TSTP Solution File: SWV256-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV256-1 : 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 : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 16:43:04 EDT 2024
% Result : Unsatisfiable 1.84s 0.72s
% Output : Refutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 2950
% Syntax : Number of formulae : 4769 (1975 unt; 0 def)
% Number of atoms : 9018 (1513 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 7021 (2772 ~;2738 |; 0 &)
% (1511 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 1581 (1579 usr;1512 prp; 0-3 aty)
% Number of functors : 195 ( 195 usr; 48 con; 0-5 aty)
% Number of variables : 4584 (4584 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f13422,plain,
$false,
inference(avatar_sat_refutation,[],[f3222,f3227,f3232,f3237,f3242,f3247,f3252,f3257,f3262,f3267,f3272,f3277,f3282,f3287,f3292,f3297,f3302,f3307,f3312,f3317,f3322,f3327,f3332,f3337,f3342,f3347,f3352,f3357,f3362,f3367,f3372,f3377,f3382,f3387,f3392,f3397,f3402,f3407,f3412,f3417,f3422,f3427,f3432,f3437,f3442,f3447,f3452,f3457,f3462,f3467,f3472,f3477,f3482,f3487,f3492,f3497,f3502,f3507,f3512,f3517,f3522,f3527,f3532,f3537,f3542,f3547,f3552,f3557,f3562,f3567,f3572,f3577,f3582,f3587,f3592,f3597,f3602,f3607,f3612,f3617,f3622,f3627,f3632,f3637,f3642,f3647,f3652,f3657,f3662,f3667,f3672,f3677,f3682,f3686,f3691,f3696,f3700,f3704,f3709,f3714,f3718,f3722,f3727,f3732,f3737,f3742,f3747,f3752,f3756,f3760,f3764,f3768,f3772,f3776,f3780,f3784,f3788,f3792,f3796,f3800,f3804,f3808,f3812,f3816,f3820,f3824,f3828,f3832,f3836,f3840,f3844,f3848,f3852,f3856,f3860,f3864,f3868,f3872,f3876,f3880,f3884,f3888,f3892,f3896,f3900,f3904,f3908,f3912,f3916,f3920,f3924,f3928,f3932,f3936,f3940,f3944,f3948,f3952,f3956,f3960,f3964,f3968,f3972,f3976,f3980,f3984,f3988,f3992,f3996,f4000,f4004,f4008,f4012,f4016,f4020,f4024,f4028,f4032,f4036,f4040,f4044,f4048,f4052,f4056,f4060,f4064,f4068,f4072,f4076,f4080,f4084,f4088,f4092,f4096,f4100,f4104,f4108,f4112,f4116,f4120,f4124,f4128,f4132,f4136,f4140,f4144,f4148,f4152,f4156,f4160,f4164,f4168,f4172,f4176,f4180,f4184,f4188,f4192,f4196,f4200,f4204,f4208,f4212,f4216,f4220,f4224,f4228,f4232,f4236,f4240,f4244,f4248,f4252,f4256,f4260,f4264,f4268,f4272,f4276,f4280,f4284,f4288,f4292,f4296,f4300,f4304,f4308,f4312,f4316,f4320,f4324,f4328,f4332,f4336,f4340,f4344,f4348,f4352,f4356,f4360,f4364,f4368,f4372,f4376,f4380,f4384,f4388,f4392,f4396,f4400,f4404,f4408,f4412,f4416,f4420,f4424,f4428,f4432,f4436,f4440,f4444,f4448,f4452,f4456,f4460,f4464,f4468,f4472,f4476,f4480,f4484,f4488,f4492,f4496,f4500,f4504,f4508,f4512,f4516,f4520,f4524,f4528,f4532,f4536,f4540,f4544,f4548,f4552,f4556,f4560,f4564,f4568,f4572,f4576,f4580,f4584,f4588,f4592,f4596,f4600,f4604,f4608,f4612,f4616,f4620,f4624,f4628,f4632,f4636,f4640,f4644,f4648,f4652,f4656,f4660,f4664,f4668,f4672,f4676,f4680,f4684,f4688,f4692,f4696,f4700,f4704,f4708,f4712,f4716,f4720,f4724,f4728,f4732,f4736,f4740,f4744,f4748,f4752,f4756,f4760,f4764,f4768,f4772,f4776,f4780,f4784,f4788,f4792,f4796,f4800,f4804,f4808,f4812,f4816,f4820,f4824,f4828,f4832,f4836,f4840,f4844,f4848,f4852,f4856,f4860,f4864,f4868,f4872,f4876,f4880,f4884,f4888,f4892,f4896,f4900,f4904,f4908,f4912,f4916,f4920,f4924,f4928,f4932,f4936,f4940,f4944,f4948,f4952,f4956,f4960,f4964,f4968,f4972,f4976,f4980,f4984,f4988,f4992,f4996,f5000,f5004,f5008,f5012,f5016,f5020,f5024,f5028,f5032,f5036,f5040,f5044,f5048,f5052,f5056,f5060,f5064,f5068,f5072,f5076,f5080,f5084,f5088,f5092,f5096,f5100,f5104,f5108,f5112,f5116