
fof(f11735,plain,
( spl0_1445
<=> ! [X45,X17] :
( c_List_Olist_ONil = c_List_Oupt(X17,c_plus(c_1,X45,tc_nat))
| c_lessequals(X17,X45,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f11725,plain,
( spl0_1444
<=> ! [X45,X17] :
( c_lessequals(X17,X45,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f11728,plain,
( ! [X45,X17] :
( c_List_Olist_ONil = c_List_Oupt(X17,c_plus(c_1,X45,tc_nat))
| c_lessequals(X17,X45,tc_nat) )
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1444 ),
inference(forward_demodulation,[],[f11726,f11227]) ).
fof(f11726,plain,
( ! [X45,X17] :
( c_lessequals(X17,X45,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat)) )
| ~ spl0_1444 ),
inference(avatar_component_clause,[],[f11725]) ).
fof(f11727,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2882,f11725]) ).
fof(f2882,plain,
! [X45,X17] :
( c_lessequals(X17,X45,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,c_Finite__Set_Ocard(c_SetInterval_OatMost(X45,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f624,f1385]) ).
fof(f624,axiom,
! [X45,X17] :
( c_lessequals(X17,X45,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,c_Suc(X45)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f11723,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2843,f11721]) ).
fof(f2843,plain,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X28),X5) ),
inference(definition_unfolding,[],[f958,f970]) ).
fof(f958,axiom,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(c_Numeral_Onumber__of(X28,X5),X5) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X28),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f11715,plain,
( spl0_1442
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1441 ),
inference(avatar_split_clause,[],[f11711,f11708,f10406,f10097,f6714,f3706,f11713]) ).
fof(f11713,plain,
( spl0_1442
<=> ! [X18] : c_insert(X18,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X18,c_plus(c_1,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f11708,plain,
( spl0_1441
<=> ! [X18] : c_insert(X18,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f11711,plain,
( ! [X18] : c_insert(X18,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X18,c_plus(c_1,X18,tc_nat),tc_nat)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1441 ),
inference(forward_demodulation,[],[f11709,f11227]) ).
fof(f11709,plain,
( ! [X18] : c_insert(X18,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat)
| ~ spl0_1441 ),
inference(avatar_component_clause,[],[f11708]) ).
fof(f11710,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2788,f11708]) ).
fof(f2788,plain,
! [X18] : c_insert(X18,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1368,f1385]) ).
fof(f1368,axiom,
! [X18] : c_SetInterval_OatLeastLessThan(X18,c_Suc(X18),tc_nat) = c_insert(X18,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f11706,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2786,f11704]) ).
fof(f11704,plain,
( spl0_1440
<=> ! [X20,X5,X24] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),c_minus(X24,X20,tc_set(X5)),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f2786,plain,
! [X24,X5,X20] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),c_minus(X24,X20,tc_set(X5)),X5,X5),
inference(definition_unfolding,[],[f1430,f1214]) ).
fof(f1430,axiom,
! [X24,X5,X20] : c_emptyset = c_inter(X20,c_minus(X24,X20,tc_set(X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f11702,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2775,f11700]) ).
fof(f11700,plain,
( spl0_1439
<=> ! [X5,X72] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f2775,plain,
! [X72,X5] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5),
inference(definition_unfolding,[],[f1547,f1557]) ).
fof(f1547,axiom,
! [X72,X5] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X72,X5),X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f11698,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2774,f11696]) ).
fof(f11696,plain,
( spl0_1438
<=> ! [X5,X72] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f2774,plain,
! [X72,X5] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X72,c_Relation_OId,tc_prod(X5,X5)),X5),X5,X5),
inference(definition_unfolding,[],[f1548,f1557]) ).
fof(f1548,axiom,
! [X72,X5] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X72,X5),X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f11691,plain,
( spl0_1437
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1436 ),
inference(avatar_split_clause,[],[f11683,f11680,f10406,f10097,f6714,f3706,f11689]) ).
fof(f11689,plain,
( spl0_1437
<=> ! [X2] : c_plus(c_1,X2,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X2,tc_nat),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f11680,plain,
( spl0_1436
<=> ! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f11683,plain,
( ! [X2] : c_plus(c_1,X2,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X2,tc_nat),X2)
| ~ spl0_112
| ~ spl0_670
| ~ spl0_1261
| ~ spl0_1338
| ~ spl0_1436 ),
inference(forward_demodulation,[],[f11681,f11227]) ).
fof(f11681,plain,
( ! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X2)
| ~ spl0_1436 ),
inference(avatar_component_clause,[],[f11680]) ).
fof(f11682,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2770,f11680]) ).
fof(f2770,plain,
! [X2] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X2),
inference(definition_unfolding,[],[f4,f1385,f1385]) ).
fof(f4,axiom,
! [X2] : c_Suc(X2) = c_Binomial_Obinomial(c_Suc(X2),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f11678,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2735,f11676]) ).
fof(f2735,axiom,
! [X26,X5] : c_UNITY_OAllowedActs(X26,X5) = c_insert(c_Relation_OId,c_UNITY_OAllowedActs(X26,X5),tc_set(tc_prod(X5,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oinsert__Id__AllowedActs_0) ).
fof(f11674,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2734,f11672]) ).
fof(f11672,plain,
( spl0_1434
<=> ! [X5,X26] : c_UNITY_OActs(X26,X5) = c_insert(c_Relation_OId,c_UNITY_OActs(X26,X5),tc_set(tc_prod(X5,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f2734,axiom,
! [X26,X5] : c_UNITY_OActs(X26,X5) = c_insert(c_Relation_OId,c_UNITY_OActs(X26,X5),tc_set(tc_prod(X5,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_Oinsert__Id__Acts_0) ).
fof(f11670,plain,
spl0_1433,
inference(avatar_split_clause,[],[f1679,f11668]) ).
fof(f11668,plain,
( spl0_1433
<=> ! [X20,X5,X24] :
( X20 = X24
| ~ c_lessequals(X20,X24,tc_set(X5))
| ~ c_lessequals(X24,X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f1679,axiom,
! [X24,X5,X20] :
( X20 = X24
| ~ c_lessequals(X20,X24,tc_set(X5))
| ~ c_lessequals(X24,X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f11666,plain,
spl0_1432,
inference(avatar_split_clause,[],[f1676,f11664]) ).
fof(f11664,plain,
( spl0_1432
<=> ! [X24,X20,X5,X19] :
( ~ c_in(X19,X20,X5)
| c_in(X19,X24,X5)
| ~ c_lessequals(X20,X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f1676,axiom,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X20,X5)
| c_in(X19,X24,X5)
| ~ c_lessequals(X20,X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11662,plain,
spl0_1431,
inference(avatar_split_clause,[],[f1672,f11660]) ).
fof(f11660,plain,
( spl0_1431
<=> ! [X20,X5,X24] :
( X20 = X24
| ~ c_lessequals(X20,X24,tc_set(X5))
| c_less(X20,X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f1672,axiom,
! [X24,X5,X20] :
( X20 = X24
| ~ c_lessequals(X20,X24,tc_set(X5))
| c_less(X20,X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f11658,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1668,f11656]) ).
fof(f11656,plain,
( spl0_1430
<=> ! [X20,X73,X5] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(X20,c_Main_OUnionE__1(X20,X73,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f1668,axiom,
! [X73,X5,X20] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(X20,c_Main_OUnionE__1(X20,X73,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f11654,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1665,f11652]) ).
fof(f11652,plain,
( spl0_1429
<=> ! [X20,X73,X5] :
( c_in(X20,c_Inter(X73,X5),X5)
| ~ c_in(X20,c_Main_OInterI__1(X20,X73,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f1665,axiom,
! [X73,X5,X20] :
( c_in(X20,c_Inter(X73,X5),X5)
| ~ c_in(X20,c_Main_OInterI__1(X20,X73,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f11650,plain,
spl0_1428,
inference(avatar_split_clause,[],[f1597,f11648]) ).
fof(f11648,plain,
( spl0_1428
<=> ! [X20,X5,X8] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_insert(X8,X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1597,axiom,
! [X8,X5,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_insert(X8,X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11646,plain,
spl0_1427,
inference(avatar_split_clause,[],[f1566,f11644]) ).
fof(f1566,axiom,
! [X8,X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| ~ c_in(c_Pair(X8,X8,X5,X5),X13,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f11640,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1530,f11638]) ).
fof(f11638,plain,
( spl0_1426
<=> ! [X20,X5,X24,X3] :
( c_lessequals(X20,X24,tc_set(X5))
| ~ c_lessequals(c_insert(X3,X20,X5),X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f1530,axiom,
! [X3,X24,X5,X20] :
( c_lessequals(X20,X24,tc_set(X5))
| ~ c_lessequals(c_insert(X3,X20,X5),X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f11636,plain,
spl0_1425,
inference(avatar_split_clause,[],[f1510,f11634]) ).
fof(f11634,plain,
( spl0_1425
<=> ! [X20,X5,X23] :
( c_emptyset = X23
| c_emptyset != c_Union(X20,X5)
| ~ c_in(X23,X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f1510,axiom,
! [X5,X23,X20] :
( c_emptyset = X23
| c_emptyset != c_Union(X20,X5)
| ~ c_in(X23,X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_0) ).
fof(f11632,plain,
spl0_1424,
inference(avatar_split_clause,[],[f1497,f11630]) ).
fof(f11630,plain,
( spl0_1424
<=> ! [X20,X73,X5] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(X20,c_Main_OUnion__iff__1(X20,X73,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f1497,axiom,
! [X73,X5,X20] :
( ~ c_in(X20,c_Union(X73,X5),X5)
| c_in(X20,c_Main_OUnion__iff__1(X20,X73,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f11628,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1487,f11626]) ).
fof(f11626,plain,
( spl0_1423
<=> ! [X20,X73,X5,X24] :
( c_lessequals(X24,X73,tc_set(X5))
| ~ c_lessequals(c_union(X20,X24,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f1487,axiom,
! [X73,X24,X5,X20] :
( c_lessequals(X24,X73,tc_set(X5))
| ~ c_lessequals(c_union(X20,X24,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f11624,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1486,f11622]) ).
fof(f11622,plain,
( spl0_1422
<=> ! [X24,X20,X5,X73] :
( c_lessequals(X20,X73,tc_set(X5))
| ~ c_lessequals(c_union(X20,X24,X5),X73,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f1486,axiom,
! [X73,X24,X5,X20] :
( c_lessequals(X20,X73,tc_set(X5))
| ~ c_lessequals(c_union(X20,X24,X5),X73,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f11620,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1472,f11618]) ).
fof(f11618,plain,
( spl0_1421
<=> ! [X20,X5,X24] : c_union(X20,X24,X5) = c_union(X20,c_minus(X24,X20,tc_set(X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1472,axiom,
! [X24,X5,X20] : c_union(X20,X24,X5) = c_union(X20,c_minus(X24,X20,tc_set(X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f11616,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1471,f11614]) ).
fof(f1471,axiom,
! [X24,X5,X20] : c_union(c_minus(X24,X20,tc_set(X5)),X20,X5) = c_union(X24,X20,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f11612,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1463,f11610]) ).
fof(f11610,plain,
( spl0_1419
<=> ! [X20,X73,X5] :
( c_in(X20,c_Inter(X73,X5),X5)
| ~ c_in(X20,c_Main_OInter__iff__1(X20,X73,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f1463,axiom,
! [X73,X5,X20] :
( c_in(X20,c_Inter(X73,X5),X5)
| ~ c_in(X20,c_Main_OInter__iff__1(X20,X73,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f11608,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1457,f11606]) ).
fof(f11606,plain,
( spl0_1418
<=> ! [X20,X5,X23] :
( c_UNIV = X23
| c_UNIV != c_Inter(X20,X5)
| ~ c_in(X23,X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f1457,axiom,
! [X5,X23,X20] :
( c_UNIV = X23
| c_UNIV != c_Inter(X20,X5)
| ~ c_in(X23,X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f11604,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1396,f11602]) ).
fof(f11602,plain,
( spl0_1417
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanLessThan(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f1396,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanLessThan(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f11600,plain,
( ~ spl0_1416
| ~ spl0_113
| ~ spl0_1114
| ~ spl0_1205 ),
inference(avatar_split_clause,[],[f9510,f9500,f8934,f3711,f11597]) ).
fof(f9500,plain,
( spl0_1205
<=> ! [X2] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f9510,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1114
| ~ spl0_1205 ),
inference(forward_demodulation,[],[f9509,f8935]) ).
fof(f9509,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1205 ),
inference(superposition,[],[f9501,f3713]) ).
fof(f9501,plain,
( ! [X2] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1205 ),
inference(avatar_component_clause,[],[f9500]) ).
fof(f11595,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1395,f11593]) ).
fof(f11593,plain,
( spl0_1415
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanLessThan(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1395,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanLessThan(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f11591,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1393,f11589]) ).
fof(f11589,plain,
( spl0_1414
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanAtMost(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f1393,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanAtMost(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f11587,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1392,f11585]) ).
fof(f11585,plain,
( spl0_1413
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanAtMost(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f1392,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThanAtMost(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f11583,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1366,f11581]) ).
fof(f11581,plain,
( spl0_1412
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OatLeastLessThan(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1366,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_less(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OatLeastLessThan(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f11579,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1365,f11577]) ).
fof(f11577,plain,
( spl0_1411
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OatLeastLessThan(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1365,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OatLeastLessThan(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f11575,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1361,f11573]) ).
fof(f11573,plain,
( spl0_1410
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OatLeastAtMost(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1361,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X17,X31,X5)
| ~ c_in(X17,c_SetInterval_OatLeastAtMost(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f11571,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1360,f11569]) ).
fof(f11569,plain,
( spl0_1409
<=> ! [X17,X31,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OatLeastAtMost(X67,X31,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1360,axiom,
! [X31,X17,X5,X67] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X67,X17,X5)
| ~ c_in(X17,c_SetInterval_OatLeastAtMost(X67,X31,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f11567,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1228,f11565]) ).
fof(f11565,plain,
( spl0_1408
<=> ! [X9,X5,X8] :
( X8 = X9
| ~ c_in(c_Pair(X8,X9,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1228,axiom,
! [X8,X9,X5] :
( X8 = X9
| ~ c_in(c_Pair(X8,X9,X5,X5),c_Relation_OId,tc_prod(X5,X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f11563,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1208,f11561]) ).
fof(f1208,axiom,
! [X10,X5,X30] : c_Pair(c_Main_Osurj__pair__1(X30,X5,X10),c_Main_Osurj__pair__2(X30,X5,X10),X5,X10) = X30,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f11559,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1206,f11557]) ).
fof(f1206,axiom,
! [X10,X1,X5] : c_Pair(c_fst(X1,X5,X10),c_snd(X1,X5,X10),X5,X10) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f11555,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1202,f11553]) ).
fof(f11553,plain,
( spl0_1405
<=> ! [X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X8,X5),c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1202,axiom,
! [X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X8,X5),c_0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f11551,plain,
spl0_1404,
inference(avatar_split_clause,[],[f1199,f11549]) ).
fof(f11549,plain,
( spl0_1404
<=> ! [X2,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X8,X5),X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1199,axiom,
! [X2,X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X8,X5),X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f11547,plain,
spl0_1403,
inference(avatar_split_clause,[],[f1188,f11545]) ).
fof(f11545,plain,
( spl0_1403
<=> ! [X2,X5,X8] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X8
| c_0 != c_Nat_Opower(X8,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f1188,axiom,
! [X2,X8,X5] :
( ~ class_Power_Orecpower(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X8
| c_0 != c_Nat_Opower(X8,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f11543,plain,
spl0_1402,
inference(avatar_split_clause,[],[f1180,f11541]) ).
fof(f11541,plain,
( spl0_1402
<=> ! [X28,X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f1180,axiom,
! [X3,X28] :
( ~ c_less(c_0,X3,tc_nat)
| c_less(c_0,c_Nat_Opower(X3,c_Numeral_Onumber__of(X28,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f11539,plain,
spl0_1401,
inference(avatar_split_clause,[],[f1136,f11537]) ).
fof(f11537,plain,
( spl0_1401
<=> ! [X2,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_less(c_0,X2,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X3,X2,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f1136,axiom,
! [X2,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_less(c_0,X2,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X3,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f11535,plain,
spl0_1400,
inference(avatar_split_clause,[],[f1123,f11533]) ).
fof(f11533,plain,
( spl0_1400
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_less(c_0,X1,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f1123,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_less(c_0,X1,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f11531,plain,
spl0_1399,
inference(avatar_split_clause,[],[f1106,f11529]) ).
fof(f11529,plain,
( spl0_1399
<=> ! [X3,X1,X30,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X1,X30,X10)
| ~ c_lessequals(c_Orderings_Omax(X3,X1,X10),X30,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f1106,axiom,
! [X3,X10,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X1,X30,X10)
| ~ c_lessequals(c_Orderings_Omax(X3,X1,X10),X30,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f11527,plain,
spl0_1398,
inference(avatar_split_clause,[],[f1105,f11525]) ).
fof(f11525,plain,
( spl0_1398
<=> ! [X10,X3,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X3,X30,X10)
| ~ c_lessequals(c_Orderings_Omax(X3,X1,X10),X30,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f1105,axiom,
! [X3,X10,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X3,X30,X10)
| ~ c_lessequals(c_Orderings_Omax(X3,X1,X10),X30,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f11523,plain,
spl0_1397,
inference(avatar_split_clause,[],[f1101,f11521]) ).
fof(f11521,plain,
( spl0_1397
<=> ! [X10,X3,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X3,X30,X10)
| ~ c_lessequals(X3,c_Orderings_Omin(X1,X30,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f1101,axiom,
! [X3,X10,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X3,X30,X10)
| ~ c_lessequals(X3,c_Orderings_Omin(X1,X30,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f11519,plain,
spl0_1396,
inference(avatar_split_clause,[],[f1100,f11517]) ).
fof(f11517,plain,
( spl0_1396
<=> ! [X3,X10,X30,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X3,X1,X10)
| ~ c_lessequals(X3,c_Orderings_Omin(X1,X30,X10),X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f1100,axiom,
! [X3,X10,X1,X30] :
( ~ class_Orderings_Olinorder(X10)
| c_lessequals(X3,X1,X10)
| ~ c_lessequals(X3,c_Orderings_Omin(X1,X30,X10),X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f11515,plain,
spl0_1395,
inference(avatar_split_clause,[],[f1098,f11513]) ).
fof(f11513,plain,
( spl0_1395
<=> ! [X5,X3,X1,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X30,X1,X5)
| ~ c_less(X30,c_Orderings_Omin(X3,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f1098,axiom,
! [X3,X1,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X30,X1,X5)
| ~ c_less(X30,c_Orderings_Omin(X3,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f11511,plain,
spl0_1394,
inference(avatar_split_clause,[],[f1097,f11509]) ).
fof(f11509,plain,
( spl0_1394
<=> ! [X5,X3,X30,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X30,X3,X5)
| ~ c_less(X30,c_Orderings_Omin(X3,X1,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f1097,axiom,
! [X3,X1,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X30,X3,X5)
| ~ c_less(X30,c_Orderings_Omin(X3,X1,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f11507,plain,
spl0_1393,
inference(avatar_split_clause,[],[f1095,f11505]) ).
fof(f11505,plain,
( spl0_1393
<=> ! [X3,X5,X1,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X1,X30,X5)
| ~ c_less(c_Orderings_Omax(X3,X1,X5),X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f1095,axiom,
! [X3,X1,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X1,X30,X5)
| ~ c_less(c_Orderings_Omax(X3,X1,X5),X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f11503,plain,
spl0_1392,
inference(avatar_split_clause,[],[f1094,f11501]) ).
fof(f11501,plain,
( spl0_1392
<=> ! [X5,X3,X1,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X3,X30,X5)
| ~ c_less(c_Orderings_Omax(X3,X1,X5),X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f1094,axiom,
! [X3,X1,X5,X30] :
( ~ class_Orderings_Olinorder(X5)
| c_less(X3,X30,X5)
| ~ c_less(c_Orderings_Omax(X3,X1,X5),X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f11499,plain,
spl0_1391,
inference(avatar_split_clause,[],[f1090,f11497]) ).
fof(f11497,plain,
( spl0_1391
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_lessequals(c_0,c_plus(X8,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f1090,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_lessequals(c_0,c_plus(X8,X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f11495,plain,
spl0_1390,
inference(avatar_split_clause,[],[f1089,f11493]) ).
fof(f11493,plain,
( spl0_1390
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,X8,X5)
| ~ c_lessequals(c_0,c_plus(X8,X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f1089,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,X8,X5)
| ~ c_lessequals(c_0,c_plus(X8,X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f11491,plain,
spl0_1389,
inference(avatar_split_clause,[],[f1056,f11489]) ).
fof(f11489,plain,
( spl0_1389
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_minus(X8,X9,X5),X5) = c_minus(X9,X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f1056,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_minus(X8,X9,X5),X5) = c_minus(X9,X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f11487,plain,
spl0_1388,
inference(avatar_split_clause,[],[f1053,f11485]) ).
fof(f11485,plain,
( spl0_1388
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X8
| c_0 != c_LOrder_Omeet(X8,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f1053,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X8
| c_0 != c_LOrder_Omeet(X8,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f11483,plain,
spl0_1387,
inference(avatar_split_clause,[],[f1051,f11481]) ).
fof(f11481,plain,
( spl0_1387
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X8
| c_0 != c_LOrder_Ojoin(X8,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f1051,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = X8
| c_0 != c_LOrder_Ojoin(X8,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f11479,plain,
spl0_1386,
inference(avatar_split_clause,[],[f1048,f11477]) ).
fof(f11477,plain,
( spl0_1386
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_lessequals(c_plus(X8,X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f1048,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_lessequals(c_plus(X8,X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f11475,plain,
spl0_1385,
inference(avatar_split_clause,[],[f1047,f11473]) ).
fof(f11473,plain,
( spl0_1385
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(X8,c_0,X5)
| ~ c_lessequals(c_plus(X8,X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f1047,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(X8,c_0,X5)
| ~ c_lessequals(c_plus(X8,X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f11471,plain,
spl0_1384,
inference(avatar_split_clause,[],[f1045,f11469]) ).
fof(f11469,plain,
( spl0_1384
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_plus(X8,X9,X5) = c_minus(X8,c_uminus(X9,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f1045,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_plus(X8,X9,X5) = c_minus(X8,c_uminus(X9,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f11467,plain,
spl0_1383,
inference(avatar_split_clause,[],[f1044,f11465]) ).
fof(f11465,plain,
( spl0_1383
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_minus(X8,X9,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f1044,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X8,X9,X5)
| c_less(c_minus(X8,X9,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f11463,plain,
spl0_1382,
inference(avatar_split_clause,[],[f1043,f11461]) ).
fof(f11461,plain,
( spl0_1382
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_minus(X8,X9,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f1043,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X8,X9,X5)
| ~ c_less(c_minus(X8,X9,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f11459,plain,
spl0_1381,
inference(avatar_split_clause,[],[f1042,f11457]) ).
fof(f11457,plain,
( spl0_1381
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_minus(X8,X9,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f1042,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X8,X9,X5)
| c_lessequals(c_minus(X8,X9,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f11455,plain,
spl0_1380,
inference(avatar_split_clause,[],[f1041,f11453]) ).
fof(f11453,plain,
( spl0_1380
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_minus(X8,X9,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f1041,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X8,X9,X5)
| ~ c_lessequals(c_minus(X8,X9,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f11451,plain,
spl0_1379,
inference(avatar_split_clause,[],[f1025,f11449]) ).
fof(f11449,plain,
( spl0_1379
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_uminus(X8,X5) = c_HOL_Oabs(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f1025,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_uminus(X8,X5) = c_HOL_Oabs(X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f11447,plain,
spl0_1378,
inference(avatar_split_clause,[],[f951,f11445]) ).
fof(f11445,plain,
( spl0_1378
<=> ! [X29,X28] : c_Numeral_Obin__add(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X29,X28),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f951,axiom,
! [X28,X29] : c_Numeral_Obin__add(c_Numeral_OBit(X29,c_Numeral_Obit_OB1),c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X29,X28),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f11443,plain,
spl0_1377,
inference(avatar_split_clause,[],[f950,f11441]) ).
fof(f11441,plain,
( spl0_1377
<=> ! [X29,X1,X28] : c_Numeral_Obin__add(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),c_Numeral_OBit(X28,X1)) = c_Numeral_OBit(c_Numeral_Obin__add(X29,X28),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f950,axiom,
! [X28,X29,X1] : c_Numeral_Obin__add(c_Numeral_OBit(X29,c_Numeral_Obit_OB0),c_Numeral_OBit(X28,X1)) = c_Numeral_OBit(c_Numeral_Obin__add(X29,X28),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f11439,plain,
spl0_1376,
inference(avatar_split_clause,[],[f886,f11437]) ).
fof(f11437,plain,
( spl0_1376
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_plus(X2,c_minus(X1,X2,tc_nat),tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f886,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_plus(X2,c_minus(X1,X2,tc_nat),tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f11435,plain,
spl0_1375,
inference(avatar_split_clause,[],[f885,f11433]) ).
fof(f11433,plain,
( spl0_1375
<=> ! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_plus(c_minus(X1,X2,tc_nat),X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f885,axiom,
! [X2,X1] :
( ~ c_lessequals(X2,X1,tc_nat)
| c_plus(c_minus(X1,X2,tc_nat),X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f11431,plain,
spl0_1374,
inference(avatar_split_clause,[],[f693,f11429]) ).
fof(f11429,plain,
( spl0_1374
<=> ! [X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f693,axiom,
! [X29] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X29,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f11427,plain,
spl0_1373,
inference(avatar_split_clause,[],[f640,f11425]) ).
fof(f11425,plain,
( spl0_1373
<=> ! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_minus(X2,c_minus(X2,X1,tc_nat),tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f640,axiom,
! [X2,X1] :
( ~ c_lessequals(X1,X2,tc_nat)
| c_minus(X2,c_minus(X2,X1,tc_nat),tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f11423,plain,
spl0_1372,
inference(avatar_split_clause,[],[f606,f11421]) ).
fof(f11421,plain,
( spl0_1372
<=> ! [X20,X5,X3] :
( c_in(c_0,X20,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f606,axiom,
! [X3,X5,X20] :
( c_in(c_0,X20,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f11419,plain,
spl0_1371,
inference(avatar_split_clause,[],[f589,f11417]) ).
fof(f11417,plain,
( spl0_1371
<=> ! [X6,X34,X3] : c_List_Oset(c_List_Olist_OCons(X3,X34,X6),X6) = c_insert(X3,c_List_Oset(X34,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f589,axiom,
! [X3,X6,X34] : c_List_Oset(c_List_Olist_OCons(X3,X34,X6),X6) = c_insert(X3,c_List_Oset(X34,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f11415,plain,
spl0_1370,
inference(avatar_split_clause,[],[f583,f11413]) ).
fof(f11413,plain,
( spl0_1370
<=> ! [X2,X5,X1] :
( c_List_Orotate(X2,X1,X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f583,axiom,
! [X2,X1,X5] :
( c_List_Orotate(X2,X1,X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f11411,plain,
spl0_1369,
inference(avatar_split_clause,[],[f543,f11409]) ).
fof(f11409,plain,
( spl0_1369
<=> ! [X17,X5,X2,X1] :
( ~ c_less(X17,X2,tc_nat)
| c_List_Onth(c_List_Oreplicate(X2,X1,X5),X17,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f543,axiom,
! [X2,X1,X17,X5] :
( ~ c_less(X17,X2,tc_nat)
| c_List_Onth(c_List_Oreplicate(X2,X1,X5),X17,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f11407,plain,
spl0_1368,
inference(avatar_split_clause,[],[f445,f11405]) ).
fof(f11405,plain,
( spl0_1368
<=> ! [X17,X34,X5,X3] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Olist__update(X34,X17,X3,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f445,axiom,
! [X3,X34,X17,X5] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Olist__update(X34,X17,X3,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f11403,plain,
spl0_1367,
inference(avatar_split_clause,[],[f432,f11401]) ).
fof(f11401,plain,
( spl0_1367
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X35
| c_List_Olast(c_append(X34,X35,X5),X5) = c_List_Olast(X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f432,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X35
| c_List_Olast(c_append(X34,X35,X5),X5) = c_List_Olast(X35,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f11399,plain,
spl0_1366,
inference(avatar_split_clause,[],[f430,f11397]) ).
fof(f11397,plain,
( spl0_1366
<=> ! [X34,X5,X3] :
( c_List_Olist_ONil = X34
| c_List_Olast(c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Olast(X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f430,axiom,
! [X3,X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olast(c_List_Olist_OCons(X3,X34,X5),X5) = c_List_Olast(X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f11380,plain,
spl0_1365,
inference(avatar_split_clause,[],[f422,f11378]) ).
fof(f11378,plain,
( spl0_1365
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X34
| c_List_Ohd(c_append(X34,X35,X5),X5) = c_List_Ohd(X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f422,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X34
| c_List_Ohd(c_append(X34,X35,X5),X5) = c_List_Ohd(X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f11376,plain,
spl0_1364,
inference(avatar_split_clause,[],[f421,f11374]) ).
fof(f421,axiom,
! [X1,X5] :
( c_List_Olist_ONil = X1
| c_List_Olist_OCons(c_List_Ohd(X1,X5),c_List_Otl(X1,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f11372,plain,
spl0_1363,
inference(avatar_split_clause,[],[f419,f11370]) ).
fof(f11370,plain,
( spl0_1363
<=> ! [X45,X18,X17] : c_List_Odrop(X18,c_List_Oupt(X17,X45),tc_nat) = c_List_Oupt(c_plus(X17,X18,tc_nat),X45) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f419,axiom,
! [X18,X45,X17] : c_List_Odrop(X18,c_List_Oupt(X17,X45),tc_nat) = c_List_Oupt(c_plus(X17,X18,tc_nat),X45),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f11368,plain,
spl0_1362,
inference(avatar_split_clause,[],[f417,f11366]) ).
fof(f11366,plain,
( spl0_1362
<=> ! [X34,X5,X2] :
( c_List_Olist_ONil = c_List_Odrop(X2,X34,X5)
| ~ c_lessequals(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f417,axiom,
! [X2,X34,X5] :
( c_List_Olist_ONil = c_List_Odrop(X2,X34,X5)
| ~ c_lessequals(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f11364,plain,
spl0_1361,
inference(avatar_split_clause,[],[f416,f11362]) ).
fof(f11362,plain,
( spl0_1361
<=> ! [X34,X5,X2] :
( c_List_Olist_ONil != c_List_Odrop(X2,X34,X5)
| c_lessequals(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f416,axiom,
! [X2,X34,X5] :
( c_List_Olist_ONil != c_List_Odrop(X2,X34,X5)
| c_lessequals(c_Nat_Osize(X34,tc_List_Olist(X5)),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f11360,plain,
spl0_1360,
inference(avatar_split_clause,[],[f316,f11358]) ).
fof(f11358,plain,
( spl0_1360
<=> ! [X9,X8] : c_div(c_uminus(X8,tc_IntDef_Oint),c_uminus(X9,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X8,X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f316,axiom,
! [X8,X9] : c_div(c_uminus(X8,tc_IntDef_Oint),c_uminus(X9,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X8,X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f11356,plain,
spl0_1359,
inference(avatar_split_clause,[],[f257,f11354]) ).
fof(f11354,plain,
( spl0_1359
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_uminus(X30,tc_IntDef_Oint),X5) = c_uminus(c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f257,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_uminus(X30,tc_IntDef_Oint),X5) = c_uminus(c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f11352,plain,
spl0_1358,
inference(avatar_split_clause,[],[f146,f11350]) ).
fof(f11350,plain,
( spl0_1358
<=> ! [X2,X0,X18] :
( c_Divides_Oop_Advd(X0,X2,tc_nat)
| ~ c_Divides_Oop_Advd(X0,c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f146,axiom,
! [X2,X0,X18] :
( c_Divides_Oop_Advd(X0,X2,tc_nat)
| ~ c_Divides_Oop_Advd(X0,c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f11348,plain,
spl0_1357,
inference(avatar_split_clause,[],[f145,f11346]) ).
fof(f11346,plain,
( spl0_1357
<=> ! [X18,X0,X2] :
( c_Divides_Oop_Advd(X0,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X0,c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f145,axiom,
! [X2,X0,X18] :
( c_Divides_Oop_Advd(X0,X18,tc_nat)
| ~ c_Divides_Oop_Advd(X0,c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f11344,plain,
spl0_1356,
inference(avatar_split_clause,[],[f132,f11342]) ).
fof(f11342,plain,
( spl0_1356
<=> ! [X20,X5,X8] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_insert(X8,X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f132,axiom,
! [X8,X5,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_insert(X8,X20,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f11333,plain,
spl0_1355,
inference(avatar_split_clause,[],[f128,f11331]) ).
fof(f11331,plain,
( spl0_1355
<=> ! [X5,X27,X26] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f128,axiom,
! [X26,X27,X5] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f11329,plain,
spl0_1354,
inference(avatar_split_clause,[],[f127,f11327]) ).
fof(f11327,plain,
( spl0_1354
<=> ! [X5,X27,X26] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f127,axiom,
! [X26,X27,X5] :
( c_in(X26,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_union(X26,X27,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f11325,plain,
spl0_1353,
inference(avatar_split_clause,[],[f126,f11323]) ).
fof(f11323,plain,
( spl0_1353
<=> ! [X20,X5] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Pow(X20,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f126,axiom,
! [X5,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_in(c_Pow(X20,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f11321,plain,
spl0_1352,
inference(avatar_split_clause,[],[f125,f11319]) ).
fof(f11319,plain,
( spl0_1352
<=> ! [X20,X5] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_Pow(X20,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f125,axiom,
! [X5,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| ~ c_in(c_Pow(X20,X5),c_Finite__Set_OFinites,tc_set(tc_set(X5))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f11317,plain,
spl0_1351,
inference(avatar_split_clause,[],[f117,f11315]) ).
fof(f11315,plain,
( spl0_1351
<=> ! [X20,X5] :
( c_emptyset = X20
| c_0 != c_Finite__Set_Ocard(X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f117,axiom,
! [X5,X20] :
( c_emptyset = X20
| c_0 != c_Finite__Set_Ocard(X20,X5)
| ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f11313,plain,
spl0_1350,
inference(avatar_split_clause,[],[f64,f11311]) ).
fof(f11311,plain,
( spl0_1350
<=> ! [X2,X1] :
( ~ c_less(c_0,X2,tc_nat)
| c_div(c_times(X1,X2,tc_nat),X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f64,axiom,
! [X2,X1] :
( ~ c_less(c_0,X2,tc_nat)
| c_div(c_times(X1,X2,tc_nat),X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f11309,plain,
spl0_1349,
inference(avatar_split_clause,[],[f62,f11307]) ).
fof(f11307,plain,
( spl0_1349
<=> ! [X2,X1] :
( ~ c_less(c_0,X2,tc_nat)
| c_div(c_times(X2,X1,tc_nat),X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f62,axiom,
! [X2,X1] :
( ~ c_less(c_0,X2,tc_nat)
| c_div(c_times(X2,X1,tc_nat),X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f11297,plain,
( spl0_1348
| ~ spl0_1046
| ~ spl0_1335 ),
inference(avatar_split_clause,[],[f11168,f10394,f8493,f11295]) ).
fof(f10394,plain,
( spl0_1335
<=> ! [X20,X5,X24] :
( c_lessequals(X20,X24,tc_set(X5))
| ~ c_in(c_Main_OsubsetI__1(X20,X24,X5),X24,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f11168,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1046
| ~ spl0_1335 ),
inference(resolution,[],[f10395,f8494]) ).
fof(f10395,plain,
( ! [X24,X5,X20] :
( ~ c_in(c_Main_OsubsetI__1(X20,X24,X5),X24,X5)
| c_lessequals(X20,X24,tc_set(X5)) )
| ~ spl0_1335 ),
inference(avatar_component_clause,[],[f10394]) ).
fof(f10931,plain,
( spl0_1347
| ~ spl0_709
| ~ spl0_1110 ),
inference(avatar_split_clause,[],[f9192,f8918,f6891,f10929]) ).
fof(f10929,plain,
( spl0_1347
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f6891,plain,
( spl0_709
<=> ! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f8918,plain,
( spl0_1110
<=> ! [X20,X5] : c_Relation_Odiag(X20,X5) = c_Relation_Oconverse(c_Relation_Odiag(X20,X5),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f9192,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_709
| ~ spl0_1110 ),
inference(superposition,[],[f8919,f6892]) ).
fof(f6892,plain,
( ! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5)
| ~ spl0_709 ),
inference(avatar_component_clause,[],[f6891]) ).
fof(f8919,plain,
( ! [X5,X20] : c_Relation_Odiag(X20,X5) = c_Relation_Oconverse(c_Relation_Odiag(X20,X5),X5,X5)
| ~ spl0_1110 ),
inference(avatar_component_clause,[],[f8918]) ).
fof(f10699,plain,
( spl0_1346
| ~ spl0_116
| ~ spl0_1080 ),
inference(avatar_split_clause,[],[f9109,f8797,f3725,f10697]) ).
fof(f10697,plain,
( spl0_1346
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f3725,plain,
( spl0_116
<=> ! [X18] : c_Divides_Oop_Advd(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f8797,plain,
( spl0_1080
<=> ! [X28,X30] :
( c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X30,tc_IntDef_Oint),X28,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f9109,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_1080 ),
inference(resolution,[],[f8798,f3726]) ).
fof(f3726,plain,
( ! [X18] : c_Divides_Oop_Advd(X18,X18,tc_IntDef_Oint)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f3725]) ).
fof(f8798,plain,
( ! [X28,X30] :
( ~ c_Divides_Oop_Advd(c_uminus(X30,tc_IntDef_Oint),X28,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint) )
| ~ spl0_1080 ),
inference(avatar_component_clause,[],[f8797]) ).
fof(f10638,plain,
( spl0_1345
| ~ spl0_116
| ~ spl0_1077 ),
inference(avatar_split_clause,[],[f9099,f8784,f3725,f10636]) ).
fof(f10636,plain,
( spl0_1345
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f8784,plain,
( spl0_1077
<=> ! [X28,X30] :
( c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f9099,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_116
| ~ spl0_1077 ),
inference(resolution,[],[f8785,f3726]) ).
fof(f8785,plain,
( ! [X28,X30] :
( ~ c_Divides_Oop_Advd(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint) )
| ~ spl0_1077 ),
inference(avatar_component_clause,[],[f8784]) ).
fof(f10432,plain,
spl0_1344,
inference(avatar_split_clause,[],[f3108,f10430]) ).
fof(f10430,plain,
( spl0_1344
<=> ! [X5,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f3108,plain,
! [X3,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X3,X5) ),
inference(forward_demodulation,[],[f3107,f956]) ).
fof(f3107,plain,
! [X3,X5] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X3,X5) ),
inference(forward_demodulation,[],[f2914,f2744]) ).
fof(f2914,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f179,f970]) ).
fof(f179,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(X3,X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10428,plain,
spl0_1343,
inference(avatar_split_clause,[],[f3038,f10426]) ).
fof(f10426,plain,
( spl0_1343
<=> ! [X5] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X5)
| ~ class_Power_Orecpower(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f3038,plain,
! [X5] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X5)
| ~ class_Power_Orecpower(X5) ),
inference(forward_demodulation,[],[f3037,f997]) ).
fof(f3037,plain,
! [X5] :
( 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),X5)
| ~ class_Power_Orecpower(X5) ),
inference(forward_demodulation,[],[f3036,f995]) ).
fof(f3036,plain,
! [X5] :
( 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),X5)
| ~ class_Power_Orecpower(X5) ),
inference(forward_demodulation,[],[f719,f997]) ).
fof(f719,axiom,
! [X5] :
( ~ class_Power_Orecpower(X5)
| 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),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10424,plain,
spl0_1342,
inference(avatar_split_clause,[],[f3031,f10422]) ).
fof(f3031,plain,
! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f3030,f997]) ).
fof(f3030,plain,
! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f3029,f995]) ).
fof(f3029,plain,
! [X5] :
( c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f169,f997]) ).
fof(f169,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_plus(c_1,c_1,X5) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10420,plain,
spl0_1341,
inference(avatar_split_clause,[],[f2855,f10418]) ).
fof(f10418,plain,
( spl0_1341
<=> ! [X20,X5,X24] :
( c_UNIV = X20
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f2855,plain,
! [X24,X5,X20] :
( c_UNIV = X20
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5) ),
inference(definition_unfolding,[],[f1439,f1214]) ).
fof(f1439,axiom,
! [X24,X5,X20] :
( c_UNIV = X20
| c_UNIV != c_inter(X20,X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10416,plain,
spl0_1340,
inference(avatar_split_clause,[],[f2854,f10414]) ).
fof(f10414,plain,
( spl0_1340
<=> ! [X20,X5,X24] :
( c_UNIV = X24
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f2854,plain,
! [X24,X5,X20] :
( c_UNIV = X24
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X20,X5),X24,X5,X5) ),
inference(definition_unfolding,[],[f1440,f1214]) ).
fof(f1440,axiom,
! [X24,X5,X20] :
( c_UNIV = X24
| c_UNIV != c_inter(X20,X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10412,plain,
spl0_1339,
inference(avatar_split_clause,[],[f2849,f10410]) ).
fof(f10410,plain,
( spl0_1339
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f2849,plain,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),X5) ),
inference(definition_unfolding,[],[f1187,f1385]) ).
fof(f1187,axiom,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_0 = c_Nat_Opower(c_0,c_Suc(X2),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10408,plain,
spl0_1338,
inference(avatar_split_clause,[],[f2781,f10406]) ).
fof(f2781,plain,
! [X18] : c_plus(c_1,c_IntDef_Oint(X18),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f213,f1385]) ).
fof(f213,axiom,
! [X18] : c_IntDef_Oint(c_Suc(X18)) = c_plus(c_1,c_IntDef_Oint(X18),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10404,plain,
spl0_1337,
inference(avatar_split_clause,[],[f2778,f10402]) ).
fof(f10402,plain,
( spl0_1337
<=> ! [X20,X5] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X20,tc_set(X5)),X5),X20,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f2778,plain,
! [X5,X20] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X20,tc_set(X5)),X5),X20,X5,X5),
inference(definition_unfolding,[],[f1419,f1214]) ).
fof(f1419,axiom,
! [X5,X20] : c_emptyset = c_inter(c_uminus(X20,tc_set(X5)),X20,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10400,plain,
spl0_1336,
inference(avatar_split_clause,[],[f2777,f10398]) ).
fof(f10398,plain,
( spl0_1336
<=> ! [X20,X5] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),c_uminus(X20,tc_set(X5)),X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f2777,plain,
! [X5,X20] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X20,X5),c_uminus(X20,tc_set(X5)),X5,X5),
inference(definition_unfolding,[],[f1420,f1214]) ).
fof(f1420,axiom,
! [X5,X20] : c_emptyset = c_inter(X20,c_uminus(X20,tc_set(X5)),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10396,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1678,f10394]) ).
fof(f1678,axiom,
! [X24,X5,X20] :
( c_lessequals(X20,X24,tc_set(X5))
| ~ c_in(c_Main_OsubsetI__1(X20,X24,X5),X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10392,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1677,f10390]) ).
fof(f10390,plain,
( spl0_1334
<=> ! [X20,X5,X24] :
( c_lessequals(X20,X24,tc_set(X5))
| c_in(c_Main_OsubsetI__1(X20,X24,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f1677,axiom,
! [X24,X5,X20] :
( c_lessequals(X20,X24,tc_set(X5))
| c_in(c_Main_OsubsetI__1(X20,X24,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10388,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1617,f10386]) ).
fof(f10386,plain,
( spl0_1333
<=> ! [X34,X5] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X34,X5),tc_List_Olist(X5)),c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f1617,axiom,
! [X34,X5] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X34,X5),tc_List_Olist(X5)),c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10384,plain,
spl0_1332,
inference(avatar_split_clause,[],[f1570,f10382]) ).
fof(f10382,plain,
( spl0_1332
<=> ! [X3,X10,X5,X1] :
( X1 = X3
| c_Datatype__Universe_ONumb(X3,X5,X10) != c_Datatype__Universe_ONumb(X1,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f1570,axiom,
! [X3,X10,X1,X5] :
( X1 = X3
| c_Datatype__Universe_ONumb(X3,X5,X10) != c_Datatype__Universe_ONumb(X1,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10380,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1569,f10378]) ).
fof(f10378,plain,
( spl0_1331
<=> ! [X3,X10,X5,X1] :
( X1 = X3
| c_Datatype__Universe_OLeaf(X3,X5,X10) != c_Datatype__Universe_OLeaf(X1,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f1569,axiom,
! [X3,X10,X1,X5] :
( X1 = X3
| c_Datatype__Universe_OLeaf(X3,X5,X10) != c_Datatype__Universe_OLeaf(X1,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10376,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1544,f10374]) ).
fof(f10374,plain,
( spl0_1330
<=> ! [X3,X10,X5,X1] :
( X1 = X3
| c_Sum__Type_OInr(X3,X10,X5) != c_Sum__Type_OInr(X1,X10,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f1544,axiom,
! [X3,X10,X1,X5] :
( X1 = X3
| c_Sum__Type_OInr(X3,X10,X5) != c_Sum__Type_OInr(X1,X10,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10372,plain,
spl0_1329,
inference(avatar_split_clause,[],[f1542,f10370]) ).
fof(f10370,plain,
( spl0_1329
<=> ! [X3,X10,X5,X1] :
( X1 = X3
| c_Sum__Type_OInl(X3,X5,X10) != c_Sum__Type_OInl(X1,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f1542,axiom,
! [X3,X10,X1,X5] :
( X1 = X3
| c_Sum__Type_OInl(X3,X5,X10) != c_Sum__Type_OInl(X1,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10368,plain,
spl0_1328,
inference(avatar_split_clause,[],[f1533,f10366]) ).