,f5120,f5124,f5128,f5132,f5136,f5140,f5144,f5148,f5152,f5156,f5160,f5164,f5168,f5172,f5176,f5180,f5184,f5188,f5192,f5196,f5200,f5204,f5208,f5212,f5216,f5220,f5224,f5228,f5232,f5236,f5240,f5244,f5248,f5252,f5256,f5260,f5264,f5268,f5272,f5276,f5280,f5284,f5288,f5292,f5296,f5300,f5304,f5308,f5312,f5316,f5320,f5324,f5328,f5332,f5336,f5340,f5344,f5348,f5352,f5356,f5360,f5364,f5368,f5372,f5376,f5380,f5384,f5388,f5392,f5396,f5400,f5404,f5408,f5412,f5416,f5420,f5424,f5428,f5432,f5436,f5440,f5444,f5448,f5452,f5456,f5460,f5464,f5468,f5472,f5476,f5480,f5484,f5488,f5492,f5496,f5500,f5504,f5508,f5512,f5516,f5520,f5524,f5528,f5532,f5536,f5540,f5544,f5548,f5552,f5556,f5560,f5564,f5568,f5572,f5576,f5580,f5584,f5588,f5592,f5596,f5600,f5604,f5608,f5612,f5616,f5620,f5624,f5628,f5632,f5636,f5640,f5644,f5648,f5652,f5656,f5660,f5664,f5668,f5672,f5676,f5680,f5684,f5688,f5692,f5696,f5700,f5704,f5708,f5712,f5716,f5720,f5724,f5728,f5732,f5736,f5740,f5744,f5748,f5752,f5756,f5760,f5764,f5768,f5772,f5776,f5780,f5784,f5788,f5792,f5796,f5800,f5804,f5808,f5812,f5816,f5820,f5824,f5828,f5832,f5836,f5840,f5844,f5848,f5852,f5856,f5860,f5864,f5868,f5872,f5876,f5881,f5886,f5891,f5895,f5899,f5903,f5908,f5912,f5917,f5921,f5925,f5929,f5934,f5939,f5944,f5949,f5953,f5958,f6725,f6729,f6733,f6737,f6741,f6745,f6749,f6754,f6758,f6762,f6766,f6770,f6775,f6780,f6785,f6789,f6793,f6797,f6802,f6806,f6810,f6814,f6818,f6822,f6826,f6830,f6835,f6840,f6845,f6850,f6855,f6860,f6865,f6870,f6875,f6880,f6885,f6890,f6895,f6900,f6905,f6910,f6914,f6918,f6922,f6926,f6930,f6934,f6939,f6944,f6949,f6953,f6957,f6961,f6965,f6969,f6973,f6978,f6983,f6987,f6992,f6997,f7001,f7005,f7009,f7013,f7017,f7021,f7025,f7029,f7034,f7039,f7043,f7048,f7052,f7057,f7068,f7073,f7080,f7084,f7088,f7092,f7096,f7100,f7104,f7108,f7112,f7116,f7120,f7125,f7129,f7133,f7137,f7141,f7145,f7149,f7153,f7157,f7161,f7165,f7169,f7173,f7177,f7181,f7185,f7189,f7193,f7197,f7201,f7205,f7209,f7213,f7217,f7221,f7225,f7229,f7233,f7237,f7241,f7245,f7249,f7253,f7257,f7261,f7265,f7269,f7274,f7278,f7282,f7286,f7290,f7294,f7298,f7302,f7306,f7310,f7314,f7318,f7322,f7326,f7330,f7334,f7338,f7342,f7346,f7350,f7354,f7358,f7362,f7366,f7370,f7374,f7378,f7383,f7387,f7392,f7396,f7401,f7405,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7463,f7467,f7471,f7475,f7479,f7483,f7487,f7491,f7495,f7499,f7503,f7507,f7511,f7515,f7519,f7523,f7527,f7531,f7535,f7539,f7543,f7547,f7551,f7555,f7559,f7563,f7567,f7571,f7575,f7579,f7583,f7587,f7591,f7595,f7599,f7603,f7607,f7611,f7615,f7619,f7623,f7627,f7631,f7635,f7639,f7643,f7647,f7652,f7657,f7661,f7665,f7669,f7697,f7731,f7742,f7751,f7760,f7764,f7768,f7772,f7776,f7781,f7785,f7789,f7793,f7797,f7801,f7805,f7809,f7813,f7818,f7822,f7827,f7831,f7835,f7839,f7843,f7847,f7851,f7855,f7859,f7863,f7867,f7872,f7876,f7880,f7884,f7888,f7892,f7896,f7900,f7904,f7908,f7912,f7921,f7925,f7929,f7933,f7937,f7941,f7945,f7949,f7953,f7957,f7961,f7965,f7969,f7973,f7977,f7981,f7985,f7989,f7993,f7997,f8001,f8005,f8009,f8013,f8017,f8021,f8025,f8029,f8033,f8037,f8041,f8045,f8049,f8053,f8057,f8061,f8065,f8069,f8074,f8078,f8082,f8087,f8091,f8095,f8099,f8103,f8107,f8111,f8115,f8119,f8123,f8127,f8132,f8136,f8140,f8150,f8273,f8277,f8282,f8286,f8290,f8294,f8298,f8302,f8306,f8310,f8314,f8318,f8323,f8327,f8331,f8335,f8339,f8343,f8347,f8351,f8355,f8359,f8363,f8367,f8371,f8375,f8379,f8383,f8387,f8391,f8395,f8399,f8403,f8408,f8412,f8416,f8420,f8424,f8428,f8432,f8436,f8440,f8444,f8448,f8452,f8456,f8460,f8464,f8468,f8472,f8476,f8480,f8484,f8488,f8493,f8497,f8501,f8505,f8509,f8513,f8517,f8521,f8525,f8529,f8533,f8537,f8541,f8545,f8549,f8553,f8557,f8561,f8565,f8569,f8573,f8577,f8581,f8585,f8589,f8593,f8597,f8601,f8605,f8609,f8613,f8617,f8621,f8626,f8630,f8634,f8658,f8738,f8757,f8804,f8829,f8858,f8862,f8866,f8870,f8875,f8879,f8883,f8887,f8891,f8895,f8899,f8903,f8907,f8911,f8915,f8919,f8923,f8927,f8931,f8935,f8939,f8943,f8947,f8951,f8955,f8959,f8963,f8967,f8971,f8975,f8979,f8983,f8987,f8992,f8996,f9000,f9004,f9008,f9012,f9016,f9020,f9024,f9028,f9032,f9036,f9040,f9044,f9049,f9053,f9057,f9061,f9065,f9069,f9073,f9077,f9081,f9085,f9089,f9093,f9097,f9101,f9105,f9109,f9113,f9117,f9121,f9125,f9129,f9133,f9137,f9141,f9145,f9149,f9153,f9157,f9161,f9166,f9170,f9175,f9179,f9186,f9190,f9194,f9198,f9202,f9206,f9218,f9275,f9320,f9354,f9395,f9411,f9422,f9437,f9441,f9445,f9449,f9453,f9457,f9461,f9466,f9470,f9474,f9478,f9482,f9486,f9490,f9494,f9498,f9502,f9506,f9510,f9514,f9518,f9522,f9526,f9530,f9534,f9538,f9542,f9546,f9550,f9554,f9558,f9562,f9566,f9570,f9574,f9578,f9582,f9586,f9590,f9594,f9598,f9602,f9606,f9610,f9614,f9618,f9622,f9626,f9630,f9634,f9638,f9642,f9646,f9650,f9654,f9658,f9662,f9666,f9670,f9674,f9678,f9682,f9686,f9690,f9694,f9698,f9702,f9706,f9710,f9715,f9723,f9727,f9731,f9735,f9739,f9743,f9747,f9751,f9783,f9789,f9817,f9870,f9918,f9986,f10157,f10161,f10165,f10169,f10173,f10183,f10187,f10191,f10195,f10199,f10203,f10207,f10211,f10215,f10219,f10229,f10233,f10237,f10241,f10245,f10249,f10253,f10257,f10261,f10265,f10270,f10274,f10278,f10282,f10287,f10292,f10296,f10300,f10304,f10309,f10313,f10317,f10321,f10325,f10329,f10333,f10337,f10341,f10345,f10349,f10357,f10361,f10365,f10369,f10373,f10377,f10381,f10385,f10389,f10393,f10397,f10401,f10405,f10409,f10413,f10417,f10421,f10425,f10429,f10433,f10437,f10441,f10445,f10449,f10453,f10457,f10461,f10465,f10469,f10473,f10477,f10485,f10489,f10493,f10497,f10501,f10505,f10509,f10513,f10517,f10521,f10525,f10529,f10533,f10537,f10541,f10545,f10549,f10553,f10557,f10561,f10565,f10570,f10574,f10578,f10582,f10586,f10590,f10594,f10598,f10602,f10606,f10610,f10614,f10618,f10622,f10626,f10630,f10634,f10638,f10642,f10646,f10650,f10654,f10658,f10662,f10666,f10670,f10674,f10678,f10682,f10686,f10690,f10694,f10698,f10702,f10706,f10738,f11128,f11202,f11458,f11697,f11701,f11705,f11709,f11713,f11717,f11721,f11725,f11729,f11733,f11737,f11741,f11745,f11749,f11753,f11757,f11761,f11765,f11769,f11773,f11777,f11790,f11794,f11798,f11802,f11806,f11810,f11814,f11818,f11822,f11826,f11845,f11849,f11853,f11857,f11861,f11865,f11869,f11873,f11877,f11881,f11885,f11889,f11893,f11897,f11901,f11905,f11909,f11913,f11917,f11921,f11925,f11929,f11933,f11937,f11941,f11945,f11949,f11953,f11957,f11961,f11965,f11969,f11973,f11977,f11981,f11985,f11989,f11993,f11997,f12001,f12005,f12009,f12013,f12017,f12021,f12025,f12029,f12033,f12037,f12041,f12047,f12051,f12055,f12059,f12063,f12067,f12071,f12075,f12079,f12083,f12088,f12092,f12096,f12100,f12105,f12112,f12116,f12120,f12124,f12129,f12141,f12145,f12150,f12182,f12186,f12190,f12194,f12198,f12207,f12211,f12965,f13159,f13351,f13403,f13407,f13411,f13415,f13419,f13421]) ).
fof(f13421,plain,
( ~ spl0_875
| spl0_1506 ),
inference(avatar_contradiction_clause,[],[f13420]) ).
fof(f13420,plain,
( $false
| ~ spl0_875
| spl0_1506 ),
inference(resolution,[],[f13350,f7642]) ).
fof(f7642,plain,
( ! [X88] : c_lessequals(c_Message_Oanalz(X88),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ spl0_875 ),
inference(avatar_component_clause,[],[f7641]) ).