fof(f10366,plain,
( spl0_1328
<=> ! [X5,X20,X9,X8] :
( X8 = X9
| c_insert(X8,X20,X5) != c_insert(X9,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f1533,axiom,
! [X8,X9,X5,X20] :
( X8 = X9
| c_insert(X8,X20,X5) != c_insert(X9,c_emptyset,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
fof(f10364,plain,
spl0_1327,
inference(avatar_split_clause,[],[f1529,f10362]) ).
fof(f10362,plain,
( spl0_1327
<=> ! [X24,X20,X5,X3] :
( c_in(X3,X24,X5)
| ~ c_lessequals(c_insert(X3,X20,X5),X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f1529,axiom,
! [X3,X24,X5,X20] :
( c_in(X3,X24,X5)
| ~ c_lessequals(c_insert(X3,X20,X5),X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10360,plain,
spl0_1326,
inference(avatar_split_clause,[],[f1517,f10358]) ).
fof(f10358,plain,
( spl0_1326
<=> ! [X20,X5,X3] : c_insert(X3,X20,X5) = c_insert(X3,c_insert(X3,X20,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f1517,axiom,
! [X3,X5,X20] : c_insert(X3,X20,X5) = c_insert(X3,c_insert(X3,X20,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10356,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1511,f10354]) ).
fof(f10354,plain,
( spl0_1325
<=> ! [X20,X5] :
( c_emptyset = c_Union(X20,X5)
| c_in(c_Main_Oempty__Union__conv__1(X20,X5),X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1511,axiom,
! [X5,X20] :
( c_emptyset = c_Union(X20,X5)
| c_in(c_Main_Oempty__Union__conv__1(X20,X5),X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10352,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1494,f10350]) ).
fof(f10350,plain,
( spl0_1324
<=> ! [X20,X5] :
( c_emptyset = c_Union(X20,X5)
| c_in(c_Main_OUnion__empty__conv__1(X20,X5),X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f1494,axiom,
! [X5,X20] :
( c_emptyset = c_Union(X20,X5)
| c_in(c_Main_OUnion__empty__conv__1(X20,X5),X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10348,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1469,f10346]) ).
fof(f10346,plain,
( spl0_1323
<=> ! [X20,X5,X24] :
( ~ c_lessequals(X20,X24,tc_set(X5))
| c_in(X20,c_Pow(X24,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1469,axiom,
! [X24,X5,X20] :
( ~ c_lessequals(X20,X24,tc_set(X5))
| c_in(X20,c_Pow(X24,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10344,plain,
spl0_1322,
inference(avatar_split_clause,[],[f1468,f10342]) ).
fof(f10342,plain,
( spl0_1322
<=> ! [X20,X5,X24] :
( c_lessequals(X20,X24,tc_set(X5))
| ~ c_in(X20,c_Pow(X24,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f1468,axiom,
! [X24,X5,X20] :
( c_lessequals(X20,X24,tc_set(X5))
| ~ c_in(X20,c_Pow(X24,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10340,plain,
spl0_1321,
inference(avatar_split_clause,[],[f1458,f10338]) ).
fof(f10338,plain,
( spl0_1321
<=> ! [X20,X5] :
( c_UNIV = c_Inter(X20,X5)
| c_in(c_Main_OInter__UNIV__conv__2__1(X20,X5),X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f1458,axiom,
! [X5,X20] :
( c_UNIV = c_Inter(X20,X5)
| c_in(c_Main_OInter__UNIV__conv__2__1(X20,X5),X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10336,plain,
spl0_1320,
inference(avatar_split_clause,[],[f1455,f10334]) ).
fof(f10334,plain,
( spl0_1320
<=> ! [X20,X5] :
( c_UNIV = c_Inter(X20,X5)
| c_in(c_Main_OInter__UNIV__conv__1__1(X20,X5),X20,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1455,axiom,
! [X5,X20] :
( c_UNIV = c_Inter(X20,X5)
| c_in(c_Main_OInter__UNIV__conv__1__1(X20,X5),X20,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10332,plain,
spl0_1319,
inference(avatar_split_clause,[],[f1436,f10330]) ).
fof(f10330,plain,
( spl0_1319
<=> ! [X24,X20,X5,X19] :
( ~ c_in(X19,X24,X5)
| ~ c_in(X19,c_minus(X20,X24,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f1436,axiom,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X24,X5)
| ~ c_in(X19,c_minus(X20,X24,tc_set(X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10328,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1435,f10326]) ).
fof(f10326,plain,
( spl0_1318
<=> ! [X24,X20,X5,X19] :
( c_in(X19,X20,X5)
| ~ c_in(X19,c_minus(X20,X24,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1435,axiom,
! [X19,X24,X5,X20] :
( c_in(X19,X20,X5)
| ~ c_in(X19,c_minus(X20,X24,tc_set(X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10324,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1433,f10322]) ).
fof(f1433,axiom,
! [X24,X5,X20] :
( ~ c_lessequals(X20,X24,tc_set(X5))
| c_emptyset = c_minus(X20,X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10320,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1432,f10318]) ).
fof(f10318,plain,
( spl0_1316
<=> ! [X20,X5,X24] :
( c_lessequals(X20,X24,tc_set(X5))
| c_emptyset != c_minus(X20,X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f1432,axiom,
! [X24,X5,X20] :
( c_lessequals(X20,X24,tc_set(X5))
| c_emptyset != c_minus(X20,X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10316,plain,
spl0_1315,
inference(avatar_split_clause,[],[f1422,f10314]) ).
fof(f10314,plain,
( spl0_1315
<=> ! [X20,X5,X24] :
( X20 = X24
| c_uminus(X20,tc_set(X5)) != c_uminus(X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f1422,axiom,
! [X24,X5,X20] :
( X20 = X24
| c_uminus(X20,tc_set(X5)) != c_uminus(X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10312,plain,
spl0_1314,
inference(avatar_split_clause,[],[f1411,f10310]) ).
fof(f10310,plain,
( spl0_1314
<=> ! [X5,X0,X17] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X17,X0,X5)
| c_in(X17,c_SetInterval_OlessThan(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f1411,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X17,X0,X5)
| c_in(X17,c_SetInterval_OlessThan(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10308,plain,
spl0_1313,
inference(avatar_split_clause,[],[f1410,f10306]) ).
fof(f10306,plain,
( spl0_1313
<=> ! [X5,X0,X17] :
( ~ class_Orderings_Oord(X5)
| c_less(X17,X0,X5)
| ~ c_in(X17,c_SetInterval_OlessThan(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1410,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X17,X0,X5)
| ~ c_in(X17,c_SetInterval_OlessThan(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10304,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1409,f10302]) ).
fof(f10302,plain,
( spl0_1312
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OlessThan(X3,X5) != c_SetInterval_OlessThan(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1409,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OlessThan(X3,X5) != c_SetInterval_OlessThan(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10300,plain,
spl0_1311,
inference(avatar_split_clause,[],[f1400,f10298]) ).
fof(f10298,plain,
( spl0_1311
<=> ! [X5,X17,X0] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X0,X17,X5)
| c_in(X17,c_SetInterval_OgreaterThan(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f1400,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_less(X0,X17,X5)
| c_in(X17,c_SetInterval_OgreaterThan(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10296,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1399,f10294]) ).
fof(f10294,plain,
( spl0_1310
<=> ! [X5,X17,X0] :
( ~ class_Orderings_Oord(X5)
| c_less(X0,X17,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThan(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f1399,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| c_less(X0,X17,X5)
| ~ c_in(X17,c_SetInterval_OgreaterThan(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10292,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1398,f10290]) ).
fof(f10290,plain,
( spl0_1309
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OgreaterThan(X3,X5) != c_SetInterval_OgreaterThan(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1398,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OgreaterThan(X3,X5) != c_SetInterval_OgreaterThan(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10288,plain,
( spl0_1308
| ~ spl0_700
| ~ spl0_779
| ~ spl0_1040 ),
inference(avatar_split_clause,[],[f8658,f8435,f7188,f6852,f10285]) ).
fof(f8435,plain,
( spl0_1040
<=> ! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X28,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f8658,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_700
| ~ spl0_779
| ~ spl0_1040 ),
inference(forward_demodulation,[],[f8655,f6854]) ).
fof(f8655,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_779
| ~ spl0_1040 ),
inference(superposition,[],[f8436,f7190]) ).
fof(f8436,plain,
( ! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X28,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1040 ),
inference(avatar_component_clause,[],[f8435]) ).
fof(f10283,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1391,f10281]) ).
fof(f10281,plain,
( spl0_1307
<=> ! [X5,X0,X67] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X67,X0,X5)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X67,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f1391,axiom,
! [X0,X5,X67] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X67,X0,X5)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X0,X67,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10279,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1387,f10277]) ).
fof(f10277,plain,
( spl0_1306
<=> ! [X67,X31] : c_IntDef_Onat(c_minus(X31,X67,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1387,axiom,
! [X31,X67] : c_IntDef_Onat(c_minus(X31,X67,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10275,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1384,f10273]) ).
fof(f10273,plain,
( spl0_1305
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X31,X67,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1384,axiom,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X67,X31,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X31,X67,tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10271,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1378,f10269]) ).
fof(f10269,plain,
( spl0_1304
<=> ! [X5,X0,X17] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X17,X0,X5)
| c_in(X17,c_SetInterval_OatMost(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1378,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X17,X0,X5)
| c_in(X17,c_SetInterval_OatMost(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10267,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1377,f10265]) ).
fof(f10265,plain,
( spl0_1303
<=> ! [X5,X0,X17] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X17,X0,X5)
| ~ c_in(X17,c_SetInterval_OatMost(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1377,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X17,X0,X5)
| ~ c_in(X17,c_SetInterval_OatMost(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10263,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1376,f10261]) ).
fof(f10261,plain,
( spl0_1302
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OatMost(X3,X5) != c_SetInterval_OatMost(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1376,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OatMost(X3,X5) != c_SetInterval_OatMost(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10259,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1372,f10257]) ).
fof(f10257,plain,
( spl0_1301
<=> ! [X5,X17,X0] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X0,X17,X5)
| c_in(X17,c_SetInterval_OatLeast(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1372,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| ~ c_lessequals(X0,X17,X5)
| c_in(X17,c_SetInterval_OatLeast(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10255,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1371,f10253]) ).
fof(f10253,plain,
( spl0_1300
<=> ! [X5,X17,X0] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X0,X17,X5)
| ~ c_in(X17,c_SetInterval_OatLeast(X0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1371,axiom,
! [X0,X17,X5] :
( ~ class_Orderings_Oord(X5)
| c_lessequals(X0,X17,X5)
| ~ c_in(X17,c_SetInterval_OatLeast(X0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10251,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1370,f10249]) ).
fof(f10249,plain,
( spl0_1299
<=> ! [X5,X1,X3] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OatLeast(X3,X5) != c_SetInterval_OatLeast(X1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f1370,axiom,
! [X3,X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| X1 = X3
| c_SetInterval_OatLeast(X3,X5) != c_SetInterval_OatLeast(X1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10247,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1364,f10245]) ).
fof(f10245,plain,
( spl0_1298
<=> ! [X18,X5,X2] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X2,X18,X5)
| c_emptyset = c_SetInterval_OatLeastLessThan(X18,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1364,axiom,
! [X2,X18,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_lessequals(X2,X18,X5)
| c_emptyset = c_SetInterval_OatLeastLessThan(X18,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10243,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1359,f10241]) ).
fof(f10241,plain,
( spl0_1297
<=> ! [X18,X5,X2] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X2,X18,X5)
| c_emptyset = c_SetInterval_OatLeastAtMost(X18,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1359,axiom,
! [X2,X18,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X2,X18,X5)
| c_emptyset = c_SetInterval_OatLeastAtMost(X18,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10239,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1358,f10237]) ).
fof(f10237,plain,
( spl0_1296
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatLeast(X0,X5) = c_uminus(c_SetInterval_OlessThan(X0,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1358,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatLeast(X0,X5) = c_uminus(c_SetInterval_OlessThan(X0,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10235,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1357,f10233]) ).
fof(f10233,plain,
( spl0_1295
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatMost(X0,X5) = c_uminus(c_SetInterval_OgreaterThan(X0,X5),tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1357,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_SetInterval_OatMost(X0,X5) = c_uminus(c_SetInterval_OgreaterThan(X0,X5),tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10231,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1356,f10229]) ).
fof(f10229,plain,
( spl0_1294
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatMost(X0,X5),tc_set(X5)) = c_SetInterval_OgreaterThan(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1356,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatMost(X0,X5),tc_set(X5)) = c_SetInterval_OgreaterThan(X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10227,plain,
spl0_1293,
inference(avatar_split_clause,[],[f1355,f10225]) ).
fof(f10225,plain,
( spl0_1293
<=> ! [X5,X0] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatLeast(X0,X5),tc_set(X5)) = c_SetInterval_OlessThan(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f1355,axiom,
! [X0,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_uminus(c_SetInterval_OatLeast(X0,X5),tc_set(X5)) = c_SetInterval_OlessThan(X0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10223,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1143,f10221]) ).
fof(f10221,plain,
( spl0_1292
<=> ! [X1,X3] :
( c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f1143,axiom,
! [X3,X1] :
( c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10219,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1142,f10217]) ).
fof(f10217,plain,
( spl0_1291
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1142,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10215,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1141,f10213]) ).
fof(f10213,plain,
( spl0_1290
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1141,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10211,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1140,f10209]) ).
fof(f10209,plain,
( spl0_1289
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1140,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10207,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1137,f10205]) ).
fof(f10205,plain,
( spl0_1288
<=> ! [X1,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1137,axiom,
! [X3,X1] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10203,plain,
( spl0_1286
| ~ spl0_1287
| ~ spl0_781
| ~ spl0_1011 ),
inference(avatar_split_clause,[],[f8605,f8318,f7197,f10200,f10197]) ).
fof(f10197,plain,
( spl0_1286
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f10200,plain,
( spl0_1287
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f7197,plain,
( spl0_781
<=> ! [X33] : c_1 = c_Nat_Opower(X33,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f8318,plain,
( spl0_1011
<=> ! [X1,X3] :
( c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f8605,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_781
| ~ spl0_1011 ),
inference(superposition,[],[f8319,f7198]) ).
fof(f7198,plain,
( ! [X33] : c_1 = c_Nat_Opower(X33,c_0,tc_nat)
| ~ spl0_781 ),
inference(avatar_component_clause,[],[f7197]) ).
fof(f8319,plain,
( ! [X3,X1] :
( ~ c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat)
| c_Parity_Oeven(X3,tc_nat) )
| ~ spl0_1011 ),
inference(avatar_component_clause,[],[f8318]) ).
fof(f10195,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1130,f10193]) ).
fof(f10193,plain,
( spl0_1285
<=> ! [X1,X3] :
( c_Parity_Oeven(X1,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1130,axiom,
! [X3,X1] :
( c_Parity_Oeven(X1,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10191,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1129,f10189]) ).
fof(f10189,plain,
( spl0_1284
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1129,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10187,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1128,f10185]) ).
fof(f10185,plain,
( spl0_1283
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1128,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10183,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1127,f10181]) ).
fof(f10181,plain,
( spl0_1282
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f1127,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10179,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1124,f10177]) ).
fof(f10177,plain,
( spl0_1281
<=> ! [X1,X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven(c_times(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1124,axiom,
! [X3,X1] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X1,tc_nat)
| ~ c_Parity_Oeven(c_times(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10175,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1118,f10173]) ).
fof(f10173,plain,
( spl0_1280
<=> ! [X1,X3] :
( c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1118,axiom,
! [X3,X1] :
( c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10171,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1117,f10169]) ).
fof(f10169,plain,
( spl0_1279
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1117,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10167,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1116,f10165]) ).
fof(f10165,plain,
( spl0_1278
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1116,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X1,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10163,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1115,f10161]) ).
fof(f10161,plain,
( spl0_1277
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1115,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10159,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1075,f10157]) ).
fof(f10157,plain,
( spl0_1276
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(c_0,X8,X5)
| c_less(c_uminus(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1075,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(c_0,X8,X5)
| c_less(c_uminus(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10155,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1074,f10153]) ).
fof(f10153,plain,
( spl0_1275
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(c_0,X8,X5)
| ~ c_less(c_uminus(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1074,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(c_0,X8,X5)
| ~ c_less(c_uminus(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10151,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1071,f10149]) ).
fof(f10149,plain,
( spl0_1274
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_lessequals(c_uminus(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1071,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(c_0,X8,X5)
| c_lessequals(c_uminus(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10147,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1070,f10145]) ).
fof(f10145,plain,
( spl0_1273
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_0,X8,X5)
| ~ c_lessequals(c_uminus(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1070,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(c_0,X8,X5)
| ~ c_lessequals(c_uminus(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10143,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1068,f10141]) ).
fof(f10141,plain,
( spl0_1272
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X8 = X9
| c_uminus(X8,X5) != c_uminus(X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1068,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X8 = X9
| c_uminus(X8,X5) != c_uminus(X9,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10139,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1065,f10137]) ).
fof(f10137,plain,
( spl0_1271
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X8,c_0,X5)
| c_less(c_0,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1065,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_less(X8,c_0,X5)
| c_less(c_0,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10135,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1064,f10133]) ).
fof(f10133,plain,
( spl0_1270
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X8,c_0,X5)
| ~ c_less(c_0,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f1064,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_less(X8,c_0,X5)
| ~ c_less(c_0,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10131,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1063,f10129]) ).
fof(f1063,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| ~ c_lessequals(X8,c_0,X5)
| c_lessequals(c_0,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10127,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1062,f10125]) ).
fof(f1062,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X5)
| c_lessequals(X8,c_0,X5)
| ~ c_lessequals(c_0,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10123,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1008,f10121]) ).
fof(f10121,plain,
( spl0_1267
<=> ! [X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(X30,X5) = c_times(X30,c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1008,axiom,
! [X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_uminus(X30,X5) = c_times(X30,c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10119,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1007,f10117]) ).
fof(f10117,plain,
( spl0_1266
<=> ! [X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X30,X5) = c_uminus(X30,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1007,axiom,
! [X5,X30] :
( ~ class_Numeral_Onumber__ring(X5)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X30,X5) = c_uminus(X30,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10115,plain,
( spl0_1265
| ~ spl0_747
| ~ spl0_975 ),
inference(avatar_split_clause,[],[f8516,f8172,f7060,f10113]) ).
fof(f10113,plain,
( spl0_1265
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f7060,plain,
( spl0_747
<=> ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f8172,plain,
( spl0_975
<=> ! [X9,X8] : c_0 = c_div(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f8516,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_747
| ~ spl0_975 ),
inference(superposition,[],[f8173,f7061]) ).
fof(f7061,plain,
( ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1
| ~ spl0_747 ),
inference(avatar_component_clause,[],[f7060]) ).
fof(f8173,plain,
( ! [X8,X9] : c_0 = c_div(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint)
| ~ spl0_975 ),
inference(avatar_component_clause,[],[f8172]) ).
fof(f10111,plain,
spl0_1264,
inference(avatar_split_clause,[],[f927,f10109]) ).
fof(f10109,plain,
( spl0_1264
<=> ! [X18,X0,X2] :
( X2 = X18
| c_plus(X18,X0,tc_nat) != c_plus(X2,X0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f927,axiom,
! [X2,X0,X18] :
( X2 = X18
| c_plus(X18,X0,tc_nat) != c_plus(X2,X0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10107,plain,
spl0_1263,
inference(avatar_split_clause,[],[f922,f10105]) ).
fof(f10105,plain,
( spl0_1263
<=> ! [X18,X0,X2] :
( X2 = X18
| c_plus(X0,X18,tc_nat) != c_plus(X0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f922,axiom,
! [X2,X0,X18] :
( X2 = X18
| c_plus(X0,X18,tc_nat) != c_plus(X0,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10103,plain,
spl0_1262,
inference(avatar_split_clause,[],[f906,f10101]) ).
fof(f10101,plain,
( spl0_1262
<=> ! [X18,X2] :
( c_0 = X18
| c_0 = X2
| c_0 != c_times(X18,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f906,axiom,
! [X2,X18] :
( c_0 = X18
| c_0 = X2
| c_0 != c_times(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10099,plain,
spl0_1261,
inference(avatar_split_clause,[],[f691,f10097]) ).
fof(f691,axiom,
! [X2,X18] : c_IntDef_Oint(c_plus(X18,X2,tc_nat)) = c_plus(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10095,plain,
spl0_1260,
inference(avatar_split_clause,[],[f654,f10093]) ).
fof(f10093,plain,
( spl0_1260
<=> ! [X18,X5,X2] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X2 = X18
| c_NatArith_Oof__nat(X2,X5) != c_NatArith_Oof__nat(X18,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f654,axiom,
! [X2,X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| X2 = X18
| c_NatArith_Oof__nat(X2,X5) != c_NatArith_Oof__nat(X18,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10091,plain,
spl0_1259,
inference(avatar_split_clause,[],[f648,f10089]) ).
fof(f10089,plain,
( spl0_1259
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_0,X2,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f648,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_0,X2,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10087,plain,
spl0_1258,
inference(avatar_split_clause,[],[f647,f10085]) ).
fof(f10085,plain,
( spl0_1258
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f647,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10083,plain,
spl0_1257,
inference(avatar_split_clause,[],[f625,f10081]) ).
fof(f10081,plain,
( spl0_1257
<=> ! [X45,X17] :
( c_0 = X45
| c_lessequals(X45,X17,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X17,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f625,axiom,
! [X45,X17] :
( c_0 = X45
| c_lessequals(X45,X17,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X17,X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10079,plain,
spl0_1256,
inference(avatar_split_clause,[],[f584,f10077]) ).
fof(f10077,plain,
( spl0_1256
<=> ! [X37,X34,X5,X35] :
( X35 = X37
| c_append(X34,X35,X5) != c_append(X34,X37,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f584,axiom,
! [X37,X34,X35,X5] :
( X35 = X37
| c_append(X34,X35,X5) != c_append(X34,X37,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10075,plain,
spl0_1255,
inference(avatar_split_clause,[],[f578,f10073]) ).
fof(f10073,plain,
( spl0_1255
<=> ! [X5,X1] :
( c_List_Orotate1(X1,X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f578,axiom,
! [X1,X5] :
( c_List_Orotate1(X1,X5) = X1
| ~ c_lessequals(c_Nat_Osize(X1,tc_List_Olist(X5)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10065,plain,
spl0_1254,
inference(avatar_split_clause,[],[f467,f10063]) ).
fof(f10063,plain,
( spl0_1254
<=> ! [X49,X50,X5,X8,X7] :
( X49 = X50
| c_List_Olist_OCons(X7,X49,X5) != c_List_Olist_OCons(X8,X50,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f467,axiom,
! [X50,X49,X8,X7,X5] :
( X49 = X50
| c_List_Olist_OCons(X7,X49,X5) != c_List_Olist_OCons(X8,X50,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10061,plain,
spl0_1253,
inference(avatar_split_clause,[],[f466,f10059]) ).
fof(f10059,plain,
( spl0_1253
<=> ! [X49,X7,X50,X5,X8] :
( X7 = X8
| c_List_Olist_OCons(X7,X49,X5) != c_List_Olist_OCons(X8,X50,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f466,axiom,
! [X50,X49,X8,X7,X5] :
( X7 = X8
| c_List_Olist_OCons(X7,X49,X5) != c_List_Olist_OCons(X8,X50,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10057,plain,
spl0_1252,
inference(avatar_split_clause,[],[f451,f10055]) ).
fof(f10055,plain,
( spl0_1252
<=> ! [X34,X5,X2] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate(X2,X34,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f451,axiom,
! [X2,X34,X5] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate(X2,X34,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10053,plain,
spl0_1251,
inference(avatar_split_clause,[],[f393,f10051]) ).
fof(f10051,plain,
( spl0_1251
<=> ! [X6,X34,X3] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X3,X34,X6),X6)
| ~ c_in(X3,c_List_Oset(X34,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f393,axiom,
! [X3,X6,X34] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X3,X34,X6),X6)
| ~ c_in(X3,c_List_Oset(X34,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10049,plain,
spl0_1250,
inference(avatar_split_clause,[],[f371,f10047]) ).
fof(f10047,plain,
( spl0_1250
<=> ! [X37,X34,X5,X35] :
( X35 = X37
| c_append(X35,X34,X5) != c_append(X37,X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f371,axiom,
! [X37,X34,X35,X5] :
( X35 = X37
| c_append(X35,X34,X5) != c_append(X37,X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10045,plain,
spl0_1249,
inference(avatar_split_clause,[],[f334,f10043]) ).
fof(f10043,plain,
( spl0_1249
<=> ! [X9,X8] : c_Divides_Oop_Amod(X9,X8,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X9,X8,tc_IntDef_Oint),X8,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f334,axiom,
! [X8,X9] : c_Divides_Oop_Amod(X9,X8,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X9,X8,tc_IntDef_Oint),X8,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10041,plain,
spl0_1248,
inference(avatar_split_clause,[],[f333,f10039]) ).
fof(f10039,plain,
( spl0_1248
<=> ! [X9,X8] : c_Divides_Oop_Amod(c_plus(X8,X9,tc_IntDef_Oint),X8,tc_IntDef_Oint) = c_Divides_Oop_Amod(X9,X8,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f333,axiom,
! [X8,X9] : c_Divides_Oop_Amod(c_plus(X8,X9,tc_IntDef_Oint),X8,tc_IntDef_Oint) = c_Divides_Oop_Amod(X9,X8,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10037,plain,
spl0_1247,
inference(avatar_split_clause,[],[f326,f10035]) ).
fof(f10035,plain,
( spl0_1247
<=> ! [X2,X3] :
( c_0 = X3
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f326,axiom,
! [X2,X3] :
( c_0 = X3
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10032,plain,
( spl0_1246
| ~ spl0_872
| ~ spl0_1245 ),
inference(avatar_split_clause,[],[f10022,f10019,f7612,f10030]) ).
fof(f10030,plain,
( spl0_1246
<=> ! [X2] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f10019,plain,
( spl0_1245
<=> ! [X2] :
( c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f10022,plain,
( ! [X2] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X2,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X2 )
| ~ spl0_872
| ~ spl0_1245 ),
inference(forward_demodulation,[],[f10020,f7614]) ).
fof(f10020,plain,
( ! [X2] :
( c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1245 ),
inference(avatar_component_clause,[],[f10019]) ).
fof(f10021,plain,
spl0_1245,
inference(avatar_split_clause,[],[f325,f10019]) ).
fof(f325,axiom,
! [X2] :
( c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10017,plain,
spl0_1244,
inference(avatar_split_clause,[],[f318,f10015]) ).
fof(f10015,plain,
( spl0_1244
<=> ! [X9,X1] :
( c_0 = X9
| c_div(c_times(X9,X1,tc_IntDef_Oint),X9,tc_IntDef_Oint) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f318,axiom,
! [X1,X9] :
( c_0 = X9
| c_div(c_times(X9,X1,tc_IntDef_Oint),X9,tc_IntDef_Oint) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10013,plain,
spl0_1243,
inference(avatar_split_clause,[],[f317,f10011]) ).
fof(f10011,plain,
( spl0_1243
<=> ! [X9,X1] :
( c_0 = X9
| c_div(c_times(X1,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f317,axiom,
! [X1,X9] :
( c_0 = X9
| c_div(c_times(X1,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10009,plain,
spl0_1242,
inference(avatar_split_clause,[],[f298,f10007]) ).
fof(f10007,plain,
( spl0_1242
<=> ! [X9] : c_IntDiv_OposDivAlg(c_Pair(c_0,X9,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_1242])]) ).
fof(f298,axiom,
! [X9] : c_IntDiv_OposDivAlg(c_Pair(c_0,X9,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10005,plain,
spl0_1241,
inference(avatar_split_clause,[],[f283,f10003]) ).
fof(f10003,plain,
( spl0_1241
<=> ! [X9,X8] : c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f283,axiom,
! [X8,X9] : c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10001,plain,
spl0_1240,
inference(avatar_split_clause,[],[f254,f9999]) ).
fof(f9999,plain,
( spl0_1240
<=> ! [X5,X28] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X28,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X28,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f254,axiom,
! [X28,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(X28,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X28,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f9997,plain,
spl0_1239,
inference(avatar_split_clause,[],[f253,f9995]) ).
fof(f9995,plain,
( spl0_1239
<=> ! [X5,X28] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X28,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X28,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f253,axiom,
! [X28,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(X28,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X28,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f9993,plain,
spl0_1238,
inference(avatar_split_clause,[],[f250,f9991]) ).
fof(f9991,plain,
( spl0_1238
<=> ! [X5,X28] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X28,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X28,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f250,axiom,
! [X28,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(X28,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X28,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f9989,plain,
spl0_1237,
inference(avatar_split_clause,[],[f249,f9987]) ).
fof(f9987,plain,
( spl0_1237
<=> ! [X5,X28] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X28,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X28,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f249,axiom,
! [X28,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(X28,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X28,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f9985,plain,
spl0_1236,
inference(avatar_split_clause,[],[f247,f9983]) ).
fof(f9983,plain,
( spl0_1236
<=> ! [X5,X28,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| X28 = X30
| c_IntDef_Oof__int(X30,X5) != c_IntDef_Oof__int(X28,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f247,axiom,
! [X28,X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| X28 = X30
| c_IntDef_Oof__int(X30,X5) != c_IntDef_Oof__int(X28,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f9976,plain,
spl0_1235,
inference(avatar_split_clause,[],[f241,f9974]) ).
fof(f9974,plain,
( spl0_1235
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X30,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f241,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_less(c_0,X30,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f9972,plain,
spl0_1234,
inference(avatar_split_clause,[],[f240,f9970]) ).
fof(f9970,plain,
( spl0_1234
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X30,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f240,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_less(c_0,X30,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f9968,plain,
spl0_1233,
inference(avatar_split_clause,[],[f239,f9966]) ).
fof(f9966,plain,
( spl0_1233
<=> ! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X30,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X30,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f239,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_lessequals(c_0,X30,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f9964,plain,
spl0_1232,
inference(avatar_split_clause,[],[f238,f9962]) ).
fof(f238,axiom,
! [X5,X30] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_lessequals(c_0,X30,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X30,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f9960,plain,
spl0_1231,
inference(avatar_split_clause,[],[f202,f9958]) ).
fof(f9958,plain,
( spl0_1231
<=> ! [X5,X8] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| c_in(c_uminus(X8,X5),c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f202,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| ~ c_in(X8,c_IntDef_OInts,X5)
| c_in(c_uminus(X8,X5),c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f9956,plain,
spl0_1230,
inference(avatar_split_clause,[],[f197,f9954]) ).
fof(f9954,plain,
( spl0_1230
<=> ! [X1] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1
| ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f197,axiom,
! [X1] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X1)) = X1
| ~ c_in(X1,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f9952,plain,
spl0_1229,
inference(avatar_split_clause,[],[f183,f9950]) ).
fof(f9950,plain,
( spl0_1229
<=> ! [X29,X18] :
( c_IntDef_Oint(X18) != c_Numeral_Onumber__of(X29,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f183,axiom,
! [X29,X18] :
( c_IntDef_Oint(X18) != c_Numeral_Onumber__of(X29,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f9948,plain,
spl0_1228,
inference(avatar_split_clause,[],[f182,f9946]) ).
fof(f9946,plain,
( spl0_1228
<=> ! [X29,X18] :
( c_IntDef_Oint(X18) != c_Numeral_Onumber__of(X29,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X29,tc_IntDef_Oint)) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f182,axiom,
! [X29,X18] :
( c_IntDef_Oint(X18) != c_Numeral_Onumber__of(X29,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X29,tc_IntDef_Oint)) = X18 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f9944,plain,
spl0_1227,
inference(avatar_split_clause,[],[f84,f9942]) ).
fof(f9942,plain,
( spl0_1227
<=> ! [X2,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f84,axiom,
! [X2,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f9940,plain,
spl0_1226,
inference(avatar_split_clause,[],[f74,f9938]) ).
fof(f9938,plain,
( spl0_1226
<=> ! [X2,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_plus(X18,X2,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f74,axiom,
! [X2,X18] : c_Divides_Oop_Amod(X18,X2,tc_nat) = c_Divides_Oop_Amod(c_plus(X18,X2,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f9936,plain,
( spl0_1225
| ~ spl0_56
| ~ spl0_960 ),
inference(avatar_split_clause,[],[f8117,f7995,f3432,f9933]) ).
fof(f7995,plain,
( spl0_960
<=> ! [X5] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f8117,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_960 ),
inference(resolution,[],[f7996,f3434]) ).
fof(f7996,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5) )
| ~ spl0_960 ),
inference(avatar_component_clause,[],[f7995]) ).
fof(f9931,plain,
spl0_1224,
inference(avatar_split_clause,[],[f73,f9929]) ).
fof(f9929,plain,
( spl0_1224
<=> ! [X2,X18] : c_Divides_Oop_Amod(c_plus(X2,X18,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X18,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f73,axiom,
! [X2,X18] : c_Divides_Oop_Amod(c_plus(X2,X18,tc_nat),X2,tc_nat) = c_Divides_Oop_Amod(X18,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f9927,plain,
spl0_1223,
inference(avatar_split_clause,[],[f32,f9925]) ).
fof(f9925,plain,
( spl0_1223
<=> ! [X10,X11,X12,X5] :
( X11 = X12
| c_Datatype__Universe_OIn1(X12,X5,X10) != c_Datatype__Universe_OIn1(X11,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f32,axiom,
! [X10,X11,X5,X12] :
( X11 = X12
| c_Datatype__Universe_OIn1(X12,X5,X10) != c_Datatype__Universe_OIn1(X11,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f9923,plain,
spl0_1222,
inference(avatar_split_clause,[],[f30,f9921]) ).
fof(f9921,plain,
( spl0_1222
<=> ! [X10,X11,X12,X5] :
( X11 = X12
| c_Datatype__Universe_OIn0(X11,X5,X10) != c_Datatype__Universe_OIn0(X12,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f30,axiom,
! [X10,X11,X5,X12] :
( X11 = X12
| c_Datatype__Universe_OIn0(X11,X5,X10) != c_Datatype__Universe_OIn0(X12,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f9919,plain,
spl0_1221,
inference(avatar_split_clause,[],[f26,f9917]) ).
fof(f9917,plain,
( spl0_1221
<=> ! [X5,X10,X9,X8] :
( X8 = X9
| c_Datatype__Universe_OAtom(X8,X5,X10) != c_Datatype__Universe_OAtom(X9,X5,X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f26,axiom,
! [X10,X8,X9,X5] :
( X8 = X9
| c_Datatype__Universe_OAtom(X8,X5,X10) != c_Datatype__Universe_OAtom(X9,X5,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f9861,plain,
( ~ spl0_1219
| spl0_1220
| ~ spl0_769
| ~ spl0_1185 ),
inference(avatar_split_clause,[],[f9763,f9419,f7148,f9859,f9855]) ).
fof(f9855,plain,
( spl0_1219
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f9859,plain,
( spl0_1220
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f7148,plain,
( spl0_769
<=> ! [X2] : c_0 = c_minus(c_0,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f9419,plain,
( spl0_1185
<=> ! [X9,X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X8 = X9
| c_0 != c_minus(X8,X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f9763,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_769
| ~ spl0_1185 ),
inference(trivial_inequality_removal,[],[f9756]) ).
fof(f9756,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_769
| ~ spl0_1185 ),
inference(superposition,[],[f9420,f7149]) ).
fof(f7149,plain,
( ! [X2] : c_0 = c_minus(c_0,X2,tc_nat)
| ~ spl0_769 ),
inference(avatar_component_clause,[],[f7148]) ).
fof(f9420,plain,
( ! [X8,X9,X5] :
( c_0 != c_minus(X8,X9,X5)
| X8 = X9
| ~ class_OrderedGroup_Oab__group__add(X5) )
| ~ spl0_1185 ),
inference(avatar_component_clause,[],[f9419]) ).
fof(f9738,plain,
( spl0_1218
| ~ spl0_854
| ~ spl0_939 ),
inference(avatar_split_clause,[],[f8100,f7908,f7492,f9735]) ).
fof(f9735,plain,
( spl0_1218
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f8100,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_854
| ~ spl0_939 ),
inference(superposition,[],[f7493,f7910]) ).
fof(f9690,plain,
( spl0_1217
| ~ spl0_91
| ~ spl0_927 ),
inference(avatar_split_clause,[],[f8083,f7860,f3607,f9688]) ).
fof(f9688,plain,
( spl0_1217
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f3607,plain,
( spl0_91
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f7860,plain,
( spl0_927
<=> ! [X5,X1] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X1,c_1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f8083,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_91
| ~ spl0_927 ),
inference(resolution,[],[f7861,f3609]) ).
fof(f3609,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f3607]) ).
fof(f7861,plain,
( ! [X1,X5] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X1,c_1,X5) = X1 )
| ~ spl0_927 ),
inference(avatar_component_clause,[],[f7860]) ).
fof(f9647,plain,
( spl0_1216
| ~ spl0_57
| ~ spl0_927 ),
inference(avatar_split_clause,[],[f8082,f7860,f3437,f9645]) ).
fof(f3437,plain,
( spl0_57
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f8082,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_57
| ~ spl0_927 ),
inference(resolution,[],[f7861,f3439]) ).
fof(f3439,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_57 ),
inference(avatar_component_clause,[],[f3437]) ).
fof(f9585,plain,
( spl0_1215
| ~ spl0_91
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8081,f7856,f3607,f9583]) ).
fof(f9583,plain,
( spl0_1215
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f7856,plain,
( spl0_926
<=> ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f8081,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_91
| ~ spl0_926 ),
inference(resolution,[],[f7857,f3609]) ).
fof(f7857,plain,
( ! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X2,X5) )
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f7856]) ).
fof(f9572,plain,
( spl0_1214
| ~ spl0_56
| ~ spl0_1006
| ~ spl0_1143 ),
inference(avatar_split_clause,[],[f9253,f9250,f8298,f3432,f9570]) ).
fof(f9570,plain,
( spl0_1214
<=> ! [X5] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X5)
| ~ class_Numeral_Onumber__ring(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f9250,plain,
( spl0_1143
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f9253,plain,
( ! [X5] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_56
| ~ spl0_1006
| ~ spl0_1143 ),
inference(forward_demodulation,[],[f9251,f8596]) ).
fof(f9251,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) )
| ~ spl0_1143 ),
inference(avatar_component_clause,[],[f9250]) ).
fof(f9550,plain,
( spl0_1213
| ~ spl0_57
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8080,f7856,f3437,f9548]) ).
fof(f9548,plain,
( spl0_1213
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f8080,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_57
| ~ spl0_926 ),
inference(resolution,[],[f7857,f3439]) ).
fof(f9534,plain,
spl0_1212,
inference(avatar_split_clause,[],[f3055,f9532]) ).
fof(f9532,plain,
( spl0_1212
<=> ! [X2,X18] :
( ~ c_lessequals(c_1,c_times(X18,X2,tc_nat),tc_nat)
| c_lessequals(c_1,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f3055,plain,
! [X2,X18] :
( ~ c_lessequals(c_1,c_times(X18,X2,tc_nat),tc_nat)
| c_lessequals(c_1,X18,tc_nat) ),
inference(forward_demodulation,[],[f2878,f2745]) ).
fof(f2878,plain,
! [X2,X18] :
( c_lessequals(c_1,X18,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X18,X2,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f936,f1385]) ).
fof(f936,axiom,
! [X2,X18] :
( c_lessequals(c_1,X18,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9530,plain,
spl0_1211,
inference(avatar_split_clause,[],[f3054,f9528]) ).
fof(f9528,plain,
( spl0_1211
<=> ! [X2,X18] :
( ~ c_lessequals(c_1,c_times(X18,X2,tc_nat),tc_nat)
| c_lessequals(c_1,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f3054,plain,
! [X2,X18] :
( ~ c_lessequals(c_1,c_times(X18,X2,tc_nat),tc_nat)
| c_lessequals(c_1,X2,tc_nat) ),
inference(forward_demodulation,[],[f2877,f2745]) ).
fof(f2877,plain,
! [X2,X18] :
( c_lessequals(c_1,X2,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X18,X2,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f937,f1385]) ).
fof(f937,axiom,
! [X2,X18] :
( c_lessequals(c_1,X2,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9526,plain,
spl0_1210,
inference(avatar_split_clause,[],[f3051,f9524]) ).
fof(f9524,plain,
( spl0_1210
<=> ! [X2,X17] :
( c_lessequals(c_1,c_Nat_Opower(X17,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X17,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f3051,plain,
! [X2,X17] :
( c_lessequals(c_1,c_Nat_Opower(X17,X2,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X17,tc_nat) ),
inference(forward_demodulation,[],[f2869,f2745]) ).
fof(f2869,plain,
! [X2,X17] :
( ~ c_lessequals(c_1,X17,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X17,X2,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1181,f1385]) ).
fof(f1181,axiom,
! [X2,X17] :
( ~ c_lessequals(c_1,X17,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X17,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9522,plain,
spl0_1209,
inference(avatar_split_clause,[],[f2985,f9520]) ).
fof(f2985,plain,
! [X2,X18] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2785,f2781]) ).
fof(f2785,plain,
! [X2,X18] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1606,f1385]) ).
fof(f1606,axiom,
! [X2,X18] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X2)),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9518,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2981,f9516]) ).
fof(f9516,plain,
( spl0_1208
<=> ! [X28] : c_Numeral_OBit(c_Numeral_Obin__add(X28,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f2981,plain,
! [X28] : c_Numeral_OBit(c_Numeral_Obin__add(X28,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2783,f2760]) ).
fof(f2783,plain,
! [X28] : c_Numeral_Obin__add(c_Numeral_OBit(X28,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X28,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f972,f954,f954]) ).
fof(f972,axiom,
! [X28] : c_Numeral_Obin__pred(c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X28),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9514,plain,
spl0_1207,
inference(avatar_split_clause,[],[f2784,f9512]) ).
fof(f9512,plain,
( spl0_1207
<=> ! [X28] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X28),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f2784,plain,
! [X28] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X28),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f964,f970,f970]) ).
fof(f964,axiom,
! [X28] : c_Numeral_Obin__minus(c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X28),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9506,plain,
( spl0_1206
| ~ spl0_95
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f8073,f7844,f3627,f9504]) ).
fof(f9504,plain,
( spl0_1206
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f3627,plain,
( spl0_95
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f7844,plain,
( spl0_923
<=> ! [X1,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omax(X1,X1,X10) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f8073,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_95
| ~ spl0_923 ),
inference(resolution,[],[f7845,f3629]) ).
fof(f3629,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_95 ),
inference(avatar_component_clause,[],[f3627]) ).
fof(f7845,plain,
( ! [X10,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omax(X1,X1,X10) = X1 )
| ~ spl0_923 ),
inference(avatar_component_clause,[],[f7844]) ).
fof(f9502,plain,
( spl0_1205
| ~ spl0_1204 ),
inference(avatar_split_clause,[],[f9498,f9495,f9500]) ).
fof(f9495,plain,
( spl0_1204
<=> ! [X2] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f9498,plain,
( ! [X2] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1204 ),
inference(forward_demodulation,[],[f9496,f2781]) ).
fof(f9496,plain,
( ! [X2] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1204 ),
inference(avatar_component_clause,[],[f9495]) ).
fof(f9497,plain,
spl0_1204,
inference(avatar_split_clause,[],[f2773,f9495]) ).
fof(f2773,plain,
! [X2] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f235,f1385]) ).
fof(f235,axiom,
! [X2] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X2)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9493,plain,
spl0_1203,
inference(avatar_split_clause,[],[f1556,f9491]) ).
fof(f9491,plain,
( spl0_1203
<=> ! [X13,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X13,X5),X5,X5) = c_Relation_ORange(X13,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1556,axiom,
! [X5,X13] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X13,X5),X5,X5) = c_Relation_ORange(X13,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9489,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1554,f9487]) ).
fof(f9487,plain,
( spl0_1202
<=> ! [X13,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X13,X5),X5,X5) = c_Relation_ODomain(X13,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1554,axiom,
! [X5,X13] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X13,X5),X5,X5) = c_Relation_ODomain(X13,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9485,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1526,f9483]) ).
fof(f9483,plain,
( spl0_1201
<=> ! [X9,X20,X5,X8] :
( ~ c_in(X8,X20,X5)
| c_in(X8,c_insert(X9,X20,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1526,axiom,
! [X8,X9,X5,X20] :
( ~ c_in(X8,X20,X5)
| c_in(X8,c_insert(X9,X20,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9481,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1483,f9479]) ).
fof(f9479,plain,
( spl0_1200
<=> ! [X24,X20,X5,X19] :
( ~ c_in(X19,X24,X5)
| c_in(X19,c_union(X20,X24,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1483,axiom,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X24,X5)
| c_in(X19,c_union(X20,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9477,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1482,f9475]) ).
fof(f9475,plain,
( spl0_1199
<=> ! [X24,X20,X5,X19] :
( ~ c_in(X19,X20,X5)
| c_in(X19,c_union(X20,X24,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1482,axiom,
! [X19,X24,X5,X20] :
( ~ c_in(X19,X20,X5)
| c_in(X19,c_union(X20,X24,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9473,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1424,f9471]) ).
fof(f9471,plain,
( spl0_1198
<=> ! [X20,X5,X19] :
( c_in(X19,X20,X5)
| c_in(X19,c_uminus(X20,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f1424,axiom,
! [X19,X5,X20] :
( c_in(X19,X20,X5)
| c_in(X19,c_uminus(X20,tc_set(X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9469,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1423,f9467]) ).