fof(f7641,plain,
( spl0_875
<=> ! [X88] : c_lessequals(c_Message_Oanalz(X88),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f13350,plain,
( ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| spl0_1506 ),
inference(avatar_component_clause,[],[f13348]) ).
fof(f13348,plain,
( spl0_1506
<=> c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f13419,plain,
spl0_1511,
inference(avatar_split_clause,[],[f96,f13417]) ).
fof(f13417,plain,
( spl0_1511
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f96,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_0) ).
fof(f13415,plain,
spl0_1510,
inference(avatar_split_clause,[],[f59,f13413]) ).
fof(f13413,plain,
( spl0_1510
<=> ! [X0,X12,X1,X26] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f59,axiom,
! [X0,X1,X26,X12] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_OlistsE_1) ).
fof(f13411,plain,
spl0_1509,
inference(avatar_split_clause,[],[f48,f13409]) ).
fof(f13409,plain,
( spl0_1509
<=> ! [X12,X1,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f48,axiom,
! [X1,X12,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oin__listsI_1) ).
fof(f13407,plain,
spl0_1508,
inference(avatar_split_clause,[],[f43,f13405]) ).
fof(f13405,plain,
( spl0_1508
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f43,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f13403,plain,
spl0_1507,
inference(avatar_split_clause,[],[f27,f13401]) ).
fof(f13401,plain,
( spl0_1507
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f27,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f13351,plain,
( ~ spl0_1506
| spl0_1
| ~ spl0_1484 ),
inference(avatar_split_clause,[],[f13294,f12094,f3219,f13348]) ).
fof(f3219,plain,
( spl0_1
<=> c_lessequals(c_Message_Oparts(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f12094,plain,
( spl0_1484
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f13294,plain,
( ~ c_lessequals(c_Message_Oanalz(v_H),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| spl0_1
| ~ spl0_1484 ),
inference(resolution,[],[f12095,f3221]) ).
fof(f3221,plain,
( ~ c_lessequals(c_Message_Oparts(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg))
| spl0_1 ),
inference(avatar_component_clause,[],[f3219]) ).
fof(f12095,plain,
( ! [X88,X20] :
( c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1484 ),
inference(avatar_component_clause,[],[f12094]) ).
fof(f13159,plain,
( ~ spl0_1504
| spl0_1505
| ~ spl0_112
| ~ spl0_1305 ),
inference(avatar_split_clause,[],[f11003,f10379,f3766,f13157,f13153]) ).
fof(f13153,plain,
( spl0_1504
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f13157,plain,
( spl0_1505
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f3766,plain,
( spl0_112
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f10379,plain,
( spl0_1305
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f11003,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_112
| ~ spl0_1305 ),
inference(resolution,[],[f10380,f3767]) ).
fof(f3767,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3766]) ).
fof(f10380,plain,
( ! [X18,X1] :
( ~ c_lessequals(c_0,c_uminus(X18,X1),X1)
| c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
| ~ spl0_1305 ),
inference(avatar_component_clause,[],[f10379]) ).
fof(f12965,plain,
( ~ spl0_1502
| spl0_1503
| ~ spl0_112
| ~ spl0_1269 ),
inference(avatar_split_clause,[],[f10789,f10227,f3766,f12963,f12959]) ).
fof(f12959,plain,
( spl0_1502
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f12963,plain,
( spl0_1503
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f10227,plain,
( spl0_1269
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f10789,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_112
| ~ spl0_1269 ),
inference(resolution,[],[f10228,f3767]) ).
fof(f10228,plain,
( ! [X48,X1] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1269 ),
inference(avatar_component_clause,[],[f10227]) ).
fof(f12211,plain,
spl0_1501,
inference(avatar_split_clause,[],[f3124,f12209]) ).
fof(f12209,plain,
( spl0_1501
<=> ! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f3124,plain,
! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2943,f2798]) ).
fof(f2798,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2016,f2544]) ).
fof(f2544,axiom,
! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f2016,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2943,plain,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1871,f2544,f2544]) ).
fof(f1871,axiom,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f12207,plain,
spl0_1500,
inference(avatar_split_clause,[],[f3108,f12205]) ).
fof(f12205,plain,
( spl0_1500
<=> ! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f3108,plain,
! [X21,X43] :
( c_less(c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X43,X21,tc_nat),tc_nat),X21,tc_nat)
| ~ c_less(c_0,X21,tc_nat) ),
inference(forward_demodulation,[],[f2923,f2851]) ).
fof(f2851,plain,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Finite__Set_Ocard(c_SetInterval_OatMost(X26,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2547,f2544]) ).
fof(f2547,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f2923,plain,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X43,tc_nat),tc_nat),tc_nat),X21,tc_nat) ),
inference(definition_unfolding,[],[f2036,f2544]) ).
fof(f2036,axiom,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__Suc__less_0) ).
fof(f12198,plain,
spl0_1499,
inference(avatar_split_clause,[],[f3061,f12196]) ).
fof(f12196,plain,
( spl0_1499
<=> ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f3061,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f3060,f2156]) ).
fof(f2156,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(f3060,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f3059,f2154]) ).
fof(f2154,axiom,
! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3059,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f1883,f2156]) ).
fof(f1883,axiom,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f12194,plain,
spl0_1498,
inference(avatar_split_clause,[],[f3047,f12192]) ).
fof(f12192,plain,
( spl0_1498
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f3047,plain,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11),
inference(forward_demodulation,[],[f2128,f2127]) ).
fof(f2127,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f2128,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__1_0) ).
fof(f12190,plain,
spl0_1497,
inference(avatar_split_clause,[],[f3043,f12188]) ).
fof(f12188,plain,
( spl0_1497
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f3043,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_Obin__mult(c_Numeral_OMin,X11)),c_Numeral_Obit_OB1),
inference(forward_demodulation,[],[f2840,f2813]) ).
fof(f2813,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
inference(definition_unfolding,[],[f2112,f2113]) ).
fof(f2113,axiom,
! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f2112,axiom,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2840,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2124,f2129,f2113,f2129]) ).
fof(f2129,axiom,
! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f2124,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__1_0) ).
fof(f12186,plain,
spl0_1496,
inference(avatar_split_clause,[],[f2953,f12184]) ).
fof(f12184,plain,
( spl0_1496
<=> ! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f2953,plain,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(definition_unfolding,[],[f1853,f2129]) ).
fof(f1853,axiom,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_0) ).
fof(f12182,plain,
spl0_1495,
inference(avatar_split_clause,[],[f2951,f12180]) ).
fof(f12180,plain,
( spl0_1495
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f2951,plain,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1854,f2129]) ).
fof(f1854,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oless__0__number__of_1) ).
fof(f12150,plain,
( spl0_1494
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380
| ~ spl0_1493 ),
inference(avatar_split_clause,[],[f12146,f12143,f10680,f10355,f6808,f5878,f12148]) ).
fof(f12148,plain,
( spl0_1494
<=> ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f5878,plain,
( spl0_640
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f6808,plain,
( spl0_678
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f10355,plain,
( spl0_1299
<=> ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f10680,plain,
( spl0_1380
<=> ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f12143,plain,
( spl0_1493
<=> ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f12146,plain,
( ! [X59,X43] :
( c_List_Olist_ONil = c_List_Oupt(X43,c_plus(c_1,X59,tc_nat))
| c_lessequals(X43,X59,tc_nat) )
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380
| ~ spl0_1493 ),
inference(forward_demodulation,[],[f12144,f11618]) ).
fof(f11618,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_plus(c_1,X0,tc_nat)
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380 ),
inference(forward_demodulation,[],[f11617,f6809]) ).
fof(f6809,plain,
( ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3
| ~ spl0_678 ),
inference(avatar_component_clause,[],[f6808]) ).
fof(f11617,plain,
( ! [X0] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat) = c_IntDef_Onat(c_IntDef_Oint(c_plus(c_1,X0,tc_nat)))
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380 ),
inference(forward_demodulation,[],[f11579,f10969]) ).
fof(f10969,plain,
( ! [X0] : c_plus(c_1,c_IntDef_Oint(X0),tc_IntDef_Oint) = c_IntDef_Oint(c_plus(c_1,X0,tc_nat))
| ~ spl0_640
| ~ spl0_1299 ),
inference(superposition,[],[f10356,f5880]) ).
fof(f5880,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_640 ),
inference(avatar_component_clause,[],[f5878]) ).
fof(f10356,plain,
( ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_1299 ),
inference(avatar_component_clause,[],[f10355]) ).
fof(f11579,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_678
| ~ spl0_1380 ),
inference(superposition,[],[f6809,f10681]) ).
fof(f10681,plain,
( ! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat))
| ~ spl0_1380 ),
inference(avatar_component_clause,[],[f10680]) ).
fof(f12144,plain,
( ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) )
| ~ spl0_1493 ),
inference(avatar_component_clause,[],[f12143]) ).
fof(f12145,plain,
spl0_1493,
inference(avatar_split_clause,[],[f2938,f12143]) ).
fof(f2938,plain,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Finite__Set_Ocard(c_SetInterval_OatMost(X59,tc_nat),tc_nat)) ),
inference(definition_unfolding,[],[f1783,f2544]) ).
fof(f1783,axiom,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt_Oupt__Suc_1) ).
fof(f12141,plain,
spl0_1492,
inference(avatar_split_clause,[],[f2899,f12139]) ).
fof(f12139,plain,
( spl0_1492
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f2899,plain,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_OMin,X11),X1) ),
inference(definition_unfolding,[],[f2117,f2129]) ).
fof(f2117,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f12129,plain,
( spl0_1491
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380
| ~ spl0_1490 ),
inference(avatar_split_clause,[],[f12125,f12122,f10680,f10355,f6808,f5878,f12127]) ).
fof(f12127,plain,
( spl0_1491
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f12122,plain,
( spl0_1490
<=> ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f12125,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_plus(c_1,X15,tc_nat),tc_nat)
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380
| ~ spl0_1490 ),
inference(forward_demodulation,[],[f12123,f11618]) ).
fof(f12123,plain,
( ! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat)
| ~ spl0_1490 ),
inference(avatar_component_clause,[],[f12122]) ).
fof(f12124,plain,
spl0_1490,
inference(avatar_split_clause,[],[f2841,f12122]) ).
fof(f2841,plain,
! [X15] : c_insert(X15,c_emptyset,tc_nat) = c_SetInterval_OatLeastLessThan(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2527,f2544]) ).
fof(f2527,axiom,
! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f12120,plain,
spl0_1489,
inference(avatar_split_clause,[],[f2839,f12118]) ).
fof(f12118,plain,
( spl0_1489
<=> ! [X13,X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2839,plain,
! [X1,X12,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_minus(X13,X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2589,f2373]) ).