fof(f9467,plain,
( spl0_1197
<=> ! [X20,X5,X19] :
( ~ c_in(X19,X20,X5)
| ~ c_in(X19,c_uminus(X20,tc_set(X5)),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1423,axiom,
! [X19,X5,X20] :
( ~ c_in(X19,X20,X5)
| ~ c_in(X19,c_uminus(X20,tc_set(X5)),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9465,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1386,f9463]) ).
fof(f9463,plain,
( spl0_1196
<=> ! [X67,X31] : c_minus(X31,X67,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1386,axiom,
! [X31,X67] : c_minus(X31,X67,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9461,plain,
( spl0_1195
| ~ spl0_31
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f8072,f7844,f3307,f9459]) ).
fof(f9459,plain,
( spl0_1195
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f3307,plain,
( spl0_31
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f8072,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_923 ),
inference(resolution,[],[f7845,f3309]) ).
fof(f3309,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3307]) ).
fof(f9457,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1383,f9455]) ).
fof(f9455,plain,
( spl0_1194
<=> ! [X67,X31] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,X67,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1383,axiom,
! [X31,X67] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X67,X31,tc_nat),tc_nat) = c_minus(X31,X67,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9453,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1363,f9451]) ).
fof(f9451,plain,
( spl0_1193
<=> ! [X5,X8] :
( ~ class_Orderings_Oorder(X5)
| c_SetInterval_OatLeastAtMost(X8,X8,X5) = c_insert(X8,c_emptyset,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1363,axiom,
! [X8,X5] :
( ~ class_Orderings_Oorder(X5)
| c_SetInterval_OatLeastAtMost(X8,X8,X5) = c_insert(X8,c_emptyset,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9449,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1112,f9447]) ).
fof(f9447,plain,
( spl0_1192
<=> ! [X29] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1112,axiom,
! [X29] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/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(f9445,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1111,f9443]) ).
fof(f9443,plain,
( spl0_1191
<=> ! [X29] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1111,axiom,
! [X29] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X29,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/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(f9441,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1093,f9439]) ).
fof(f9439,plain,
( spl0_1190
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X8
| c_less(c_0,c_HOL_Oabs(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1093,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X8
| c_less(c_0,c_HOL_Oabs(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9437,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1086,f9435]) ).
fof(f1086,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X1,X5)
| c_OrderedGroup_Opprt(X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9433,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1085,f9431]) ).
fof(f9431,plain,
( spl0_1188
<=> ! [X5,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X3,c_0,X5)
| c_0 = c_OrderedGroup_Opprt(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1085,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X3,c_0,X5)
| c_0 = c_OrderedGroup_Opprt(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9429,plain,
spl0_1187,
inference(avatar_split_clause,[],[f1081,f9427]) ).
fof(f9427,plain,
( spl0_1187
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X1,c_0,X5)
| c_OrderedGroup_Onprt(X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f1081,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(X1,c_0,X5)
| c_OrderedGroup_Onprt(X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9425,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1080,f9423]) ).
fof(f1080,axiom,
! [X3,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| ~ c_lessequals(c_0,X3,X5)
| c_0 = c_OrderedGroup_Onprt(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9421,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1040,f9419]) ).
fof(f1040,axiom,
! [X8,X9,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| X8 = X9
| c_0 != c_minus(X8,X9,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9417,plain,
( spl0_1184
| ~ spl0_95
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8071,f7840,f3627,f9415]) ).
fof(f9415,plain,
( spl0_1184
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f7840,plain,
( spl0_922
<=> ! [X1,X10] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omin(X1,X1,X10) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f8071,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_95
| ~ spl0_922 ),
inference(resolution,[],[f7841,f3629]) ).
fof(f7841,plain,
( ! [X10,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omin(X1,X1,X10) = X1 )
| ~ spl0_922 ),
inference(avatar_component_clause,[],[f7840]) ).
fof(f9413,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1024,f9411]) ).
fof(f1024,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_lessequals(c_0,X1,X5)
| c_HOL_Oabs(X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9409,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1022,f9407]) ).
fof(f9407,plain,
( spl0_1182
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X8,X5) = c_HOL_Oabs(c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f1022,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X8,X5) = c_HOL_Oabs(c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9405,plain,
spl0_1181,
inference(avatar_split_clause,[],[f1020,f9403]) ).
fof(f9403,plain,
( spl0_1181
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X8
| ~ c_lessequals(c_HOL_Oabs(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f1020,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X8
| ~ c_lessequals(c_HOL_Oabs(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9401,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1019,f9399]) ).
fof(f9399,plain,
( spl0_1180
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X8,X5) = c_HOL_Oabs(c_HOL_Oabs(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1019,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_HOL_Oabs(X8,X5) = c_HOL_Oabs(c_HOL_Oabs(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9397,plain,
spl0_1179,
inference(avatar_split_clause,[],[f988,f9395]) ).
fof(f9395,plain,
( spl0_1179
<=> ! [X5,X28] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB1),X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f988,axiom,
! [X28,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X28,c_Numeral_Obit_OB1),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9393,plain,
spl0_1178,
inference(avatar_split_clause,[],[f968,f9391]) ).
fof(f9389,plain,
spl0_1177,
inference(avatar_split_clause,[],[f945,f9387]) ).
fof(f9387,plain,
( spl0_1177
<=> ! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_0,c_minus(X2,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f945,axiom,
! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_0,c_minus(X2,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9385,plain,
spl0_1176,
inference(avatar_split_clause,[],[f944,f9383]) ).
fof(f9383,plain,
( spl0_1176
<=> ! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_0,c_minus(X2,X18,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f944,axiom,
! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_0,c_minus(X2,X18,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9381,plain,
spl0_1175,
inference(avatar_split_clause,[],[f920,f9379]) ).
fof(f9379,plain,
( spl0_1175
<=> ! [X2,X18] :
( c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_times(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f920,axiom,
! [X2,X18] :
( c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_times(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9377,plain,
spl0_1174,
inference(avatar_split_clause,[],[f919,f9375]) ).
fof(f9375,plain,
( spl0_1174
<=> ! [X18,X2] :
( c_less(c_0,X18,tc_nat)
| ~ c_less(c_0,c_times(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f919,axiom,
! [X2,X18] :
( c_less(c_0,X18,tc_nat)
| ~ c_less(c_0,c_times(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9373,plain,
( spl0_1173
| ~ spl0_31
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8070,f7840,f3307,f9371]) ).
fof(f9371,plain,
( spl0_1173
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f8070,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_922 ),
inference(resolution,[],[f7841,f3309]) ).
fof(f9369,plain,
spl0_1172,
inference(avatar_split_clause,[],[f871,f9367]) ).
fof(f9367,plain,
( spl0_1172
<=> ! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_0,c_plus(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f871,axiom,
! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_0,c_plus(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9365,plain,
spl0_1171,
inference(avatar_split_clause,[],[f870,f9363]) ).
fof(f9363,plain,
( spl0_1171
<=> ! [X18,X2] :
( ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_plus(X18,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f870,axiom,
! [X2,X18] :
( ~ c_less(c_0,X18,tc_nat)
| c_less(c_0,c_plus(X18,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9361,plain,
spl0_1170,
inference(avatar_split_clause,[],[f692,f9359]) ).
fof(f9359,plain,
( spl0_1170
<=> ! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f692,axiom,
! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X29,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9357,plain,
spl0_1169,
inference(avatar_split_clause,[],[f655,f9355]) ).
fof(f9355,plain,
( spl0_1169
<=> ! [X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X18
| ~ c_lessequals(c_NatArith_Oof__nat(X18,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f655,axiom,
! [X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X18
| ~ c_lessequals(c_NatArith_Oof__nat(X18,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9353,plain,
spl0_1168,
inference(avatar_split_clause,[],[f575,f9351]) ).
fof(f9351,plain,
( spl0_1168
<=> ! [X5,X3] : c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) = c_List_Orev(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f575,axiom,
! [X3,X5] : c_List_Olist_OCons(X3,c_List_Olist_ONil,X5) = c_List_Orev(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f9349,plain,
spl0_1167,
inference(avatar_split_clause,[],[f572,f9347]) ).
fof(f9347,plain,
( spl0_1167
<=> ! [X2,X5,X3] : c_List_Oreplicate(X2,X3,X5) = c_List_Orev(c_List_Oreplicate(X2,X3,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f572,axiom,
! [X2,X3,X5] : c_List_Oreplicate(X2,X3,X5) = c_List_Orev(c_List_Oreplicate(X2,X3,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9345,plain,
spl0_1166,
inference(avatar_split_clause,[],[f553,f9343]) ).
fof(f9343,plain,
( spl0_1166
<=> ! [X35,X6,X3,X1] :
( ~ c_List_Oop_Amem(X3,X35,X6)
| c_List_Oop_Amem(X3,c_List_Olist_OCons(X1,X35,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f553,axiom,
! [X3,X1,X6,X35] :
( ~ c_List_Oop_Amem(X3,X35,X6)
| c_List_Oop_Amem(X3,c_List_Olist_OCons(X1,X35,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9341,plain,
spl0_1165,
inference(avatar_split_clause,[],[f454,f9339]) ).
fof(f9339,plain,
( spl0_1165
<=> ! [X45,X17] : c_Nat_Osize(c_List_Oupt(X17,X45),tc_List_Olist(tc_nat)) = c_minus(X45,X17,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f454,axiom,
! [X45,X17] : c_Nat_Osize(c_List_Oupt(X17,X45),tc_List_Olist(tc_nat)) = c_minus(X45,X17,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9337,plain,
spl0_1164,
inference(avatar_split_clause,[],[f450,f9335]) ).
fof(f9335,plain,
( spl0_1164
<=> ! [X34,X5] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate1(X34,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f450,axiom,
! [X34,X5] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orotate1(X34,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9333,plain,
spl0_1163,
inference(avatar_split_clause,[],[f449,f9331]) ).
fof(f9331,plain,
( spl0_1163
<=> ! [X34,X5] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orev(X34,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f449,axiom,
! [X34,X5] : c_Nat_Osize(X34,tc_List_Olist(X5)) = c_Nat_Osize(c_List_Orev(X34,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9329,plain,
( spl0_1162
| ~ spl0_68
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8065,f7824,f3492,f9327]) ).
fof(f9327,plain,
( spl0_1162
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f3492,plain,
( spl0_68
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f7824,plain,
( spl0_918
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X1,c_1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f8065,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_68
| ~ spl0_918 ),
inference(resolution,[],[f7825,f3494]) ).
fof(f3494,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_68 ),
inference(avatar_component_clause,[],[f3492]) ).
fof(f7825,plain,
( ! [X1,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X1,c_1,X5) = X1 )
| ~ spl0_918 ),
inference(avatar_component_clause,[],[f7824]) ).
fof(f9325,plain,
spl0_1161,
inference(avatar_split_clause,[],[f436,f9323]) ).
fof(f9323,plain,
( spl0_1161
<=> ! [X34,X5,X1] : c_List_Olast(c_append(X34,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f436,axiom,
! [X1,X34,X5] : c_List_Olast(c_append(X34,c_List_Olist_OCons(X1,c_List_Olist_ONil,X5),X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9321,plain,
spl0_1160,
inference(avatar_split_clause,[],[f435,f9319]) ).
fof(f9319,plain,
( spl0_1160
<=> ! [X2,X5,X1] :
( c_0 = X2
| c_List_Olast(c_List_Oreplicate(X2,X1,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f435,axiom,
! [X2,X1,X5] :
( c_0 = X2
| c_List_Olast(c_List_Oreplicate(X2,X1,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9317,plain,
spl0_1159,
inference(avatar_split_clause,[],[f434,f9315]) ).
fof(f9315,plain,
( spl0_1159
<=> ! [X5,X46] :
( c_List_Olist_ONil = X46
| c_in(c_List_Olast(X46,X5),c_List_Oset(X46,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f434,axiom,
! [X46,X5] :
( c_List_Olist_ONil = X46
| c_in(c_List_Olast(X46,X5),c_List_Oset(X46,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9313,plain,
spl0_1158,
inference(avatar_split_clause,[],[f425,f9311]) ).
fof(f425,axiom,
! [X1,X45] :
( ~ c_less(X1,X45,tc_nat)
| c_List_Ohd(c_List_Oupt(X1,X45),tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9309,plain,
spl0_1157,
inference(avatar_split_clause,[],[f424,f9307]) ).
fof(f9307,plain,
( spl0_1157
<=> ! [X2,X5,X1] :
( c_0 = X2
| c_List_Ohd(c_List_Oreplicate(X2,X1,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f424,axiom,
! [X2,X1,X5] :
( c_0 = X2
| c_List_Ohd(c_List_Oreplicate(X2,X1,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9305,plain,
spl0_1156,
inference(avatar_split_clause,[],[f423,f9303]) ).
fof(f9303,plain,
( spl0_1156
<=> ! [X34,X5] :
( c_List_Olist_ONil = X34
| c_in(c_List_Ohd(X34,X5),c_List_Oset(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f423,axiom,
! [X34,X5] :
( c_List_Olist_ONil = X34
| c_in(c_List_Ohd(X34,X5),c_List_Oset(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9301,plain,
spl0_1155,
inference(avatar_split_clause,[],[f380,f9299]) ).
fof(f9299,plain,
( spl0_1155
<=> ! [X5,X1,X3] : c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f380,axiom,
! [X3,X1,X5] : c_List_Obutlast(c_append(X1,c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9297,plain,
spl0_1154,
inference(avatar_split_clause,[],[f304,f9295]) ).
fof(f9295,plain,
( spl0_1154
<=> ! [X9,X8] :
( ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f304,axiom,
! [X8,X9] :
( ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9293,plain,
spl0_1153,
inference(avatar_split_clause,[],[f303,f9291]) ).
fof(f9291,plain,
( spl0_1153
<=> ! [X9,X8] :
( ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f303,axiom,
! [X8,X9] :
( ~ c_less(c_0,X9,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9289,plain,
spl0_1152,
inference(avatar_split_clause,[],[f296,f9287]) ).
fof(f9287,plain,
( spl0_1152
<=> ! [X9,X8] :
( ~ c_less(X9,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f296,axiom,
! [X8,X9] :
( ~ c_less(X9,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9285,plain,
( spl0_1151
| ~ spl0_19
| ~ spl0_918 ),
inference(avatar_split_clause,[],[f8064,f7824,f3247,f9283]) ).
fof(f9283,plain,
( spl0_1151
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f3247,plain,
( spl0_19
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f8064,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_19
| ~ spl0_918 ),
inference(resolution,[],[f7825,f3249]) ).
fof(f3249,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f3247]) ).
fof(f9281,plain,
spl0_1150,
inference(avatar_split_clause,[],[f295,f9279]) ).
fof(f9279,plain,
( spl0_1150
<=> ! [X9,X8] :
( ~ c_less(X9,c_0,tc_IntDef_Oint)
| c_less(X9,c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f295,axiom,
! [X8,X9] :
( ~ c_less(X9,c_0,tc_IntDef_Oint)
| c_less(X9,c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9277,plain,
spl0_1149,
inference(avatar_split_clause,[],[f259,f9275]) ).
fof(f9275,plain,
( spl0_1149
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_NatArith_Oof__nat(X2,X5) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X2,tc_IntDef_Oint),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f259,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_NatArith_Oof__nat(X2,X5) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X2,tc_IntDef_Oint),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9273,plain,
spl0_1148,
inference(avatar_split_clause,[],[f195,f9271]) ).
fof(f9271,plain,
( spl0_1148
<=> ! [X28,X30] :
( ~ c_less(X28,X30,tc_IntDef_Oint)
| c_lessequals(X28,c_minus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f195,axiom,
! [X28,X30] :
( ~ c_less(X28,X30,tc_IntDef_Oint)
| c_lessequals(X28,c_minus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9269,plain,
spl0_1147,
inference(avatar_split_clause,[],[f194,f9267]) ).
fof(f9267,plain,
( spl0_1147
<=> ! [X28,X30] :
( c_less(X28,X30,tc_IntDef_Oint)
| ~ c_lessequals(X28,c_minus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f194,axiom,
! [X28,X30] :
( c_less(X28,X30,tc_IntDef_Oint)
| ~ c_lessequals(X28,c_minus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9265,plain,
spl0_1146,
inference(avatar_split_clause,[],[f193,f9263]) ).
fof(f9263,plain,
( spl0_1146
<=> ! [X28,X30] :
( ~ c_lessequals(X28,X30,tc_IntDef_Oint)
| c_less(X28,c_plus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f193,axiom,
! [X28,X30] :
( ~ c_lessequals(X28,X30,tc_IntDef_Oint)
| c_less(X28,c_plus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9261,plain,
spl0_1145,
inference(avatar_split_clause,[],[f192,f9259]) ).
fof(f9259,plain,
( spl0_1145
<=> ! [X28,X30] :
( c_lessequals(X28,X30,tc_IntDef_Oint)
| ~ c_less(X28,c_plus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f192,axiom,
! [X28,X30] :
( c_lessequals(X28,X30,tc_IntDef_Oint)
| ~ c_less(X28,c_plus(X30,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9257,plain,
spl0_1144,
inference(avatar_split_clause,[],[f189,f9255]) ).
fof(f9255,plain,
( spl0_1144
<=> ! [X28,X30] : c_plus(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X30,X28,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f189,axiom,
! [X28,X30] : c_plus(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X30,X28,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f9252,plain,
spl0_1143,
inference(avatar_split_clause,[],[f186,f9250]) ).
fof(f186,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9248,plain,
spl0_1142,
inference(avatar_split_clause,[],[f151,f9246]) ).
fof(f9246,plain,
( spl0_1142
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f151,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9244,plain,
spl0_1141,
inference(avatar_split_clause,[],[f148,f9242]) ).
fof(f9242,plain,
( spl0_1141
<=> ! [X2,X1] : c_GCD_Ogcd(c_Pair(X1,c_times(X1,X2,tc_nat),tc_nat,tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f148,axiom,
! [X2,X1] : c_GCD_Ogcd(c_Pair(X1,c_times(X1,X2,tc_nat),tc_nat,tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9240,plain,
( spl0_1140
| ~ spl0_68
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8063,f7820,f3492,f9238]) ).
fof(f9238,plain,
( spl0_1140
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f7820,plain,
( spl0_917
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f8063,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_68
| ~ spl0_917 ),
inference(resolution,[],[f7821,f3494]) ).
fof(f7821,plain,
( ! [X1,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X1,X5) = X1 )
| ~ spl0_917 ),
inference(avatar_component_clause,[],[f7820]) ).
fof(f9236,plain,
spl0_1139,
inference(avatar_split_clause,[],[f77,f9234]) ).
fof(f9234,plain,
( spl0_1139
<=> ! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f77,axiom,
! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9232,plain,
spl0_1138,
inference(avatar_split_clause,[],[f75,f9230]) ).
fof(f9230,plain,
( spl0_1138
<=> ! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f75,axiom,
! [X2,X18] :
( ~ c_less(c_0,X2,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9228,plain,
spl0_1137,
inference(avatar_split_clause,[],[f19,f9226]) ).
fof(f19,axiom,
! [X10,X8,X9,X5] : c_0 = c_Nat_Osize(c_Pair(X8,X9,X5,X10),tc_prod(X5,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9224,plain,
spl0_1136,
inference(avatar_split_clause,[],[f7,f9222]) ).
fof(f9222,plain,
( spl0_1136
<=> ! [X4,X5,X3] :
( c_Datatype_Ooption_OSome(X3,X5) = X4
| ~ c_in(X3,c_Datatype_Oo2s(X4,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f7,axiom,
! [X3,X4,X5] :
( c_Datatype_Ooption_OSome(X3,X5) = X4
| ~ c_in(X3,c_Datatype_Oo2s(X4,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9206,plain,
( spl0_1135
| ~ spl0_19
| ~ spl0_917 ),
inference(avatar_split_clause,[],[f8062,f7820,f3247,f9204]) ).
fof(f9204,plain,
( spl0_1135
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f8062,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_19
| ~ spl0_917 ),
inference(resolution,[],[f7821,f3249]) ).
fof(f9191,plain,
( spl0_1134
| ~ spl0_13
| ~ spl0_916 ),
inference(avatar_split_clause,[],[f8061,f7816,f3217,f9189]) ).
fof(f9189,plain,
( spl0_1134
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f7816,plain,
( spl0_916
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X8,X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f8061,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_13
| ~ spl0_916 ),
inference(resolution,[],[f7817,f3219]) ).
fof(f7817,plain,
( ! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X8,X8,X5) )
| ~ spl0_916 ),
inference(avatar_component_clause,[],[f7816]) ).
fof(f9166,plain,
( spl0_1133
| ~ spl0_13
| ~ spl0_915 ),
inference(avatar_split_clause,[],[f8060,f7812,f3217,f9164]) ).
fof(f9164,plain,
( spl0_1133
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f7812,plain,
( spl0_915
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X1,c_0,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f8060,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_13
| ~ spl0_915 ),
inference(resolution,[],[f7813,f3219]) ).
fof(f7813,plain,
( ! [X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X1,c_0,X5) = X1 )
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f7812]) ).
fof(f9108,plain,
( spl0_1132
| ~ spl0_56
| ~ spl0_1006
| ~ spl0_1079 ),
inference(avatar_split_clause,[],[f8795,f8792,f8298,f3432,f9106]) ).
fof(f9106,plain,
( spl0_1132
<=> ! [X8] : c_uminus(X8,tc_IntDef_Oint) = c_div(X8,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f8792,plain,
( spl0_1079
<=> ! [X8] : c_div(X8,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X8,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f8795,plain,
( ! [X8] : c_uminus(X8,tc_IntDef_Oint) = c_div(X8,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_1006
| ~ spl0_1079 ),
inference(forward_demodulation,[],[f8793,f8596]) ).
fof(f8793,plain,
( ! [X8] : c_div(X8,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X8,tc_IntDef_Oint)
| ~ spl0_1079 ),
inference(avatar_component_clause,[],[f8792]) ).
fof(f9088,plain,
( spl0_1131
| spl0_668
| ~ spl0_1065 ),
inference(avatar_split_clause,[],[f9045,f8736,f6705,f9085]) ).
fof(f8736,plain,
( spl0_1065
<=> ! [X20,X5] :
( c_0 = c_Finite__Set_Ocard(X20,X5)
| c_in(X20,c_Finite__Set_OFinites,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f9045,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_668
| ~ spl0_1065 ),
inference(resolution,[],[f8737,f6707]) ).
fof(f8737,plain,
( ! [X5,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X5))
| c_0 = c_Finite__Set_Ocard(X20,X5) )
| ~ spl0_1065 ),
inference(avatar_component_clause,[],[f8736]) ).
fof(f9020,plain,
( spl0_1130
| ~ spl0_113
| ~ spl0_1114
| ~ spl0_1123 ),
inference(avatar_split_clause,[],[f8981,f8972,f8934,f3711,f9017]) ).
fof(f9017,plain,
( spl0_1130
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f8972,plain,
( spl0_1123
<=> ! [X2] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f8981,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1114
| ~ spl0_1123 ),
inference(forward_demodulation,[],[f8980,f8935]) ).
fof(f8980,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_1123 ),
inference(superposition,[],[f8973,f3713]) ).
fof(f8973,plain,
( ! [X2] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1123 ),
inference(avatar_component_clause,[],[f8972]) ).
fof(f9001,plain,
spl0_1129,
inference(avatar_split_clause,[],[f3103,f8999]) ).
fof(f8999,plain,
( spl0_1129
<=> ! [X5,X3] :
( c_IntDef_Oiszero(c_0,X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f3103,plain,
! [X3,X5] :
( c_IntDef_Oiszero(c_0,X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X3,X5) ),
inference(inner_rewriting,[],[f3102]) ).
fof(f3102,plain,
! [X3,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X3,X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X3,X5) ),
inference(forward_demodulation,[],[f3101,f956]) ).
fof(f3101,plain,
! [X3,X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X5),X5)
| ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X3,X5) ),
inference(forward_demodulation,[],[f2910,f2744]) ).
fof(f2910,plain,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X5),X5) ),
inference(definition_unfolding,[],[f178,f970]) ).
fof(f178,axiom,
! [X3,X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 != c_Numeral_Onumber__of(X3,X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f8997,plain,
spl0_1128,
inference(avatar_split_clause,[],[f2988,f8995]) ).
fof(f8995,plain,
( spl0_1128
<=> ! [X5,X11,X10] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f2988,plain,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10),
inference(forward_demodulation,[],[f2790,f2745]) ).
fof(f2790,plain,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10),
inference(definition_unfolding,[],[f50,f1385]) ).
fof(f50,axiom,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X11,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f8993,plain,
spl0_1127,
inference(avatar_split_clause,[],[f2987,f8991]) ).
fof(f8991,plain,
( spl0_1127
<=> ! [X5,X11,X10] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f2987,plain,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10),
inference(forward_demodulation,[],[f2789,f2745]) ).
fof(f2789,plain,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10),
inference(definition_unfolding,[],[f51,f1385]) ).
fof(f51,axiom,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X11,X5,X10),X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f8989,plain,
spl0_1126,
inference(avatar_split_clause,[],[f2861,f8987]) ).
fof(f8987,plain,
( spl0_1126
<=> ! [X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X3,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f2861,plain,
! [X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X3,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1120,f1385]) ).
fof(f1120,axiom,
! [X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f8985,plain,
spl0_1125,
inference(avatar_split_clause,[],[f2851,f8983]) ).
fof(f8983,plain,
( spl0_1125
<=> ! [X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X3,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f2851,plain,
! [X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X3,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1119,f1385]) ).
fof(f1119,axiom,
! [X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X3),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f8978,plain,
( spl0_1124
| ~ spl0_8
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8058,f7808,f3192,f8976]) ).
fof(f8976,plain,
( spl0_1124
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f3192,plain,
( spl0_8
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f7808,plain,
( spl0_914
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f8058,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_8
| ~ spl0_914 ),
inference(resolution,[],[f7809,f3194]) ).
fof(f3194,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f3192]) ).
fof(f7809,plain,
( ! [X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X1,X5) = X1 )
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f7808]) ).
fof(f8974,plain,
( spl0_1123
| ~ spl0_1122 ),
inference(avatar_split_clause,[],[f8970,f8967,f8972]) ).
fof(f8967,plain,
( spl0_1122
<=> ! [X2] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f8970,plain,
( ! [X2] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X2),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1122 ),
inference(forward_demodulation,[],[f8968,f2781]) ).
fof(f8968,plain,
( ! [X2] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1122 ),
inference(avatar_component_clause,[],[f8967]) ).
fof(f8969,plain,
spl0_1122,
inference(avatar_split_clause,[],[f2772,f8967]) ).
fof(f2772,plain,
! [X2] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f229,f1385]) ).
fof(f229,axiom,
! [X2] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X2)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f8965,plain,
( spl0_1121
| ~ spl0_796
| ~ spl0_1120 ),
inference(avatar_split_clause,[],[f8961,f8958,f7257,f8963]) ).
fof(f8963,plain,
( spl0_1121
<=> ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f8958,plain,
( spl0_1120
<=> ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X5,X5)),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f8961,plain,
( ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X5)
| ~ spl0_796
| ~ spl0_1120 ),
inference(forward_demodulation,[],[f8959,f7258]) ).
fof(f8959,plain,
( ! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X5,X5)),X5)
| ~ spl0_1120 ),
inference(avatar_component_clause,[],[f8958]) ).
fof(f8960,plain,
spl0_1120,
inference(avatar_split_clause,[],[f2746,f8958]) ).
fof(f2746,plain,
! [X5] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X5,X5)),X5),
inference(definition_unfolding,[],[f1550,f1557]) ).
fof(f1550,axiom,
! [X5] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f8956,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1673,f8954]) ).
fof(f8954,plain,
( spl0_1119
<=> ! [X9,X5,X8] :
( X8 = X9
| ~ c_in(X9,c_insert(X8,c_emptyset,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1673,axiom,
! [X8,X9,X5] :
( X8 = X9
| ~ c_in(X9,c_insert(X8,c_emptyset,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8952,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1671,f8950]) ).
fof(f8950,plain,
( spl0_1118
<=> ! [X20,X5,X24] :
( ~ c_less(X20,X24,tc_set(X5))
| c_lessequals(X20,X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1671,axiom,
! [X24,X5,X20] :
( ~ c_less(X20,X24,tc_set(X5))
| c_lessequals(X20,X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8948,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1670,f8946]) ).
fof(f8946,plain,
( spl0_1117
<=> ! [X20,X5,X24] :
( ~ c_lessequals(X24,X20,tc_set(X5))
| ~ c_less(X20,X24,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1670,axiom,
! [X24,X5,X20] :
( ~ c_lessequals(X24,X20,tc_set(X5))
| ~ c_less(X20,X24,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8944,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1512,f8942]) ).
fof(f8942,plain,
( spl0_1116
<=> ! [X20,X5] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X20,X5)
| c_emptyset = c_Union(X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1512,axiom,
! [X5,X20] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X20,X5)
| c_emptyset = c_Union(X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f8940,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1495,f8938]) ).
fof(f8938,plain,
( spl0_1115
<=> ! [X20,X5] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X20,X5)
| c_emptyset = c_Union(X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1495,axiom,
! [X5,X20] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X20,X5)
| c_emptyset = c_Union(X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f8936,plain,
( spl0_1114
| ~ spl0_8
| ~ spl0_913 ),
inference(avatar_split_clause,[],[f8056,f7804,f3192,f8934]) ).
fof(f7804,plain,
( spl0_913
<=> ! [X5,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X1,c_0,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f8056,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_8
| ~ spl0_913 ),
inference(resolution,[],[f7805,f3194]) ).
fof(f7805,plain,
( ! [X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X1,c_0,X5) = X1 )
| ~ spl0_913 ),
inference(avatar_component_clause,[],[f7804]) ).
fof(f8932,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1459,f8930]) ).
fof(f8930,plain,
( spl0_1113
<=> ! [X20,X5] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X20,X5)
| c_UNIV = c_Inter(X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1459,axiom,
! [X5,X20] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X20,X5)
| c_UNIV = c_Inter(X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f8928,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1456,f8926]) ).
fof(f8926,plain,
( spl0_1112
<=> ! [X20,X5] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X20,X5)
| c_UNIV = c_Inter(X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1456,axiom,
! [X5,X20] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X20,X5)
| c_UNIV = c_Inter(X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f8924,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1229,f8922]) ).
fof(f1229,axiom,
! [X3,X5] : c_in(c_Pair(X3,X3,X5,X5),c_Relation_OId,tc_prod(X5,X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f8920,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1224,f8918]) ).
fof(f1224,axiom,
! [X5,X20] : c_Relation_Odiag(X20,X5) = c_Relation_Oconverse(c_Relation_Odiag(X20,X5),X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f8916,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1207,f8914]) ).
fof(f1207,axiom,
! [X10,X1,X8,X5] : c_snd(c_Pair(X8,X1,X10,X5),X10,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f8912,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1205,f8910]) ).
fof(f1205,axiom,
! [X10,X1,X9,X5] : c_fst(c_Pair(X1,X9,X5,X10),X5,X10) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f8908,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1183,f8906]) ).
fof(f8906,plain,
( spl0_1107
<=> ! [X2,X3] :
( c_0 = X3
| c_less(c_0,c_Nat_Opower(X3,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1183,axiom,
! [X2,X3] :
( c_0 = X3
| c_less(c_0,c_Nat_Opower(X3,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f8904,plain,
spl0_1106,
inference(avatar_split_clause,[],[f1182,f8902]) ).
fof(f8902,plain,
( spl0_1106
<=> ! [X2] :
( c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_0,X2,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f1182,axiom,
! [X2] :
( c_0 = X2
| ~ c_less(c_0,c_Nat_Opower(c_0,X2,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f8900,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1135,f8898]) ).
fof(f8898,plain,
( spl0_1105
<=> ! [X2,X3] :
( c_less(c_0,X2,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X2,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1135,axiom,
! [X2,X3] :
( c_less(c_0,X2,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f8896,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1122,f8894]) ).
fof(f8894,plain,
( spl0_1104
<=> ! [X1,X3] :
( c_less(c_0,X1,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1122,axiom,
! [X3,X1] :
( c_less(c_0,X1,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f8892,plain,
( spl0_1103
| ~ spl0_699
| ~ spl0_866
| ~ spl0_909 ),
inference(avatar_split_clause,[],[f8045,f7788,f7541,f6847,f8889]) ).
fof(f8889,plain,
( spl0_1103
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f7788,plain,
( spl0_909
<=> ! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X28,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f8045,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_699
| ~ spl0_866
| ~ spl0_909 ),
inference(forward_demodulation,[],[f8043,f6849]) ).
fof(f8043,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_866
| ~ spl0_909 ),
inference(superposition,[],[f7789,f7543]) ).
fof(f7789,plain,
( ! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X28,c_Numeral_Obit_OB0))
| ~ spl0_909 ),
inference(avatar_component_clause,[],[f7788]) ).
fof(f8887,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1088,f8885]) ).
fof(f8885,plain,
( spl0_1102
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(X8,c_uminus(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1088,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(X8,c_uminus(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f8883,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1060,f8881]) ).
fof(f8881,plain,
( spl0_1101
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = X8
| c_0 != c_uminus(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1060,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = X8
| c_0 != c_uminus(X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
fof(f8879,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1054,f8877]) ).
fof(f8877,plain,
( spl0_1100
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1054,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f8875,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1052,f8873]) ).
fof(f8873,plain,
( spl0_1099
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1052,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f8871,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1038,f8869]) ).
fof(f8869,plain,
( spl0_1098
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(X8,X5) = c_minus(c_0,X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1038,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(X8,X5) = c_minus(c_0,X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f8867,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1016,f8865]) ).
fof(f8865,plain,
( spl0_1097
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X8
| c_0 != c_HOL_Oabs(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1016,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = X8
| c_0 != c_HOL_Oabs(X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f8863,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1012,f8861]) ).
fof(f8861,plain,
( spl0_1096
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(c_uminus(X8,X5),X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1012,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_plus(c_uminus(X8,X5),X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f8859,plain,
spl0_1095,
inference(avatar_split_clause,[],[f880,f8857]) ).
fof(f8857,plain,
( spl0_1095
<=> ! [X2,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_0 = c_minus(X18,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f880,axiom,
! [X2,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_0 = c_minus(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f8855,plain,
spl0_1094,
inference(avatar_split_clause,[],[f879,f8853]) ).
fof(f879,axiom,
! [X2,X18] :
( c_lessequals(X18,X2,tc_nat)
| c_0 != c_minus(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f8851,plain,
spl0_1093,
inference(avatar_split_clause,[],[f690,f8849]) ).
fof(f690,axiom,
! [X29] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X29,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f8847,plain,
( spl0_1092
| ~ spl0_86
| ~ spl0_889 ),
inference(avatar_split_clause,[],[f8022,f7706,f3582,f8845]) ).
fof(f8845,plain,
( spl0_1092
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f3582,plain,
( spl0_86
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f7706,plain,
( spl0_889
<=> ! [X5,X1] :
( ~ class_LOrder_Omeet__semilorder(X5)
| c_LOrder_Omeet(X1,X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f8022,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_86
| ~ spl0_889 ),
inference(resolution,[],[f7707,f3584]) ).
fof(f3584,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_86 ),
inference(avatar_component_clause,[],[f3582]) ).
fof(f7707,plain,
( ! [X1,X5] :
( ~ class_LOrder_Omeet__semilorder(X5)
| c_LOrder_Omeet(X1,X1,X5) = X1 )
| ~ spl0_889 ),
inference(avatar_component_clause,[],[f7706]) ).
fof(f8843,plain,
spl0_1091,
inference(avatar_split_clause,[],[f673,f8841]) ).
fof(f8841,plain,
( spl0_1091
<=> ! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X29,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f673,axiom,
! [X29] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X29,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X29,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f8839,plain,
spl0_1090,
inference(avatar_split_clause,[],[f652,f8837]) ).
fof(f8837,plain,
( spl0_1090
<=> ! [X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X18
| c_0 != c_NatArith_Oof__nat(X18,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f652,axiom,
! [X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = X18
| c_0 != c_NatArith_Oof__nat(X18,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
fof(f8835,plain,
spl0_1089,
inference(avatar_split_clause,[],[f600,f8833]) ).
fof(f8833,plain,
( spl0_1089
<=> ! [X34,X5,X2] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Orotate(X2,X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f600,axiom,
! [X2,X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Orotate(X2,X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f8831,plain,
spl0_1088,
inference(avatar_split_clause,[],[f571,f8829]) ).
fof(f8829,plain,
( spl0_1088
<=> ! [X34,X5,X35] :
( X34 = X35
| c_List_Orev(X34,X5) != c_List_Orev(X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f571,axiom,
! [X34,X35,X5] :
( X34 = X35
| c_List_Orev(X34,X5) != c_List_Orev(X35,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f8827,plain,
spl0_1087,
inference(avatar_split_clause,[],[f444,f8825]) ).
fof(f8825,plain,
( spl0_1087
<=> ! [X34,X5] :
( c_List_Olist_ONil = X34
| c_less(c_0,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f444,axiom,
! [X34,X5] :
( c_List_Olist_ONil = X34
| c_less(c_0,c_Nat_Osize(X34,tc_List_Olist(X5)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f8823,plain,
spl0_1086,
inference(avatar_split_clause,[],[f389,f8821]) ).
fof(f8821,plain,
( spl0_1086
<=> ! [X36,X5] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X36,X5)
| c_List_Olist_ONil = c_List_Oconcat(X36,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f389,axiom,
! [X36,X5] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X36,X5)
| c_List_Olist_ONil = c_List_Oconcat(X36,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f8819,plain,
spl0_1085,
inference(avatar_split_clause,[],[f382,f8817]) ).
fof(f8817,plain,
( spl0_1085
<=> ! [X41,X43,X40,X42] :
( X41 = X43
| c_List_Ochar_OChar(X40,X41) != c_List_Ochar_OChar(X42,X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f382,axiom,
! [X40,X41,X42,X43] :
( X41 = X43
| c_List_Ochar_OChar(X40,X41) != c_List_Ochar_OChar(X42,X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f8815,plain,
spl0_1084,
inference(avatar_split_clause,[],[f381,f8813]) ).
fof(f8813,plain,
( spl0_1084
<=> ! [X41,X40,X42,X43] :
( X40 = X42
| c_List_Ochar_OChar(X40,X41) != c_List_Ochar_OChar(X42,X43) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f381,axiom,
! [X40,X41,X42,X43] :
( X40 = X42
| c_List_Ochar_OChar(X40,X41) != c_List_Ochar_OChar(X42,X43) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f8811,plain,
spl0_1083,
inference(avatar_split_clause,[],[f350,f8809]) ).
fof(f8809,plain,
( spl0_1083
<=> ! [X36,X5] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X36,X5)
| c_List_Olist_ONil = c_List_Oconcat(X36,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f350,axiom,
! [X36,X5] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X36,X5)
| c_List_Olist_ONil = c_List_Oconcat(X36,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f8807,plain,
spl0_1082,
inference(avatar_split_clause,[],[f329,f8805]) ).
fof(f8805,plain,
( spl0_1082
<=> ! [X28,X30] :
( ~ c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X30,tc_IntDef_Oint),X28,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f329,axiom,
! [X28,X30] :
( ~ c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X30,tc_IntDef_Oint),X28,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f8803,plain,
( spl0_1081
| ~ spl0_28
| ~ spl0_889 ),
inference(avatar_split_clause,[],[f8021,f7706,f3292,f8801]) ).
fof(f8801,plain,
( spl0_1081
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f3292,plain,
( spl0_28
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f8021,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_889 ),
inference(resolution,[],[f7707,f3294]) ).
fof(f3294,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3292]) ).
fof(f8799,plain,
spl0_1080,
inference(avatar_split_clause,[],[f328,f8797]) ).
fof(f328,axiom,
! [X28,X30] :
( c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X30,tc_IntDef_Oint),X28,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f8794,plain,
spl0_1079,
inference(avatar_split_clause,[],[f308,f8792]) ).
fof(f308,axiom,
! [X8] : c_div(X8,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X8,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f8790,plain,
spl0_1078,
inference(avatar_split_clause,[],[f281,f8788]) ).
fof(f8788,plain,
( spl0_1078
<=> ! [X28,X30] :
( ~ c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f281,axiom,
! [X28,X30] :
( ~ c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f8786,plain,
spl0_1077,
inference(avatar_split_clause,[],[f280,f8784]) ).
fof(f280,axiom,
! [X28,X30] :
( c_Divides_Oop_Advd(X30,X28,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X30,c_uminus(X28,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f8782,plain,
spl0_1076,
inference(avatar_split_clause,[],[f271,f8780]) ).
fof(f8780,plain,
( spl0_1076
<=> ! [X28,X30] :
( c_less(X28,X30,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X28),c_IntDef_Onat(X30),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f271,axiom,
! [X28,X30] :
( c_less(X28,X30,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X28),c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f8778,plain,
spl0_1075,
inference(avatar_split_clause,[],[f270,f8776]) ).
fof(f8776,plain,
( spl0_1075
<=> ! [X28,X30] :
( c_less(c_0,X30,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X28),c_IntDef_Onat(X30),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f270,axiom,
! [X28,X30] :
( c_less(c_0,X30,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X28),c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f8774,plain,
spl0_1074,
inference(avatar_split_clause,[],[f269,f8772]) ).
fof(f8772,plain,
( spl0_1074
<=> ! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f269,axiom,
! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_less(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f8770,plain,
spl0_1073,
inference(avatar_split_clause,[],[f268,f8768]) ).
fof(f8768,plain,
( spl0_1073
<=> ! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f268,axiom,
! [X2,X18] :
( c_less(X18,X2,tc_nat)
| ~ c_less(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f8766,plain,
spl0_1072,
inference(avatar_split_clause,[],[f267,f8764]) ).
fof(f8764,plain,
( spl0_1072
<=> ! [X2,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f267,axiom,
! [X2,X18] :
( ~ c_lessequals(X18,X2,tc_nat)
| c_lessequals(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f8762,plain,
spl0_1071,
inference(avatar_split_clause,[],[f266,f8760]) ).
fof(f8760,plain,
( spl0_1071
<=> ! [X2,X18] :
( c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f266,axiom,
! [X2,X18] :
( c_lessequals(X18,X2,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X18),c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f8758,plain,
( spl0_1070
| ~ spl0_93
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f8020,f7702,f3617,f8756]) ).
fof(f8756,plain,
( spl0_1070
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f3617,plain,
( spl0_93
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f7702,plain,
( spl0_888
<=> ! [X5,X1] :
( ~ class_LOrder_Ojoin__semilorder(X5)
| c_LOrder_Ojoin(X1,X1,X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f8020,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_93
| ~ spl0_888 ),
inference(resolution,[],[f7703,f3619]) ).
fof(f3619,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f3617]) ).
fof(f7703,plain,
( ! [X1,X5] :
( ~ class_LOrder_Ojoin__semilorder(X5)
| c_LOrder_Ojoin(X1,X1,X5) = X1 )
| ~ spl0_888 ),
inference(avatar_component_clause,[],[f7702]) ).
fof(f8754,plain,
spl0_1069,
inference(avatar_split_clause,[],[f248,f8752]) ).
fof(f8752,plain,
( spl0_1069
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_IntDef_Oint(X2),X5) = c_NatArith_Oof__nat(X2,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f248,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_IntDef_Oof__int(c_IntDef_Oint(X2),X5) = c_NatArith_Oof__nat(X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f8750,plain,
spl0_1068,
inference(avatar_split_clause,[],[f245,f8748]) ).
fof(f8748,plain,
( spl0_1068
<=> ! [X5,X28] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X28
| c_0 != c_IntDef_Oof__int(X28,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f245,axiom,
! [X28,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = X28
| c_0 != c_IntDef_Oof__int(X28,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
fof(f8746,plain,
spl0_1067,
inference(avatar_split_clause,[],[f231,f8744]) ).
fof(f8744,plain,
( spl0_1067
<=> ! [X18,X2] :
( c_0 = X18
| c_IntDef_Oint(X18) != c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f231,axiom,
! [X2,X18] :
( c_0 = X18
| c_IntDef_Oint(X18) != c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f8742,plain,
spl0_1066,
inference(avatar_split_clause,[],[f230,f8740]) ).
fof(f8740,plain,
( spl0_1066
<=> ! [X2,X18] :
( c_0 = X2
| c_IntDef_Oint(X18) != c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f230,axiom,
! [X2,X18] :
( c_0 = X2
| c_IntDef_Oint(X18) != c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8738,plain,
spl0_1065,
inference(avatar_split_clause,[],[f120,f8736]) ).
fof(f120,axiom,
! [X5,X20] :
( c_0 = c_Finite__Set_Ocard(X20,X5)
| c_in(X20,c_Finite__Set_OFinites,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8734,plain,
spl0_1064,
inference(avatar_split_clause,[],[f116,f8732]) ).
fof(f8732,plain,
( spl0_1064
<=> ! [X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMin(c_insert(X1,c_emptyset,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f116,axiom,
! [X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMin(c_insert(X1,c_emptyset,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8730,plain,
spl0_1063,
inference(avatar_split_clause,[],[f106,f8728]) ).
fof(f8728,plain,
( spl0_1063
<=> ! [X5,X1] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMax(c_insert(X1,c_emptyset,X5),X5) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f106,axiom,
! [X1,X5] :
( ~ class_Orderings_Olinorder(X5)
| c_Finite__Set_OMax(c_insert(X1,c_emptyset,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8726,plain,
spl0_1062,
inference(avatar_split_clause,[],[f76,f8724]) ).