fof(f2373,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f2589,axiom,
! [X1,X12,X13] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__disjoint_0) ).
fof(f12116,plain,
spl0_1488,
inference(avatar_split_clause,[],[f2828,f12114]) ).
fof(f12114,plain,
( spl0_1488
<=> ! [X85,X1] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f2828,plain,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2706,f2716]) ).
fof(f2716,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f2706,axiom,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f12112,plain,
spl0_1487,
inference(avatar_split_clause,[],[f2827,f12110]) ).
fof(f12110,plain,
( spl0_1487
<=> ! [X85,X1] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f2827,plain,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Otrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),X1,X1),
inference(definition_unfolding,[],[f2707,f2716]) ).
fof(f2707,axiom,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f12105,plain,
( spl0_1486
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380
| ~ spl0_1485 ),
inference(avatar_split_clause,[],[f12101,f12098,f10680,f10355,f6808,f5878,f12103]) ).
fof(f12103,plain,
( spl0_1486
<=> ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f12098,plain,
( spl0_1485
<=> ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f12101,plain,
( ! [X21] : c_plus(c_1,X21,tc_nat) = c_Binomial_Obinomial(c_plus(c_1,X21,tc_nat),X21)
| ~ spl0_640
| ~ spl0_678
| ~ spl0_1299
| ~ spl0_1380
| ~ spl0_1485 ),
inference(forward_demodulation,[],[f12099,f11618]) ).
fof(f12099,plain,
( ! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21)
| ~ spl0_1485 ),
inference(avatar_component_clause,[],[f12098]) ).
fof(f12100,plain,
spl0_1485,
inference(avatar_split_clause,[],[f2823,f12098]) ).
fof(f2823,plain,
! [X21] : c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat) = c_Binomial_Obinomial(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X21),
inference(definition_unfolding,[],[f1163,f2544,f2544]) ).
fof(f1163,axiom,
! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f12096,plain,
spl0_1484,
inference(avatar_split_clause,[],[f2792,f12094]) ).
fof(f2792,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_1) ).
fof(f12092,plain,
spl0_1483,
inference(avatar_split_clause,[],[f2791,f12090]) ).
fof(f12090,plain,
( spl0_1483
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f2791,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__subset__iff_0) ).
fof(f12088,plain,
( ~ spl0_1482
| ~ spl0_641
| ~ spl0_1134
| ~ spl0_1238 ),
inference(avatar_split_clause,[],[f9719,f9713,f9091,f5883,f12085]) ).
fof(f12085,plain,
( spl0_1482
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f5883,plain,
( spl0_641
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f9091,plain,
( spl0_1134
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f9713,plain,
( spl0_1238
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f9719,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1134
| ~ spl0_1238 ),
inference(forward_demodulation,[],[f9718,f9092]) ).
fof(f9092,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1134 ),
inference(avatar_component_clause,[],[f9091]) ).
fof(f9718,plain,
( ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1238 ),
inference(superposition,[],[f9714,f5885]) ).
fof(f5885,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_641 ),
inference(avatar_component_clause,[],[f5883]) ).
fof(f9714,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1238 ),
inference(avatar_component_clause,[],[f9713]) ).
fof(f12083,plain,
spl0_1481,
inference(avatar_split_clause,[],[f2788,f12081]) ).
fof(f12081,plain,
( spl0_1481
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f2788,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Number_0) ).
fof(f12079,plain,
spl0_1480,
inference(avatar_split_clause,[],[f2787,f12077]) ).
fof(f12077,plain,
( spl0_1480
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f2787,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Nonce_0) ).
fof(f12075,plain,
spl0_1479,
inference(avatar_split_clause,[],[f2785,f12073]) ).
fof(f12073,plain,
( spl0_1479
<=> ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f2785,axiom,
! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Key_0) ).
fof(f12071,plain,
spl0_1478,
inference(avatar_split_clause,[],[f2784,f12069]) ).
fof(f12069,plain,
( spl0_1478
<=> ! [X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f2784,axiom,
! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Hash_0) ).
fof(f12067,plain,
spl0_1477,
inference(avatar_split_clause,[],[f2782,f12065]) ).
fof(f12065,plain,
( spl0_1477
<=> ! [X102,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f2782,axiom,
! [X88,X102] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__Agent_0) ).
fof(f12063,plain,
spl0_1476,
inference(avatar_split_clause,[],[f2780,f12061]) ).
fof(f12061,plain,
( spl0_1476
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f2780,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__cut__eq_0) ).
fof(f12059,plain,
spl0_1475,
inference(avatar_split_clause,[],[f2725,f12057]) ).
fof(f12057,plain,
( spl0_1475
<=> ! [X18,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f2725,axiom,
! [X1,X18,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f12055,plain,
spl0_1474,
inference(avatar_split_clause,[],[f2689,f12053]) ).
fof(f12053,plain,
( spl0_1474
<=> ! [X13,X12,X0,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f2689,axiom,
! [X0,X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_1) ).
fof(f12051,plain,
spl0_1473,
inference(avatar_split_clause,[],[f2656,f12049]) ).
fof(f12049,plain,
( spl0_1473
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f2656,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__iff_1) ).
fof(f12047,plain,
spl0_1472,
inference(avatar_split_clause,[],[f2652,f12045]) ).
fof(f12045,plain,
( spl0_1472
<=> ! [X12,X1,X24] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f2652,axiom,
! [X1,X24,X12] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_0) ).