fof(f8724,plain,
( spl0_1062
<=> ! [X2,X1] :
( ~ c_less(X1,X2,tc_nat)
| c_Divides_Oop_Amod(X1,X2,tc_nat) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f76,axiom,
! [X2,X1] :
( ~ c_less(X1,X2,tc_nat)
| c_Divides_Oop_Amod(X1,X2,tc_nat) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8722,plain,
spl0_1061,
inference(avatar_split_clause,[],[f65,f8720]) ).
fof(f8720,plain,
( spl0_1061
<=> ! [X2] :
( ~ c_less(c_0,X2,tc_nat)
| c_1 = c_div(X2,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f65,axiom,
! [X2] :
( ~ c_less(c_0,X2,tc_nat)
| c_1 = c_div(X2,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8718,plain,
spl0_1060,
inference(avatar_split_clause,[],[f57,f8716]) ).
fof(f8716,plain,
( spl0_1060
<=> ! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_0 = c_div(X18,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f57,axiom,
! [X2,X18] :
( ~ c_less(X18,X2,tc_nat)
| c_0 = c_div(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8713,plain,
spl0_1059,
inference(avatar_split_clause,[],[f42,f8711]) ).
fof(f8711,plain,
( spl0_1059
<=> ! [X5,X10,X11,X0,X12] : c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_ONumb(X0,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f42,axiom,
! [X10,X0,X11,X5,X12] : c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_ONumb(X0,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb_0) ).
fof(f8709,plain,
spl0_1058,
inference(avatar_split_clause,[],[f35,f8707]) ).
fof(f8707,plain,
( spl0_1058
<=> ! [X11,X10,X12,X5,X8] : c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_OLeaf(X8,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f35,axiom,
! [X10,X11,X8,X5,X12] : c_Datatype__Universe_OScons(X11,X12,X5,X10) != c_Datatype__Universe_OLeaf(X8,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons_0) ).
fof(f8705,plain,
spl0_1057,
inference(avatar_split_clause,[],[f27,f8703]) ).
fof(f8703,plain,
( spl0_1057
<=> ! [X10,X11,X12,X5,X8] : c_Datatype__Universe_OAtom(X8,X5,X10) != c_Datatype__Universe_OScons(X11,X12,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f27,axiom,
! [X10,X11,X8,X5,X12] : c_Datatype__Universe_OAtom(X8,X5,X10) != c_Datatype__Universe_OScons(X11,X12,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f8701,plain,
spl0_1056,
inference(avatar_split_clause,[],[f21,f8699]) ).
fof(f8699,plain,
( spl0_1056
<=> ! [X9,X5,X10] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X9,X10,X5),tc_sum(X5,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f21,axiom,
! [X10,X9,X5] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X9,X10,X5),tc_sum(X5,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8697,plain,
spl0_1055,
inference(avatar_split_clause,[],[f20,f8695]) ).
fof(f8695,plain,
( spl0_1055
<=> ! [X5,X8,X10] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X8,X5,X10),tc_sum(X5,X10)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f20,axiom,
! [X10,X8,X5] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X8,X5,X10),tc_sum(X5,X10)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8693,plain,
spl0_1054,
inference(avatar_split_clause,[],[f16,f8691]) ).
fof(f8691,plain,
( spl0_1054
<=> ! [X5,X8,X7] :
( X7 = X8
| c_Datatype_Ooption_OSome(X7,X5) != c_Datatype_Ooption_OSome(X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f16,axiom,
! [X8,X7,X5] :
( X7 = X8
| c_Datatype_Ooption_OSome(X7,X5) != c_Datatype_Ooption_OSome(X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8689,plain,
spl0_1053,
inference(avatar_split_clause,[],[f11,f8687]) ).
fof(f8687,plain,
( spl0_1053
<=> ! [X6,X3] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X3,X6),X6) = c_insert(X3,c_emptyset,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f11,axiom,
! [X3,X6] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X3,X6),X6) = c_insert(X3,c_emptyset,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8685,plain,
spl0_1052,
inference(avatar_split_clause,[],[f10,f8683]) ).
fof(f8683,plain,
( spl0_1052
<=> ! [X5,X3] :
( c_Datatype_Ooption_ONone = X3
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X3,X5),X5) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f10,axiom,
! [X3,X5] :
( c_Datatype_Ooption_ONone = X3
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X3,X5),X5) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8681,plain,
spl0_1051,
inference(avatar_split_clause,[],[f9,f8679]) ).
fof(f8679,plain,
( spl0_1051
<=> ! [X5,X3] :
( c_Datatype_Ooption_ONone = X3
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X3,X5),X5) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f9,axiom,
! [X3,X5] :
( c_Datatype_Ooption_ONone = X3
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X3,X5),X5) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8671,plain,
( spl0_1050
| ~ spl0_870
| ~ spl0_1003 ),
inference(avatar_split_clause,[],[f8579,f8286,f7567,f8669]) ).
fof(f8669,plain,
( spl0_1050
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f7567,plain,
( spl0_870
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f8286,plain,
( spl0_1003
<=> ! [X45,X17] :
( ~ c_lessequals(X45,X17,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,X45) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f8579,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_870
| ~ spl0_1003 ),
inference(resolution,[],[f8287,f7568]) ).
fof(f7568,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_870 ),
inference(avatar_component_clause,[],[f7567]) ).
fof(f8287,plain,
( ! [X45,X17] :
( ~ c_lessequals(X45,X17,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,X45) )
| ~ spl0_1003 ),
inference(avatar_component_clause,[],[f8286]) ).
fof(f8623,plain,
( spl0_1049
| ~ spl0_798
| ~ spl0_1020 ),
inference(avatar_split_clause,[],[f8614,f8354,f7265,f8621]) ).
fof(f8621,plain,
( spl0_1049
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f8614,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_798
| ~ spl0_1020 ),
inference(superposition,[],[f7266,f8355]) ).
fof(f8576,plain,
( spl0_1048
| ~ spl0_798
| ~ spl0_994 ),
inference(avatar_split_clause,[],[f8563,f8249,f7265,f8574]) ).
fof(f8574,plain,
( spl0_1048
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f8563,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_798
| ~ spl0_994 ),
inference(superposition,[],[f7266,f8250]) ).
fof(f8555,plain,
( spl0_1047
| ~ spl0_29
| ~ spl0_888 ),
inference(avatar_split_clause,[],[f8019,f7702,f3297,f8553]) ).
fof(f8553,plain,
( spl0_1047
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f3297,plain,
( spl0_29
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f8019,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_29
| ~ spl0_888 ),
inference(resolution,[],[f7703,f3299]) ).
fof(f3299,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f3297]) ).
fof(f8495,plain,
( ~ spl0_78
| spl0_1046
| ~ spl0_666
| ~ spl0_886 ),
inference(avatar_split_clause,[],[f8018,f7694,f6697,f8493,f3542]) ).
fof(f3542,plain,
( spl0_78
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f6697,plain,
( spl0_666
<=> ! [X1] : c_NatArith_Oof__nat(X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f7694,plain,
( spl0_886
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_NatArith_Oof__nat(X2,X5),c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f8018,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_666
| ~ spl0_886 ),
inference(superposition,[],[f7695,f6698]) ).
fof(f6698,plain,
( ! [X1] : c_NatArith_Oof__nat(X1,tc_nat) = X1
| ~ spl0_666 ),
inference(avatar_component_clause,[],[f6697]) ).
fof(f7695,plain,
( ! [X2,X5] :
( c_in(c_NatArith_Oof__nat(X2,X5),c_IntDef_ONats,X5)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5) )
| ~ spl0_886 ),
inference(avatar_component_clause,[],[f7694]) ).
fof(f8457,plain,
spl0_1045,
inference(avatar_split_clause,[],[f3056,f8455]) ).
fof(f8455,plain,
( spl0_1045
<=> ! [X30] :
( ~ c_less(c_1,c_IntDef_Onat(X30),tc_nat)
| c_less(c_1,X30,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f3056,plain,
! [X30] :
( ~ c_less(c_1,c_IntDef_Onat(X30),tc_nat)
| c_less(c_1,X30,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2880,f2745]) ).
fof(f2880,plain,
! [X30] :
( c_less(c_1,X30,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X30),tc_nat) ),
inference(definition_unfolding,[],[f187,f1385]) ).
fof(f187,axiom,
! [X30] :
( c_less(c_1,X30,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8453,plain,
spl0_1044,
inference(avatar_split_clause,[],[f3044,f8451]) ).
fof(f8451,plain,
( spl0_1044
<=> ! [X30] :
( c_less(c_1,c_IntDef_Onat(X30),tc_nat)
| ~ c_less(c_1,X30,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f3044,plain,
! [X30] :
( c_less(c_1,c_IntDef_Onat(X30),tc_nat)
| ~ c_less(c_1,X30,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2862,f2745]) ).
fof(f2862,plain,
! [X30] :
( ~ c_less(c_1,X30,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X30),tc_nat) ),
inference(definition_unfolding,[],[f188,f1385]) ).
fof(f188,axiom,
! [X30] :
( ~ c_less(c_1,X30,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8449,plain,
( spl0_1043
| ~ spl0_819
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f7633,f7512,f7352,f8447]) ).
fof(f8447,plain,
( spl0_1043
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f7352,plain,
( spl0_819
<=> ! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f7512,plain,
( spl0_859
<=> ! [X18,X0] : c_Divides_Oop_Advd(X0,c_times(X18,X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f7633,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_819
| ~ spl0_859 ),
inference(resolution,[],[f7513,f7353]) ).
fof(f7353,plain,
( ! [X18] :
( ~ c_Divides_Oop_Advd(c_0,X18,tc_IntDef_Oint)
| c_0 = X18 )
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7352]) ).
fof(f7513,plain,
( ! [X0,X18] : c_Divides_Oop_Advd(X0,c_times(X18,X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f7512]) ).
fof(f8445,plain,
spl0_1042,
inference(avatar_split_clause,[],[f3040,f8443]) ).
fof(f8443,plain,
( spl0_1042
<=> ! [X2,X18] :
( c_1 != c_times(X18,X2,tc_nat)
| c_1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f3040,plain,
! [X2,X18] :
( c_1 != c_times(X18,X2,tc_nat)
| c_1 = X2 ),
inference(forward_demodulation,[],[f2857,f2745]) ).
fof(f2857,plain,
! [X2,X18] :
( c_1 = X2
| c_times(X18,X2,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f904,f1385]) ).
fof(f904,axiom,
! [X2,X18] :
( c_1 = X2
| c_Suc(c_0) != c_times(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_1) ).
fof(f8441,plain,
spl0_1041,
inference(avatar_split_clause,[],[f3039,f8439]) ).
fof(f8439,plain,
( spl0_1041
<=> ! [X2,X18] :
( c_1 != c_times(X18,X2,tc_nat)
| c_1 = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f3039,plain,
! [X2,X18] :
( c_1 != c_times(X18,X2,tc_nat)
| c_1 = X18 ),
inference(forward_demodulation,[],[f2856,f2745]) ).
fof(f2856,plain,
! [X2,X18] :
( c_1 = X18
| c_times(X18,X2,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f903,f1385]) ).
fof(f903,axiom,
! [X2,X18] :
( c_1 = X18
| c_Suc(c_0) != c_times(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
fof(f8437,plain,
spl0_1040,
inference(avatar_split_clause,[],[f2776,f8435]) ).
fof(f2776,plain,
! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X28,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f973,f954]) ).
fof(f973,axiom,
! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X28,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8433,plain,
spl0_1039,
inference(avatar_split_clause,[],[f2765,f8431]) ).
fof(f8431,plain,
( spl0_1039
<=> ! [X5,X1] : c_Relation_OImage(c_Relation_Odiag(X1,X5),X1,X5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f2765,plain,
! [X1,X5] : c_Relation_OImage(c_Relation_Odiag(X1,X5),X1,X5,X5) = X1,
inference(definition_unfolding,[],[f1444,f1214]) ).
fof(f1444,axiom,
! [X1,X5] : c_inter(X1,X1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8429,plain,
spl0_1038,
inference(avatar_split_clause,[],[f2764,f8427]) ).
fof(f8427,plain,
( spl0_1038
<=> ! [X5,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X5),X1,X5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f2764,plain,
! [X1,X5] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X5),X1,X5,X5) = X1,
inference(definition_unfolding,[],[f1442,f1214]) ).
fof(f1442,axiom,
! [X1,X5] : c_inter(c_UNIV,X1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8425,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2763,f8423]) ).
fof(f2763,plain,
! [X1,X5] : c_Relation_OImage(c_Relation_Odiag(X1,X5),c_UNIV,X5,X5) = X1,
inference(definition_unfolding,[],[f1443,f1214]) ).
fof(f1443,axiom,
! [X1,X5] : c_inter(X1,c_UNIV,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8421,plain,
spl0_1036,
inference(avatar_split_clause,[],[f2757,f8419]) ).
fof(f8419,plain,
( spl0_1036
<=> ! [X0] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f2757,plain,
! [X0] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1,f1385]) ).
fof(f1,axiom,
! [X0] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8417,plain,
spl0_1035,
inference(avatar_split_clause,[],[f2732,f8415]) ).
fof(f8415,plain,
( spl0_1035
<=> ! [X5,X26] : c_in(c_Relation_OId,c_UNITY_OAllowedActs(X26,X5),tc_set(tc_prod(X5,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f2732,axiom,
! [X26,X5] : c_in(c_Relation_OId,c_UNITY_OAllowedActs(X26,X5),tc_set(tc_prod(X5,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_OId__in__AllowedActs_0) ).
fof(f8413,plain,
spl0_1034,
inference(avatar_split_clause,[],[f2731,f8411]) ).
fof(f8411,plain,
( spl0_1034
<=> ! [X5,X26] : c_in(c_Relation_OId,c_UNITY_OActs(X26,X5),tc_set(tc_prod(X5,X5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f2731,axiom,
! [X26,X5] : c_in(c_Relation_OId,c_UNITY_OActs(X26,X5),tc_set(tc_prod(X5,X5))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_OId__in__Acts_0) ).
fof(f8409,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1631,f8407]) ).
fof(f8407,plain,
( spl0_1033
<=> ! [X13,X5] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X13,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f1631,axiom,
! [X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X13,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8405,plain,
( spl0_1032
| ~ spl0_819
| ~ spl0_858 ),
inference(avatar_split_clause,[],[f7632,f7508,f7352,f8403]) ).
fof(f8403,plain,
( spl0_1032
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f7508,plain,
( spl0_858
<=> ! [X18,X0] : c_Divides_Oop_Advd(X0,c_times(X0,X18,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f7632,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_819
| ~ spl0_858 ),
inference(resolution,[],[f7509,f7353]) ).
fof(f7509,plain,
( ! [X0,X18] : c_Divides_Oop_Advd(X0,c_times(X0,X18,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_858 ),
inference(avatar_component_clause,[],[f7508]) ).
fof(f8401,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1630,f8399]) ).
fof(f8399,plain,
( spl0_1031
<=> ! [X13,X5] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X13,X5),tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1630,axiom,
! [X5,X13] :
( ~ c_Wellfounded__Recursion_Owf(X13,X5)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X13,X5),tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8397,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1603,f8395]) ).
fof(f8395,plain,
( spl0_1030
<=> ! [X2,X18] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1603,axiom,
! [X2,X18] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8393,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1602,f8391]) ).
fof(f8391,plain,
( spl0_1029
<=> ! [X18,X2] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1602,axiom,
! [X2,X18] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X18,X2,tc_nat,tc_nat)),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8389,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1559,f8387]) ).
fof(f8387,plain,
( spl0_1028
<=> ! [X13,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X13,X5)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X13,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f1559,axiom,
! [X5,X13] :
( ~ c_Wellfounded__Recursion_Oacyclic(X13,X5)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X13,X5,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8385,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1558,f8383]) ).
fof(f8383,plain,
( spl0_1027
<=> ! [X13,X5] :
( c_Wellfounded__Recursion_Oacyclic(X13,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X13,X5,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1558,axiom,
! [X5,X13] :
( c_Wellfounded__Recursion_Oacyclic(X13,X5)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X13,X5,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8381,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1545,f8379]) ).
fof(f8379,plain,
( spl0_1026
<=> ! [X9,X5,X8,X10] : c_Sum__Type_OInl(X8,X5,X10) != c_Sum__Type_OInr(X9,X10,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1545,axiom,
! [X10,X8,X9,X5] : c_Sum__Type_OInl(X8,X5,X10) != c_Sum__Type_OInr(X9,X10,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl_0) ).
fof(f8377,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1508,f8375]) ).
fof(f8375,plain,
( spl0_1025
<=> ! [X5,X1] : c_uminus(c_uminus(X1,tc_set(X5)),tc_set(X5)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1508,axiom,
! [X1,X5] : c_uminus(c_uminus(X1,tc_set(X5)),tc_set(X5)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8373,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1500,f8371]) ).
fof(f8371,plain,
( spl0_1024
<=> ! [X20,X5] :
( c_emptyset = X20
| c_in(c_Main_Oall__not__in__conv__1(X20,X5),X20,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1500,axiom,
! [X5,X20] :
( c_emptyset = X20
| c_in(c_Main_Oall__not__in__conv__1(X20,X5),X20,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8369,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1477,f8367]) ).
fof(f8367,plain,
( spl0_1023
<=> ! [X20,X5,X24] :
( c_emptyset = X24
| c_emptyset != c_union(X20,X24,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1477,axiom,
! [X24,X5,X20] :
( c_emptyset = X24
| c_emptyset != c_union(X20,X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8365,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1476,f8363]) ).
fof(f8363,plain,
( spl0_1022
<=> ! [X20,X5,X24] :
( c_emptyset = X20
| c_emptyset != c_union(X20,X24,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1476,axiom,
! [X24,X5,X20] :
( c_emptyset = X20
| c_emptyset != c_union(X20,X24,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8361,plain,
( spl0_1021
| ~ spl0_112
| ~ spl0_816 ),
inference(avatar_split_clause,[],[f7570,f7340,f3706,f8358]) ).
fof(f7340,plain,
( spl0_816
<=> ! [X2] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f7570,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_112
| ~ spl0_816 ),
inference(superposition,[],[f7341,f3708]) ).
fof(f7341,plain,
( ! [X2] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint))
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7340]) ).
fof(f8356,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1467,f8354]) ).
fof(f1467,axiom,
! [X5] : c_Pow(c_emptyset,X5) = c_insert(c_emptyset,c_emptyset,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8352,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1231,f8350]) ).
fof(f8350,plain,
( spl0_1019
<=> ! [X6,X72] : c_Relation_OId = c_Nat_Opower(X72,c_0,tc_set(tc_prod(X6,X6))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1231,axiom,
! [X72,X6] : c_Relation_OId = c_Nat_Opower(X72,c_0,tc_set(tc_prod(X6,X6))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8348,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1230,f8346]) ).
fof(f8346,plain,
( spl0_1018
<=> ! [X5,X1] : c_Nat_Opower(X1,c_1,tc_set(tc_prod(X5,X5))) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1230,axiom,
! [X1,X5] : c_Nat_Opower(X1,c_1,tc_set(tc_prod(X5,X5))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8344,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1223,f8342]) ).
fof(f8342,plain,
( spl0_1017
<=> ! [X5,X1,X10] : c_Relation_Oconverse(c_Relation_Oconverse(X1,X5,X10),X10,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1223,axiom,
! [X10,X1,X5] : c_Relation_Oconverse(c_Relation_Oconverse(X1,X5,X10),X10,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8340,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1139,f8338]) ).
fof(f8338,plain,
( spl0_1016
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1139,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8336,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1138,f8334]) ).
fof(f8334,plain,
( spl0_1015
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1138,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X3,X1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8332,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1134,f8330]) ).
fof(f8330,plain,
( spl0_1014
<=> ! [X2,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X2,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1134,axiom,
! [X2,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X2,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8328,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1126,f8326]) ).
fof(f8326,plain,
( spl0_1013
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X1,tc_nat)
| c_Parity_Oeven(c_times(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1126,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X1,tc_nat)
| c_Parity_Oeven(c_times(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8324,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1125,f8322]) ).
fof(f8322,plain,
( spl0_1012
<=> ! [X1,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X3,X1,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1125,axiom,
! [X3,X1] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8320,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1121,f8318]) ).
fof(f1121,axiom,
! [X3,X1] :
( c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X3,X1,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8316,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1057,f8314]) ).
fof(f1057,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_uminus(c_uminus(X1,X5),X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8312,plain,
spl0_1009,
inference(avatar_split_clause,[],[f995,f8310]) ).
fof(f8310,plain,
( spl0_1009
<=> ! [X28] : c_Numeral_Obin__succ(c_Numeral_OBit(X28,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X28),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f8308,plain,
spl0_1008,
inference(avatar_split_clause,[],[f991,f8306]) ).
fof(f8306,plain,
( spl0_1008
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f991,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8304,plain,
spl0_1007,
inference(avatar_split_clause,[],[f977,f8302]) ).
fof(f8302,plain,
( spl0_1007
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f977,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ class_Ring__and__Field_Oordered__idom(X5)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8300,plain,
spl0_1006,
inference(avatar_split_clause,[],[f959,f8298]) ).
fof(f959,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_Numeral_Onumber__of(c_Numeral_OMin,X5) = c_uminus(c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8296,plain,
spl0_1005,
inference(avatar_split_clause,[],[f873,f8294]) ).
fof(f8294,plain,
( spl0_1005
<=> ! [X2,X18] :
( c_0 = X2
| c_0 != c_plus(X18,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f873,axiom,
! [X2,X18] :
( c_0 = X2
| c_0 != c_plus(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8292,plain,
spl0_1004,
inference(avatar_split_clause,[],[f872,f8290]) ).
fof(f8290,plain,
( spl0_1004
<=> ! [X18,X2] :
( c_0 = X18
| c_0 != c_plus(X18,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f872,axiom,
! [X2,X18] :
( c_0 = X18
| c_0 != c_plus(X18,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8288,plain,
spl0_1003,
inference(avatar_split_clause,[],[f627,f8286]) ).
fof(f627,axiom,
! [X45,X17] :
( ~ c_lessequals(X45,X17,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X17,X45) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8284,plain,
spl0_1002,
inference(avatar_split_clause,[],[f599,f8282]) ).
fof(f8282,plain,
( spl0_1002
<=> ! [X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Orotate1(X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f599,axiom,
! [X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Orotate1(X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8280,plain,
spl0_1001,
inference(avatar_split_clause,[],[f598,f8278]) ).
fof(f8278,plain,
( spl0_1001
<=> ! [X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Orev(X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f598,axiom,
! [X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Orev(X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8276,plain,
( ~ spl0_56
| spl0_1000
| ~ spl0_834
| ~ spl0_945 ),
inference(avatar_split_clause,[],[f8112,f7933,f7412,f8273,f3432]) ).
fof(f8273,plain,
( spl0_1000
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f7412,plain,
( spl0_834
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f7933,plain,
( spl0_945
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f8112,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_834
| ~ spl0_945 ),
inference(superposition,[],[f7413,f7935]) ).
fof(f7935,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_945 ),
inference(avatar_component_clause,[],[f7933]) ).
fof(f7413,plain,
( ! [X5] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5)
| ~ class_Numeral_Onumber__ring(X5) )
| ~ spl0_834 ),
inference(avatar_component_clause,[],[f7412]) ).
fof(f8271,plain,
spl0_999,
inference(avatar_split_clause,[],[f595,f8269]) ).
fof(f8269,plain,
( spl0_999
<=> ! [X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Oremdups(X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f595,axiom,
! [X34,X5] : c_List_Oset(X34,X5) = c_List_Oset(c_List_Oremdups(X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8267,plain,
spl0_998,
inference(avatar_split_clause,[],[f585,f8265]) ).
fof(f8265,plain,
( spl0_998
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X34
| c_append(X34,X35,X5) != X35 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f585,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X34
| c_append(X34,X35,X5) != X35 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8263,plain,
spl0_997,
inference(avatar_split_clause,[],[f581,f8261]) ).
fof(f8261,plain,
( spl0_997
<=> ! [X34,X5,X2] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Orotate(X2,X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f581,axiom,
! [X2,X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Orotate(X2,X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8259,plain,
spl0_996,
inference(avatar_split_clause,[],[f561,f8257]) ).
fof(f8257,plain,
( spl0_996
<=> ! [X34,X5,X3] : c_List_Oremove1(X3,c_List_Olist_OCons(X3,X34,X5),X5) = X34 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f561,axiom,
! [X3,X34,X5] : c_List_Oremove1(X3,c_List_Olist_OCons(X3,X34,X5),X5) = X34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8255,plain,
spl0_995,
inference(avatar_split_clause,[],[f533,f8253]) ).
fof(f8253,plain,
( spl0_995
<=> ! [X34,X5,X1] : c_List_Onth(c_List_Olist_OCons(X1,X34,X5),c_0,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f533,axiom,
! [X1,X34,X5] : c_List_Onth(c_List_Olist_OCons(X1,X34,X5),c_0,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8251,plain,
spl0_994,
inference(avatar_split_clause,[],[f480,f8249]) ).
fof(f8247,plain,
spl0_993,
inference(avatar_split_clause,[],[f448,f8245]) ).
fof(f8245,plain,
( spl0_993
<=> ! [X5,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X1,X3,X5),tc_List_Olist(X5)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f448,axiom,
! [X3,X1,X5] : c_Nat_Osize(c_List_Oreplicate(X1,X3,X5),tc_List_Olist(X5)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8243,plain,
spl0_992,
inference(avatar_split_clause,[],[f438,f8241]) ).
fof(f8241,plain,
( spl0_992
<=> ! [X34,X5] :
( c_List_Olist_ONil = X34
| c_0 != c_Nat_Osize(X34,tc_List_Olist(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f438,axiom,
! [X34,X5] :
( c_List_Olist_ONil = X34
| c_0 != c_Nat_Osize(X34,tc_List_Olist(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8239,plain,
spl0_991,
inference(avatar_split_clause,[],[f406,f8237]) ).
fof(f8237,plain,
( spl0_991
<=> ! [X34,X5,X44] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Osublist(X34,X44,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f406,axiom,
! [X44,X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Osublist(X34,X44,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8235,plain,
spl0_990,
inference(avatar_split_clause,[],[f405,f8233]) ).
fof(f8233,plain,
( spl0_990
<=> ! [X34,X5,X2] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Orotate(X2,X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f405,axiom,
! [X2,X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Orotate(X2,X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8231,plain,
spl0_989,
inference(avatar_split_clause,[],[f404,f8229]) ).
fof(f8229,plain,
( spl0_989
<=> ! [X34,X5,X2] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_List_Orotate(X2,X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f404,axiom,
! [X2,X34,X5] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_List_Orotate(X2,X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8227,plain,
spl0_988,
inference(avatar_split_clause,[],[f401,f8225]) ).
fof(f8225,plain,
( spl0_988
<=> ! [X34,X5,X3] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Oremove1(X3,X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f401,axiom,
! [X3,X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Oremove1(X3,X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8223,plain,
spl0_987,
inference(avatar_split_clause,[],[f400,f8221]) ).
fof(f8221,plain,
( spl0_987
<=> ! [X34,X5,X17] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Odrop(X17,X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f400,axiom,
! [X34,X17,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Odrop(X17,X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8219,plain,
spl0_986,
inference(avatar_split_clause,[],[f397,f8217]) ).
fof(f8217,plain,
( spl0_986
<=> ! [X34,X5,X35] :
( c_List_Odistinct(X35,X5)
| ~ c_List_Odistinct(c_append(X34,X35,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f397,axiom,
! [X34,X35,X5] :
( c_List_Odistinct(X35,X5)
| ~ c_List_Odistinct(c_append(X34,X35,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8215,plain,
spl0_985,
inference(avatar_split_clause,[],[f396,f8213]) ).
fof(f8213,plain,
( spl0_985
<=> ! [X34,X5,X35] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_append(X34,X35,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f396,axiom,
! [X34,X5,X35] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_append(X34,X35,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8211,plain,
spl0_984,
inference(avatar_split_clause,[],[f394,f8209]) ).
fof(f8209,plain,
( spl0_984
<=> ! [X6,X34,X3] :
( c_List_Odistinct(X34,X6)
| ~ c_List_Odistinct(c_List_Olist_OCons(X3,X34,X6),X6) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f394,axiom,
! [X3,X6,X34] :
( c_List_Odistinct(X34,X6)
| ~ c_List_Odistinct(c_List_Olist_OCons(X3,X34,X6),X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8207,plain,
spl0_983,
inference(avatar_split_clause,[],[f374,f8205]) ).
fof(f8205,plain,
( spl0_983
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X35
| c_append(X34,X35,X5) != X34 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f374,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X35
| c_append(X34,X35,X5) != X34 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8203,plain,
spl0_982,
inference(avatar_split_clause,[],[f368,f8201]) ).
fof(f8201,plain,
( spl0_982
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_append(X34,X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f368,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_append(X34,X35,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f8199,plain,
spl0_981,
inference(avatar_split_clause,[],[f352,f8197]) ).
fof(f8197,plain,
( spl0_981
<=> ! [X34,X5,X35] :
( c_List_Olist_ONil = X35
| c_List_Olist_ONil != c_append(X34,X35,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f352,axiom,
! [X34,X35,X5] :
( c_List_Olist_ONil = X35
| c_List_Olist_ONil != c_append(X34,X35,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).
fof(f8195,plain,
spl0_980,
inference(avatar_split_clause,[],[f338,f8193]) ).
fof(f8193,plain,
( spl0_980
<=> ! [X9,X8] : c_0 = c_Divides_Oop_Amod(c_times(X9,X8,tc_IntDef_Oint),X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f338,axiom,
! [X8,X9] : c_0 = c_Divides_Oop_Amod(c_times(X9,X8,tc_IntDef_Oint),X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8191,plain,
( ~ spl0_979
| ~ spl0_798
| ~ spl0_939 ),
inference(avatar_split_clause,[],[f8101,f7908,f7265,f8188]) ).
fof(f8188,plain,
( spl0_979
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f8101,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_798
| ~ spl0_939 ),
inference(superposition,[],[f7266,f7910]) ).
fof(f8186,plain,
spl0_978,
inference(avatar_split_clause,[],[f337,f8184]) ).
fof(f8184,plain,
( spl0_978
<=> ! [X9,X8] : c_0 = c_Divides_Oop_Amod(c_times(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f337,axiom,
! [X8,X9] : c_0 = c_Divides_Oop_Amod(c_times(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8182,plain,
spl0_977,
inference(avatar_split_clause,[],[f324,f8180]) ).
fof(f324,axiom,
! [X2,X3] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),X2,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8178,plain,
spl0_976,
inference(avatar_split_clause,[],[f312,f8176]) ).
fof(f8176,plain,
( spl0_976
<=> ! [X8] :
( c_0 = X8
| c_1 = c_div(X8,X8,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f312,axiom,
! [X8] :
( c_0 = X8
| c_1 = c_div(X8,X8,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8174,plain,
spl0_975,
inference(avatar_split_clause,[],[f282,f8172]) ).
fof(f282,axiom,
! [X8,X9] : c_0 = c_div(c_Divides_Oop_Amod(X8,X9,tc_IntDef_Oint),X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8170,plain,
spl0_974,
inference(avatar_split_clause,[],[f264,f8168]) ).
fof(f8168,plain,
( spl0_974
<=> ! [X30] :
( ~ c_less(c_0,X30,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X30),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f264,axiom,
! [X30] :
( ~ c_less(c_0,X30,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8166,plain,
spl0_973,
inference(avatar_split_clause,[],[f263,f8164]) ).
fof(f8164,plain,
( spl0_973
<=> ! [X30] :
( c_less(c_0,X30,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X30),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f263,axiom,
! [X30] :
( c_less(c_0,X30,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X30),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8162,plain,
spl0_972,
inference(avatar_split_clause,[],[f262,f8160]) ).
fof(f8160,plain,
( spl0_972
<=> ! [X2] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f262,axiom,
! [X2] :
( ~ c_less(c_0,X2,tc_nat)
| c_less(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8158,plain,
spl0_971,
inference(avatar_split_clause,[],[f261,f8156]) ).
fof(f8156,plain,
( spl0_971
<=> ! [X2] :
( c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f261,axiom,
! [X2] :
( c_less(c_0,X2,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8154,plain,
spl0_970,
inference(avatar_split_clause,[],[f221,f8152]) ).
fof(f8152,plain,
( spl0_970
<=> ! [X30] :
( c_lessequals(c_0,X30,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X30)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f221,axiom,
! [X30] :
( c_lessequals(c_0,X30,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X30)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8150,plain,
spl0_969,
inference(avatar_split_clause,[],[f220,f8148]) ).
fof(f8148,plain,
( spl0_969
<=> ! [X30] :
( ~ c_lessequals(c_0,X30,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X30)) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f220,axiom,
! [X30] :
( ~ c_lessequals(c_0,X30,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X30)) = X30 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8145,plain,
spl0_968,
inference(avatar_split_clause,[],[f190,f8143]) ).
fof(f190,axiom,
! [X30] :
( c_0 = X30
| ~ c_less(c_HOL_Oabs(X30,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8141,plain,
spl0_967,
inference(avatar_split_clause,[],[f85,f8139]) ).
fof(f8139,plain,
( spl0_967
<=> ! [X13,X20,X5] :
( c_emptyset = X20
| c_emptyset != c_Equiv__Relations_Oquotient(X20,X13,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f85,axiom,
! [X5,X13,X20] :
( c_emptyset = X20
| c_emptyset != c_Equiv__Relations_Oquotient(X20,X13,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
fof(f8137,plain,
spl0_966,
inference(avatar_split_clause,[],[f83,f8135]) ).
fof(f8135,plain,
( spl0_966
<=> ! [X2,X18] : c_0 = c_div(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f83,axiom,
! [X2,X18] : c_0 = c_div(c_Divides_Oop_Amod(X18,X2,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8133,plain,
spl0_965,
inference(avatar_split_clause,[],[f81,f8131]) ).
fof(f8131,plain,
( spl0_965
<=> ! [X2,X18] : c_0 = c_Divides_Oop_Amod(c_times(X18,X2,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f81,axiom,
! [X2,X18] : c_0 = c_Divides_Oop_Amod(c_times(X18,X2,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8129,plain,
spl0_964,
inference(avatar_split_clause,[],[f79,f8127]) ).
fof(f8127,plain,
( spl0_964
<=> ! [X2,X18] : c_0 = c_Divides_Oop_Amod(c_times(X2,X18,tc_nat),X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f79,axiom,
! [X2,X18] : c_0 = c_Divides_Oop_Amod(c_times(X2,X18,tc_nat),X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8125,plain,
spl0_963,
inference(avatar_split_clause,[],[f34,f8123]) ).
fof(f8123,plain,
( spl0_963
<=> ! [X5,X0,X8,X10] : c_Datatype__Universe_OLeaf(X8,X5,X10) != c_Datatype__Universe_ONumb(X0,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f34,axiom,
! [X10,X0,X8,X5] : c_Datatype__Universe_OLeaf(X8,X5,X10) != c_Datatype__Universe_ONumb(X0,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Numb_0) ).
fof(f8121,plain,
spl0_962,
inference(avatar_split_clause,[],[f31,f8119]) ).
fof(f8119,plain,
( spl0_962
<=> ! [X11,X5,X12,X10] : c_Datatype__Universe_OIn0(X11,X5,X10) != c_Datatype__Universe_OIn1(X12,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f31,axiom,
! [X10,X11,X5,X12] : c_Datatype__Universe_OIn0(X11,X5,X10) != c_Datatype__Universe_OIn1(X12,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f8008,plain,
( spl0_961
| ~ spl0_44
| ~ spl0_844 ),
inference(avatar_split_clause,[],[f7610,f7452,f3372,f8005]) ).
fof(f8005,plain,
( spl0_961
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f7452,plain,
( spl0_844
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f7610,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_44
| ~ spl0_844 ),
inference(resolution,[],[f7453,f3374]) ).
fof(f3374,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_44 ),
inference(avatar_component_clause,[],[f3372]) ).
fof(f7453,plain,
( ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) )
| ~ spl0_844 ),
inference(avatar_component_clause,[],[f7452]) ).
fof(f7997,plain,
spl0_960,
inference(avatar_split_clause,[],[f3028,f7995]) ).
fof(f3028,plain,
! [X5] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X5)
| ~ class_Numeral_Onumber__ring(X5) ),
inference(forward_demodulation,[],[f1011,f997]) ).
fof(f1011,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f7993,plain,
spl0_959,
inference(avatar_split_clause,[],[f2980,f7991]) ).
fof(f7991,plain,
( spl0_959
<=> ! [X18] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X18,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2980,plain,
! [X18] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X18,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2780,f2745]) ).
fof(f2780,plain,
! [X18] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X18,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f141,f1385]) ).
fof(f141,axiom,
! [X18] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X18,tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f7989,plain,
spl0_958,
inference(avatar_split_clause,[],[f2979,f7987]) ).
fof(f7987,plain,
( spl0_958
<=> ! [X18] : c_1 = c_GCD_Ogcd(c_Pair(X18,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2979,plain,
! [X18] : c_1 = c_GCD_Ogcd(c_Pair(X18,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2779,f2745]) ).
fof(f2779,plain,
! [X18] : c_1 = c_GCD_Ogcd(c_Pair(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f140,f1385]) ).
fof(f140,axiom,
! [X18] : c_1 = c_GCD_Ogcd(c_Pair(X18,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f7985,plain,
spl0_957,
inference(avatar_split_clause,[],[f2751,f7983]) ).
fof(f7983,plain,
( spl0_957
<=> ! [X2] : c_less(X2,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2751,plain,
! [X2] : c_less(X2,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1633,f1385]) ).
fof(f1633,axiom,
! [X2] : c_less(X2,c_Suc(X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f7981,plain,
( spl0_956
| ~ spl0_44
| ~ spl0_843 ),
inference(avatar_split_clause,[],[f7609,f7448,f3372,f7978]) ).
fof(f7978,plain,
( spl0_956
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f7448,plain,
( spl0_843
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f7609,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_44
| ~ spl0_843 ),
inference(resolution,[],[f7449,f3374]) ).
fof(f7449,plain,
( ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) )
| ~ spl0_843 ),
inference(avatar_component_clause,[],[f7448]) ).
fof(f7976,plain,
spl0_955,
inference(avatar_split_clause,[],[f2750,f7974]) ).
fof(f7974,plain,
( spl0_955
<=> ! [X2] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2750,plain,
! [X2] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X2,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1635,f1385]) ).
fof(f1635,axiom,
! [X2] : c_less(c_0,c_Suc(X2),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f7972,plain,
spl0_954,
inference(avatar_split_clause,[],[f1820,f7970]) ).
fof(f7970,plain,
( spl0_954
<=> ! [X84,X83] :
( ~ class_Finite__Set_Ofinite(X84)
| ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_sum(X84,X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1820,axiom,
! [X83,X84] :
( ~ class_Finite__Set_Ofinite(X84)
| ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_sum(X84,X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f7968,plain,
spl0_953,
inference(avatar_split_clause,[],[f1814,f7966]) ).
fof(f7966,plain,
( spl0_953
<=> ! [X84,X83] :
( ~ class_Finite__Set_Ofinite(X84)
| ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_prod(X84,X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1814,axiom,
! [X83,X84] :
( ~ class_Finite__Set_Ofinite(X84)
| ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_prod(X84,X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f7964,plain,
spl0_952,
inference(avatar_split_clause,[],[f1764,f7962]) ).
fof(f7962,plain,
( spl0_952
<=> ! [X84,X83] :
( ~ class_Finite__Set_Ofinite(X84)
| ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_fun(X84,X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1764,axiom,
! [X83,X84] :
( ~ class_Finite__Set_Ofinite(X84)
| ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_fun(X84,X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f7960,plain,
spl0_951,
inference(avatar_split_clause,[],[f1662,f7958]) ).
fof(f7958,plain,
( spl0_951
<=> ! [X67,X31] : c_in(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1662,axiom,
! [X31,X67] : c_in(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f7956,plain,
spl0_950,
inference(avatar_split_clause,[],[f1661,f7954]) ).
fof(f7954,plain,
( spl0_950
<=> ! [X67,X31] : c_in(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f1661,axiom,
! [X31,X67] : c_in(c_SetInterval_OgreaterThanLessThan(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f7952,plain,
spl0_949,
inference(avatar_split_clause,[],[f1660,f7950]) ).
fof(f7950,plain,
( spl0_949
<=> ! [X67,X31] : c_in(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1660,axiom,
! [X31,X67] : c_in(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f7948,plain,
spl0_948,
inference(avatar_split_clause,[],[f1659,f7946]) ).
fof(f7946,plain,
( spl0_948
<=> ! [X67,X31] : c_in(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1659,axiom,
! [X31,X67] : c_in(c_SetInterval_OgreaterThanAtMost(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7944,plain,
spl0_947,
inference(avatar_split_clause,[],[f1657,f7942]) ).
fof(f7942,plain,
( spl0_947
<=> ! [X67,X31] : c_in(c_SetInterval_OatLeastLessThan(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f1657,axiom,
! [X31,X67] : c_in(c_SetInterval_OatLeastLessThan(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f7940,plain,
spl0_946,
inference(avatar_split_clause,[],[f1656,f7938]) ).
fof(f7938,plain,
( spl0_946
<=> ! [X67,X31] : c_in(c_SetInterval_OatLeastLessThan(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1656,axiom,
! [X31,X67] : c_in(c_SetInterval_OatLeastLessThan(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7936,plain,
( spl0_945
| ~ spl0_56
| ~ spl0_840 ),
inference(avatar_split_clause,[],[f7606,f7436,f3432,f7933]) ).
fof(f7436,plain,
( spl0_840
<=> ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f7606,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_840 ),
inference(resolution,[],[f7437,f3434]) ).
fof(f7437,plain,
( ! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) )
| ~ spl0_840 ),
inference(avatar_component_clause,[],[f7436]) ).
fof(f7931,plain,
spl0_944,
inference(avatar_split_clause,[],[f1655,f7929]) ).
fof(f7929,plain,
( spl0_944
<=> ! [X67,X31] : c_in(c_SetInterval_OatLeastAtMost(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1655,axiom,
! [X31,X67] : c_in(c_SetInterval_OatLeastAtMost(X67,X31,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f7927,plain,
spl0_943,
inference(avatar_split_clause,[],[f1654,f7925]) ).
fof(f7925,plain,
( spl0_943
<=> ! [X67,X31] : c_in(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1654,axiom,
! [X31,X67] : c_in(c_SetInterval_OatLeastAtMost(X67,X31,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7923,plain,
spl0_942,
inference(avatar_split_clause,[],[f1605,f7921]) ).
fof(f1605,axiom,
! [X2,X18] : c_lessequals(c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint),c_IntDef_Oint(X18),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7919,plain,
spl0_941,
inference(avatar_split_clause,[],[f1540,f7917]) ).
fof(f7917,plain,
( spl0_941
<=> ! [X20,X5] :
( c_emptyset = X20
| ~ c_lessequals(X20,c_emptyset,tc_set(X5)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1540,axiom,
! [X5,X20] :
( c_emptyset = X20
| ~ c_lessequals(X20,c_emptyset,tc_set(X5)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f7915,plain,
spl0_940,
inference(avatar_split_clause,[],[f1501,f7913]) ).
fof(f1501,axiom,
! [X1,X5] : c_Set_Ocontents(c_insert(X1,c_emptyset,X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f7911,plain,
spl0_939,
inference(avatar_split_clause,[],[f1375,f7908]) ).
fof(f1375,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
fof(f7906,plain,
spl0_938,
inference(avatar_split_clause,[],[f1333,f7904]) ).
fof(f7904,plain,
( spl0_938
<=> ! [X5,X8] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(X8,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1333,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(X8,c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f7902,plain,
spl0_937,
inference(avatar_split_clause,[],[f1332,f7900]) ).
fof(f7900,plain,
( spl0_937
<=> ! [X5,X8] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(c_0,X8,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1332,axiom,
! [X8,X5] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X5)
| c_0 = c_times(c_0,X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f7898,plain,
spl0_936,
inference(avatar_split_clause,[],[f1315,f7896]) ).
fof(f7896,plain,
( spl0_936
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(c_1,X19,X5) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1315,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(c_1,X19,X5) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f7894,plain,
spl0_935,
inference(avatar_split_clause,[],[f1314,f7892]) ).
fof(f7892,plain,
( spl0_935
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(X9,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1314,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(X9,c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f7890,plain,
spl0_934,
inference(avatar_split_clause,[],[f1311,f7888]) ).
fof(f7888,plain,
( spl0_934
<=> ! [X5,X19] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(X19,c_1,X5) = X19 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1311,axiom,
! [X19,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_times(X19,c_1,X5) = X19 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f7886,plain,
spl0_933,
inference(avatar_split_clause,[],[f1310,f7884]) ).
fof(f7884,plain,
( spl0_933
<=> ! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(c_0,X9,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1310,axiom,
! [X9,X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_times(c_0,X9,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f7882,plain,
spl0_932,
inference(avatar_split_clause,[],[f1220,f7880]) ).
fof(f7880,plain,
( spl0_932
<=> ! [X5,X1] : c_Relation_ORange(c_Relation_Odiag(X1,X5),X5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1220,axiom,
! [X1,X5] : c_Relation_ORange(c_Relation_Odiag(X1,X5),X5,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f7878,plain,
spl0_931,
inference(avatar_split_clause,[],[f1218,f7876]) ).
fof(f7876,plain,
( spl0_931
<=> ! [X5,X1,X10] : c_Relation_Orel__comp(X1,c_Relation_OId,X5,X10,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1218,axiom,
! [X10,X1,X5] : c_Relation_Orel__comp(X1,c_Relation_OId,X5,X10,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f7874,plain,
spl0_930,
inference(avatar_split_clause,[],[f1212,f7872]) ).
fof(f7872,plain,
( spl0_930
<=> ! [X5,X1,X10] : c_Relation_Orel__comp(c_Relation_OId,X1,X10,X10,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1212,axiom,
! [X10,X1,X5] : c_Relation_Orel__comp(c_Relation_OId,X1,X10,X10,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f7870,plain,
spl0_929,
inference(avatar_split_clause,[],[f1210,f7868]) ).
fof(f7868,plain,
( spl0_929
<=> ! [X5,X1] : c_Relation_ODomain(c_Relation_Odiag(X1,X5),X5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1210,axiom,
! [X1,X5] : c_Relation_ODomain(c_Relation_Odiag(X1,X5),X5,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f7866,plain,
spl0_928,
inference(avatar_split_clause,[],[f1198,f7864]) ).
fof(f7864,plain,
( spl0_928
<=> ! [X5,X8] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(X8,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1198,axiom,
! [X8,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(X8,c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f7862,plain,
spl0_927,
inference(avatar_split_clause,[],[f1195,f7860]) ).
fof(f1195,axiom,
! [X1,X5] :
( ~ class_Power_Orecpower(X5)
| c_Nat_Opower(X1,c_1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f7858,plain,
spl0_926,
inference(avatar_split_clause,[],[f1194,f7856]) ).
fof(f1194,axiom,
! [X2,X5] :
( ~ class_Power_Orecpower(X5)
| c_1 = c_Nat_Opower(c_1,X2,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f7854,plain,
spl0_925,
inference(avatar_split_clause,[],[f1133,f7852]) ).
fof(f7852,plain,
( spl0_925
<=> ! [X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f1133,axiom,
! [X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f7850,plain,
spl0_924,
inference(avatar_split_clause,[],[f1132,f7848]) ).
fof(f7848,plain,
( spl0_924
<=> ! [X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f1132,axiom,
! [X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f7846,plain,
spl0_923,
inference(avatar_split_clause,[],[f1108,f7844]) ).
fof(f1108,axiom,
! [X10,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omax(X1,X1,X10) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f7842,plain,
spl0_922,
inference(avatar_split_clause,[],[f1103,f7840]) ).
fof(f1103,axiom,
! [X10,X1] :
( ~ class_Orderings_Olinorder(X10)
| c_Orderings_Omin(X1,X1,X10) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f7838,plain,
spl0_921,
inference(avatar_split_clause,[],[f1092,f7836]) ).
fof(f7836,plain,
( spl0_921
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f1092,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f7834,plain,
spl0_920,
inference(avatar_split_clause,[],[f1091,f7832]) ).
fof(f7832,plain,
( spl0_920
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1091,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f7830,plain,
spl0_919,
inference(avatar_split_clause,[],[f1082,f7828]) ).
fof(f1082,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_lessequals(c_OrderedGroup_Onprt(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f7826,plain,
spl0_918,
inference(avatar_split_clause,[],[f1059,f7824]) ).
fof(f1059,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(X1,c_1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f7822,plain,
spl0_917,
inference(avatar_split_clause,[],[f1058,f7820]) ).
fof(f1058,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Omonoid__mult(X5)
| c_times(c_1,X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f7818,plain,
spl0_916,
inference(avatar_split_clause,[],[f1046,f7816]) ).
fof(f1046,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_minus(X8,X8,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f7814,plain,
spl0_915,
inference(avatar_split_clause,[],[f1039,f7812]) ).
fof(f1039,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_minus(X1,c_0,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f7810,plain,
spl0_914,
inference(avatar_split_clause,[],[f1037,f7808]) ).
fof(f1037,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(c_0,X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f7806,plain,
spl0_913,
inference(avatar_split_clause,[],[f1026,f7804]) ).
fof(f1026,axiom,
! [X1,X5] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X5)
| c_plus(X1,c_0,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f7802,plain,
spl0_912,
inference(avatar_split_clause,[],[f1023,f7800]) ).
fof(f7800,plain,
( spl0_912
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_HOL_Oabs(X8,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1023,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| ~ c_less(c_HOL_Oabs(X8,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f7798,plain,
spl0_911,
inference(avatar_split_clause,[],[f1021,f7796]) ).
fof(f7796,plain,
( spl0_911
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_HOL_Oabs(c_0,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1021,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_HOL_Oabs(c_0,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f7794,plain,
spl0_910,
inference(avatar_split_clause,[],[f1018,f7792]) ).
fof(f7792,plain,
( spl0_910
<=> ! [X5,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_0,c_HOL_Oabs(X8,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1018,axiom,
! [X8,X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_lessequals(c_0,c_HOL_Oabs(X8,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7790,plain,
spl0_909,
inference(avatar_split_clause,[],[f994,f7788]) ).
fof(f994,axiom,
! [X28] : c_Numeral_OBit(X28,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X28,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f7786,plain,
spl0_908,
inference(avatar_split_clause,[],[f706,f7784]) ).
fof(f706,axiom,
! [X28] : c_IntDef_Onat(c_Numeral_Onumber__of(X28,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X28,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f7782,plain,
spl0_907,
inference(avatar_split_clause,[],[f659,f7780]) ).
fof(f7780,plain,
( spl0_907
<=> ! [X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_NatArith_Oof__nat(X18,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f659,axiom,
! [X18,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_NatArith_Oof__nat(X18,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f7778,plain,
spl0_906,
inference(avatar_split_clause,[],[f656,f7776]) ).
fof(f7776,plain,
( spl0_906
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_NatArith_Oof__nat(c_0,X5),c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f656,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_NatArith_Oof__nat(c_0,X5),c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7774,plain,
spl0_905,
inference(avatar_split_clause,[],[f646,f7772]) ).
fof(f7772,plain,
( spl0_905
<=> ! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_NatArith_Oof__nat(X2,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f646,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_NatArith_Oof__nat(X2,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7770,plain,
( ~ spl0_903
| spl0_904
| ~ spl0_698
| ~ spl0_834 ),
inference(avatar_split_clause,[],[f7600,f7412,f6842,f7767,f7763]) ).
fof(f7763,plain,
( spl0_903
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f7767,plain,
( spl0_904
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f7600,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_698
| ~ spl0_834 ),
inference(superposition,[],[f7413,f6844]) ).
fof(f7761,plain,
spl0_902,
inference(avatar_split_clause,[],[f620,f7759]) ).
fof(f7759,plain,
( spl0_902
<=> ! [X6,X1,X3] : c_List_Otl(c_List_Olist_OCons(X3,X1,X6),X6) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f620,axiom,
! [X3,X1,X6] : c_List_Otl(c_List_Olist_OCons(X3,X1,X6),X6) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7757,plain,
spl0_901,
inference(avatar_split_clause,[],[f593,f7755]) ).
fof(f7755,plain,
( spl0_901
<=> ! [X34,X5] :
( c_List_Olist_ONil = X34
| c_emptyset != c_List_Oset(X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f593,axiom,
! [X34,X5] :
( c_List_Olist_ONil = X34
| c_emptyset != c_List_Oset(X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty_0) ).
fof(f7753,plain,
spl0_900,
inference(avatar_split_clause,[],[f576,f7751]) ).
fof(f7751,plain,
( spl0_900
<=> ! [X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Orotate1(X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f576,axiom,
! [X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Orotate1(X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7749,plain,
spl0_899,
inference(avatar_split_clause,[],[f556,f7747]) ).
fof(f7747,plain,
( spl0_899
<=> ! [X5,X3] :
( c_List_Olist_ONil = X3
| c_List_Olist_ONil != c_List_Oremdups(X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f556,axiom,
! [X3,X5] :
( c_List_Olist_ONil = X3
| c_List_Olist_ONil != c_List_Oremdups(X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_0) ).
fof(f7745,plain,
spl0_898,
inference(avatar_split_clause,[],[f429,f7743]) ).
fof(f7743,plain,
( spl0_898
<=> ! [X5,X3] : c_List_Olast(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f429,axiom,
! [X3,X5] : c_List_Olast(c_List_Olist_OCons(X3,c_List_Olist_ONil,X5),X5) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7741,plain,
spl0_897,
inference(avatar_split_clause,[],[f420,f7739]) ).
fof(f7739,plain,
( spl0_897
<=> ! [X34,X5,X1] : c_List_Ohd(c_List_Olist_OCons(X1,X34,X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f420,axiom,
! [X1,X34,X5] : c_List_Ohd(c_List_Olist_OCons(X1,X34,X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7737,plain,
spl0_896,
inference(avatar_split_clause,[],[f403,f7735]) ).
fof(f7735,plain,
( spl0_896
<=> ! [X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Orev(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f403,axiom,
! [X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Orev(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7733,plain,
spl0_895,
inference(avatar_split_clause,[],[f402,f7731]) ).
fof(f7731,plain,
( spl0_895
<=> ! [X34,X5] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_List_Orev(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f402,axiom,
! [X34,X5] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_List_Orev(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7729,plain,
spl0_894,
inference(avatar_split_clause,[],[f391,f7727]) ).
fof(f7727,plain,
( spl0_894
<=> ! [X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Orotate1(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f391,axiom,
! [X34,X5] :
( ~ c_List_Odistinct(X34,X5)
| c_List_Odistinct(c_List_Orotate1(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7725,plain,
spl0_893,
inference(avatar_split_clause,[],[f390,f7723]) ).
fof(f7723,plain,
( spl0_893
<=> ! [X34,X5] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_List_Orotate1(X34,X5),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f390,axiom,
! [X34,X5] :
( c_List_Odistinct(X34,X5)
| ~ c_List_Odistinct(c_List_Orotate1(X34,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7721,plain,
( spl0_892
| ~ spl0_52
| ~ spl0_827 ),
inference(avatar_split_clause,[],[f7580,f7384,f3412,f7718]) ).
fof(f7718,plain,
( spl0_892
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f3412,plain,
( spl0_52
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f7384,plain,
( spl0_827
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f7580,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_827 ),
inference(resolution,[],[f7385,f3414]) ).
fof(f3414,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f3412]) ).
fof(f7385,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) )
| ~ spl0_827 ),
inference(avatar_component_clause,[],[f7384]) ).
fof(f7716,plain,
spl0_891,
inference(avatar_split_clause,[],[f378,f7714]) ).
fof(f7714,plain,
( spl0_891
<=> ! [X6,X3] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X3,c_List_Olist_ONil,X6),X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f378,axiom,
! [X3,X6] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X3,c_List_Olist_ONil,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7712,plain,
spl0_890,
inference(avatar_split_clause,[],[f354,f7710]) ).
fof(f7710,plain,
( spl0_890
<=> ! [X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Orev(X34,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f354,axiom,
! [X34,X5] :
( c_List_Olist_ONil = X34
| c_List_Olist_ONil != c_List_Orev(X34,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7708,plain,
spl0_889,
inference(avatar_split_clause,[],[f340,f7706]) ).
fof(f340,axiom,
! [X1,X5] :
( ~ class_LOrder_Omeet__semilorder(X5)
| c_LOrder_Omeet(X1,X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7704,plain,
spl0_888,
inference(avatar_split_clause,[],[f339,f7702]) ).
fof(f339,axiom,
! [X1,X5] :
( ~ class_LOrder_Ojoin__semilorder(X5)
| c_LOrder_Ojoin(X1,X1,X5) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7700,plain,
spl0_887,
inference(avatar_split_clause,[],[f331,f7698]) ).
fof(f7698,plain,
( spl0_887
<=> ! [X8] : c_0 = c_Divides_Oop_Amod(X8,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f331,axiom,
! [X8] : c_0 = c_Divides_Oop_Amod(X8,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f7696,plain,
spl0_886,
inference(avatar_split_clause,[],[f260,f7694]) ).
fof(f260,axiom,
! [X2,X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_NatArith_Oof__nat(X2,X5),c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7692,plain,
spl0_885,
inference(avatar_split_clause,[],[f233,f7690]) ).
fof(f233,axiom,
! [X2,X18] : ~ c_less(c_IntDef_Oint(X2),c_uminus(c_IntDef_Oint(X18),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7688,plain,
spl0_884,
inference(avatar_split_clause,[],[f226,f7686]) ).
fof(f7686,plain,
( spl0_884
<=> ! [X30] :
( ~ c_lessequals(X30,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X30) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f226,axiom,
! [X30] :
( ~ c_lessequals(X30,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X30) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7684,plain,
spl0_883,
inference(avatar_split_clause,[],[f217,f7682]) ).
fof(f7682,plain,
( spl0_883
<=> ! [X2] :
( c_0 = X2
| ~ c_lessequals(c_IntDef_Oint(X2),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f217,axiom,
! [X2] :
( c_0 = X2
| ~ c_lessequals(c_IntDef_Oint(X2),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7680,plain,
spl0_882,
inference(avatar_split_clause,[],[f216,f7678]) ).
fof(f216,axiom,
! [X2,X18] :
( X2 = X18
| c_IntDef_Oint(X18) != c_IntDef_Oint(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7676,plain,
( spl0_881
| ~ spl0_25
| ~ spl0_826 ),
inference(avatar_split_clause,[],[f7578,f7380,f3277,f7673]) ).
fof(f7673,plain,
( spl0_881
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f3277,plain,
( spl0_25
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f7380,plain,
( spl0_826
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_1 = c_NatArith_Oof__nat(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f7578,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_25
| ~ spl0_826 ),
inference(resolution,[],[f7381,f3279]) ).
fof(f3279,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f3277]) ).
fof(f7381,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_1 = c_NatArith_Oof__nat(c_1,X5) )
| ~ spl0_826 ),
inference(avatar_component_clause,[],[f7380]) ).
fof(f7671,plain,
spl0_880,
inference(avatar_split_clause,[],[f149,f7669]) ).
fof(f7669,plain,
( spl0_880
<=> ! [X1] : c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f149,axiom,
! [X1] : c_GCD_Ogcd(c_Pair(X1,X1,tc_nat,tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7667,plain,
spl0_879,
inference(avatar_split_clause,[],[f139,f7665]) ).
fof(f7665,plain,
( spl0_879
<=> ! [X1] : c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f139,axiom,
! [X1] : c_GCD_Ogcd(c_Pair(c_0,X1,tc_nat,tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7663,plain,
spl0_878,
inference(avatar_split_clause,[],[f138,f7661]) ).
fof(f7661,plain,
( spl0_878
<=> ! [X1] : c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f138,axiom,
! [X1] : c_GCD_Ogcd(c_Pair(X1,c_0,tc_nat,tc_nat)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7659,plain,
spl0_877,
inference(avatar_split_clause,[],[f18,f7657]) ).
fof(f7657,plain,
( spl0_877
<=> ! [X5,X8] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X8,X5),tc_Datatype_Ooption(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f18,axiom,
! [X8,X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X8,X5),tc_Datatype_Ooption(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7655,plain,
spl0_876,
inference(avatar_split_clause,[],[f12,f7653]) ).
fof(f7653,plain,
( spl0_876
<=> ! [X4,X5] :
( c_Datatype_Ooption_ONone = X4
| c_Datatype_Oo2s(X4,X5) != c_emptyset ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f12,axiom,
! [X4,X5] :
( c_Datatype_Ooption_ONone = X4
| c_Datatype_Oo2s(X4,X5) != c_emptyset ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7650,plain,
spl0_875,
inference(avatar_split_clause,[],[f8,f7648]) ).
fof(f7648,plain,
( spl0_875
<=> ! [X5,X3] : c_in(X3,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X3,X5),X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f8,axiom,
! [X3,X5] : c_in(X3,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X3,X5),X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7642,plain,
( spl0_874
| ~ spl0_54
| ~ spl0_818 ),
inference(avatar_split_clause,[],[f7574,f7348,f3422,f7639]) ).
fof(f7639,plain,
( spl0_874
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f3422,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f7348,plain,
( spl0_818
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f7574,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_818 ),
inference(resolution,[],[f7349,f3424]) ).
fof(f3424,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3422]) ).
fof(f7349,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) )
| ~ spl0_818 ),
inference(avatar_component_clause,[],[f7348]) ).
fof(f7623,plain,
( spl0_873
| ~ spl0_26
| ~ spl0_817 ),
inference(avatar_split_clause,[],[f7573,f7344,f3282,f7620]) ).
fof(f7620,plain,
( spl0_873
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f3282,plain,
( spl0_26
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f7344,plain,
( spl0_817
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f7573,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_26
| ~ spl0_817 ),
inference(resolution,[],[f7345,f3284]) ).
fof(f3284,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3282]) ).
fof(f7345,plain,
( ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) )
| ~ spl0_817 ),
inference(avatar_component_clause,[],[f7344]) ).
fof(f7615,plain,
( spl0_872
| ~ spl0_113
| ~ spl0_814 ),
inference(avatar_split_clause,[],[f7563,f7332,f3711,f7612]) ).
fof(f7332,plain,
( spl0_814
<=> ! [X18] : c_IntDef_Oint(X18) = c_HOL_Oabs(c_IntDef_Oint(X18),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f7563,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_814 ),
inference(superposition,[],[f7333,f3713]) ).
fof(f7333,plain,
( ! [X18] : c_IntDef_Oint(X18) = c_HOL_Oabs(c_IntDef_Oint(X18),tc_IntDef_Oint)
| ~ spl0_814 ),
inference(avatar_component_clause,[],[f7332]) ).
fof(f7605,plain,
( spl0_871
| ~ spl0_112
| ~ spl0_814 ),
inference(avatar_split_clause,[],[f7562,f7332,f3706,f7602]) ).
fof(f7562,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_814 ),
inference(superposition,[],[f7333,f3708]) ).
fof(f7569,plain,
( spl0_870
| ~ spl0_805
| ~ spl0_808 ),
inference(avatar_split_clause,[],[f7558,f7308,f7296,f7567]) ).
fof(f7296,plain,
( spl0_805
<=> ! [X1] : c_div(X1,c_1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f7558,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_805
| ~ spl0_808 ),
inference(superposition,[],[f7309,f7297]) ).
fof(f7297,plain,
( ! [X1] : c_div(X1,c_1,tc_nat) = X1
| ~ spl0_805 ),
inference(avatar_component_clause,[],[f7296]) ).
fof(f7556,plain,
spl0_869,
inference(avatar_split_clause,[],[f3053,f7554]) ).
fof(f7554,plain,
( spl0_869
<=> ! [X18] :
( ~ c_Divides_Oop_Advd(X18,c_1,tc_nat)
| c_1 = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f3053,plain,
! [X18] :
( ~ c_Divides_Oop_Advd(X18,c_1,tc_nat)
| c_1 = X18 ),
inference(forward_demodulation,[],[f3052,f2745]) ).
fof(f3052,plain,
! [X18] :
( c_1 = X18
| ~ c_Divides_Oop_Advd(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2876,f2745]) ).
fof(f2876,plain,
! [X18] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X18
| ~ c_Divides_Oop_Advd(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f68,f1385,f1385]) ).
fof(f68,axiom,
! [X18] :
( c_Suc(c_0) = X18
| ~ c_Divides_Oop_Advd(X18,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7552,plain,
spl0_868,
inference(avatar_split_clause,[],[f2967,f7550]) ).
fof(f7550,plain,
( spl0_868
<=> ! [X5,X24] : c_emptyset = c_Relation_OImage(c_emptyset,X24,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2967,plain,
! [X24,X5] : c_emptyset = c_Relation_OImage(c_emptyset,X24,X5,X5),
inference(forward_demodulation,[],[f2756,f1227]) ).
fof(f1227,axiom,
! [X5] : c_emptyset = c_Relation_Odiag(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2756,plain,
! [X24,X5] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X5),X24,X5,X5),
inference(definition_unfolding,[],[f1445,f1214]) ).
fof(f1445,axiom,
! [X24,X5] : c_emptyset = c_inter(c_emptyset,X24,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7548,plain,
spl0_867,
inference(avatar_split_clause,[],[f2760,f7546]) ).
fof(f7544,plain,
spl0_866,
inference(avatar_split_clause,[],[f2758,f7541]) ).
fof(f2758,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f974,f954]) ).
fof(f974,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7539,plain,
spl0_865,
inference(avatar_split_clause,[],[f2745,f7536]) ).
fof(f7536,plain,
( spl0_865
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f7534,plain,
spl0_864,
inference(avatar_split_clause,[],[f2741,f7532]) ).
fof(f7532,plain,
( spl0_864
<=> ! [X18] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2741,plain,
! [X18] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X18,tc_nat),tc_nat),
inference(definition_unfolding,[],[f864,f1385]) ).
fof(f864,axiom,
! [X18] : c_0 != c_Suc(X18),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
fof(f7530,plain,
spl0_863,
inference(avatar_split_clause,[],[f1663,f7528]) ).
fof(f7528,plain,
( spl0_863
<=> ! [X0] : c_in(c_SetInterval_OlessThan(X0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f1663,axiom,
! [X0] : c_in(c_SetInterval_OlessThan(X0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7526,plain,
spl0_862,
inference(avatar_split_clause,[],[f1658,f7524]) ).
fof(f7524,plain,
( spl0_862
<=> ! [X0] : c_in(c_SetInterval_OatMost(X0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f1658,axiom,
! [X0] : c_in(c_SetInterval_OatMost(X0,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7522,plain,
spl0_861,
inference(avatar_split_clause,[],[f1629,f7520]) ).
fof(f7520,plain,
( spl0_861
<=> ! [X20,X5] : c_in(c_List_Olist_ONil,c_List_Olists(X20,X5),tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1629,axiom,
! [X5,X20] : c_in(c_List_Olist_ONil,c_List_Olists(X20,X5),tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7518,plain,
spl0_860,
inference(avatar_split_clause,[],[f1613,f7516]) ).
fof(f7516,plain,
( spl0_860
<=> ! [X34,X5] : c_in(c_List_Oset(X34,X5),c_Finite__Set_OFinites,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1613,axiom,
! [X34,X5] : c_in(c_List_Oset(X34,X5),c_Finite__Set_OFinites,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7514,plain,
spl0_859,
inference(avatar_split_clause,[],[f1610,f7512]) ).
fof(f1610,axiom,
! [X0,X18] : c_Divides_Oop_Advd(X0,c_times(X18,X0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7510,plain,
spl0_858,
inference(avatar_split_clause,[],[f1609,f7508]) ).
fof(f1609,axiom,
! [X0,X18] : c_Divides_Oop_Advd(X0,c_times(X0,X18,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7506,plain,
spl0_857,
inference(avatar_split_clause,[],[f1594,f7504]) ).
fof(f7504,plain,
( spl0_857
<=> ! [X18,X0] : c_Divides_Oop_Advd(X0,c_times(X18,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1594,axiom,
! [X0,X18] : c_Divides_Oop_Advd(X0,c_times(X18,X0,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7502,plain,
spl0_856,
inference(avatar_split_clause,[],[f1593,f7500]) ).
fof(f7500,plain,
( spl0_856
<=> ! [X18,X0] : c_Divides_Oop_Advd(X0,c_times(X0,X18,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1593,axiom,
! [X0,X18] : c_Divides_Oop_Advd(X0,c_times(X0,X18,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7498,plain,
spl0_855,
inference(avatar_split_clause,[],[f1546,f7496]) ).
fof(f7496,plain,
( spl0_855
<=> ! [X5,X10] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1546,axiom,
! [X10,X5] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7494,plain,
spl0_854,
inference(avatar_split_clause,[],[f1525,f7492]) ).
fof(f1525,axiom,
! [X3,X5,X20] : c_in(X3,c_insert(X3,X20,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7490,plain,
spl0_853,
inference(avatar_split_clause,[],[f1509,f7488]) ).
fof(f7488,plain,
( spl0_853
<=> ! [X20,X5] : c_emptyset = c_minus(c_emptyset,X20,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f1509,axiom,
! [X5,X20] : c_emptyset = c_minus(c_emptyset,X20,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7486,plain,
spl0_852,
inference(avatar_split_clause,[],[f1489,f7484]) ).
fof(f7484,plain,
( spl0_852
<=> ! [X5,X1] : c_Union(c_Pow(X1,X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1489,axiom,
! [X1,X5] : c_Union(c_Pow(X1,X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7482,plain,
spl0_851,
inference(avatar_split_clause,[],[f1431,f7480]) ).
fof(f7480,plain,
( spl0_851
<=> ! [X5,X1] : c_minus(X1,c_emptyset,tc_set(X5)) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f1431,axiom,
! [X1,X5] : c_minus(X1,c_emptyset,tc_set(X5)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7478,plain,
spl0_850,
inference(avatar_split_clause,[],[f1429,f7476]) ).
fof(f7476,plain,
( spl0_850
<=> ! [X20,X5] : c_emptyset = c_minus(X20,X20,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f1429,axiom,
! [X5,X20] : c_emptyset = c_minus(X20,X20,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7474,plain,
spl0_849,
inference(avatar_split_clause,[],[f1428,f7472]) ).
fof(f7472,plain,
( spl0_849
<=> ! [X20,X5] : c_emptyset = c_minus(X20,c_UNIV,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1428,axiom,
! [X5,X20] : c_emptyset = c_minus(X20,c_UNIV,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7470,plain,
spl0_848,
inference(avatar_split_clause,[],[f1390,f7468]) ).
fof(f7468,plain,
( spl0_848
<=> ! [X1] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1390,axiom,
! [X1] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X1,tc_nat),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7466,plain,
spl0_847,
inference(avatar_split_clause,[],[f1235,f7464]) ).
fof(f7464,plain,
( spl0_847
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f1235,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_1 = c_HOL_Oabs(c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7462,plain,
spl0_846,
inference(avatar_split_clause,[],[f1215,f7460]) ).
fof(f7460,plain,
( spl0_846
<=> ! [X5,X72,X10] : c_emptyset = c_Relation_OImage(X72,c_emptyset,X10,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1215,axiom,
! [X72,X10,X5] : c_emptyset = c_Relation_OImage(X72,c_emptyset,X10,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7458,plain,
spl0_845,
inference(avatar_split_clause,[],[f1213,f7456]) ).
fof(f7456,plain,
( spl0_845
<=> ! [X5,X1] : c_Relation_OImage(c_Relation_OId,X1,X5,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1213,axiom,
! [X1,X5] : c_Relation_OImage(c_Relation_OId,X1,X5,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7454,plain,
spl0_844,
inference(avatar_split_clause,[],[f1084,f7452]) ).
fof(f1084,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Opprt(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7450,plain,
spl0_843,
inference(avatar_split_clause,[],[f1079,f7448]) ).
fof(f1079,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group(X5)
| c_0 = c_OrderedGroup_Onprt(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7446,plain,
spl0_842,
inference(avatar_split_clause,[],[f1067,f7444]) ).
fof(f7444,plain,
( spl0_842
<=> ! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_uminus(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1067,axiom,
! [X5] :
( ~ class_OrderedGroup_Oab__group__add(X5)
| c_0 = c_uminus(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
fof(f7442,plain,
spl0_841,
inference(avatar_split_clause,[],[f1017,f7440]) ).
fof(f7440,plain,
( spl0_841
<=> ! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = c_HOL_Oabs(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1017,axiom,
! [X5] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X5)
| c_0 = c_HOL_Oabs(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7438,plain,
spl0_840,
inference(avatar_split_clause,[],[f1010,f7436]) ).
fof(f1010,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7434,plain,
spl0_839,
inference(avatar_split_clause,[],[f1003,f7432]) ).
fof(f7432,plain,
( spl0_839
<=> ! [X22,X5,X1] : c_Numeral_Obit_Obit__rec(X22,X1,c_Numeral_Obit_OB1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f1003,axiom,
! [X1,X22,X5] : c_Numeral_Obit_Obit__rec(X22,X1,c_Numeral_Obit_OB1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7430,plain,
spl0_838,
inference(avatar_split_clause,[],[f1002,f7428]) ).
fof(f7428,plain,
( spl0_838
<=> ! [X5,X1,X21] : c_Numeral_Obit_Obit__rec(X1,X21,c_Numeral_Obit_OB0,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f1002,axiom,
! [X21,X1,X5] : c_Numeral_Obit_Obit__rec(X1,X21,c_Numeral_Obit_OB0,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7426,plain,
spl0_837,
inference(avatar_split_clause,[],[f999,f7424]) ).
fof(f7424,plain,
( spl0_837
<=> ! [X22,X5,X1] : c_Numeral_Obit_Obit__case(X22,X1,c_Numeral_Obit_OB1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f999,axiom,
! [X1,X22,X5] : c_Numeral_Obit_Obit__case(X22,X1,c_Numeral_Obit_OB1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7422,plain,
spl0_836,
inference(avatar_split_clause,[],[f998,f7420]) ).
fof(f7420,plain,
( spl0_836
<=> ! [X5,X1,X21] : c_Numeral_Obit_Obit__case(X1,X21,c_Numeral_Obit_OB0,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f998,axiom,
! [X21,X1,X5] : c_Numeral_Obit_Obit__case(X1,X21,c_Numeral_Obit_OB0,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7418,plain,
spl0_835,
inference(avatar_split_clause,[],[f985,f7416]) ).
fof(f985,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7414,plain,
spl0_834,
inference(avatar_split_clause,[],[f984,f7412]) ).
fof(f984,axiom,
! [X5] :
( ~ class_Numeral_Onumber__ring(X5)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X5),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7410,plain,
spl0_833,
inference(avatar_split_clause,[],[f930,f7408]) ).
fof(f7408,plain,
( spl0_833
<=> ! [X2] :
( c_0 = X2
| c_less(c_0,X2,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f930,axiom,
! [X2] :
( c_0 = X2
| c_less(c_0,X2,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7406,plain,
spl0_832,
inference(avatar_split_clause,[],[f929,f7404]) ).
fof(f7404,plain,
( spl0_832
<=> ! [X45,X17] : ~ c_less(c_plus(X45,X17,tc_nat),X17,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f929,axiom,
! [X45,X17] : ~ c_less(c_plus(X45,X17,tc_nat),X17,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7402,plain,
spl0_831,
inference(avatar_split_clause,[],[f928,f7400]) ).
fof(f7400,plain,
( spl0_831
<=> ! [X45,X17] : ~ c_less(c_plus(X17,X45,tc_nat),X17,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f928,axiom,
! [X45,X17] : ~ c_less(c_plus(X17,X45,tc_nat),X17,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7398,plain,
spl0_830,
inference(avatar_split_clause,[],[f889,f7396]) ).
fof(f7396,plain,
( spl0_830
<=> ! [X2] :
( c_0 = X2
| ~ c_less(X2,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f889,axiom,
! [X2] :
( c_0 = X2
| ~ c_less(X2,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7394,plain,
spl0_829,
inference(avatar_split_clause,[],[f883,f7392]) ).
fof(f883,axiom,
! [X17] :
( c_0 = X17
| ~ c_lessequals(X17,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7390,plain,
spl0_828,
inference(avatar_split_clause,[],[f881,f7388]) ).
fof(f7388,plain,
( spl0_828
<=> ! [X18,X2] : c_lessequals(c_minus(X18,X2,tc_nat),X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f881,axiom,
! [X2,X18] : c_lessequals(c_minus(X18,X2,tc_nat),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7386,plain,
spl0_827,
inference(avatar_split_clause,[],[f653,f7384]) ).
fof(f653,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_0 = c_NatArith_Oof__nat(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f7382,plain,
spl0_826,
inference(avatar_split_clause,[],[f649,f7380]) ).
fof(f649,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_1 = c_NatArith_Oof__nat(c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7378,plain,
spl0_825,
inference(avatar_split_clause,[],[f631,f7376]) ).
fof(f7376,plain,
( spl0_825
<=> ! [X5,X35,X10] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X35,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f631,axiom,
! [X10,X35,X5] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X35,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7374,plain,
spl0_824,
inference(avatar_split_clause,[],[f629,f7372]) ).
fof(f7372,plain,
( spl0_824
<=> ! [X6,X34,X69] : c_List_Olist_ONil = c_List_Ozip(X34,c_List_Olist_ONil,X6,X69) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f629,axiom,
! [X6,X69,X34] : c_List_Olist_ONil = c_List_Ozip(X34,c_List_Olist_ONil,X6,X69),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7370,plain,
spl0_823,
inference(avatar_split_clause,[],[f573,f7368]) ).
fof(f7368,plain,
( spl0_823
<=> ! [X5,X1] : c_List_Orev(c_List_Orev(X1,X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f573,axiom,
! [X1,X5] : c_List_Orev(c_List_Orev(X1,X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7366,plain,
spl0_822,
inference(avatar_split_clause,[],[f552,f7364]) ).
fof(f7364,plain,
( spl0_822
<=> ! [X3,X5,X35] : c_List_Oop_Amem(X3,c_List_Olist_OCons(X3,X35,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f552,axiom,
! [X3,X35,X5] : c_List_Oop_Amem(X3,c_List_Olist_OCons(X3,X35,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7362,plain,
spl0_821,
inference(avatar_split_clause,[],[f472,f7360]) ).
fof(f7360,plain,
( spl0_821
<=> ! [X6,X29,X17] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X17,X29,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f472,axiom,
! [X29,X6,X17] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X17,X29,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7358,plain,
spl0_820,
inference(avatar_split_clause,[],[f383,f7356]) ).
fof(f7356,plain,
( spl0_820
<=> ! [X41,X40] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X40,X41),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f383,axiom,
! [X40,X41] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X40,X41),tc_List_Ochar),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7354,plain,
spl0_819,
inference(avatar_split_clause,[],[f319,f7352]) ).
fof(f319,axiom,
! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7350,plain,
spl0_818,
inference(avatar_split_clause,[],[f246,f7348]) ).
fof(f246,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| c_0 = c_IntDef_Oof__int(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
fof(f7346,plain,
spl0_817,
inference(avatar_split_clause,[],[f242,f7344]) ).
fof(f242,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_1 = c_IntDef_Oof__int(c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7342,plain,
spl0_816,
inference(avatar_split_clause,[],[f228,f7340]) ).
fof(f228,axiom,
! [X2] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X2),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7338,plain,
spl0_815,
inference(avatar_split_clause,[],[f214,f7336]) ).
fof(f7336,plain,
( spl0_815
<=> ! [X2] :
( c_0 = X2
| c_0 != c_IntDef_Oint(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f214,axiom,
! [X2] :
( c_0 = X2
| c_0 != c_IntDef_Oint(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7334,plain,
spl0_814,
inference(avatar_split_clause,[],[f208,f7332]) ).
fof(f208,axiom,
! [X18] : c_IntDef_Oint(X18) = c_HOL_Oabs(c_IntDef_Oint(X18),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7330,plain,
spl0_813,
inference(avatar_split_clause,[],[f94,f7328]) ).
fof(f7328,plain,
( spl0_813
<=> ! [X22,X5,X1] : c_Extraction_Osumbool_Osumbool__rec(X22,X1,c_Extraction_Osumbool_ORight,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f94,axiom,
! [X1,X22,X5] : c_Extraction_Osumbool_Osumbool__rec(X22,X1,c_Extraction_Osumbool_ORight,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7326,plain,
spl0_812,
inference(avatar_split_clause,[],[f93,f7324]) ).
fof(f7324,plain,
( spl0_812
<=> ! [X5,X1,X21] : c_Extraction_Osumbool_Osumbool__rec(X1,X21,c_Extraction_Osumbool_OLeft,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f93,axiom,
! [X21,X1,X5] : c_Extraction_Osumbool_Osumbool__rec(X1,X21,c_Extraction_Osumbool_OLeft,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7322,plain,
spl0_811,
inference(avatar_split_clause,[],[f90,f7320]) ).
fof(f7320,plain,
( spl0_811
<=> ! [X22,X5,X1] : c_Extraction_Osumbool_Osumbool__case(X22,X1,c_Extraction_Osumbool_ORight,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f90,axiom,
! [X1,X22,X5] : c_Extraction_Osumbool_Osumbool__case(X22,X1,c_Extraction_Osumbool_ORight,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7318,plain,
spl0_810,
inference(avatar_split_clause,[],[f89,f7316]) ).
fof(f7316,plain,
( spl0_810
<=> ! [X5,X1,X21] : c_Extraction_Osumbool_Osumbool__case(X1,X21,c_Extraction_Osumbool_OLeft,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f89,axiom,
! [X21,X1,X5] : c_Extraction_Osumbool_Osumbool__case(X1,X21,c_Extraction_Osumbool_OLeft,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7314,plain,
spl0_809,
inference(avatar_split_clause,[],[f66,f7312]) ).
fof(f7312,plain,
( spl0_809
<=> ! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f66,axiom,
! [X18] :
( c_0 = X18
| ~ c_Divides_Oop_Advd(c_0,X18,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7310,plain,
spl0_808,
inference(avatar_split_clause,[],[f56,f7308]) ).
fof(f56,axiom,
! [X2,X18] : c_lessequals(c_div(X18,X2,tc_nat),X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7306,plain,
spl0_807,
inference(avatar_split_clause,[],[f43,f7304]) ).
fof(f7304,plain,
( spl0_807
<=> ! [X5,X11,X10] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X11,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f43,axiom,
! [X10,X11,X5] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X11,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7302,plain,
spl0_806,
inference(avatar_split_clause,[],[f22,f7300]) ).
fof(f7300,plain,
( spl0_806
<=> ! [X5,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X5),X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f22,axiom,
! [X1,X5] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X1,X5),X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7298,plain,
spl0_805,
inference(avatar_split_clause,[],[f2977,f7296]) ).
fof(f2977,plain,
! [X1] : c_div(X1,c_1,tc_nat) = X1,
inference(forward_demodulation,[],[f2771,f2745]) ).
fof(f2771,plain,
! [X1] : c_div(X1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X1,
inference(definition_unfolding,[],[f55,f1385]) ).
fof(f55,axiom,
! [X1] : c_div(X1,c_Suc(c_0),tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7294,plain,
spl0_804,
inference(avatar_split_clause,[],[f2975,f7291]) ).
fof(f7291,plain,
( spl0_804
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2975,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2768,f2745]) ).
fof(f2768,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,[],[f905,f1385]) ).
fof(f905,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
fof(f7289,plain,
spl0_803,
inference(avatar_split_clause,[],[f2973,f7287]) ).
fof(f7287,plain,
( spl0_803
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2973,plain,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_nat),
inference(forward_demodulation,[],[f2767,f2745]) ).
fof(f2767,plain,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f72,f1385]) ).
fof(f72,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7285,plain,
spl0_802,
inference(avatar_split_clause,[],[f2972,f7282]) ).
fof(f2972,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f708,f997]) ).
fof(f708,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7280,plain,
spl0_801,
inference(avatar_split_clause,[],[f2970,f7278]) ).
fof(f7278,plain,
( spl0_801
<=> ! [X6,X1] : c_append(c_List_Olist_ONil,X1,X6) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2970,plain,
! [X1,X6] : c_append(c_List_Olist_ONil,X1,X6) = X1,
inference(forward_demodulation,[],[f2762,f355]) ).
fof(f355,axiom,
! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
fof(f2762,plain,
! [X1,X6] : c_append(c_List_Orev(c_List_Olist_ONil,X6),X1,X6) = X1,
inference(definition_unfolding,[],[f427,f426]) ).
fof(f427,axiom,
! [X1,X6] : c_List_Oitrev(c_List_Olist_ONil,X1,X6) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7276,plain,
spl0_800,
inference(avatar_split_clause,[],[f2968,f7273]) ).
fof(f7273,plain,
( spl0_800
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2968,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2759,f997]) ).
fof(f2759,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f966,f970]) ).
fof(f966,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7271,plain,
spl0_799,
inference(avatar_split_clause,[],[f1636,f7269]) ).
fof(f7269,plain,
( spl0_799
<=> ! [X5,X3] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X3,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f1636,axiom,
! [X3,X5] :
( ~ class_Orderings_Oorder(X5)
| c_lessequals(X3,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7267,plain,
spl0_798,
inference(avatar_split_clause,[],[f1528,f7265]) ).
fof(f1528,axiom,
! [X8,X5,X20] : c_emptyset != c_insert(X8,X20,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
fof(f7263,plain,
spl0_797,
inference(avatar_split_clause,[],[f1480,f7261]) ).
fof(f7261,plain,
( spl0_797
<=> ! [X5,X1] : c_union(X1,c_emptyset,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f1480,axiom,
! [X1,X5] : c_union(X1,c_emptyset,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7259,plain,
spl0_796,
inference(avatar_split_clause,[],[f1479,f7257]) ).
fof(f1479,axiom,
! [X1,X5] : c_union(c_emptyset,X1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7255,plain,
spl0_795,
inference(avatar_split_clause,[],[f1475,f7253]) ).
fof(f7253,plain,
( spl0_795
<=> ! [X5,X1] : c_union(X1,X1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f1475,axiom,
! [X1,X5] : c_union(X1,X1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7251,plain,
spl0_794,
inference(avatar_split_clause,[],[f1474,f7249]) ).
fof(f1474,axiom,
! [X5,X20] : c_UNIV = c_union(X20,c_UNIV,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7247,plain,
spl0_793,
inference(avatar_split_clause,[],[f1473,f7245]) ).
fof(f1473,axiom,
! [X24,X5] : c_UNIV = c_union(c_UNIV,X24,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7243,plain,
spl0_792,
inference(avatar_split_clause,[],[f1421,f7241]) ).
fof(f1421,axiom,
! [X5] : c_UNIV = c_uminus(c_emptyset,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7239,plain,
spl0_791,
inference(avatar_split_clause,[],[f1417,f7237]) ).
fof(f1417,axiom,
! [X5] : c_emptyset = c_uminus(c_UNIV,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7235,plain,
spl0_790,
inference(avatar_split_clause,[],[f1352,f7233]) ).
fof(f7233,plain,
( spl0_790
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1352,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_lessequals(c_0,c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7231,plain,
spl0_789,
inference(avatar_split_clause,[],[f1340,f7229]) ).
fof(f7229,plain,
( spl0_789
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f1340,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| c_less(c_0,c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7227,plain,
spl0_788,
inference(avatar_split_clause,[],[f1335,f7225]) ).
fof(f7225,plain,
( spl0_788
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1335,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_less(c_1,c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7223,plain,
spl0_787,
inference(avatar_split_clause,[],[f1334,f7221]) ).
fof(f7221,plain,
( spl0_787
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_1,c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f1334,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__semidom(X5)
| ~ c_lessequals(c_1,c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7219,plain,
spl0_786,
inference(avatar_split_clause,[],[f1222,f7217]) ).
fof(f7217,plain,
( spl0_786
<=> ! [X5] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1222,axiom,
! [X5] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7215,plain,
spl0_785,
inference(avatar_split_clause,[],[f1221,f7213]) ).
fof(f7213,plain,
( spl0_785
<=> ! [X5,X10] : c_emptyset = c_Relation_ORange(c_emptyset,X10,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1221,axiom,
! [X10,X5] : c_emptyset = c_Relation_ORange(c_emptyset,X10,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7211,plain,
spl0_784,
inference(avatar_split_clause,[],[f1219,f7209]) ).
fof(f7209,plain,
( spl0_784
<=> ! [X5] : c_UNIV = c_Relation_ORange(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1219,axiom,
! [X5] : c_UNIV = c_Relation_ORange(c_Relation_OId,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7207,plain,
spl0_783,
inference(avatar_split_clause,[],[f1211,f7205]) ).
fof(f7205,plain,
( spl0_783
<=> ! [X5,X10] : c_emptyset = c_Relation_ODomain(c_emptyset,X5,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1211,axiom,
! [X10,X5] : c_emptyset = c_Relation_ODomain(c_emptyset,X5,X10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7203,plain,
spl0_782,
inference(avatar_split_clause,[],[f1209,f7201]) ).
fof(f7201,plain,
( spl0_782
<=> ! [X5] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X5,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f1209,axiom,
! [X5] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X5,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7199,plain,
spl0_781,
inference(avatar_split_clause,[],[f1185,f7197]) ).
fof(f1185,axiom,
! [X33] : c_1 = c_Nat_Opower(X33,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7195,plain,
spl0_780,
inference(avatar_split_clause,[],[f1110,f7193]) ).
fof(f7193,plain,
( spl0_780
<=> ! [X5,X3] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X3,X3,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f1110,axiom,
! [X3,X5] :
( ~ class_Orderings_Oorder(X5)
| ~ c_less(X3,X3,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7191,plain,
spl0_779,
inference(avatar_split_clause,[],[f997,f7188]) ).
fof(f7186,plain,
spl0_778,
inference(avatar_split_clause,[],[f943,f7184]) ).
fof(f943,axiom,
! [X1] : c_minus(X1,c_0,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7182,plain,
spl0_777,
inference(avatar_split_clause,[],[f941,f7180]) ).
fof(f941,axiom,
! [X1] : c_plus(c_0,X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7178,plain,
spl0_776,
inference(avatar_split_clause,[],[f939,f7176]) ).
fof(f7176,plain,
( spl0_776
<=> ! [X2] : c_0 = c_times(c_0,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f939,axiom,
! [X2] : c_0 = c_times(c_0,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7174,plain,
spl0_775,
inference(avatar_split_clause,[],[f897,f7172]) ).
fof(f7172,plain,
( spl0_775
<=> ! [X18] : c_0 = c_times(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f897,axiom,
! [X18] : c_0 = c_times(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7170,plain,
spl0_774,
inference(avatar_split_clause,[],[f895,f7168]) ).
fof(f7168,plain,
( spl0_774
<=> ! [X2] : c_0 = c_Orderings_Omin(X2,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f895,axiom,
! [X2] : c_0 = c_Orderings_Omin(X2,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7166,plain,
spl0_773,
inference(avatar_split_clause,[],[f894,f7164]) ).
fof(f7164,plain,
( spl0_773
<=> ! [X2] : c_0 = c_Orderings_Omin(c_0,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f894,axiom,
! [X2] : c_0 = c_Orderings_Omin(c_0,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7162,plain,
spl0_772,
inference(avatar_split_clause,[],[f892,f7160]) ).