fof(f12041,plain,
spl0_1471,
inference(avatar_split_clause,[],[f2646,f12039]) ).
fof(f12039,plain,
( spl0_1471
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f2646,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_1) ).
fof(f12037,plain,
spl0_1470,
inference(avatar_split_clause,[],[f2645,f12035]) ).
fof(f12035,plain,
( spl0_1470
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f2645,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__subset__iff_0) ).
fof(f12033,plain,
spl0_1469,
inference(avatar_split_clause,[],[f2631,f12031]) ).
fof(f12031,plain,
( spl0_1469
<=> ! [X13,X12,X1] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f2631,axiom,
! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel_0) ).
fof(f12029,plain,
spl0_1468,
inference(avatar_split_clause,[],[f2630,f12027]) ).
fof(f12027,plain,
( spl0_1468
<=> ! [X13,X12,X1] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f2630,axiom,
! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__Diff__cancel2_0) ).
fof(f12025,plain,
spl0_1467,
inference(avatar_split_clause,[],[f2622,f12023]) ).
fof(f12023,plain,
( spl0_1467
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f2622,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__iff_2) ).
fof(f12021,plain,
spl0_1466,
inference(avatar_split_clause,[],[f2616,f12019]) ).
fof(f12019,plain,
( spl0_1466
<=> ! [X12,X1,X24] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f2616,axiom,
! [X1,X24,X12] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f12017,plain,
spl0_1465,
inference(avatar_split_clause,[],[f2555,f12015]) ).
fof(f12015,plain,
( spl0_1465
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f2555,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f12013,plain,
spl0_1464,
inference(avatar_split_clause,[],[f2554,f12011]) ).
fof(f12011,plain,
( spl0_1464
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f2554,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f12009,plain,
spl0_1463,
inference(avatar_split_clause,[],[f2552,f12007]) ).
fof(f12007,plain,
( spl0_1463
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f2552,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f12005,plain,
spl0_1462,
inference(avatar_split_clause,[],[f2551,f12003]) ).
fof(f12003,plain,
( spl0_1462
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f2551,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f12001,plain,
spl0_1461,
inference(avatar_split_clause,[],[f2525,f11999]) ).
fof(f11999,plain,
( spl0_1461
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f2525,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f11997,plain,
spl0_1460,
inference(avatar_split_clause,[],[f2524,f11995]) ).
fof(f11995,plain,
( spl0_1460
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f2524,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f11993,plain,
spl0_1459,
inference(avatar_split_clause,[],[f2520,f11991]) ).
fof(f11991,plain,
( spl0_1459
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f2520,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f11989,plain,
spl0_1458,
inference(avatar_split_clause,[],[f2519,f11987]) ).
fof(f11987,plain,
( spl0_1458
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f2519,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f11985,plain,
spl0_1457,
inference(avatar_split_clause,[],[f2387,f11983]) ).
fof(f11983,plain,
( spl0_1457
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f2387,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_0) ).
fof(f11981,plain,
spl0_1456,
inference(avatar_split_clause,[],[f2367,f11979]) ).
fof(f11979,plain,
( spl0_1456
<=> ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f2367,axiom,
! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osurj__pair_0) ).
fof(f11977,plain,
spl0_1455,
inference(avatar_split_clause,[],[f2365,f11975]) ).
fof(f11975,plain,
( spl0_1455
<=> ! [X2,X1,X3] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f2365,axiom,
! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Opair__collapse_0) ).
fof(f11973,plain,
spl0_1454,
inference(avatar_split_clause,[],[f2361,f11971]) ).
fof(f11971,plain,
( spl0_1454
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f2361,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f11969,plain,
spl0_1453,
inference(avatar_split_clause,[],[f2358,f11967]) ).
fof(f11967,plain,
( spl0_1453
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f2358,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Ozero__le__power__abs_0) ).
fof(f11965,plain,
spl0_1452,
inference(avatar_split_clause,[],[f2347,f11963]) ).
fof(f11963,plain,
( spl0_1452
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f2347,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__eq__0__iff_0) ).
fof(f11961,plain,
spl0_1451,
inference(avatar_split_clause,[],[f2339,f11959]) ).
fof(f11959,plain,
( spl0_1451
<=> ! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f2339,axiom,
! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f11957,plain,
spl0_1450,
inference(avatar_split_clause,[],[f2295,f11955]) ).
fof(f11955,plain,
( spl0_1450
<=> ! [X0,X21] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f2295,axiom,
! [X21,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_2) ).
fof(f11953,plain,
spl0_1449,
inference(avatar_split_clause,[],[f2282,f11951]) ).
fof(f11951,plain,
( spl0_1449
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f2282,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_2) ).
fof(f11949,plain,
spl0_1448,
inference(avatar_split_clause,[],[f2265,f11947]) ).
fof(f11947,plain,
( spl0_1448
<=> ! [X2,X48,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f2265,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f11945,plain,
spl0_1447,
inference(avatar_split_clause,[],[f2264,f11943]) ).
fof(f11943,plain,
( spl0_1447
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f2264,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f11941,plain,
spl0_1446,
inference(avatar_split_clause,[],[f2260,f11939]) ).
fof(f11939,plain,
( spl0_1446
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f2260,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f11937,plain,
spl0_1445,
inference(avatar_split_clause,[],[f2259,f11935]) ).