fof(f7160,plain,
( spl0_772
<=> ! [X1] : c_Orderings_Omax(X1,c_0,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f892,axiom,
! [X1] : c_Orderings_Omax(X1,c_0,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7158,plain,
spl0_771,
inference(avatar_split_clause,[],[f891,f7156]) ).
fof(f7156,plain,
( spl0_771
<=> ! [X1] : c_Orderings_Omax(c_0,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f891,axiom,
! [X1] : c_Orderings_Omax(c_0,X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7154,plain,
spl0_770,
inference(avatar_split_clause,[],[f882,f7152]) ).
fof(f882,axiom,
! [X18] : c_0 = c_minus(X18,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7150,plain,
spl0_769,
inference(avatar_split_clause,[],[f875,f7148]) ).
fof(f875,axiom,
! [X2] : c_0 = c_minus(c_0,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7146,plain,
spl0_768,
inference(avatar_split_clause,[],[f867,f7144]) ).
fof(f867,axiom,
! [X1] : c_plus(X1,c_0,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7142,plain,
spl0_767,
inference(avatar_split_clause,[],[f628,f7140]) ).
fof(f7140,plain,
( spl0_767
<=> ! [X3,X5,X68] : c_List_Olist_OCons(X3,X68,X5) != X68 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f628,axiom,
! [X3,X68,X5] : c_List_Olist_OCons(X3,X68,X5) != X68,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
fof(f7138,plain,
spl0_766,
inference(avatar_split_clause,[],[f604,f7136]) ).
fof(f7136,plain,
( spl0_766
<=> ! [X20,X5] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X20,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f604,axiom,
! [X5,X20] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X20,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7134,plain,
spl0_765,
inference(avatar_split_clause,[],[f603,f7132]) ).
fof(f7132,plain,
( spl0_765
<=> ! [X34,X5] : c_List_Olist_ONil = c_List_Osublist(X34,c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f603,axiom,
! [X34,X5] : c_List_Olist_ONil = c_List_Osublist(X34,c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7130,plain,
spl0_764,
inference(avatar_split_clause,[],[f588,f7128]) ).
fof(f7128,plain,
( spl0_764
<=> ! [X34,X5] : c_append(X34,c_List_Olist_ONil,X5) = X34 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f588,axiom,
! [X34,X5] : c_append(X34,c_List_Olist_ONil,X5) = X34,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv_1) ).
fof(f7126,plain,
spl0_763,
inference(avatar_split_clause,[],[f582,f7124]) ).
fof(f7124,plain,
( spl0_763
<=> ! [X2,X5] : c_List_Olist_ONil = c_List_Orotate(X2,c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f582,axiom,
! [X2,X5] : c_List_Olist_ONil = c_List_Orotate(X2,c_List_Olist_ONil,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7122,plain,
spl0_762,
inference(avatar_split_clause,[],[f563,f7120]) ).
fof(f563,axiom,
! [X3,X6] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X3,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7118,plain,
spl0_761,
inference(avatar_split_clause,[],[f560,f7116]) ).
fof(f7116,plain,
( spl0_761
<=> ! [X6,X3] : c_List_Olist_ONil = c_List_Oremove1(X3,c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f560,axiom,
! [X3,X6] : c_List_Olist_ONil = c_List_Oremove1(X3,c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7114,plain,
spl0_760,
inference(avatar_split_clause,[],[f548,f7112]) ).
fof(f548,axiom,
! [X3,X6,X34] : ~ c_List_Onull(c_List_Olist_OCons(X3,X34,X6),X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7110,plain,
spl0_759,
inference(avatar_split_clause,[],[f469,f7108]) ).
fof(f7108,plain,
( spl0_759
<=> ! [X6,X51] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X51,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f469,axiom,
! [X51,X6] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X51,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7106,plain,
spl0_758,
inference(avatar_split_clause,[],[f465,f7104]) ).
fof(f7104,plain,
( spl0_758
<=> ! [X5,X7,X49] : c_List_Olist_ONil != c_List_Olist_OCons(X7,X49,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f465,axiom,
! [X49,X7,X5] : c_List_Olist_ONil != c_List_Olist_OCons(X7,X49,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f7102,plain,
spl0_757,
inference(avatar_split_clause,[],[f456,f7100]) ).
fof(f7100,plain,
( spl0_757
<=> ! [X6,X13] : c_emptyset = c_List_Olexn(X13,c_0,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f456,axiom,
! [X6,X13] : c_emptyset = c_List_Olexn(X13,c_0,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7098,plain,
spl0_756,
inference(avatar_split_clause,[],[f439,f7096]) ).
fof(f7096,plain,
( spl0_756
<=> ! [X5] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f439,axiom,
! [X5] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7094,plain,
spl0_755,
inference(avatar_split_clause,[],[f410,f7092]) ).
fof(f7092,plain,
( spl0_755
<=> ! [X5,X1] : c_List_Odrop(c_0,X1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f410,axiom,
! [X1,X5] : c_List_Odrop(c_0,X1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7090,plain,
spl0_754,
inference(avatar_split_clause,[],[f409,f7088]) ).
fof(f7088,plain,
( spl0_754
<=> ! [X6,X2] : c_List_Olist_ONil = c_List_Odrop(X2,c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f409,axiom,
! [X2,X6] : c_List_Olist_ONil = c_List_Odrop(X2,c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7086,plain,
spl0_753,
inference(avatar_split_clause,[],[f335,f7084]) ).
fof(f7084,plain,
( spl0_753
<=> ! [X9] : c_0 = c_Divides_Oop_Amod(c_0,X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f335,axiom,
! [X9] : c_0 = c_Divides_Oop_Amod(c_0,X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7082,plain,
spl0_752,
inference(avatar_split_clause,[],[f332,f7080]) ).
fof(f7080,plain,
( spl0_752
<=> ! [X8] : c_0 = c_Divides_Oop_Amod(X8,X8,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f332,axiom,
! [X8] : c_0 = c_Divides_Oop_Amod(X8,X8,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7078,plain,
spl0_751,
inference(avatar_split_clause,[],[f330,f7076]) ).
fof(f7076,plain,
( spl0_751
<=> ! [X8] : c_0 = c_Divides_Oop_Amod(X8,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f330,axiom,
! [X8] : c_0 = c_Divides_Oop_Amod(X8,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7074,plain,
spl0_750,
inference(avatar_split_clause,[],[f315,f7072]) ).
fof(f7072,plain,
( spl0_750
<=> ! [X9] : c_0 = c_div(c_0,X9,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f315,axiom,
! [X9] : c_0 = c_div(c_0,X9,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7070,plain,
spl0_749,
inference(avatar_split_clause,[],[f307,f7068]) ).
fof(f7068,plain,
( spl0_749
<=> ! [X1] : c_div(X1,c_1,tc_IntDef_Oint) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f307,axiom,
! [X1] : c_div(X1,c_1,tc_IntDef_Oint) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7066,plain,
spl0_748,
inference(avatar_split_clause,[],[f305,f7064]) ).
fof(f7064,plain,
( spl0_748
<=> ! [X33] : c_1 = c_Nat_Opower(X33,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f305,axiom,
! [X33] : c_1 = c_Nat_Opower(X33,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7062,plain,
spl0_747,
inference(avatar_split_clause,[],[f273,f7060]) ).
fof(f273,axiom,
! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_IntDef_Oint) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7058,plain,
spl0_746,
inference(avatar_split_clause,[],[f205,f7056]) ).
fof(f7056,plain,
( spl0_746
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_1,c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f205,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_1,c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7054,plain,
spl0_745,
inference(avatar_split_clause,[],[f204,f7052]) ).
fof(f7052,plain,
( spl0_745
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_0,c_IntDef_ONats,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f204,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| c_in(c_0,c_IntDef_ONats,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7050,plain,
spl0_744,
inference(avatar_split_clause,[],[f199,f7048]) ).
fof(f7048,plain,
( spl0_744
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_1,c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f199,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_1,c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7046,plain,
spl0_743,
inference(avatar_split_clause,[],[f198,f7044]) ).
fof(f7044,plain,
( spl0_743
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_0,c_IntDef_OInts,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f198,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X5)
| c_in(c_0,c_IntDef_OInts,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7042,plain,
spl0_742,
inference(avatar_split_clause,[],[f191,f7039]) ).
fof(f7039,plain,
( spl0_742
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f191,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f7037,plain,
spl0_741,
inference(avatar_split_clause,[],[f86,f7035]) ).
fof(f7035,plain,
( spl0_741
<=> ! [X13,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X13,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f86,axiom,
! [X5,X13] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X13,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
fof(f7033,plain,
spl0_740,
inference(avatar_split_clause,[],[f82,f7031]) ).
fof(f7031,plain,
( spl0_740
<=> ! [X2] : c_0 = c_Divides_Oop_Amod(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f82,axiom,
! [X2] : c_0 = c_Divides_Oop_Amod(X2,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7029,plain,
spl0_739,
inference(avatar_split_clause,[],[f71,f7027]) ).
fof(f71,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(c_0,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7025,plain,
spl0_738,
inference(avatar_split_clause,[],[f54,f7023]) ).
fof(f7023,plain,
( spl0_738
<=> ! [X18] : c_0 = c_div(c_0,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f54,axiom,
! [X18] : c_0 = c_div(c_0,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7021,plain,
spl0_737,
inference(avatar_split_clause,[],[f53,f7019]) ).
fof(f7019,plain,
( spl0_737
<=> ! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f53,axiom,
! [X1] : c_Divides_Oop_Amod(X1,c_0,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7017,plain,
spl0_736,
inference(avatar_split_clause,[],[f52,f7015]) ).
fof(f7015,plain,
( spl0_736
<=> ! [X8] : c_0 = c_div(X8,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f52,axiom,
! [X8] : c_0 = c_div(X8,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7013,plain,
spl0_735,
inference(avatar_split_clause,[],[f24,f7011]) ).
fof(f7011,plain,
( spl0_735
<=> ! [X5,X1] : c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f24,axiom,
! [X1,X5] : c_Datatype_Ounit_Ounit__rec(X1,c_Product__Type_OUnity,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7009,plain,
spl0_734,
inference(avatar_split_clause,[],[f23,f7007]) ).
fof(f7007,plain,
( spl0_734
<=> ! [X5,X1] : c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f23,axiom,
! [X1,X5] : c_Datatype_Ounit_Ounit__case(X1,c_Product__Type_OUnity,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7005,plain,
spl0_733,
inference(avatar_split_clause,[],[f17,f7003]) ).
fof(f7003,plain,
( spl0_733
<=> ! [X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f17,axiom,
! [X5] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f6999,plain,
( spl0_732
| ~ spl0_112
| ~ spl0_671 ),
inference(avatar_split_clause,[],[f6987,f6718,f3706,f6996]) ).
fof(f6718,plain,
( spl0_671
<=> ! [X2] : c_lessequals(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f6987,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_671 ),
inference(superposition,[],[f6719,f3708]) ).
fof(f6719,plain,
( ! [X2] : c_lessequals(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint)
| ~ spl0_671 ),
inference(avatar_component_clause,[],[f6718]) ).
fof(f6993,plain,
( ~ spl0_731
| ~ spl0_113
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f6979,f6710,f3711,f6990]) ).
fof(f6990,plain,
( spl0_731
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f6710,plain,
( spl0_669
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f6979,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_669 ),
inference(superposition,[],[f6711,f3713]) ).
fof(f6711,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint)
| ~ spl0_669 ),
inference(avatar_component_clause,[],[f6710]) ).
fof(f6984,plain,
( ~ spl0_730
| ~ spl0_112
| ~ spl0_669 ),
inference(avatar_split_clause,[],[f6978,f6710,f3706,f6981]) ).
fof(f6981,plain,
( spl0_730
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f6978,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_669 ),
inference(superposition,[],[f6711,f3708]) ).
fof(f6977,plain,
spl0_729,
inference(avatar_split_clause,[],[f2974,f6974]) ).
fof(f6974,plain,
( spl0_729
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2974,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f232,f215]) ).
fof(f215,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f232,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f6972,plain,
spl0_728,
inference(avatar_split_clause,[],[f2969,f6970]) ).
fof(f6970,plain,
( spl0_728
<=> ! [X1] : c_Binomial_Obinomial(X1,c_1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2969,plain,
! [X1] : c_Binomial_Obinomial(X1,c_1) = X1,
inference(forward_demodulation,[],[f2761,f2745]) ).
fof(f2761,plain,
! [X1] : c_Binomial_Obinomial(X1,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X1,
inference(definition_unfolding,[],[f2,f1385]) ).
fof(f2,axiom,
! [X1] : c_Binomial_Obinomial(X1,c_Suc(c_0)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f6968,plain,
spl0_727,
inference(avatar_split_clause,[],[f2744,f6965]) ).
fof(f6963,plain,
spl0_726,
inference(avatar_split_clause,[],[f2729,f6961]) ).
fof(f6961,plain,
( spl0_726
<=> ! [X5,X26] : c_emptyset != c_UNITY_OActs(X26,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2729,axiom,
! [X26,X5] : c_emptyset != c_UNITY_OActs(X26,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNITY_OActs__nonempty_0) ).
fof(f6959,plain,
spl0_725,
inference(avatar_split_clause,[],[f1818,f6957]) ).
fof(f6957,plain,
( spl0_725
<=> ! [X83] :
( ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_set(X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1818,axiom,
! [X83] :
( ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_set(X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6955,plain,
spl0_724,
inference(avatar_split_clause,[],[f1696,f6953]) ).
fof(f6953,plain,
( spl0_724
<=> ! [X83] :
( ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X83)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1696,axiom,
! [X83] :
( ~ class_Finite__Set_Ofinite(X83)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X83)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6951,plain,
spl0_723,
inference(avatar_split_clause,[],[f1680,f6949]) ).
fof(f1680,axiom,
! [X5,X20] : c_lessequals(X20,X20,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6947,plain,
spl0_722,
inference(avatar_split_clause,[],[f1669,f6945]) ).
fof(f6945,plain,
( spl0_722
<=> ! [X20,X5] : c_lessequals(c_emptyset,X20,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1669,axiom,
! [X5,X20] : c_lessequals(c_emptyset,X20,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6943,plain,
spl0_721,
inference(avatar_split_clause,[],[f1612,f6941]) ).
fof(f6941,plain,
( spl0_721
<=> ! [X34,X5] : c_List_Odistinct(c_List_Oremdups(X34,X5),X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1612,axiom,
! [X34,X5] : c_List_Odistinct(c_List_Oremdups(X34,X5),X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6939,plain,
spl0_720,
inference(avatar_split_clause,[],[f1596,f6937]) ).
fof(f6937,plain,
( spl0_720
<=> ! [X5] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1596,axiom,
! [X5] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6935,plain,
spl0_719,
inference(avatar_split_clause,[],[f1555,f6933]) ).
fof(f6933,plain,
( spl0_719
<=> ! [X5] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1555,axiom,
! [X5] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f6931,plain,
spl0_718,
inference(avatar_split_clause,[],[f1539,f6929]) ).
fof(f1539,axiom,
! [X5,X20] : c_lessequals(X20,c_UNIV,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f6927,plain,
spl0_717,
inference(avatar_split_clause,[],[f1532,f6925]) ).
fof(f6925,plain,
( spl0_717
<=> ! [X20,X5] : ~ c_less(X20,c_emptyset,tc_set(X5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1532,axiom,
! [X5,X20] : ~ c_less(X20,c_emptyset,tc_set(X5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f6923,plain,
spl0_716,
inference(avatar_split_clause,[],[f1492,f6921]) ).
fof(f6921,plain,
( spl0_716
<=> ! [X5] : c_emptyset = c_Union(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1492,axiom,
! [X5] : c_emptyset = c_Union(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f6919,plain,
spl0_715,
inference(avatar_split_clause,[],[f1490,f6917]) ).
fof(f1490,axiom,
! [X5] : c_UNIV = c_Union(c_UNIV,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f6915,plain,
spl0_714,
inference(avatar_split_clause,[],[f1466,f6913]) ).
fof(f1466,axiom,
! [X5] : c_UNIV = c_Pow(c_UNIV,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f6911,plain,
spl0_713,
inference(avatar_split_clause,[],[f1460,f6909]) ).
fof(f6909,plain,
( spl0_713
<=> ! [X5] : c_UNIV = c_Inter(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1460,axiom,
! [X5] : c_UNIV = c_Inter(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f6907,plain,
spl0_712,
inference(avatar_split_clause,[],[f1453,f6905]) ).
fof(f1453,axiom,
! [X5] : c_emptyset = c_Inter(c_UNIV,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f6903,plain,
spl0_711,
inference(avatar_split_clause,[],[f1408,f6900]) ).
fof(f6900,plain,
( spl0_711
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f1408,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f6898,plain,
spl0_710,
inference(avatar_split_clause,[],[f1369,f6895]) ).
fof(f6895,plain,
( spl0_710
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f1369,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f6893,plain,
spl0_709,
inference(avatar_split_clause,[],[f1227,f6891]) ).
fof(f6889,plain,
spl0_708,
inference(avatar_split_clause,[],[f1005,f6886]) ).
fof(f6886,plain,
( spl0_708
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f1005,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__2_0) ).
fof(f6884,plain,
spl0_707,
inference(avatar_split_clause,[],[f1004,f6881]) ).
fof(f6881,plain,
( spl0_707
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1004,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__1_0) ).
fof(f6879,plain,
spl0_706,
inference(avatar_split_clause,[],[f993,f6877]) ).
fof(f6877,plain,
( spl0_706
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f993,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f6875,plain,
spl0_705,
inference(avatar_split_clause,[],[f992,f6873]) ).
fof(f6873,plain,
( spl0_705
<=> ! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f992,axiom,
! [X5] :
( ~ class_Ring__and__Field_Oordered__idom(X5)
| ~ c_IntDef_Oneg(c_0,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f6871,plain,
spl0_704,
inference(avatar_split_clause,[],[f976,f6869]) ).
fof(f6869,plain,
( spl0_704
<=> ! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_IntDef_Oiszero(c_1,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f976,axiom,
! [X5] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X5)
| ~ c_IntDef_Oiszero(c_1,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f6867,plain,
spl0_703,
inference(avatar_split_clause,[],[f971,f6865]) ).
fof(f971,axiom,
! [X28] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X28),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6863,plain,
spl0_702,
inference(avatar_split_clause,[],[f956,f6861]) ).
fof(f6861,plain,
( spl0_702
<=> ! [X1] : c_Numeral_Obin__add(X1,c_Numeral_OPls) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f6859,plain,
spl0_701,
inference(avatar_split_clause,[],[f955,f6857]) ).
fof(f6855,plain,
spl0_700,
inference(avatar_split_clause,[],[f947,f6852]) ).
fof(f947,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
fof(f6850,plain,
spl0_699,
inference(avatar_split_clause,[],[f946,f6847]) ).
fof(f946,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
fof(f6845,plain,
spl0_698,
inference(avatar_split_clause,[],[f707,f6842]) ).
fof(f707,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f6840,plain,
spl0_697,
inference(avatar_split_clause,[],[f626,f6838]) ).
fof(f6838,plain,
( spl0_697
<=> ! [X17] : c_List_Olist_ONil = c_List_Oupt(X17,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f626,axiom,
! [X17] : c_List_Olist_ONil = c_List_Oupt(X17,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6836,plain,
spl0_696,
inference(avatar_split_clause,[],[f619,f6834]) ).
fof(f6834,plain,
( spl0_696
<=> ! [X6] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f619,axiom,
! [X6] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6832,plain,
spl0_695,
inference(avatar_split_clause,[],[f594,f6830]) ).
fof(f6830,plain,
( spl0_695
<=> ! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f594,axiom,
! [X5] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
fof(f6828,plain,
spl0_694,
inference(avatar_split_clause,[],[f577,f6826]) ).
fof(f6826,plain,
( spl0_694
<=> ! [X5] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f577,axiom,
! [X5] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6824,plain,
spl0_693,
inference(avatar_split_clause,[],[f559,f6822]) ).
fof(f6822,plain,
( spl0_693
<=> ! [X5] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f559,axiom,
! [X5] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).
fof(f6820,plain,
spl0_692,
inference(avatar_split_clause,[],[f529,f6817]) ).
fof(f6817,plain,
( spl0_692
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f529,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__9_0) ).
fof(f6815,plain,
spl0_691,
inference(avatar_split_clause,[],[f528,f6812]) ).
fof(f6812,plain,
( spl0_691
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f528,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__8_0) ).
fof(f6810,plain,
spl0_690,
inference(avatar_split_clause,[],[f527,f6807]) ).
fof(f6807,plain,
( spl0_690
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f527,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__7_0) ).
fof(f6805,plain,
spl0_689,
inference(avatar_split_clause,[],[f526,f6802]) ).
fof(f6802,plain,
( spl0_689
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f526,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__6_0) ).
fof(f6800,plain,
spl0_688,
inference(avatar_split_clause,[],[f525,f6797]) ).
fof(f6797,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f525,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__5_0) ).
fof(f6795,plain,
spl0_687,
inference(avatar_split_clause,[],[f524,f6792]) ).
fof(f6792,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f524,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__4_0) ).
fof(f6790,plain,
spl0_686,
inference(avatar_split_clause,[],[f523,f6787]) ).
fof(f6787,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f523,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__3_0) ).
fof(f6785,plain,
spl0_685,
inference(avatar_split_clause,[],[f522,f6782]) ).
fof(f6782,plain,
( spl0_685
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f522,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__2_0) ).
fof(f6780,plain,
spl0_684,
inference(avatar_split_clause,[],[f521,f6777]) ).
fof(f6777,plain,
( spl0_684
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f521,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__1_0) ).
fof(f6775,plain,
spl0_683,
inference(avatar_split_clause,[],[f520,f6772]) ).
fof(f6772,plain,
( spl0_683
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f520,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__16_0) ).
fof(f6770,plain,
spl0_682,
inference(avatar_split_clause,[],[f519,f6767]) ).
fof(f6767,plain,
( spl0_682
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f519,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__15_0) ).
fof(f6765,plain,
spl0_681,
inference(avatar_split_clause,[],[f518,f6762]) ).
fof(f6762,plain,
( spl0_681
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f518,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__14_0) ).
fof(f6760,plain,
spl0_680,
inference(avatar_split_clause,[],[f517,f6757]) ).
fof(f6757,plain,
( spl0_680
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f517,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__13_0) ).
fof(f6755,plain,
spl0_679,
inference(avatar_split_clause,[],[f516,f6752]) ).
fof(f6752,plain,
( spl0_679
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f516,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__12_0) ).
fof(f6750,plain,
spl0_678,
inference(avatar_split_clause,[],[f515,f6747]) ).
fof(f6747,plain,
( spl0_678
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f515,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__11_0) ).
fof(f6745,plain,
spl0_677,
inference(avatar_split_clause,[],[f514,f6742]) ).
fof(f6742,plain,
( spl0_677
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f514,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onibble_Osize__10_0) ).
fof(f6740,plain,
spl0_676,
inference(avatar_split_clause,[],[f479,f6738]) ).
fof(f479,axiom,
! [X5] : c_UNIV = c_List_Olists(c_UNIV,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6736,plain,
spl0_675,
inference(avatar_split_clause,[],[f408,f6734]) ).
fof(f6734,plain,
( spl0_675
<=> ! [X45,X17] : c_List_Odistinct(c_List_Oupt(X17,X45),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f408,axiom,
! [X45,X17] : c_List_Odistinct(c_List_Oupt(X17,X45),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6732,plain,
spl0_674,
inference(avatar_split_clause,[],[f384,f6730]) ).
fof(f6730,plain,
( spl0_674
<=> ! [X6] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f384,axiom,
! [X6] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6728,plain,
spl0_673,
inference(avatar_split_clause,[],[f377,f6726]) ).
fof(f6726,plain,
( spl0_673
<=> ! [X6] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f377,axiom,
! [X6] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6724,plain,
spl0_672,
inference(avatar_split_clause,[],[f355,f6722]) ).
fof(f6722,plain,
( spl0_672
<=> ! [X5] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f6720,plain,
spl0_671,
inference(avatar_split_clause,[],[f265,f6718]) ).
fof(f265,axiom,
! [X2] : c_lessequals(c_0,c_IntDef_Oint(X2),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6716,plain,
spl0_670,
inference(avatar_split_clause,[],[f225,f6714]) ).
fof(f225,axiom,
! [X1] : c_IntDef_Onat(c_IntDef_Oint(X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6712,plain,
spl0_669,
inference(avatar_split_clause,[],[f219,f6710]) ).
fof(f219,axiom,
! [X0] : ~ c_less(c_IntDef_Oint(X0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6708,plain,
~ spl0_668,
inference(avatar_split_clause,[],[f150,f6705]) ).
fof(f150,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
fof(f6703,plain,
spl0_667,
inference(avatar_split_clause,[],[f137,f6701]) ).
fof(f6701,plain,
( spl0_667
<=> ! [X5,X1] : c_Fun_Oid(X1,X5) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f137,axiom,
! [X1,X5] : c_Fun_Oid(X1,X5) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6699,plain,
spl0_666,
inference(avatar_split_clause,[],[f136,f6697]) ).
fof(f136,axiom,
! [X1] : c_NatArith_Oof__nat(X1,tc_nat) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6695,plain,
spl0_665,
inference(avatar_split_clause,[],[f119,f6693]) ).
fof(f6693,plain,
( spl0_665
<=> ! [X5] : c_0 = c_Finite__Set_Ocard(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f119,axiom,
! [X5] : c_0 = c_Finite__Set_Ocard(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6691,plain,
spl0_664,
inference(avatar_split_clause,[],[f96,f6688]) ).
fof(f6688,plain,
( spl0_664
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f96,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f6686,plain,
spl0_663,
inference(avatar_split_clause,[],[f95,f6683]) ).
fof(f6683,plain,
( spl0_663
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f95,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f6681,plain,
spl0_662,
inference(avatar_split_clause,[],[f25,f6678]) ).
fof(f6678,plain,
( spl0_662
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f25,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Osize_0) ).
fof(f6676,plain,
spl0_661,
inference(avatar_split_clause,[],[f14,f6674]) ).
fof(f6674,plain,
( spl0_661
<=> ! [X5,X7] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X7,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f14,axiom,
! [X7,X5] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X7,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f6672,plain,
spl0_660,
inference(avatar_split_clause,[],[f13,f6670]) ).
fof(f6670,plain,
( spl0_660
<=> ! [X5] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f13,axiom,
! [X5] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6668,plain,
spl0_659,
inference(avatar_split_clause,[],[f6,f6666]) ).
fof(f6666,plain,
( spl0_659
<=> ! [X2] : c_1 = c_Binomial_Obinomial(X2,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f6,axiom,
! [X2] : c_1 = c_Binomial_Obinomial(X2,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6664,plain,
spl0_658,
inference(avatar_split_clause,[],[f5,f6662]) ).
fof(f6662,plain,
( spl0_658
<=> ! [X2] : c_Binomial_Obinomial(X2,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f5,axiom,
! [X2] : c_Binomial_Obinomial(X2,c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f5900,plain,
( ~ spl0_657
| ~ spl0_113
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f5890,f3721,f3711,f5897]) ).
fof(f5897,plain,
( spl0_657
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f3721,plain,
( spl0_115
<=> ! [X2] : ~ c_IntDef_Oneg(c_IntDef_Oint(X2),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f5890,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_115 ),
inference(superposition,[],[f3722,f3713]) ).
fof(f3722,plain,
( ! [X2] : ~ c_IntDef_Oneg(c_IntDef_Oint(X2),tc_IntDef_Oint)
| ~ spl0_115 ),
inference(avatar_component_clause,[],[f3721]) ).
fof(f5895,plain,
( ~ spl0_656
| ~ spl0_112
| ~ spl0_115 ),
inference(avatar_split_clause,[],[f5889,f3721,f3706,f5892]) ).
fof(f5892,plain,
( spl0_656
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f5889,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_112
| ~ spl0_115 ),
inference(superposition,[],[f3722,f3708]) ).
fof(f5888,plain,
spl0_655,
inference(avatar_split_clause,[],[f2984,f5885]) ).
fof(f5885,plain,
( spl0_655
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2984,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f327,f305]) ).
fof(f327,axiom,
! [X3] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X3,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f5883,plain,
spl0_654,
inference(avatar_split_clause,[],[f2965,f5881]) ).
fof(f5881,plain,
( spl0_654
<=> ! [X0] : c_Divides_Oop_Advd(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2965,plain,
! [X0] : c_Divides_Oop_Advd(c_1,X0,tc_nat),
inference(forward_demodulation,[],[f2749,f2745]) ).
fof(f2749,plain,
! [X0] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X0,tc_nat),
inference(definition_unfolding,[],[f1592,f1385]) ).
fof(f1592,axiom,
! [X0] : c_Divides_Oop_Advd(c_Suc(c_0),X0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f5879,plain,
spl0_653,
inference(avatar_split_clause,[],[f2963,f5876]) ).
fof(f5876,plain,
( spl0_653
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2963,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f218,f215]) ).
fof(f218,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f5874,plain,
spl0_652,
inference(avatar_split_clause,[],[f2962,f5871]) ).
fof(f5871,plain,
( spl0_652
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2962,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2747,f2745]) ).
fof(f2747,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f185,f1385]) ).
fof(f185,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5869,plain,
spl0_651,
inference(avatar_split_clause,[],[f2727,f5867]) ).
fof(f5867,plain,
( spl0_651
<=> ! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2727,axiom,
! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5865,plain,
spl0_650,
inference(avatar_split_clause,[],[f2726,f5863]) ).
fof(f5863,plain,
( spl0_650
<=> ! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2726,axiom,
! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5861,plain,
spl0_649,
inference(avatar_split_clause,[],[f2725,f5859]) ).
fof(f5859,plain,
( spl0_649
<=> ! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2725,axiom,
! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5857,plain,
spl0_648,
inference(avatar_split_clause,[],[f2724,f5855]) ).
fof(f5855,plain,
( spl0_648
<=> ! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2724,axiom,
! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5853,plain,
spl0_647,
inference(avatar_split_clause,[],[f2723,f5851]) ).
fof(f5851,plain,
( spl0_647
<=> ! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2723,axiom,
! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5849,plain,
spl0_646,
inference(avatar_split_clause,[],[f2722,f5847]) ).
fof(f5847,plain,
( spl0_646
<=> ! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2722,axiom,
! [X85] :
( ~ class_Wellfounded__Recursion_Owellorder(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5845,plain,
spl0_645,
inference(avatar_split_clause,[],[f2721,f5843]) ).
fof(f5843,plain,
( spl0_645
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f2721,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5841,plain,
spl0_644,
inference(avatar_split_clause,[],[f2716,f5839]) ).
fof(f5839,plain,
( spl0_644
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f2716,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5837,plain,
spl0_643,
inference(avatar_split_clause,[],[f2715,f5835]) ).
fof(f5835,plain,
( spl0_643
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2715,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5833,plain,
spl0_642,
inference(avatar_split_clause,[],[f2714,f5831]) ).
fof(f5831,plain,
( spl0_642
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f2714,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5829,plain,
spl0_641,
inference(avatar_split_clause,[],[f2713,f5827]) ).
fof(f5827,plain,
( spl0_641
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f2713,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5825,plain,
spl0_640,
inference(avatar_split_clause,[],[f2712,f5823]) ).
fof(f5823,plain,
( spl0_640
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f2712,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5821,plain,
spl0_639,
inference(avatar_split_clause,[],[f2711,f5819]) ).
fof(f5819,plain,
( spl0_639
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f2711,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5817,plain,
spl0_638,
inference(avatar_split_clause,[],[f2708,f5815]) ).
fof(f5815,plain,
( spl0_638
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f2708,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5813,plain,
spl0_637,
inference(avatar_split_clause,[],[f2707,f5811]) ).
fof(f5811,plain,
( spl0_637
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2707,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5809,plain,
spl0_636,
inference(avatar_split_clause,[],[f2706,f5807]) ).
fof(f5807,plain,
( spl0_636
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f2706,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5805,plain,
spl0_635,
inference(avatar_split_clause,[],[f2703,f5803]) ).
fof(f5803,plain,
( spl0_635
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f2703,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5801,plain,
spl0_634,
inference(avatar_split_clause,[],[f2700,f5799]) ).
fof(f5799,plain,
( spl0_634
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f2700,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5797,plain,
spl0_633,
inference(avatar_split_clause,[],[f2699,f5795]) ).
fof(f5795,plain,
( spl0_633
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f2699,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5793,plain,
spl0_632,
inference(avatar_split_clause,[],[f2698,f5791]) ).
fof(f5791,plain,
( spl0_632
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2698,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5789,plain,
spl0_631,
inference(avatar_split_clause,[],[f2697,f5787]) ).
fof(f5787,plain,
( spl0_631
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2697,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5785,plain,
spl0_630,
inference(avatar_split_clause,[],[f2694,f5783]) ).
fof(f5783,plain,
( spl0_630
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f2694,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5781,plain,
spl0_629,
inference(avatar_split_clause,[],[f2693,f5779]) ).
fof(f5779,plain,
( spl0_629
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f2693,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5777,plain,
spl0_628,
inference(avatar_split_clause,[],[f2688,f5775]) ).
fof(f5775,plain,
( spl0_628
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2688,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5773,plain,
spl0_627,
inference(avatar_split_clause,[],[f2685,f5771]) ).
fof(f5771,plain,
( spl0_627
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2685,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5769,plain,
spl0_626,
inference(avatar_split_clause,[],[f2684,f5767]) ).
fof(f5767,plain,
( spl0_626
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2684,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5765,plain,
spl0_625,
inference(avatar_split_clause,[],[f2683,f5763]) ).
fof(f5763,plain,
( spl0_625
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2683,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5761,plain,
spl0_624,
inference(avatar_split_clause,[],[f2681,f5759]) ).
fof(f5759,plain,
( spl0_624
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2681,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5757,plain,
spl0_623,
inference(avatar_split_clause,[],[f2675,f5755]) ).
fof(f5755,plain,
( spl0_623
<=> ! [X85] :
( ~ class_Ring__and__Field_Osemiring__0(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2675,axiom,
! [X85] :
( ~ class_Ring__and__Field_Osemiring__0(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5753,plain,
spl0_622,
inference(avatar_split_clause,[],[f2667,f5751]) ).
fof(f5751,plain,
( spl0_622
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2667,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5749,plain,
spl0_621,
inference(avatar_split_clause,[],[f2666,f5747]) ).
fof(f5747,plain,
( spl0_621
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2666,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5745,plain,
spl0_620,
inference(avatar_split_clause,[],[f2665,f5743]) ).
fof(f5743,plain,
( spl0_620
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2665,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5741,plain,
spl0_619,
inference(avatar_split_clause,[],[f2664,f5739]) ).
fof(f5739,plain,
( spl0_619
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2664,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5737,plain,
spl0_618,
inference(avatar_split_clause,[],[f2663,f5735]) ).
fof(f5735,plain,
( spl0_618
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2663,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5733,plain,
spl0_617,
inference(avatar_split_clause,[],[f2661,f5731]) ).
fof(f5731,plain,
( spl0_617
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2661,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5729,plain,
spl0_616,
inference(avatar_split_clause,[],[f2660,f5727]) ).
fof(f5727,plain,
( spl0_616
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2660,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5725,plain,
spl0_615,
inference(avatar_split_clause,[],[f2659,f5723]) ).
fof(f5723,plain,
( spl0_615
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2659,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5721,plain,
spl0_614,
inference(avatar_split_clause,[],[f2658,f5719]) ).
fof(f5719,plain,
( spl0_614
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2658,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5717,plain,
spl0_613,
inference(avatar_split_clause,[],[f2657,f5715]) ).
fof(f5715,plain,
( spl0_613
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2657,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5713,plain,
spl0_612,
inference(avatar_split_clause,[],[f2652,f5711]) ).
fof(f5711,plain,
( spl0_612
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2652,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5709,plain,
spl0_611,
inference(avatar_split_clause,[],[f2651,f5707]) ).
fof(f5707,plain,
( spl0_611
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2651,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5705,plain,
spl0_610,
inference(avatar_split_clause,[],[f2650,f5703]) ).
fof(f5703,plain,
( spl0_610
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2650,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring__1(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5701,plain,
spl0_609,
inference(avatar_split_clause,[],[f2648,f5699]) ).
fof(f5699,plain,
( spl0_609
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2648,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5697,plain,
spl0_608,
inference(avatar_split_clause,[],[f2646,f5695]) ).
fof(f5695,plain,
( spl0_608
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2646,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5693,plain,
spl0_607,
inference(avatar_split_clause,[],[f2641,f5691]) ).
fof(f5691,plain,
( spl0_607
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2641,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5689,plain,
spl0_606,
inference(avatar_split_clause,[],[f2640,f5687]) ).
fof(f5687,plain,
( spl0_606
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2640,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5685,plain,
spl0_605,
inference(avatar_split_clause,[],[f2639,f5683]) ).
fof(f5683,plain,
( spl0_605
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2639,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5681,plain,
spl0_604,
inference(avatar_split_clause,[],[f2638,f5679]) ).
fof(f5679,plain,
( spl0_604
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2638,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5677,plain,
spl0_603,
inference(avatar_split_clause,[],[f2636,f5675]) ).
fof(f5675,plain,
( spl0_603
<=> ! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2636,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5673,plain,
spl0_602,
inference(avatar_split_clause,[],[f2635,f5671]) ).
fof(f5671,plain,
( spl0_602
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2635,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5669,plain,
spl0_601,
inference(avatar_split_clause,[],[f2630,f5667]) ).
fof(f5667,plain,
( spl0_601
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2630,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5665,plain,
spl0_600,
inference(avatar_split_clause,[],[f2627,f5663]) ).
fof(f5663,plain,
( spl0_600
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2627,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5661,plain,
spl0_599,
inference(avatar_split_clause,[],[f2626,f5659]) ).
fof(f5659,plain,
( spl0_599
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2626,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5657,plain,
spl0_598,
inference(avatar_split_clause,[],[f2625,f5655]) ).
fof(f5655,plain,
( spl0_598
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f2625,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5653,plain,
spl0_597,
inference(avatar_split_clause,[],[f2624,f5651]) ).
fof(f5651,plain,
( spl0_597
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2624,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5649,plain,
spl0_596,
inference(avatar_split_clause,[],[f2621,f5647]) ).
fof(f5647,plain,
( spl0_596
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2621,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5645,plain,
spl0_595,
inference(avatar_split_clause,[],[f2620,f5643]) ).
fof(f5643,plain,
( spl0_595
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2620,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5641,plain,
spl0_594,
inference(avatar_split_clause,[],[f2619,f5639]) ).
fof(f5639,plain,
( spl0_594
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2619,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5637,plain,
spl0_593,
inference(avatar_split_clause,[],[f2618,f5635]) ).
fof(f5635,plain,
( spl0_593
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2618,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5633,plain,
spl0_592,
inference(avatar_split_clause,[],[f2617,f5631]) ).
fof(f5631,plain,
( spl0_592
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2617,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5629,plain,
spl0_591,
inference(avatar_split_clause,[],[f2616,f5627]) ).
fof(f5627,plain,
( spl0_591
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2616,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5625,plain,
spl0_590,
inference(avatar_split_clause,[],[f2615,f5623]) ).
fof(f5623,plain,
( spl0_590
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2615,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5621,plain,
spl0_589,
inference(avatar_split_clause,[],[f2614,f5619]) ).
fof(f5619,plain,
( spl0_589
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2614,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5617,plain,
spl0_588,
inference(avatar_split_clause,[],[f2612,f5615]) ).
fof(f5615,plain,
( spl0_588
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2612,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5613,plain,
spl0_587,
inference(avatar_split_clause,[],[f2611,f5611]) ).
fof(f5611,plain,
( spl0_587
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2611,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5609,plain,
spl0_586,
inference(avatar_split_clause,[],[f2610,f5607]) ).
fof(f5607,plain,
( spl0_586
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2610,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5605,plain,
spl0_585,
inference(avatar_split_clause,[],[f2609,f5603]) ).
fof(f5603,plain,
( spl0_585
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2609,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5601,plain,
spl0_584,
inference(avatar_split_clause,[],[f2608,f5599]) ).
fof(f5599,plain,
( spl0_584
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2608,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5597,plain,
spl0_583,
inference(avatar_split_clause,[],[f2603,f5595]) ).
fof(f5595,plain,
( spl0_583
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2603,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5593,plain,
spl0_582,
inference(avatar_split_clause,[],[f2602,f5591]) ).
fof(f5591,plain,
( spl0_582
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2602,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5589,plain,
spl0_581,
inference(avatar_split_clause,[],[f2601,f5587]) ).
fof(f5587,plain,
( spl0_581
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2601,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__ring(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5585,plain,
spl0_580,
inference(avatar_split_clause,[],[f2598,f5583]) ).
fof(f5583,plain,
( spl0_580
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2598,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5581,plain,
spl0_579,
inference(avatar_split_clause,[],[f2595,f5579]) ).
fof(f5579,plain,
( spl0_579
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2595,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5577,plain,
spl0_578,
inference(avatar_split_clause,[],[f2594,f5575]) ).
fof(f5575,plain,
( spl0_578
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2594,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5573,plain,
spl0_577,
inference(avatar_split_clause,[],[f2592,f5571]) ).
fof(f5571,plain,
( spl0_577
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2592,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5569,plain,
spl0_576,
inference(avatar_split_clause,[],[f2591,f5567]) ).
fof(f5567,plain,
( spl0_576
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2591,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5565,plain,
spl0_575,
inference(avatar_split_clause,[],[f2590,f5563]) ).
fof(f5563,plain,
( spl0_575
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2590,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5561,plain,
spl0_574,
inference(avatar_split_clause,[],[f2589,f5559]) ).
fof(f5559,plain,
( spl0_574
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2589,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5557,plain,
spl0_573,
inference(avatar_split_clause,[],[f2586,f5555]) ).
fof(f5555,plain,
( spl0_573
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2586,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5553,plain,
spl0_572,
inference(avatar_split_clause,[],[f2585,f5551]) ).
fof(f5551,plain,
( spl0_572
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2585,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5549,plain,
spl0_571,
inference(avatar_split_clause,[],[f2557,f5547]) ).
fof(f5547,plain,
( spl0_571
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2557,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5545,plain,
spl0_570,
inference(avatar_split_clause,[],[f2555,f5543]) ).
fof(f5543,plain,
( spl0_570
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2555,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5541,plain,
spl0_569,
inference(avatar_split_clause,[],[f2552,f5539]) ).
fof(f5539,plain,
( spl0_569
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2552,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5537,plain,
spl0_568,
inference(avatar_split_clause,[],[f2551,f5535]) ).
fof(f5535,plain,
( spl0_568
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2551,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5533,plain,
spl0_567,
inference(avatar_split_clause,[],[f2550,f5531]) ).
fof(f5531,plain,
( spl0_567
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2550,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5529,plain,
spl0_566,
inference(avatar_split_clause,[],[f2549,f5527]) ).
fof(f5527,plain,
( spl0_566
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2549,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5525,plain,
spl0_565,
inference(avatar_split_clause,[],[f2548,f5523]) ).
fof(f5523,plain,
( spl0_565
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2548,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5521,plain,
spl0_564,
inference(avatar_split_clause,[],[f2547,f5519]) ).
fof(f5519,plain,
( spl0_564
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2547,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5517,plain,
spl0_563,
inference(avatar_split_clause,[],[f2545,f5515]) ).
fof(f5515,plain,
( spl0_563
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2545,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5513,plain,
spl0_562,
inference(avatar_split_clause,[],[f2544,f5511]) ).
fof(f5511,plain,
( spl0_562
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2544,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5509,plain,
spl0_561,
inference(avatar_split_clause,[],[f2542,f5507]) ).
fof(f5507,plain,
( spl0_561
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2542,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5505,plain,
spl0_560,
inference(avatar_split_clause,[],[f2539,f5503]) ).
fof(f5503,plain,
( spl0_560
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2539,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5501,plain,
spl0_559,
inference(avatar_split_clause,[],[f2538,f5499]) ).
fof(f5499,plain,
( spl0_559
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2538,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5497,plain,
spl0_558,
inference(avatar_split_clause,[],[f2536,f5495]) ).
fof(f5495,plain,
( spl0_558
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2536,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5493,plain,
spl0_557,
inference(avatar_split_clause,[],[f2535,f5491]) ).
fof(f5491,plain,
( spl0_557
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2535,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5489,plain,
spl0_556,
inference(avatar_split_clause,[],[f2534,f5487]) ).
fof(f5487,plain,
( spl0_556
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2534,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5485,plain,
spl0_555,
inference(avatar_split_clause,[],[f2533,f5483]) ).
fof(f5483,plain,
( spl0_555
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2533,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5481,plain,
spl0_554,
inference(avatar_split_clause,[],[f2532,f5479]) ).
fof(f5479,plain,
( spl0_554
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2532,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5477,plain,
spl0_553,
inference(avatar_split_clause,[],[f2531,f5475]) ).
fof(f5475,plain,
( spl0_553
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2531,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5473,plain,
spl0_552,
inference(avatar_split_clause,[],[f2530,f5471]) ).
fof(f5471,plain,
( spl0_552
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2530,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5469,plain,
spl0_551,
inference(avatar_split_clause,[],[f2529,f5467]) ).
fof(f5467,plain,
( spl0_551
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2529,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5465,plain,
spl0_550,
inference(avatar_split_clause,[],[f2525,f5463]) ).
fof(f5463,plain,
( spl0_550
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2525,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5461,plain,
spl0_549,
inference(avatar_split_clause,[],[f2524,f5459]) ).
fof(f5459,plain,
( spl0_549
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2524,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5457,plain,
spl0_548,
inference(avatar_split_clause,[],[f2523,f5455]) ).
fof(f5455,plain,
( spl0_548
<=> ! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2523,axiom,
! [X85] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5453,plain,
spl0_547,
inference(avatar_split_clause,[],[f2522,f5451]) ).
fof(f5451,plain,
( spl0_547
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2522,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5449,plain,
spl0_546,
inference(avatar_split_clause,[],[f2517,f5447]) ).
fof(f5447,plain,
( spl0_546
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2517,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5445,plain,
spl0_545,
inference(avatar_split_clause,[],[f2515,f5443]) ).
fof(f5443,plain,
( spl0_545
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2515,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5441,plain,
spl0_544,
inference(avatar_split_clause,[],[f2514,f5439]) ).
fof(f5439,plain,
( spl0_544
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2514,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5437,plain,
spl0_543,
inference(avatar_split_clause,[],[f2513,f5435]) ).
fof(f5435,plain,
( spl0_543
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2513,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5433,plain,
spl0_542,
inference(avatar_split_clause,[],[f2512,f5431]) ).
fof(f5431,plain,
( spl0_542
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2512,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5429,plain,
spl0_541,
inference(avatar_split_clause,[],[f2510,f5427]) ).
fof(f5427,plain,
( spl0_541
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2510,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5425,plain,
spl0_540,
inference(avatar_split_clause,[],[f2509,f5423]) ).
fof(f5423,plain,
( spl0_540
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2509,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5421,plain,
spl0_539,
inference(avatar_split_clause,[],[f2508,f5419]) ).
fof(f5419,plain,
( spl0_539
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2508,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5417,plain,
spl0_538,
inference(avatar_split_clause,[],[f2507,f5415]) ).
fof(f5415,plain,
( spl0_538
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2507,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5413,plain,
spl0_537,
inference(avatar_split_clause,[],[f2506,f5411]) ).
fof(f5411,plain,
( spl0_537
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2506,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5409,plain,
spl0_536,
inference(avatar_split_clause,[],[f2505,f5407]) ).
fof(f5407,plain,
( spl0_536
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2505,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5405,plain,
spl0_535,
inference(avatar_split_clause,[],[f2504,f5403]) ).
fof(f5403,plain,
( spl0_535
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2504,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5401,plain,
spl0_534,
inference(avatar_split_clause,[],[f2503,f5399]) ).
fof(f5399,plain,
( spl0_534
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2503,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5397,plain,
spl0_533,
inference(avatar_split_clause,[],[f2502,f5395]) ).
fof(f5395,plain,
( spl0_533
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2502,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5393,plain,
spl0_532,
inference(avatar_split_clause,[],[f2501,f5391]) ).
fof(f5391,plain,
( spl0_532
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2501,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5389,plain,
spl0_531,
inference(avatar_split_clause,[],[f2500,f5387]) ).
fof(f5387,plain,
( spl0_531
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2500,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5385,plain,
spl0_530,
inference(avatar_split_clause,[],[f2499,f5383]) ).
fof(f5383,plain,
( spl0_530
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2499,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5381,plain,
spl0_529,
inference(avatar_split_clause,[],[f2498,f5379]) ).
fof(f5379,plain,
( spl0_529
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2498,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5377,plain,
spl0_528,
inference(avatar_split_clause,[],[f2497,f5375]) ).
fof(f5375,plain,
( spl0_528
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2497,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5373,plain,
spl0_527,
inference(avatar_split_clause,[],[f2496,f5371]) ).
fof(f5371,plain,
( spl0_527
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2496,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5369,plain,
spl0_526,
inference(avatar_split_clause,[],[f2495,f5367]) ).
fof(f5367,plain,
( spl0_526
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2495,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5365,plain,
spl0_525,
inference(avatar_split_clause,[],[f2494,f5363]) ).
fof(f5363,plain,
( spl0_525
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2494,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5361,plain,
spl0_524,
inference(avatar_split_clause,[],[f2493,f5359]) ).
fof(f5359,plain,
( spl0_524
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2493,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5357,plain,
spl0_523,
inference(avatar_split_clause,[],[f2492,f5355]) ).
fof(f5355,plain,
( spl0_523
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2492,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5353,plain,
spl0_522,
inference(avatar_split_clause,[],[f2491,f5351]) ).
fof(f5351,plain,
( spl0_522
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2491,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5349,plain,
spl0_521,
inference(avatar_split_clause,[],[f2490,f5347]) ).
fof(f5347,plain,
( spl0_521
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2490,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5345,plain,
spl0_520,
inference(avatar_split_clause,[],[f2489,f5343]) ).
fof(f5343,plain,
( spl0_520
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2489,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5341,plain,
spl0_519,
inference(avatar_split_clause,[],[f2488,f5339]) ).
fof(f5339,plain,
( spl0_519
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2488,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5337,plain,
spl0_518,
inference(avatar_split_clause,[],[f2487,f5335]) ).
fof(f5335,plain,
( spl0_518
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2487,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5333,plain,
spl0_517,
inference(avatar_split_clause,[],[f2486,f5331]) ).
fof(f5331,plain,
( spl0_517
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2486,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5329,plain,
spl0_516,
inference(avatar_split_clause,[],[f2485,f5327]) ).
fof(f5327,plain,
( spl0_516
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2485,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5325,plain,
spl0_515,
inference(avatar_split_clause,[],[f2484,f5323]) ).
fof(f5323,plain,
( spl0_515
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2484,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5321,plain,
spl0_514,
inference(avatar_split_clause,[],[f2483,f5319]) ).
fof(f5319,plain,
( spl0_514
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2483,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5317,plain,
spl0_513,
inference(avatar_split_clause,[],[f2482,f5315]) ).
fof(f5315,plain,
( spl0_513
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2482,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5313,plain,
spl0_512,
inference(avatar_split_clause,[],[f2481,f5311]) ).
fof(f5311,plain,
( spl0_512
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2481,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5309,plain,
spl0_511,
inference(avatar_split_clause,[],[f2480,f5307]) ).
fof(f5307,plain,
( spl0_511
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2480,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5305,plain,
spl0_510,
inference(avatar_split_clause,[],[f2479,f5303]) ).
fof(f5303,plain,
( spl0_510
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2479,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5301,plain,
spl0_509,
inference(avatar_split_clause,[],[f2478,f5299]) ).
fof(f5299,plain,
( spl0_509
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2478,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5297,plain,
spl0_508,
inference(avatar_split_clause,[],[f2477,f5295]) ).
fof(f5295,plain,
( spl0_508
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2477,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5293,plain,
spl0_507,
inference(avatar_split_clause,[],[f2476,f5291]) ).
fof(f5291,plain,
( spl0_507
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2476,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5289,plain,
spl0_506,
inference(avatar_split_clause,[],[f2473,f5287]) ).
fof(f5287,plain,
( spl0_506
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2473,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5285,plain,
spl0_505,
inference(avatar_split_clause,[],[f2471,f5283]) ).
fof(f5283,plain,
( spl0_505
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2471,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5281,plain,
spl0_504,
inference(avatar_split_clause,[],[f2470,f5279]) ).
fof(f5279,plain,
( spl0_504
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2470,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5277,plain,
spl0_503,
inference(avatar_split_clause,[],[f2468,f5275]) ).
fof(f5275,plain,
( spl0_503
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2468,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5273,plain,
spl0_502,
inference(avatar_split_clause,[],[f2465,f5271]) ).
fof(f5271,plain,
( spl0_502
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2465,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5269,plain,
spl0_501,
inference(avatar_split_clause,[],[f2464,f5267]) ).
fof(f5267,plain,
( spl0_501
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2464,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5265,plain,
spl0_500,
inference(avatar_split_clause,[],[f2463,f5263]) ).
fof(f5263,plain,
( spl0_500
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2463,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5261,plain,
spl0_499,
inference(avatar_split_clause,[],[f2461,f5259]) ).
fof(f5259,plain,
( spl0_499
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2461,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5257,plain,
spl0_498,
inference(avatar_split_clause,[],[f2460,f5255]) ).
fof(f5255,plain,
( spl0_498
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2460,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5253,plain,
spl0_497,
inference(avatar_split_clause,[],[f2459,f5251]) ).
fof(f5251,plain,
( spl0_497
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2459,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__semidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5249,plain,
spl0_496,
inference(avatar_split_clause,[],[f2456,f5247]) ).
fof(f5247,plain,
( spl0_496
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2456,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5245,plain,
spl0_495,
inference(avatar_split_clause,[],[f2455,f5243]) ).
fof(f5243,plain,
( spl0_495
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2455,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5241,plain,
spl0_494,
inference(avatar_split_clause,[],[f2454,f5239]) ).
fof(f5239,plain,
( spl0_494
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2454,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5237,plain,
spl0_493,
inference(avatar_split_clause,[],[f2453,f5235]) ).
fof(f5235,plain,
( spl0_493
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2453,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5233,plain,
spl0_492,
inference(avatar_split_clause,[],[f2451,f5231]) ).
fof(f5231,plain,
( spl0_492
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group__join(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2451,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group__join(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5229,plain,
spl0_491,
inference(avatar_split_clause,[],[f2450,f5227]) ).
fof(f5227,plain,
( spl0_491
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group__meet(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2450,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group__meet(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5225,plain,
spl0_490,
inference(avatar_split_clause,[],[f2449,f5223]) ).
fof(f5223,plain,
( spl0_490
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group__abs(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2449,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group__abs(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5221,plain,
spl0_489,
inference(avatar_split_clause,[],[f2448,f5219]) ).
fof(f5219,plain,
( spl0_489
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Opordered__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2448,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Opordered__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5217,plain,
spl0_488,
inference(avatar_split_clause,[],[f2447,f5215]) ).
fof(f5215,plain,
( spl0_488
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Olordered__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2447,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Olordered__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5213,plain,
spl0_487,
inference(avatar_split_clause,[],[f2446,f5211]) ).
fof(f5211,plain,
( spl0_487
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2446,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5209,plain,
spl0_486,
inference(avatar_split_clause,[],[f2445,f5207]) ).
fof(f5207,plain,
( spl0_486
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2445,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5205,plain,
spl0_485,
inference(avatar_split_clause,[],[f2444,f5203]) ).
fof(f5203,plain,
( spl0_485
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2444,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5201,plain,
spl0_484,
inference(avatar_split_clause,[],[f2443,f5199]) ).
fof(f5199,plain,
( spl0_484
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Oaxclass__abs__if(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2443,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Oaxclass__abs__if(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5197,plain,
spl0_483,
inference(avatar_split_clause,[],[f2442,f5195]) ).
fof(f5195,plain,
( spl0_483
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2442,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5193,plain,
spl0_482,
inference(avatar_split_clause,[],[f2441,f5191]) ).
fof(f5191,plain,
( spl0_482
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2441,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5189,plain,
spl0_481,
inference(avatar_split_clause,[],[f2440,f5187]) ).
fof(f5187,plain,
( spl0_481
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2440,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5185,plain,
spl0_480,
inference(avatar_split_clause,[],[f2439,f5183]) ).
fof(f5183,plain,
( spl0_480
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2439,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5181,plain,
spl0_479,
inference(avatar_split_clause,[],[f2438,f5179]) ).
fof(f5179,plain,
( spl0_479
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2438,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5177,plain,
spl0_478,
inference(avatar_split_clause,[],[f2437,f5175]) ).
fof(f5175,plain,
( spl0_478
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2437,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5173,plain,
spl0_477,
inference(avatar_split_clause,[],[f2436,f5171]) ).
fof(f5171,plain,
( spl0_477
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2436,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5169,plain,
spl0_476,
inference(avatar_split_clause,[],[f2435,f5167]) ).
fof(f5167,plain,
( spl0_476
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2435,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5165,plain,
spl0_475,
inference(avatar_split_clause,[],[f2433,f5163]) ).
fof(f5163,plain,
( spl0_475
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2433,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5161,plain,
spl0_474,
inference(avatar_split_clause,[],[f2432,f5159]) ).
fof(f5159,plain,
( spl0_474
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2432,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5157,plain,
spl0_473,
inference(avatar_split_clause,[],[f2431,f5155]) ).
fof(f5155,plain,
( spl0_473
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2431,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5153,plain,
spl0_472,
inference(avatar_split_clause,[],[f2430,f5151]) ).
fof(f5151,plain,
( spl0_472
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2430,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5149,plain,
spl0_471,
inference(avatar_split_clause,[],[f2429,f5147]) ).
fof(f5147,plain,
( spl0_471
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2429,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5145,plain,
spl0_470,
inference(avatar_split_clause,[],[f2424,f5143]) ).
fof(f5143,plain,
( spl0_470
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2424,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5141,plain,
spl0_469,
inference(avatar_split_clause,[],[f2423,f5139]) ).
fof(f5139,plain,
( spl0_469
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2423,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5137,plain,
spl0_468,
inference(avatar_split_clause,[],[f2422,f5135]) ).
fof(f5135,plain,
( spl0_468
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2422,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5133,plain,
spl0_467,
inference(avatar_split_clause,[],[f2421,f5131]) ).
fof(f5131,plain,
( spl0_467
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2421,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5129,plain,
spl0_466,
inference(avatar_split_clause,[],[f2420,f5127]) ).
fof(f5127,plain,
( spl0_466
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2420,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5125,plain,
spl0_465,
inference(avatar_split_clause,[],[f2419,f5123]) ).
fof(f5123,plain,
( spl0_465
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2419,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5121,plain,
spl0_464,
inference(avatar_split_clause,[],[f2418,f5119]) ).
fof(f5119,plain,
( spl0_464
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2418,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5117,plain,
spl0_463,
inference(avatar_split_clause,[],[f2417,f5115]) ).
fof(f5115,plain,
( spl0_463
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oidom(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2417,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oidom(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5113,plain,
spl0_462,
inference(avatar_split_clause,[],[f2415,f5111]) ).
fof(f5111,plain,
( spl0_462
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__semidom(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2415,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__semidom(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5109,plain,
spl0_461,
inference(avatar_split_clause,[],[f2414,f5107]) ).
fof(f5107,plain,
( spl0_461
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2414,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5105,plain,
spl0_460,
inference(avatar_split_clause,[],[f2413,f5103]) ).
fof(f5103,plain,
( spl0_460
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2413,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5101,plain,
spl0_459,
inference(avatar_split_clause,[],[f2412,f5099]) ).
fof(f5099,plain,
( spl0_459
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group__join(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2412,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group__join(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5097,plain,
spl0_458,
inference(avatar_split_clause,[],[f2411,f5095]) ).
fof(f5095,plain,
( spl0_458
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group__meet(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2411,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group__meet(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5093,plain,
spl0_457,
inference(avatar_split_clause,[],[f2410,f5091]) ).
fof(f5091,plain,
( spl0_457
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group__abs(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2410,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Olordered__ab__group__abs(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5089,plain,
spl0_456,
inference(avatar_split_clause,[],[f2408,f5087]) ).
fof(f5087,plain,
( spl0_456
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2408,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5085,plain,
spl0_455,
inference(avatar_split_clause,[],[f2407,f5083]) ).
fof(f5083,plain,
( spl0_455
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Olordered__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2407,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Olordered__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5081,plain,
spl0_454,
inference(avatar_split_clause,[],[f2406,f5079]) ).
fof(f5079,plain,
( spl0_454
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__ring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2406,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__ring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5077,plain,
spl0_453,
inference(avatar_split_clause,[],[f2405,f5075]) ).
fof(f5075,plain,
( spl0_453
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oaxclass__abs__if(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2405,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oaxclass__abs__if(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5073,plain,
spl0_452,
inference(avatar_split_clause,[],[f2404,f5071]) ).
fof(f5071,plain,
( spl0_452
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2404,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5069,plain,
spl0_451,
inference(avatar_split_clause,[],[f2403,f5067]) ).
fof(f5067,plain,
( spl0_451
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2403,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5065,plain,
spl0_450,
inference(avatar_split_clause,[],[f2402,f5063]) ).
fof(f5063,plain,
( spl0_450
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2402,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5061,plain,
spl0_449,
inference(avatar_split_clause,[],[f2401,f5059]) ).
fof(f5059,plain,
( spl0_449
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2401,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5057,plain,
spl0_448,
inference(avatar_split_clause,[],[f2400,f5055]) ).
fof(f5055,plain,
( spl0_448
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2400,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5053,plain,
spl0_447,
inference(avatar_split_clause,[],[f2399,f5051]) ).
fof(f5051,plain,
( spl0_447
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2399,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5049,plain,
spl0_446,
inference(avatar_split_clause,[],[f2398,f5047]) ).
fof(f5047,plain,
( spl0_446
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2398,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5045,plain,
spl0_445,
inference(avatar_split_clause,[],[f2397,f5043]) ).
fof(f5043,plain,
( spl0_445
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2397,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5041,plain,
spl0_444,
inference(avatar_split_clause,[],[f2396,f5039]) ).
fof(f5039,plain,
( spl0_444
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2396,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5037,plain,
spl0_443,
inference(avatar_split_clause,[],[f2395,f5035]) ).
fof(f5035,plain,
( spl0_443
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2395,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5033,plain,
spl0_442,
inference(avatar_split_clause,[],[f2394,f5031]) ).
fof(f5031,plain,
( spl0_442
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2394,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5029,plain,
spl0_441,
inference(avatar_split_clause,[],[f2393,f5027]) ).
fof(f5027,plain,
( spl0_441
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2393,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5025,plain,
spl0_440,
inference(avatar_split_clause,[],[f2392,f5023]) ).
fof(f5023,plain,
( spl0_440
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2392,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5021,plain,
spl0_439,
inference(avatar_split_clause,[],[f2391,f5019]) ).
fof(f5019,plain,
( spl0_439
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2391,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5017,plain,
spl0_438,
inference(avatar_split_clause,[],[f2390,f5015]) ).
fof(f5015,plain,
( spl0_438
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2390,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5013,plain,
spl0_437,
inference(avatar_split_clause,[],[f2389,f5011]) ).
fof(f5011,plain,
( spl0_437
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2389,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5009,plain,
spl0_436,
inference(avatar_split_clause,[],[f2388,f5007]) ).
fof(f5007,plain,
( spl0_436
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2388,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5005,plain,
spl0_435,
inference(avatar_split_clause,[],[f2387,f5003]) ).
fof(f5003,plain,
( spl0_435
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2387,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5001,plain,
spl0_434,
inference(avatar_split_clause,[],[f2384,f4999]) ).
fof(f4999,plain,
( spl0_434
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2384,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f4997,plain,
spl0_433,
inference(avatar_split_clause,[],[f2382,f4995]) ).
fof(f4995,plain,
( spl0_433
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2382,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f4993,plain,
spl0_432,
inference(avatar_split_clause,[],[f2380,f4991]) ).
fof(f4991,plain,
( spl0_432
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2380,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f4989,plain,
spl0_431,
inference(avatar_split_clause,[],[f2377,f4987]) ).
fof(f4987,plain,
( spl0_431
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2377,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f4985,plain,
spl0_430,
inference(avatar_split_clause,[],[f2376,f4983]) ).
fof(f4983,plain,
( spl0_430
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2376,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f4981,plain,
spl0_429,
inference(avatar_split_clause,[],[f2375,f4979]) ).
fof(f4979,plain,
( spl0_429
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2375,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f4977,plain,
spl0_428,
inference(avatar_split_clause,[],[f2374,f4975]) ).
fof(f4975,plain,
( spl0_428
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2374,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f4973,plain,
spl0_427,
inference(avatar_split_clause,[],[f2372,f4971]) ).
fof(f4971,plain,
( spl0_427
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2372,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f4969,plain,
spl0_426,
inference(avatar_split_clause,[],[f2371,f4967]) ).
fof(f4967,plain,
( spl0_426
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2371,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f4965,plain,
spl0_425,
inference(avatar_split_clause,[],[f2370,f4963]) ).
fof(f4963,plain,
( spl0_425
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2370,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4961,plain,
spl0_424,
inference(avatar_split_clause,[],[f2369,f4959]) ).
fof(f4959,plain,
( spl0_424
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2369,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4957,plain,
spl0_423,
inference(avatar_split_clause,[],[f2368,f4955]) ).
fof(f4955,plain,
( spl0_423
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2368,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4953,plain,
spl0_422,
inference(avatar_split_clause,[],[f2367,f4951]) ).
fof(f4951,plain,
( spl0_422
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2367,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4949,plain,
spl0_421,
inference(avatar_split_clause,[],[f2366,f4947]) ).
fof(f4947,plain,
( spl0_421
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2366,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4945,plain,
spl0_420,
inference(avatar_split_clause,[],[f2365,f4943]) ).
fof(f4943,plain,
( spl0_420
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2365,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4941,plain,
spl0_419,
inference(avatar_split_clause,[],[f2364,f4939]) ).
fof(f4939,plain,
( spl0_419
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__ring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2364,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__idom(X85)
| class_Ring__and__Field_Ocomm__ring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4937,plain,
spl0_418,
inference(avatar_split_clause,[],[f2300,f4935]) ).
fof(f4935,plain,
( spl0_418
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2300,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4933,plain,
spl0_417,
inference(avatar_split_clause,[],[f2297,f4931]) ).
fof(f4931,plain,
( spl0_417
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2297,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4929,plain,
spl0_416,
inference(avatar_split_clause,[],[f2296,f4927]) ).
fof(f4927,plain,
( spl0_416
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2296,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4925,plain,
spl0_415,
inference(avatar_split_clause,[],[f2295,f4923]) ).
fof(f4923,plain,
( spl0_415
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2295,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4921,plain,
spl0_414,
inference(avatar_split_clause,[],[f2294,f4919]) ).
fof(f4919,plain,
( spl0_414
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2294,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4917,plain,
spl0_413,
inference(avatar_split_clause,[],[f2293,f4915]) ).
fof(f4915,plain,
( spl0_413
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2293,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4913,plain,
spl0_412,
inference(avatar_split_clause,[],[f2292,f4911]) ).
fof(f4911,plain,
( spl0_412
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2292,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4909,plain,
spl0_411,
inference(avatar_split_clause,[],[f2291,f4907]) ).
fof(f4907,plain,
( spl0_411
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2291,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4905,plain,
spl0_410,
inference(avatar_split_clause,[],[f2290,f4903]) ).
fof(f4903,plain,
( spl0_410
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2290,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Oordered__semiring__strict(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4901,plain,
spl0_409,
inference(avatar_split_clause,[],[f2289,f4899]) ).
fof(f4899,plain,
( spl0_409
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2289,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4897,plain,
spl0_408,
inference(avatar_split_clause,[],[f2288,f4895]) ).
fof(f4895,plain,
( spl0_408
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2288,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4893,plain,
spl0_407,
inference(avatar_split_clause,[],[f2287,f4891]) ).
fof(f4891,plain,
( spl0_407
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2287,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4889,plain,
spl0_406,
inference(avatar_split_clause,[],[f2286,f4887]) ).
fof(f4887,plain,
( spl0_406
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2286,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4885,plain,
spl0_405,
inference(avatar_split_clause,[],[f2284,f4883]) ).
fof(f4883,plain,
( spl0_405
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2284,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4881,plain,
spl0_404,
inference(avatar_split_clause,[],[f2283,f4879]) ).
fof(f4879,plain,
( spl0_404
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2283,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4877,plain,
spl0_403,
inference(avatar_split_clause,[],[f2282,f4875]) ).
fof(f4875,plain,
( spl0_403
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2282,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4873,plain,
spl0_402,
inference(avatar_split_clause,[],[f2281,f4871]) ).
fof(f4871,plain,
( spl0_402
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2281,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4869,plain,
spl0_401,
inference(avatar_split_clause,[],[f2280,f4867]) ).
fof(f4867,plain,
( spl0_401
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2280,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4865,plain,
spl0_400,
inference(avatar_split_clause,[],[f2279,f4863]) ).
fof(f4863,plain,
( spl0_400
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2279,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4861,plain,
spl0_399,
inference(avatar_split_clause,[],[f2278,f4859]) ).
fof(f4859,plain,
( spl0_399
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2278,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4857,plain,
spl0_398,
inference(avatar_split_clause,[],[f2277,f4855]) ).
fof(f4855,plain,
( spl0_398
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2277,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4853,plain,
spl0_397,
inference(avatar_split_clause,[],[f2274,f4851]) ).
fof(f4851,plain,
( spl0_397
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2274,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4849,plain,
spl0_396,
inference(avatar_split_clause,[],[f2273,f4847]) ).
fof(f4847,plain,
( spl0_396
<=> ! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2273,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4845,plain,
spl0_395,
inference(avatar_split_clause,[],[f2272,f4843]) ).
fof(f4843,plain,
( spl0_395
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2272,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4841,plain,
spl0_394,
inference(avatar_split_clause,[],[f2271,f4839]) ).
fof(f4839,plain,
( spl0_394
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2271,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Opordered__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4837,plain,
spl0_393,
inference(avatar_split_clause,[],[f2270,f4835]) ).
fof(f4835,plain,
( spl0_393
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2270,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Opordered__cancel__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4833,plain,
spl0_392,
inference(avatar_split_clause,[],[f2269,f4831]) ).
fof(f4831,plain,
( spl0_392
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2269,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4829,plain,
spl0_391,
inference(avatar_split_clause,[],[f2268,f4827]) ).
fof(f4827,plain,
( spl0_391
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2268,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4825,plain,
spl0_390,
inference(avatar_split_clause,[],[f2266,f4823]) ).
fof(f4823,plain,
( spl0_390
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group__join(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2266,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group__join(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4821,plain,
spl0_389,
inference(avatar_split_clause,[],[f2265,f4819]) ).
fof(f4819,plain,
( spl0_389
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2265,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4817,plain,
spl0_388,
inference(avatar_split_clause,[],[f2264,f4815]) ).
fof(f4815,plain,
( spl0_388
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group__meet(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2264,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group__meet(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4813,plain,
spl0_387,
inference(avatar_split_clause,[],[f2263,f4811]) ).
fof(f4811,plain,
( spl0_387
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2263,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4809,plain,
spl0_386,
inference(avatar_split_clause,[],[f2262,f4807]) ).
fof(f4807,plain,
( spl0_386
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2262,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4805,plain,
spl0_385,
inference(avatar_split_clause,[],[f2261,f4803]) ).
fof(f4803,plain,
( spl0_385
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2261,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4801,plain,
spl0_384,
inference(avatar_split_clause,[],[f2260,f4799]) ).
fof(f4799,plain,
( spl0_384
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2260,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4797,plain,
spl0_383,
inference(avatar_split_clause,[],[f2259,f4795]) ).
fof(f4795,plain,
( spl0_383
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group__abs(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2259,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Olordered__ab__group__abs(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4793,plain,
spl0_382,
inference(avatar_split_clause,[],[f2256,f4791]) ).
fof(f4791,plain,
( spl0_382
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2256,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4789,plain,
spl0_381,
inference(avatar_split_clause,[],[f2254,f4787]) ).
fof(f4787,plain,
( spl0_381
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2254,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4785,plain,
spl0_380,
inference(avatar_split_clause,[],[f2253,f4783]) ).
fof(f4783,plain,
( spl0_380
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2253,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4781,plain,
spl0_379,
inference(avatar_split_clause,[],[f2251,f4779]) ).
fof(f4779,plain,
( spl0_379
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2251,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4777,plain,
spl0_378,
inference(avatar_split_clause,[],[f2248,f4775]) ).
fof(f4775,plain,
( spl0_378
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2248,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4773,plain,
spl0_377,
inference(avatar_split_clause,[],[f2247,f4771]) ).
fof(f4771,plain,
( spl0_377
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2247,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4769,plain,
spl0_376,
inference(avatar_split_clause,[],[f2246,f4767]) ).
fof(f4767,plain,
( spl0_376
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2246,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4765,plain,
spl0_375,
inference(avatar_split_clause,[],[f2245,f4763]) ).
fof(f4763,plain,
( spl0_375
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2245,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4761,plain,
spl0_374,
inference(avatar_split_clause,[],[f2244,f4759]) ).
fof(f4759,plain,
( spl0_374
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f2244,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4757,plain,
spl0_373,
inference(avatar_split_clause,[],[f2243,f4755]) ).
fof(f4755,plain,
( spl0_373
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2243,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4753,plain,
spl0_372,
inference(avatar_split_clause,[],[f2242,f4751]) ).
fof(f4751,plain,
( spl0_372
<=> ! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Opordered__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2242,axiom,
! [X85] :
( ~ class_Ring__and__Field_Olordered__ring(X85)
| class_Ring__and__Field_Opordered__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4749,plain,
spl0_371,
inference(avatar_split_clause,[],[f2241,f4747]) ).
fof(f4747,plain,
( spl0_371
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2241,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4745,plain,
spl0_370,
inference(avatar_split_clause,[],[f2240,f4743]) ).
fof(f4743,plain,
( spl0_370
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2240,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4741,plain,
spl0_369,
inference(avatar_split_clause,[],[f2239,f4739]) ).
fof(f4739,plain,
( spl0_369
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2239,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4737,plain,
spl0_368,
inference(avatar_split_clause,[],[f2238,f4735]) ).
fof(f4735,plain,
( spl0_368
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2238,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4733,plain,
spl0_367,
inference(avatar_split_clause,[],[f2236,f4731]) ).
fof(f4731,plain,
( spl0_367
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2236,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4729,plain,
spl0_366,
inference(avatar_split_clause,[],[f2234,f4727]) ).
fof(f4727,plain,
( spl0_366
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2234,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4725,plain,
spl0_365,
inference(avatar_split_clause,[],[f2231,f4723]) ).
fof(f4723,plain,
( spl0_365
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2231,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4721,plain,
spl0_364,
inference(avatar_split_clause,[],[f2229,f4719]) ).
fof(f4719,plain,
( spl0_364
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2229,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4717,plain,
spl0_363,
inference(avatar_split_clause,[],[f2227,f4715]) ).
fof(f4715,plain,
( spl0_363
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2227,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4713,plain,
spl0_362,
inference(avatar_split_clause,[],[f2224,f4711]) ).
fof(f4711,plain,
( spl0_362
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2224,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4709,plain,
spl0_361,
inference(avatar_split_clause,[],[f2223,f4707]) ).
fof(f4707,plain,
( spl0_361
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Oring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2223,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Oring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4705,plain,
spl0_360,
inference(avatar_split_clause,[],[f2222,f4703]) ).
fof(f4703,plain,
( spl0_360
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2222,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4701,plain,
spl0_359,
inference(avatar_split_clause,[],[f2221,f4699]) ).
fof(f4699,plain,
( spl0_359
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2221,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4697,plain,
spl0_358,
inference(avatar_split_clause,[],[f2219,f4695]) ).
fof(f4695,plain,
( spl0_358
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2219,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4693,plain,
spl0_357,
inference(avatar_split_clause,[],[f2218,f4691]) ).
fof(f4691,plain,
( spl0_357
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2218,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4689,plain,
spl0_356,
inference(avatar_split_clause,[],[f2217,f4687]) ).
fof(f4687,plain,
( spl0_356
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2217,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4685,plain,
spl0_355,
inference(avatar_split_clause,[],[f2216,f4683]) ).
fof(f4683,plain,
( spl0_355
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2216,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4681,plain,
spl0_354,
inference(avatar_split_clause,[],[f2215,f4679]) ).
fof(f4679,plain,
( spl0_354
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2215,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4677,plain,
spl0_353,
inference(avatar_split_clause,[],[f2214,f4675]) ).
fof(f4675,plain,
( spl0_353
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2214,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4673,plain,
spl0_352,
inference(avatar_split_clause,[],[f2213,f4671]) ).
fof(f4671,plain,
( spl0_352
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2213,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4669,plain,
spl0_351,
inference(avatar_split_clause,[],[f2212,f4667]) ).
fof(f4667,plain,
( spl0_351
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2212,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4665,plain,
spl0_350,
inference(avatar_split_clause,[],[f2211,f4663]) ).
fof(f4663,plain,
( spl0_350
<=> ! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__ring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2211,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oidom(X85)
| class_Ring__and__Field_Ocomm__ring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4661,plain,
spl0_349,
inference(avatar_split_clause,[],[f2175,f4659]) ).
fof(f4659,plain,
( spl0_349
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2175,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4657,plain,
spl0_348,
inference(avatar_split_clause,[],[f2174,f4655]) ).
fof(f4655,plain,
( spl0_348
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2174,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4653,plain,
spl0_347,
inference(avatar_split_clause,[],[f2173,f4651]) ).
fof(f4651,plain,
( spl0_347
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2173,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4649,plain,
spl0_346,
inference(avatar_split_clause,[],[f2172,f4647]) ).
fof(f4647,plain,
( spl0_346
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2172,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4645,plain,
spl0_345,
inference(avatar_split_clause,[],[f2171,f4643]) ).
fof(f4643,plain,
( spl0_345
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2171,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4641,plain,
spl0_344,
inference(avatar_split_clause,[],[f2169,f4639]) ).
fof(f4639,plain,
( spl0_344
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2169,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4637,plain,
spl0_343,
inference(avatar_split_clause,[],[f2168,f4635]) ).
fof(f4635,plain,
( spl0_343
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2168,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4633,plain,
spl0_342,
inference(avatar_split_clause,[],[f2167,f4631]) ).
fof(f4631,plain,
( spl0_342
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2167,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4629,plain,
spl0_341,
inference(avatar_split_clause,[],[f2166,f4627]) ).
fof(f4627,plain,
( spl0_341
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2166,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4625,plain,
spl0_340,
inference(avatar_split_clause,[],[f2165,f4623]) ).
fof(f4623,plain,
( spl0_340
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2165,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4621,plain,
spl0_339,
inference(avatar_split_clause,[],[f2164,f4619]) ).
fof(f4619,plain,
( spl0_339
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2164,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4617,plain,
spl0_338,
inference(avatar_split_clause,[],[f2163,f4615]) ).
fof(f4615,plain,
( spl0_338
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2163,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4613,plain,
spl0_337,
inference(avatar_split_clause,[],[f2160,f4611]) ).
fof(f4611,plain,
( spl0_337
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2160,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4609,plain,
spl0_336,
inference(avatar_split_clause,[],[f2159,f4607]) ).
fof(f4607,plain,
( spl0_336
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2159,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4605,plain,
spl0_335,
inference(avatar_split_clause,[],[f2154,f4603]) ).
fof(f4603,plain,
( spl0_335
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2154,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4601,plain,
spl0_334,
inference(avatar_split_clause,[],[f2153,f4599]) ).
fof(f4599,plain,
( spl0_334
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2153,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4597,plain,
spl0_333,
inference(avatar_split_clause,[],[f2150,f4595]) ).
fof(f4595,plain,
( spl0_333
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2150,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4593,plain,
spl0_332,
inference(avatar_split_clause,[],[f2149,f4591]) ).
fof(f4591,plain,
( spl0_332
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2149,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4589,plain,
spl0_331,
inference(avatar_split_clause,[],[f2147,f4587]) ).
fof(f4587,plain,
( spl0_331
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2147,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4585,plain,
spl0_330,
inference(avatar_split_clause,[],[f2146,f4583]) ).
fof(f4583,plain,
( spl0_330
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2146,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4581,plain,
spl0_329,
inference(avatar_split_clause,[],[f2145,f4579]) ).
fof(f4579,plain,
( spl0_329
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2145,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4577,plain,
spl0_328,
inference(avatar_split_clause,[],[f2144,f4575]) ).
fof(f4575,plain,
( spl0_328
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2144,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4573,plain,
spl0_327,
inference(avatar_split_clause,[],[f2143,f4571]) ).
fof(f4571,plain,
( spl0_327
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2143,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4569,plain,
spl0_326,
inference(avatar_split_clause,[],[f2142,f4567]) ).
fof(f4567,plain,
( spl0_326
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2142,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4565,plain,
spl0_325,
inference(avatar_split_clause,[],[f2138,f4563]) ).
fof(f4563,plain,
( spl0_325
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2138,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4561,plain,
spl0_324,
inference(avatar_split_clause,[],[f2136,f4559]) ).
fof(f4559,plain,
( spl0_324
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2136,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4557,plain,
spl0_323,
inference(avatar_split_clause,[],[f2133,f4555]) ).
fof(f4555,plain,
( spl0_323
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2133,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4553,plain,
spl0_322,
inference(avatar_split_clause,[],[f2130,f4551]) ).
fof(f4551,plain,
( spl0_322
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2130,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4549,plain,
spl0_321,
inference(avatar_split_clause,[],[f2129,f4547]) ).
fof(f4547,plain,
( spl0_321
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2129,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4545,plain,
spl0_320,
inference(avatar_split_clause,[],[f2127,f4543]) ).
fof(f4543,plain,
( spl0_320
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2127,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4541,plain,
spl0_319,
inference(avatar_split_clause,[],[f2126,f4539]) ).
fof(f4539,plain,
( spl0_319
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2126,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4537,plain,
spl0_318,
inference(avatar_split_clause,[],[f2125,f4535]) ).
fof(f4535,plain,
( spl0_318
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2125,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4533,plain,
spl0_317,
inference(avatar_split_clause,[],[f2122,f4531]) ).
fof(f4531,plain,
( spl0_317
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2122,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4529,plain,
spl0_316,
inference(avatar_split_clause,[],[f2121,f4527]) ).
fof(f4527,plain,
( spl0_316
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2121,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4525,plain,
spl0_315,
inference(avatar_split_clause,[],[f2119,f4523]) ).
fof(f4523,plain,
( spl0_315
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2119,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4521,plain,
spl0_314,
inference(avatar_split_clause,[],[f2113,f4519]) ).
fof(f4519,plain,
( spl0_314
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2113,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4517,plain,
spl0_313,
inference(avatar_split_clause,[],[f2112,f4515]) ).
fof(f4515,plain,
( spl0_313
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2112,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4513,plain,
spl0_312,
inference(avatar_split_clause,[],[f2110,f4511]) ).
fof(f4511,plain,
( spl0_312
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2110,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4509,plain,
spl0_311,
inference(avatar_split_clause,[],[f2109,f4507]) ).
fof(f4507,plain,
( spl0_311
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2109,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__semiring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4505,plain,
spl0_310,
inference(avatar_split_clause,[],[f2102,f4503]) ).
fof(f4503,plain,
( spl0_310
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2102,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4501,plain,
spl0_309,
inference(avatar_split_clause,[],[f2101,f4499]) ).
fof(f4499,plain,
( spl0_309
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2101,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4497,plain,
spl0_308,
inference(avatar_split_clause,[],[f2099,f4495]) ).
fof(f4495,plain,
( spl0_308
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2099,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4493,plain,
spl0_307,
inference(avatar_split_clause,[],[f2098,f4491]) ).
fof(f4491,plain,
( spl0_307
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2098,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4489,plain,
spl0_306,
inference(avatar_split_clause,[],[f2097,f4487]) ).
fof(f4487,plain,
( spl0_306
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2097,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4485,plain,
spl0_305,
inference(avatar_split_clause,[],[f2095,f4483]) ).
fof(f4483,plain,
( spl0_305
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2095,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4481,plain,
spl0_304,
inference(avatar_split_clause,[],[f2094,f4479]) ).
fof(f4479,plain,
( spl0_304
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2094,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4477,plain,
spl0_303,
inference(avatar_split_clause,[],[f2093,f4475]) ).
fof(f4475,plain,
( spl0_303
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Oring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2093,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Oring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4473,plain,
spl0_302,
inference(avatar_split_clause,[],[f2092,f4471]) ).
fof(f4471,plain,
( spl0_302
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2092,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4469,plain,
spl0_301,
inference(avatar_split_clause,[],[f2091,f4467]) ).
fof(f4467,plain,
( spl0_301
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2091,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4465,plain,
spl0_300,
inference(avatar_split_clause,[],[f2090,f4463]) ).
fof(f4463,plain,
( spl0_300
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2090,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4461,plain,
spl0_299,
inference(avatar_split_clause,[],[f2089,f4459]) ).
fof(f4459,plain,
( spl0_299
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2089,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4457,plain,
spl0_298,
inference(avatar_split_clause,[],[f2088,f4455]) ).
fof(f4455,plain,
( spl0_298
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2088,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4453,plain,
spl0_297,
inference(avatar_split_clause,[],[f2087,f4451]) ).
fof(f4451,plain,
( spl0_297
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2087,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4449,plain,
spl0_296,
inference(avatar_split_clause,[],[f2086,f4447]) ).
fof(f4447,plain,
( spl0_296
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2086,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4445,plain,
spl0_295,
inference(avatar_split_clause,[],[f2083,f4443]) ).
fof(f4443,plain,
( spl0_295
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2083,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4441,plain,
spl0_294,
inference(avatar_split_clause,[],[f2081,f4439]) ).
fof(f4439,plain,
( spl0_294
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2081,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4437,plain,
spl0_293,
inference(avatar_split_clause,[],[f2079,f4435]) ).
fof(f4435,plain,
( spl0_293
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2079,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4433,plain,
spl0_292,
inference(avatar_split_clause,[],[f2076,f4431]) ).
fof(f4431,plain,
( spl0_292
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2076,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4429,plain,
spl0_291,
inference(avatar_split_clause,[],[f2075,f4427]) ).
fof(f4427,plain,
( spl0_291
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2075,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4425,plain,
spl0_290,
inference(avatar_split_clause,[],[f2074,f4423]) ).
fof(f4423,plain,
( spl0_290
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2074,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4421,plain,
spl0_289,
inference(avatar_split_clause,[],[f2071,f4419]) ).
fof(f4419,plain,
( spl0_289
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2071,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4417,plain,
spl0_288,
inference(avatar_split_clause,[],[f2068,f4415]) ).
fof(f4415,plain,
( spl0_288
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2068,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4413,plain,
spl0_287,
inference(avatar_split_clause,[],[f2067,f4411]) ).
fof(f4411,plain,
( spl0_287
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2067,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4409,plain,
spl0_286,
inference(avatar_split_clause,[],[f2065,f4407]) ).
fof(f4407,plain,
( spl0_286
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2065,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4405,plain,
spl0_285,
inference(avatar_split_clause,[],[f2064,f4403]) ).
fof(f4403,plain,
( spl0_285
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2064,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4401,plain,
spl0_284,
inference(avatar_split_clause,[],[f2063,f4399]) ).
fof(f4399,plain,
( spl0_284
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2063,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4397,plain,
spl0_283,
inference(avatar_split_clause,[],[f2062,f4395]) ).
fof(f4395,plain,
( spl0_283
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2062,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4393,plain,
spl0_282,
inference(avatar_split_clause,[],[f2061,f4391]) ).
fof(f4391,plain,
( spl0_282
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2061,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4389,plain,
spl0_281,
inference(avatar_split_clause,[],[f2059,f4387]) ).
fof(f4387,plain,
( spl0_281
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2059,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4385,plain,
spl0_280,
inference(avatar_split_clause,[],[f2056,f4383]) ).
fof(f4383,plain,
( spl0_280
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2056,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4381,plain,
spl0_279,
inference(avatar_split_clause,[],[f2055,f4379]) ).
fof(f4379,plain,
( spl0_279
<=> ! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2055,axiom,
! [X85] :
( ~ class_Ring__and__Field_Ocomm__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4377,plain,
spl0_278,
inference(avatar_split_clause,[],[f2051,f4375]) ).
fof(f4375,plain,
( spl0_278
<=> ! [X85] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2051,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4373,plain,
spl0_277,
inference(avatar_split_clause,[],[f2049,f4371]) ).
fof(f4371,plain,
( spl0_277
<=> ! [X85] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2049,axiom,
! [X85] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4369,plain,
spl0_276,
inference(avatar_split_clause,[],[f2041,f4367]) ).
fof(f4367,plain,
( spl0_276
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2041,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4365,plain,
spl0_275,
inference(avatar_split_clause,[],[f2040,f4363]) ).
fof(f4363,plain,
( spl0_275
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2040,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4361,plain,
spl0_274,
inference(avatar_split_clause,[],[f2039,f4359]) ).
fof(f4359,plain,
( spl0_274
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2039,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4357,plain,
spl0_273,
inference(avatar_split_clause,[],[f2038,f4355]) ).
fof(f4355,plain,
( spl0_273
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2038,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4353,plain,
spl0_272,
inference(avatar_split_clause,[],[f2037,f4351]) ).
fof(f4351,plain,
( spl0_272
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2037,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4349,plain,
spl0_271,
inference(avatar_split_clause,[],[f2036,f4347]) ).
fof(f4347,plain,
( spl0_271
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2036,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4345,plain,
spl0_270,
inference(avatar_split_clause,[],[f2035,f4343]) ).
fof(f4343,plain,
( spl0_270
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2035,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4341,plain,
spl0_269,
inference(avatar_split_clause,[],[f2034,f4339]) ).
fof(f4339,plain,
( spl0_269
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2034,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4337,plain,
spl0_268,
inference(avatar_split_clause,[],[f2033,f4335]) ).
fof(f4335,plain,
( spl0_268
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2033,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4333,plain,
spl0_267,
inference(avatar_split_clause,[],[f2032,f4331]) ).
fof(f4331,plain,
( spl0_267
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2032,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4329,plain,
spl0_266,
inference(avatar_split_clause,[],[f2031,f4327]) ).
fof(f4327,plain,
( spl0_266
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2031,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4325,plain,
spl0_265,
inference(avatar_split_clause,[],[f2030,f4323]) ).
fof(f4323,plain,
( spl0_265
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2030,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4321,plain,
spl0_264,
inference(avatar_split_clause,[],[f2029,f4319]) ).
fof(f4319,plain,
( spl0_264
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2029,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4317,plain,
spl0_263,
inference(avatar_split_clause,[],[f2028,f4315]) ).
fof(f4315,plain,
( spl0_263
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2028,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4313,plain,
spl0_262,
inference(avatar_split_clause,[],[f2027,f4311]) ).
fof(f4311,plain,
( spl0_262
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2027,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4309,plain,
spl0_261,
inference(avatar_split_clause,[],[f2026,f4307]) ).
fof(f4307,plain,
( spl0_261
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2026,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4305,plain,
spl0_260,
inference(avatar_split_clause,[],[f2025,f4303]) ).
fof(f4303,plain,
( spl0_260
<=> ! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2025,axiom,
! [X85] :
( ~ class_Power_Orecpower(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4301,plain,
spl0_259,
inference(avatar_split_clause,[],[f2022,f4299]) ).
fof(f4299,plain,
( spl0_259
<=> ! [X85] :
( ~ class_Orderings_Oorder(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2022,axiom,
! [X85] :
( ~ class_Orderings_Oorder(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4297,plain,
spl0_258,
inference(avatar_split_clause,[],[f2021,f4295]) ).
fof(f4295,plain,
( spl0_258
<=> ! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2021,axiom,
! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4293,plain,
spl0_257,
inference(avatar_split_clause,[],[f2020,f4291]) ).
fof(f4291,plain,
( spl0_257
<=> ! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2020,axiom,
! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4289,plain,
spl0_256,
inference(avatar_split_clause,[],[f2019,f4287]) ).
fof(f4287,plain,
( spl0_256
<=> ! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2019,axiom,
! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4285,plain,
spl0_255,
inference(avatar_split_clause,[],[f2018,f4283]) ).
fof(f4283,plain,
( spl0_255
<=> ! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2018,axiom,
! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4281,plain,
spl0_254,
inference(avatar_split_clause,[],[f2017,f4279]) ).
fof(f4279,plain,
( spl0_254
<=> ! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2017,axiom,
! [X85] :
( ~ class_Orderings_Olinorder(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4277,plain,
spl0_253,
inference(avatar_split_clause,[],[f2014,f4275]) ).
fof(f4275,plain,
( spl0_253
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2014,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4273,plain,
spl0_252,
inference(avatar_split_clause,[],[f2013,f4271]) ).
fof(f4271,plain,
( spl0_252
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2013,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4269,plain,
spl0_251,
inference(avatar_split_clause,[],[f2009,f4267]) ).
fof(f4267,plain,
( spl0_251
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2009,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4265,plain,
spl0_250,
inference(avatar_split_clause,[],[f2008,f4263]) ).
fof(f4263,plain,
( spl0_250
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2008,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4261,plain,
spl0_249,
inference(avatar_split_clause,[],[f2007,f4259]) ).
fof(f4259,plain,
( spl0_249
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2007,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4257,plain,
spl0_248,
inference(avatar_split_clause,[],[f2004,f4255]) ).
fof(f4255,plain,
( spl0_248
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2004,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4253,plain,
spl0_247,
inference(avatar_split_clause,[],[f2002,f4251]) ).
fof(f4251,plain,
( spl0_247
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2002,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4249,plain,
spl0_246,
inference(avatar_split_clause,[],[f2001,f4247]) ).
fof(f4247,plain,
( spl0_246
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2001,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4245,plain,
spl0_245,
inference(avatar_split_clause,[],[f2000,f4243]) ).
fof(f4243,plain,
( spl0_245
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2000,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4241,plain,
spl0_244,
inference(avatar_split_clause,[],[f1999,f4239]) ).
fof(f4239,plain,
( spl0_244
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1999,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4237,plain,
spl0_243,
inference(avatar_split_clause,[],[f1998,f4235]) ).
fof(f4235,plain,
( spl0_243
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1998,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4233,plain,
spl0_242,
inference(avatar_split_clause,[],[f1994,f4231]) ).
fof(f4231,plain,
( spl0_242
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1994,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4229,plain,
spl0_241,
inference(avatar_split_clause,[],[f1993,f4227]) ).
fof(f4227,plain,
( spl0_241
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1993,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4225,plain,
spl0_240,
inference(avatar_split_clause,[],[f1992,f4223]) ).
fof(f4223,plain,
( spl0_240
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1992,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4221,plain,
spl0_239,
inference(avatar_split_clause,[],[f1989,f4219]) ).
fof(f4219,plain,
( spl0_239
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1989,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4217,plain,
spl0_238,
inference(avatar_split_clause,[],[f1987,f4215]) ).
fof(f4215,plain,
( spl0_238
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1987,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4213,plain,
spl0_237,
inference(avatar_split_clause,[],[f1985,f4211]) ).
fof(f4211,plain,
( spl0_237
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1985,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4209,plain,
spl0_236,
inference(avatar_split_clause,[],[f1984,f4207]) ).
fof(f4207,plain,
( spl0_236
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1984,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4205,plain,
spl0_235,
inference(avatar_split_clause,[],[f1983,f4203]) ).
fof(f4203,plain,
( spl0_235
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1983,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4201,plain,
spl0_234,
inference(avatar_split_clause,[],[f1982,f4199]) ).
fof(f4199,plain,
( spl0_234
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1982,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4197,plain,
spl0_233,
inference(avatar_split_clause,[],[f1981,f4195]) ).
fof(f4195,plain,
( spl0_233
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1981,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4193,plain,
spl0_232,
inference(avatar_split_clause,[],[f1979,f4191]) ).
fof(f4191,plain,
( spl0_232
<=> ! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1979,axiom,
! [X85] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4189,plain,
spl0_231,
inference(avatar_split_clause,[],[f1978,f4187]) ).
fof(f4187,plain,
( spl0_231
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Olinorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1978,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Olinorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4185,plain,
spl0_230,
inference(avatar_split_clause,[],[f1975,f4183]) ).
fof(f4183,plain,
( spl0_230
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1975,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4181,plain,
spl0_229,
inference(avatar_split_clause,[],[f1973,f4179]) ).
fof(f4179,plain,
( spl0_229
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1973,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4177,plain,
spl0_228,
inference(avatar_split_clause,[],[f1972,f4175]) ).
fof(f4175,plain,
( spl0_228
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1972,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4173,plain,
spl0_227,
inference(avatar_split_clause,[],[f1971,f4171]) ).
fof(f4171,plain,
( spl0_227
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1971,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4169,plain,
spl0_226,
inference(avatar_split_clause,[],[f1970,f4167]) ).
fof(f4167,plain,
( spl0_226
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1970,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4165,plain,
spl0_225,
inference(avatar_split_clause,[],[f1969,f4163]) ).
fof(f4163,plain,
( spl0_225
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1969,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4161,plain,
spl0_224,
inference(avatar_split_clause,[],[f1968,f4159]) ).
fof(f4159,plain,
( spl0_224
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1968,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4157,plain,
spl0_223,
inference(avatar_split_clause,[],[f1967,f4155]) ).
fof(f4155,plain,
( spl0_223
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1967,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4153,plain,
spl0_222,
inference(avatar_split_clause,[],[f1966,f4151]) ).
fof(f4151,plain,
( spl0_222
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1966,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4149,plain,
spl0_221,
inference(avatar_split_clause,[],[f1965,f4147]) ).
fof(f4147,plain,
( spl0_221
<=> ! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1965,axiom,
! [X85] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4145,plain,
spl0_220,
inference(avatar_split_clause,[],[f1962,f4143]) ).
fof(f4143,plain,
( spl0_220
<=> ! [X85] :
( ~ class_OrderedGroup_Omonoid__mult(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1962,axiom,
! [X85] :
( ~ class_OrderedGroup_Omonoid__mult(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4141,plain,
spl0_219,
inference(avatar_split_clause,[],[f1961,f4139]) ).
fof(f4139,plain,
( spl0_219
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1961,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4137,plain,
spl0_218,
inference(avatar_split_clause,[],[f1960,f4135]) ).
fof(f4135,plain,
( spl0_218
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1960,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4133,plain,
spl0_217,
inference(avatar_split_clause,[],[f1959,f4131]) ).
fof(f4131,plain,
( spl0_217
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1959,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4129,plain,
spl0_216,
inference(avatar_split_clause,[],[f1958,f4127]) ).
fof(f4127,plain,
( spl0_216
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1958,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4125,plain,
spl0_215,
inference(avatar_split_clause,[],[f1957,f4123]) ).
fof(f4123,plain,
( spl0_215
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1957,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4121,plain,
spl0_214,
inference(avatar_split_clause,[],[f1955,f4119]) ).
fof(f4119,plain,
( spl0_214
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1955,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4117,plain,
spl0_213,
inference(avatar_split_clause,[],[f1953,f4115]) ).
fof(f4115,plain,
( spl0_213
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1953,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4113,plain,
spl0_212,
inference(avatar_split_clause,[],[f1952,f4111]) ).
fof(f4111,plain,
( spl0_212
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1952,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4109,plain,
spl0_211,
inference(avatar_split_clause,[],[f1951,f4107]) ).
fof(f4107,plain,
( spl0_211
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1951,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4105,plain,
spl0_210,
inference(avatar_split_clause,[],[f1950,f4103]) ).
fof(f4103,plain,
( spl0_210
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1950,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4101,plain,
spl0_209,
inference(avatar_split_clause,[],[f1947,f4099]) ).
fof(f4099,plain,
( spl0_209
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1947,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4097,plain,
spl0_208,
inference(avatar_split_clause,[],[f1945,f4095]) ).
fof(f4095,plain,
( spl0_208
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1945,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4093,plain,
spl0_207,
inference(avatar_split_clause,[],[f1944,f4091]) ).
fof(f4091,plain,
( spl0_207
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1944,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4089,plain,
spl0_206,
inference(avatar_split_clause,[],[f1943,f4087]) ).
fof(f4087,plain,
( spl0_206
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1943,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4085,plain,
spl0_205,
inference(avatar_split_clause,[],[f1942,f4083]) ).
fof(f4083,plain,
( spl0_205
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1942,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4081,plain,
spl0_204,
inference(avatar_split_clause,[],[f1941,f4079]) ).
fof(f4079,plain,
( spl0_204
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1941,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4077,plain,
spl0_203,
inference(avatar_split_clause,[],[f1940,f4075]) ).
fof(f4075,plain,
( spl0_203
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1940,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4073,plain,
spl0_202,
inference(avatar_split_clause,[],[f1939,f4071]) ).
fof(f4071,plain,
( spl0_202
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1939,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4069,plain,
spl0_201,
inference(avatar_split_clause,[],[f1938,f4067]) ).
fof(f4067,plain,
( spl0_201
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1938,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4065,plain,
spl0_200,
inference(avatar_split_clause,[],[f1936,f4063]) ).
fof(f4063,plain,
( spl0_200
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1936,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4061,plain,
spl0_199,
inference(avatar_split_clause,[],[f1934,f4059]) ).
fof(f4059,plain,
( spl0_199
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1934,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4057,plain,
spl0_198,
inference(avatar_split_clause,[],[f1933,f4055]) ).
fof(f4055,plain,
( spl0_198
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1933,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4053,plain,
spl0_197,
inference(avatar_split_clause,[],[f1932,f4051]) ).
fof(f4051,plain,
( spl0_197
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1932,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4049,plain,
spl0_196,
inference(avatar_split_clause,[],[f1931,f4047]) ).
fof(f4047,plain,
( spl0_196
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1931,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4045,plain,
spl0_195,
inference(avatar_split_clause,[],[f1928,f4043]) ).
fof(f4043,plain,
( spl0_195
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1928,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4041,plain,
spl0_194,
inference(avatar_split_clause,[],[f1926,f4039]) ).
fof(f4039,plain,
( spl0_194
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1926,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4037,plain,
spl0_193,
inference(avatar_split_clause,[],[f1925,f4035]) ).
fof(f4035,plain,
( spl0_193
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1925,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4033,plain,
spl0_192,
inference(avatar_split_clause,[],[f1924,f4031]) ).
fof(f4031,plain,
( spl0_192
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1924,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4029,plain,
spl0_191,
inference(avatar_split_clause,[],[f1923,f4027]) ).
fof(f4027,plain,
( spl0_191
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1923,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4025,plain,
spl0_190,
inference(avatar_split_clause,[],[f1922,f4023]) ).
fof(f4023,plain,
( spl0_190
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1922,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4021,plain,
spl0_189,
inference(avatar_split_clause,[],[f1921,f4019]) ).
fof(f4019,plain,
( spl0_189
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1921,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4017,plain,
spl0_188,
inference(avatar_split_clause,[],[f1920,f4015]) ).
fof(f4015,plain,
( spl0_188
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1920,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4013,plain,
spl0_187,
inference(avatar_split_clause,[],[f1918,f4011]) ).
fof(f4011,plain,
( spl0_187
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1918,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4009,plain,
spl0_186,
inference(avatar_split_clause,[],[f1916,f4007]) ).
fof(f4007,plain,
( spl0_186
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1916,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4005,plain,
spl0_185,
inference(avatar_split_clause,[],[f1915,f4003]) ).
fof(f4003,plain,
( spl0_185
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1915,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4001,plain,
spl0_184,
inference(avatar_split_clause,[],[f1914,f3999]) ).
fof(f3999,plain,
( spl0_184
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1914,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f3997,plain,
spl0_183,
inference(avatar_split_clause,[],[f1913,f3995]) ).
fof(f3995,plain,
( spl0_183
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1913,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f3993,plain,
spl0_182,
inference(avatar_split_clause,[],[f1912,f3991]) ).
fof(f3991,plain,
( spl0_182
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1912,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f3989,plain,
spl0_181,
inference(avatar_split_clause,[],[f1911,f3987]) ).
fof(f3987,plain,
( spl0_181
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1911,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f3985,plain,
spl0_180,
inference(avatar_split_clause,[],[f1908,f3983]) ).
fof(f3983,plain,
( spl0_180
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1908,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f3981,plain,
spl0_179,
inference(avatar_split_clause,[],[f1906,f3979]) ).
fof(f3979,plain,
( spl0_179
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1906,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f3977,plain,
spl0_178,
inference(avatar_split_clause,[],[f1905,f3975]) ).
fof(f3975,plain,
( spl0_178
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1905,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X85)
| class_OrderedGroup_Olordered__ab__group(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f3973,plain,
spl0_177,
inference(avatar_split_clause,[],[f1904,f3971]) ).
fof(f3971,plain,
( spl0_177
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1904,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f3969,plain,
spl0_176,
inference(avatar_split_clause,[],[f1903,f3967]) ).
fof(f3967,plain,
( spl0_176
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1903,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f3965,plain,
spl0_175,
inference(avatar_split_clause,[],[f1902,f3963]) ).
fof(f3963,plain,
( spl0_175
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1902,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3961,plain,
spl0_174,
inference(avatar_split_clause,[],[f1901,f3959]) ).
fof(f3959,plain,
( spl0_174
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1901,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3957,plain,
spl0_173,
inference(avatar_split_clause,[],[f1900,f3955]) ).
fof(f3955,plain,
( spl0_173
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1900,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3953,plain,
spl0_172,
inference(avatar_split_clause,[],[f1898,f3951]) ).
fof(f3951,plain,
( spl0_172
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1898,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3949,plain,
spl0_171,
inference(avatar_split_clause,[],[f1896,f3947]) ).
fof(f3947,plain,
( spl0_171
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1896,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3945,plain,
spl0_170,
inference(avatar_split_clause,[],[f1895,f3943]) ).
fof(f3943,plain,
( spl0_170
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1895,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3941,plain,
spl0_169,
inference(avatar_split_clause,[],[f1894,f3939]) ).
fof(f3939,plain,
( spl0_169
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_LOrder_Olorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1894,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_LOrder_Olorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3937,plain,
spl0_168,
inference(avatar_split_clause,[],[f1891,f3935]) ).
fof(f3935,plain,
( spl0_168
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1891,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3933,plain,
spl0_167,
inference(avatar_split_clause,[],[f1889,f3931]) ).
fof(f3931,plain,
( spl0_167
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1889,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3929,plain,
spl0_166,
inference(avatar_split_clause,[],[f1888,f3927]) ).
fof(f3927,plain,
( spl0_166
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1888,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3925,plain,
spl0_165,
inference(avatar_split_clause,[],[f1887,f3923]) ).
fof(f3923,plain,
( spl0_165
<=> ! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1887,axiom,
! [X85] :
( ~ class_OrderedGroup_Olordered__ab__group(X85)
| class_OrderedGroup_Opordered__ab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3921,plain,
spl0_164,
inference(avatar_split_clause,[],[f1886,f3919]) ).
fof(f3919,plain,
( spl0_164
<=> ! [X85] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1886,axiom,
! [X85] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3917,plain,
spl0_163,
inference(avatar_split_clause,[],[f1882,f3915]) ).
fof(f3915,plain,
( spl0_163
<=> ! [X85] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1882,axiom,
! [X85] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3913,plain,
spl0_162,
inference(avatar_split_clause,[],[f1875,f3911]) ).
fof(f3911,plain,
( spl0_162
<=> ! [X85] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1875,axiom,
! [X85] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3909,plain,
spl0_161,
inference(avatar_split_clause,[],[f1867,f3907]) ).
fof(f3907,plain,
( spl0_161
<=> ! [X85] :
( ~ class_OrderedGroup_Oab__group__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1867,axiom,
! [X85] :
( ~ class_OrderedGroup_Oab__group__add(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3905,plain,
spl0_160,
inference(avatar_split_clause,[],[f1866,f3903]) ).
fof(f3903,plain,
( spl0_160
<=> ! [X85] :
( ~ class_OrderedGroup_Oab__group__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1866,axiom,
! [X85] :
( ~ class_OrderedGroup_Oab__group__add(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3901,plain,
spl0_159,
inference(avatar_split_clause,[],[f1861,f3899]) ).
fof(f3899,plain,
( spl0_159
<=> ! [X85] :
( ~ class_OrderedGroup_Oab__group__add(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1861,axiom,
! [X85] :
( ~ class_OrderedGroup_Oab__group__add(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3897,plain,
spl0_158,
inference(avatar_split_clause,[],[f1859,f3895]) ).
fof(f3895,plain,
( spl0_158
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1859,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocomm__monoid__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3893,plain,
spl0_157,
inference(avatar_split_clause,[],[f1857,f3891]) ).
fof(f3891,plain,
( spl0_157
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1857,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3889,plain,
spl0_156,
inference(avatar_split_clause,[],[f1856,f3887]) ).
fof(f3887,plain,
( spl0_156
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1856,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3885,plain,
spl0_155,
inference(avatar_split_clause,[],[f1853,f3883]) ).
fof(f3883,plain,
( spl0_155
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Numeral_Onumber(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1853,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Numeral_Onumber(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3881,plain,
spl0_154,
inference(avatar_split_clause,[],[f1851,f3879]) ).
fof(f3879,plain,
( spl0_154
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__ring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1851,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__ring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3877,plain,
spl0_153,
inference(avatar_split_clause,[],[f1850,f3875]) ).
fof(f3875,plain,
( spl0_153
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1850,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3873,plain,
spl0_152,
inference(avatar_split_clause,[],[f1849,f3871]) ).
fof(f3871,plain,
( spl0_152
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Oring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1849,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Oring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3869,plain,
spl0_151,
inference(avatar_split_clause,[],[f1848,f3867]) ).
fof(f3867,plain,
( spl0_151
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1848,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__1__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3865,plain,
spl0_150,
inference(avatar_split_clause,[],[f1847,f3863]) ).
fof(f3863,plain,
( spl0_150
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1847,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3861,plain,
spl0_149,
inference(avatar_split_clause,[],[f1846,f3859]) ).
fof(f3859,plain,
( spl0_149
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1846,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3857,plain,
spl0_148,
inference(avatar_split_clause,[],[f1845,f3855]) ).
fof(f3855,plain,
( spl0_148
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1845,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocomm__monoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3853,plain,
spl0_147,
inference(avatar_split_clause,[],[f1844,f3851]) ).
fof(f3851,plain,
( spl0_147
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Omonoid__mult(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1844,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Omonoid__mult(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3849,plain,
spl0_146,
inference(avatar_split_clause,[],[f1843,f3847]) ).
fof(f3847,plain,
( spl0_146
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1843,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Oaxclass__0__neq__1(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3845,plain,
spl0_145,
inference(avatar_split_clause,[],[f1842,f3843]) ).
fof(f3843,plain,
( spl0_145
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_HOL_Oone(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1842,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_HOL_Oone(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3841,plain,
spl0_144,
inference(avatar_split_clause,[],[f1840,f3839]) ).
fof(f3839,plain,
( spl0_144
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1840,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__ring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3837,plain,
spl0_143,
inference(avatar_split_clause,[],[f1839,f3835]) ).
fof(f3835,plain,
( spl0_143
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1839,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3833,plain,
spl0_142,
inference(avatar_split_clause,[],[f1838,f3831]) ).
fof(f3831,plain,
( spl0_142
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Oring(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1838,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Oring(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3829,plain,
spl0_141,
inference(avatar_split_clause,[],[f1837,f3827]) ).
fof(f3827,plain,
( spl0_141
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1837,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__0__cancel(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3825,plain,
spl0_140,
inference(avatar_split_clause,[],[f1836,f3823]) ).
fof(f3823,plain,
( spl0_140
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1836,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Oab__group__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3821,plain,
spl0_139,
inference(avatar_split_clause,[],[f1835,f3819]) ).
fof(f3819,plain,
( spl0_139
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1835,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3817,plain,
spl0_138,
inference(avatar_split_clause,[],[f1834,f3815]) ).
fof(f3815,plain,
( spl0_138
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1834,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_OrderedGroup_Ocancel__semigroup__add(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3813,plain,
spl0_137,
inference(avatar_split_clause,[],[f1832,f3811]) ).
fof(f3811,plain,
( spl0_137
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1832,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Ocomm__semiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3809,plain,
spl0_136,
inference(avatar_split_clause,[],[f1831,f3807]) ).
fof(f3807,plain,
( spl0_136
<=> ! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1831,axiom,
! [X85] :
( ~ class_Numeral_Onumber__ring(X85)
| class_Ring__and__Field_Osemiring__0(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3805,plain,
spl0_135,
inference(avatar_split_clause,[],[f1828,f3803]) ).
fof(f3803,plain,
( spl0_135
<=> ! [X85] :
( ~ class_LOrder_Omeet__semilorder(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1828,axiom,
! [X85] :
( ~ class_LOrder_Omeet__semilorder(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3801,plain,
spl0_134,
inference(avatar_split_clause,[],[f1827,f3799]) ).
fof(f3799,plain,
( spl0_134
<=> ! [X85] :
( ~ class_LOrder_Omeet__semilorder(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1827,axiom,
! [X85] :
( ~ class_LOrder_Omeet__semilorder(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3797,plain,
spl0_133,
inference(avatar_split_clause,[],[f1826,f3795]) ).
fof(f3795,plain,
( spl0_133
<=> ! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_LOrder_Ojoin__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1826,axiom,
! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_LOrder_Ojoin__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3793,plain,
spl0_132,
inference(avatar_split_clause,[],[f1825,f3791]) ).
fof(f3791,plain,
( spl0_132
<=> ! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1825,axiom,
! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3789,plain,
spl0_131,
inference(avatar_split_clause,[],[f1824,f3787]) ).
fof(f3787,plain,
( spl0_131
<=> ! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1824,axiom,
! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3785,plain,
spl0_130,
inference(avatar_split_clause,[],[f1823,f3783]) ).
fof(f3783,plain,
( spl0_130
<=> ! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_LOrder_Omeet__semilorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1823,axiom,
! [X85] :
( ~ class_LOrder_Olorder(X85)
| class_LOrder_Omeet__semilorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3781,plain,
spl0_129,
inference(avatar_split_clause,[],[f1822,f3779]) ).
fof(f3779,plain,
( spl0_129
<=> ! [X85] :
( ~ class_LOrder_Ojoin__semilorder(X85)
| class_Orderings_Oorder(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1822,axiom,
! [X85] :
( ~ class_LOrder_Ojoin__semilorder(X85)
| class_Orderings_Oorder(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3777,plain,
spl0_128,
inference(avatar_split_clause,[],[f1821,f3775]) ).
fof(f3775,plain,
( spl0_128
<=> ! [X85] :
( ~ class_LOrder_Ojoin__semilorder(X85)
| class_Orderings_Oord(X85) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1821,axiom,
! [X85] :
( ~ class_LOrder_Ojoin__semilorder(X85)
| class_Orderings_Oord(X85) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3773,plain,
spl0_127,
inference(avatar_split_clause,[],[f1666,f3771]) ).
fof(f1666,axiom,
! [X3,X5] : c_in(X3,c_UNIV,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3769,plain,
spl0_126,
inference(avatar_split_clause,[],[f1634,f3767]) ).
fof(f3767,plain,
( spl0_126
<=> ! [X2] : ~ c_less(X2,X2,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1634,axiom,
! [X2] : ~ c_less(X2,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3765,plain,
spl0_125,
inference(avatar_split_clause,[],[f1632,f3763]) ).
fof(f1632,axiom,
! [X2] : c_lessequals(c_0,X2,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3761,plain,
spl0_124,
inference(avatar_split_clause,[],[f1608,f3759]) ).
fof(f3759,plain,
( spl0_124
<=> ! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1608,axiom,
! [X18] : c_Divides_Oop_Advd(c_1,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3757,plain,
spl0_123,
inference(avatar_split_clause,[],[f1607,f3755]) ).
fof(f3755,plain,
( spl0_123
<=> ! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1607,axiom,
! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3753,plain,
spl0_122,
inference(avatar_split_clause,[],[f1591,f3751]) ).
fof(f3751,plain,
( spl0_122
<=> ! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1591,axiom,
! [X18] : c_Divides_Oop_Advd(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3749,plain,
spl0_121,
inference(avatar_split_clause,[],[f1513,f3747]) ).
fof(f3747,plain,
( spl0_121
<=> ! [X5,X19] : ~ c_in(X19,c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1513,axiom,
! [X19,X5] : ~ c_in(X19,c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3745,plain,
spl0_120,
inference(avatar_split_clause,[],[f996,f3742]) ).
fof(f3742,plain,
( spl0_120
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f996,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f3740,plain,
spl0_119,
inference(avatar_split_clause,[],[f932,f3738]) ).
fof(f3738,plain,
( spl0_119
<=> ! [X2] : ~ c_less(X2,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f932,axiom,
! [X2] : ~ c_less(X2,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3736,plain,
spl0_118,
inference(avatar_split_clause,[],[f890,f3733]) ).
fof(f890,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3731,plain,
spl0_117,
inference(avatar_split_clause,[],[f550,f3729]) ).
fof(f3729,plain,
( spl0_117
<=> ! [X6,X3] : ~ c_List_Oop_Amem(X3,c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f550,axiom,
! [X3,X6] : ~ c_List_Oop_Amem(X3,c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3727,plain,
spl0_116,
inference(avatar_split_clause,[],[f323,f3725]) ).
fof(f323,axiom,
! [X18] : c_Divides_Oop_Advd(X18,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3723,plain,
spl0_115,
inference(avatar_split_clause,[],[f234,f3721]) ).
fof(f234,axiom,
! [X2] : ~ c_IntDef_Oneg(c_IntDef_Oint(X2),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3719,plain,
spl0_114,
inference(avatar_split_clause,[],[f227,f3716]) ).
fof(f3716,plain,
( spl0_114
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f227,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3714,plain,
spl0_113,
inference(avatar_split_clause,[],[f215,f3711]) ).
fof(f3709,plain,
spl0_112,
inference(avatar_split_clause,[],[f212,f3706]) ).
fof(f212,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3704,plain,
spl0_111,
inference(avatar_split_clause,[],[f70,f3702]) ).
fof(f3702,plain,
( spl0_111
<=> ! [X18] : c_Divides_Oop_Advd(X18,X18,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f70,axiom,
! [X18] : c_Divides_Oop_Advd(X18,X18,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3700,plain,
spl0_110,
inference(avatar_split_clause,[],[f1817,f3698]) ).
fof(f3698,plain,
( spl0_110
<=> ! [X83] : class_Orderings_Oorder(tc_set(X83)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1817,axiom,
! [X83] : class_Orderings_Oorder(tc_set(X83)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3696,plain,
spl0_109,
inference(avatar_split_clause,[],[f1816,f3694]) ).
fof(f3694,plain,
( spl0_109
<=> ! [X83] : class_Orderings_Oord(tc_set(X83)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1816,axiom,
! [X83] : class_Orderings_Oord(tc_set(X83)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3692,plain,
spl0_108,
inference(avatar_split_clause,[],[f1694,f3689]) ).
fof(f3689,plain,
( spl0_108
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1694,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3687,plain,
spl0_107,
inference(avatar_split_clause,[],[f1692,f3684]) ).
fof(f3684,plain,
( spl0_107
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1692,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3682,plain,
spl0_106,
inference(avatar_split_clause,[],[f1691,f3680]) ).
fof(f3680,plain,
( spl0_106
<=> ! [X5] : c_Wellfounded__Recursion_Owf(c_emptyset,X5) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1691,axiom,
! [X5] : c_Wellfounded__Recursion_Owf(c_emptyset,X5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3678,plain,
~ spl0_105,
inference(avatar_split_clause,[],[f1470,f3675]) ).
fof(f3675,plain,
( spl0_105
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1470,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3673,plain,
~ spl0_104,
inference(avatar_split_clause,[],[f1151,f3670]) ).
fof(f3670,plain,
( spl0_104
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1151,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3668,plain,
spl0_103,
inference(avatar_split_clause,[],[f1144,f3665]) ).
fof(f3665,plain,
( spl0_103
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1144,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3663,plain,
spl0_102,
inference(avatar_split_clause,[],[f1131,f3660]) ).
fof(f3660,plain,
( spl0_102
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1131,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3658,plain,
~ spl0_101,
inference(avatar_split_clause,[],[f1001,f3655]) ).
fof(f3655,plain,
( spl0_101
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1001,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).
fof(f3653,plain,
spl0_100,
inference(avatar_split_clause,[],[f547,f3651]) ).
fof(f3651,plain,
( spl0_100
<=> ! [X6] : c_List_Onull(c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f547,axiom,
! [X6] : c_List_Onull(c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3649,plain,
spl0_99,
inference(avatar_split_clause,[],[f392,f3647]) ).
fof(f3647,plain,
( spl0_99
<=> ! [X6] : c_List_Odistinct(c_List_Olist_ONil,X6) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f392,axiom,
! [X6] : c_List_Odistinct(c_List_Olist_ONil,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3645,plain,
~ spl0_98,
inference(avatar_split_clause,[],[f211,f3642]) ).
fof(f211,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3640,plain,
~ spl0_97,
inference(avatar_split_clause,[],[f92,f3637]) ).
fof(f3637,plain,
( spl0_97
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f92,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2_0) ).
fof(f3635,plain,
spl0_96,
inference(avatar_split_clause,[],[f1812,f3632]) ).
fof(f3632,plain,
( spl0_96
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1812,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3630,plain,
spl0_95,
inference(avatar_split_clause,[],[f1811,f3627]) ).
fof(f1811,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3625,plain,
spl0_94,
inference(avatar_split_clause,[],[f1810,f3622]) ).
fof(f3622,plain,
( spl0_94
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1810,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3620,plain,
spl0_93,
inference(avatar_split_clause,[],[f1809,f3617]) ).
fof(f1809,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3615,plain,
spl0_92,
inference(avatar_split_clause,[],[f1807,f3612]) ).
fof(f3612,plain,
( spl0_92
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1807,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3610,plain,
spl0_91,
inference(avatar_split_clause,[],[f1806,f3607]) ).
fof(f1806,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3605,plain,
spl0_90,
inference(avatar_split_clause,[],[f1804,f3602]) ).
fof(f3602,plain,
( spl0_90
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1804,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3600,plain,
spl0_89,
inference(avatar_split_clause,[],[f1803,f3597]) ).
fof(f3597,plain,
( spl0_89
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1803,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3595,plain,
spl0_88,
inference(avatar_split_clause,[],[f1802,f3592]) ).
fof(f3592,plain,
( spl0_88
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1802,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3590,plain,
spl0_87,
inference(avatar_split_clause,[],[f1801,f3587]) ).
fof(f3587,plain,
( spl0_87
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1801,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3585,plain,
spl0_86,
inference(avatar_split_clause,[],[f1800,f3582]) ).
fof(f1800,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3580,plain,
spl0_85,
inference(avatar_split_clause,[],[f1799,f3577]) ).
fof(f3577,plain,
( spl0_85
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1799,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3575,plain,
spl0_84,
inference(avatar_split_clause,[],[f1798,f3572]) ).
fof(f3572,plain,
( spl0_84
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1798,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3570,plain,
spl0_83,
inference(avatar_split_clause,[],[f1797,f3567]) ).
fof(f3567,plain,
( spl0_83
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1797,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3565,plain,
spl0_82,
inference(avatar_split_clause,[],[f1796,f3562]) ).
fof(f3562,plain,
( spl0_82
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1796,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3560,plain,
spl0_81,
inference(avatar_split_clause,[],[f1795,f3557]) ).
fof(f3557,plain,
( spl0_81
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1795,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3555,plain,
spl0_80,
inference(avatar_split_clause,[],[f1794,f3552]) ).
fof(f3552,plain,
( spl0_80
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1794,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3550,plain,
spl0_79,
inference(avatar_split_clause,[],[f1793,f3547]) ).
fof(f3547,plain,
( spl0_79
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1793,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3545,plain,
spl0_78,
inference(avatar_split_clause,[],[f1792,f3542]) ).
fof(f1792,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3540,plain,
spl0_77,
inference(avatar_split_clause,[],[f1791,f3537]) ).
fof(f3537,plain,
( spl0_77
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1791,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3535,plain,
spl0_76,
inference(avatar_split_clause,[],[f1790,f3532]) ).
fof(f3532,plain,
( spl0_76
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1790,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3530,plain,
spl0_75,
inference(avatar_split_clause,[],[f1789,f3527]) ).
fof(f3527,plain,
( spl0_75
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1789,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3525,plain,
spl0_74,
inference(avatar_split_clause,[],[f1788,f3522]) ).
fof(f3522,plain,
( spl0_74
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1788,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3520,plain,
spl0_73,
inference(avatar_split_clause,[],[f1787,f3517]) ).
fof(f3517,plain,
( spl0_73
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1787,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3515,plain,
spl0_72,
inference(avatar_split_clause,[],[f1786,f3512]) ).
fof(f3512,plain,
( spl0_72
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1786,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3510,plain,
spl0_71,
inference(avatar_split_clause,[],[f1785,f3507]) ).
fof(f3507,plain,
( spl0_71
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1785,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3505,plain,
spl0_70,
inference(avatar_split_clause,[],[f1784,f3502]) ).
fof(f3502,plain,
( spl0_70
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1784,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3500,plain,
spl0_69,
inference(avatar_split_clause,[],[f1783,f3497]) ).
fof(f3497,plain,
( spl0_69
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1783,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3495,plain,
spl0_68,
inference(avatar_split_clause,[],[f1782,f3492]) ).
fof(f1782,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3490,plain,
spl0_67,
inference(avatar_split_clause,[],[f1781,f3487]) ).
fof(f3487,plain,
( spl0_67
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1781,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3485,plain,
spl0_66,
inference(avatar_split_clause,[],[f1780,f3482]) ).
fof(f3482,plain,
( spl0_66
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1780,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3480,plain,
spl0_65,
inference(avatar_split_clause,[],[f1779,f3477]) ).
fof(f3477,plain,
( spl0_65
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1779,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3475,plain,
spl0_64,
inference(avatar_split_clause,[],[f1778,f3472]) ).
fof(f3472,plain,
( spl0_64
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1778,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3470,plain,
spl0_63,
inference(avatar_split_clause,[],[f1777,f3467]) ).
fof(f3467,plain,
( spl0_63
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1777,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3465,plain,
spl0_62,
inference(avatar_split_clause,[],[f1776,f3462]) ).
fof(f3462,plain,
( spl0_62
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1776,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3460,plain,
spl0_61,
inference(avatar_split_clause,[],[f1771,f3457]) ).
fof(f3457,plain,
( spl0_61
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1771,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3455,plain,
spl0_60,
inference(avatar_split_clause,[],[f1766,f3452]) ).
fof(f3452,plain,
( spl0_60
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1766,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3450,plain,
spl0_59,
inference(avatar_split_clause,[],[f1763,f3447]) ).
fof(f3447,plain,
( spl0_59
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1763,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3445,plain,
spl0_58,
inference(avatar_split_clause,[],[f1762,f3442]) ).
fof(f3442,plain,
( spl0_58
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1762,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3440,plain,
spl0_57,
inference(avatar_split_clause,[],[f1757,f3437]) ).
fof(f1757,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3435,plain,
spl0_56,
inference(avatar_split_clause,[],[f1754,f3432]) ).
fof(f1754,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3430,plain,
spl0_55,
inference(avatar_split_clause,[],[f1752,f3427]) ).
fof(f3427,plain,
( spl0_55
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1752,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3425,plain,
spl0_54,
inference(avatar_split_clause,[],[f1751,f3422]) ).
fof(f1751,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3420,plain,
spl0_53,
inference(avatar_split_clause,[],[f1750,f3417]) ).
fof(f3417,plain,
( spl0_53
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1750,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3415,plain,
spl0_52,
inference(avatar_split_clause,[],[f1749,f3412]) ).
fof(f1749,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3410,plain,
spl0_51,
inference(avatar_split_clause,[],[f1748,f3407]) ).
fof(f3407,plain,
( spl0_51
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1748,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3405,plain,
spl0_50,
inference(avatar_split_clause,[],[f1746,f3402]) ).
fof(f3402,plain,
( spl0_50
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1746,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3400,plain,
spl0_49,
inference(avatar_split_clause,[],[f1745,f3397]) ).
fof(f3397,plain,
( spl0_49
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1745,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3395,plain,
spl0_48,
inference(avatar_split_clause,[],[f1744,f3392]) ).
fof(f3392,plain,
( spl0_48
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1744,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3390,plain,
spl0_47,
inference(avatar_split_clause,[],[f1743,f3387]) ).
fof(f3387,plain,
( spl0_47
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1743,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3385,plain,
spl0_46,
inference(avatar_split_clause,[],[f1742,f3382]) ).
fof(f3382,plain,
( spl0_46
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1742,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3380,plain,
spl0_45,
inference(avatar_split_clause,[],[f1741,f3377]) ).
fof(f3377,plain,
( spl0_45
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1741,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3375,plain,
spl0_44,
inference(avatar_split_clause,[],[f1740,f3372]) ).
fof(f1740,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3370,plain,
spl0_43,
inference(avatar_split_clause,[],[f1739,f3367]) ).
fof(f1739,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3365,plain,
spl0_42,
inference(avatar_split_clause,[],[f1738,f3362]) ).
fof(f3362,plain,
( spl0_42
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1738,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3360,plain,
spl0_41,
inference(avatar_split_clause,[],[f1737,f3357]) ).
fof(f3357,plain,
( spl0_41
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1737,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3355,plain,
spl0_40,
inference(avatar_split_clause,[],[f1736,f3352]) ).
fof(f3352,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1736,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3350,plain,
spl0_39,
inference(avatar_split_clause,[],[f1735,f3347]) ).
fof(f3347,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1735,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3345,plain,
spl0_38,
inference(avatar_split_clause,[],[f1734,f3342]) ).
fof(f3342,plain,
( spl0_38
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1734,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3340,plain,
spl0_37,
inference(avatar_split_clause,[],[f1733,f3337]) ).
fof(f3337,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1733,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3335,plain,
spl0_36,
inference(avatar_split_clause,[],[f1732,f3332]) ).
fof(f3332,plain,
( spl0_36
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1732,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3330,plain,
spl0_35,
inference(avatar_split_clause,[],[f1730,f3327]) ).
fof(f3327,plain,
( spl0_35
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1730,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3325,plain,
spl0_34,
inference(avatar_split_clause,[],[f1729,f3322]) ).
fof(f3322,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1729,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3320,plain,
spl0_33,
inference(avatar_split_clause,[],[f1728,f3317]) ).
fof(f3317,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1728,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3315,plain,
spl0_32,
inference(avatar_split_clause,[],[f1727,f3312]) ).
fof(f3312,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1727,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3310,plain,
spl0_31,
inference(avatar_split_clause,[],[f1726,f3307]) ).
fof(f1726,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3305,plain,
spl0_30,
inference(avatar_split_clause,[],[f1725,f3302]) ).
fof(f3302,plain,
( spl0_30
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1725,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3300,plain,
spl0_29,
inference(avatar_split_clause,[],[f1724,f3297]) ).
fof(f1724,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3295,plain,
spl0_28,
inference(avatar_split_clause,[],[f1723,f3292]) ).
fof(f1723,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3290,plain,
spl0_27,
inference(avatar_split_clause,[],[f1722,f3287]) ).
fof(f3287,plain,
( spl0_27
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1722,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3285,plain,
spl0_26,
inference(avatar_split_clause,[],[f1721,f3282]) ).
fof(f1721,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3280,plain,
spl0_25,
inference(avatar_split_clause,[],[f1719,f3277]) ).
fof(f1719,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3275,plain,
spl0_24,
inference(avatar_split_clause,[],[f1718,f3272]) ).
fof(f3272,plain,
( spl0_24
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1718,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3270,plain,
spl0_23,
inference(avatar_split_clause,[],[f1717,f3267]) ).
fof(f3267,plain,
( spl0_23
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1717,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3265,plain,
spl0_22,
inference(avatar_split_clause,[],[f1716,f3262]) ).
fof(f3262,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1716,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3260,plain,
spl0_21,
inference(avatar_split_clause,[],[f1715,f3257]) ).
fof(f3257,plain,
( spl0_21
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1715,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3255,plain,
spl0_20,
inference(avatar_split_clause,[],[f1714,f3252]) ).
fof(f3252,plain,
( spl0_20
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1714,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3250,plain,
spl0_19,
inference(avatar_split_clause,[],[f1713,f3247]) ).
fof(f1713,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3245,plain,
spl0_18,
inference(avatar_split_clause,[],[f1712,f3242]) ).
fof(f3242,plain,
( spl0_18
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1712,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3240,plain,
spl0_17,
inference(avatar_split_clause,[],[f1711,f3237]) ).
fof(f3237,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1711,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3235,plain,
spl0_16,
inference(avatar_split_clause,[],[f1710,f3232]) ).
fof(f3232,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1710,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3230,plain,
spl0_15,
inference(avatar_split_clause,[],[f1708,f3227]) ).
fof(f3227,plain,
( spl0_15
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1708,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3225,plain,
spl0_14,
inference(avatar_split_clause,[],[f1707,f3222]) ).
fof(f3222,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1707,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3220,plain,
spl0_13,
inference(avatar_split_clause,[],[f1706,f3217]) ).
fof(f1706,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3215,plain,
spl0_12,
inference(avatar_split_clause,[],[f1705,f3212]) ).
fof(f3212,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1705,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3210,plain,
spl0_11,
inference(avatar_split_clause,[],[f1704,f3207]) ).
fof(f3207,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1704,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3205,plain,
spl0_10,
inference(avatar_split_clause,[],[f1703,f3202]) ).
fof(f3202,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1703,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3200,plain,
spl0_9,
inference(avatar_split_clause,[],[f1702,f3197]) ).
fof(f3197,plain,
( spl0_9
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1702,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3195,plain,
spl0_8,
inference(avatar_split_clause,[],[f1701,f3192]) ).
fof(f1701,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3190,plain,
spl0_7,
inference(avatar_split_clause,[],[f1700,f3187]) ).
fof(f3187,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1700,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3185,plain,
spl0_6,
inference(avatar_split_clause,[],[f1699,f3182]) ).
fof(f3182,plain,
( spl0_6
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1699,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3180,plain,
spl0_5,
inference(avatar_split_clause,[],[f1698,f3177]) ).
fof(f3177,plain,
( spl0_5
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1698,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3175,plain,
spl0_4,
inference(avatar_split_clause,[],[f2739,f3172]) ).
fof(f2739,axiom,
c_UNITY_OAllowedActs(v_F,t_a) = c_UNITY_OAllowedActs(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3170,plain,
spl0_3,
inference(avatar_split_clause,[],[f2738,f3167]) ).
fof(f2738,axiom,
c_UNITY_OActs(v_F,t_a) = c_UNITY_OActs(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3165,plain,
spl0_2,
inference(avatar_split_clause,[],[f2737,f3162]) ).
fof(f2737,axiom,
c_UNITY_OInit(v_F,t_a) = c_UNITY_OInit(v_G,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3160,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2740,f3157]) ).
fof(f2740,axiom,
v_F != v_G,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : COM010-1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n007.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 21:26:23 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.10/0.31 % (18933)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.42 % (18937)WARNING: value z3 for option sas not known
% 0.15/0.42 % (18939)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)
% 0.15/0.42 % (18937)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.42 % (18938)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.42 % (18935)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.42 % (18936)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.42 % (18941)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.42 % (18940)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 1.76/0.70 TRYING [1]
% 5.66/1.19 TRYING [2]
% 7.76/1.50 % (18939)First to succeed.
% 8.02/1.55 TRYING [1]
% 8.02/1.59 % (18939)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-18933"
% 8.02/1.60 % (18939)Refutation found. Thanks to Tanya!
% 8.02/1.60 % SZS status Unsatisfiable for theBenchmark
% 8.02/1.60 % SZS output start Proof for theBenchmark
% See solution above
% 8.52/1.66 % (18939)------------------------------
% 8.52/1.66 % (18939)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 8.52/1.66 % (18939)Termination reason: Refutation
% 8.52/1.66
% 8.52/1.66 % (18939)Memory used [KB]: 17187
% 8.52/1.66 % (18939)Time elapsed: 1.168 s
% 8.52/1.66 % (18939)Instructions burned: 2105 (million)
% 8.52/1.66 % (18933)Success in time 1.319 s
%------------------------------------------------------------------------------