fof(f11935,plain,
( spl0_1445
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f2259,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f11933,plain,
spl0_1444,
inference(avatar_split_clause,[],[f2257,f11931]) ).
fof(f11931,plain,
( spl0_1444
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f2257,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f11929,plain,
spl0_1443,
inference(avatar_split_clause,[],[f2256,f11927]) ).
fof(f11927,plain,
( spl0_1443
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f2256,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f11925,plain,
spl0_1442,
inference(avatar_split_clause,[],[f2254,f11923]) ).
fof(f11923,plain,
( spl0_1442
<=> ! [X48,X1,X0,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f2254,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f11921,plain,
spl0_1441,
inference(avatar_split_clause,[],[f2253,f11919]) ).
fof(f11919,plain,
( spl0_1441
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f2253,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f11917,plain,
spl0_1440,
inference(avatar_split_clause,[],[f2249,f11915]) ).
fof(f11915,plain,
( spl0_1440
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f2249,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f11913,plain,
spl0_1439,
inference(avatar_split_clause,[],[f2248,f11911]) ).
fof(f11911,plain,
( spl0_1439
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f2248,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f11909,plain,
spl0_1438,
inference(avatar_split_clause,[],[f2215,f11907]) ).
fof(f11907,plain,
( spl0_1438
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f2215,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f11905,plain,
spl0_1437,
inference(avatar_split_clause,[],[f2212,f11903]) ).
fof(f11903,plain,
( spl0_1437
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f2212,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f11901,plain,
spl0_1436,
inference(avatar_split_clause,[],[f2210,f11899]) ).
fof(f11899,plain,
( spl0_1436
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f2210,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f11897,plain,
spl0_1435,
inference(avatar_split_clause,[],[f2207,f11895]) ).
fof(f11895,plain,
( spl0_1435
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f2207,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f11893,plain,
spl0_1434,
inference(avatar_split_clause,[],[f2206,f11891]) ).
fof(f11891,plain,
( spl0_1434
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f2206,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f11889,plain,
spl0_1433,
inference(avatar_split_clause,[],[f2204,f11887]) ).
fof(f11887,plain,
( spl0_1433
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f2204,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f11885,plain,
spl0_1432,
inference(avatar_split_clause,[],[f2203,f11883]) ).
fof(f11883,plain,
( spl0_1432
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f2203,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f11881,plain,
spl0_1431,
inference(avatar_split_clause,[],[f2202,f11879]) ).
fof(f11879,plain,
( spl0_1431
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f2202,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f11877,plain,
spl0_1430,
inference(avatar_split_clause,[],[f2201,f11875]) ).
fof(f11875,plain,
( spl0_1430
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f2201,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f11873,plain,
spl0_1429,
inference(avatar_split_clause,[],[f2200,f11871]) ).
fof(f11871,plain,
( spl0_1429
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f2200,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f11869,plain,
spl0_1428,
inference(avatar_split_clause,[],[f2184,f11867]) ).
fof(f11867,plain,
( spl0_1428
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f2184,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f11865,plain,
spl0_1427,
inference(avatar_split_clause,[],[f2110,f11863]) ).
fof(f11863,plain,
( spl0_1427
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f2110,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f11861,plain,
spl0_1426,
inference(avatar_split_clause,[],[f2109,f11859]) ).
fof(f11859,plain,
( spl0_1426
<=> ! [X11,X3,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f2109,axiom,
! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f11857,plain,
spl0_1425,
inference(avatar_split_clause,[],[f2045,f11855]) ).
fof(f11855,plain,
( spl0_1425
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f2045,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f11853,plain,
spl0_1424,
inference(avatar_split_clause,[],[f2044,f11851]) ).
fof(f11851,plain,
( spl0_1424
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f2044,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f11849,plain,
spl0_1423,
inference(avatar_split_clause,[],[f1852,f11847]) ).
fof(f11847,plain,
( spl0_1423
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f1852,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_1) ).
fof(f11845,plain,
spl0_1422,
inference(avatar_split_clause,[],[f1799,f11843]) ).
fof(f11843,plain,
( spl0_1422
<=> ! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f1799,axiom,
! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f11826,plain,
spl0_1421,
inference(avatar_split_clause,[],[f1765,f11824]) ).
fof(f11824,plain,
( spl0_1421
<=> ! [X0,X12,X1] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f1765,axiom,
! [X0,X1,X12] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__singleton_1) ).
fof(f11822,plain,
spl0_1420,
inference(avatar_split_clause,[],[f1748,f11820]) ).
fof(f11820,plain,
( spl0_1420
<=> ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f1748,axiom,
! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset_Osimps__2_0) ).
fof(f11818,plain,
spl0_1419,
inference(avatar_split_clause,[],[f1742,f11816]) ).
fof(f11816,plain,
( spl0_1419
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f1742,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__length01_0) ).
fof(f11814,plain,
spl0_1418,
inference(avatar_split_clause,[],[f1702,f11812]) ).
fof(f11812,plain,
( spl0_1418
<=> ! [X43,X3,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f1702,axiom,
! [X21,X3,X1,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__replicate_0) ).
fof(f11810,plain,
spl0_1417,
inference(avatar_split_clause,[],[f1604,f11808]) ).
fof(f11808,plain,
( spl0_1417
<=> ! [X43,X0,X23,X1] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f1604,axiom,
! [X0,X1,X23,X43] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__list__update_0) ).
fof(f11806,plain,
spl0_1416,
inference(avatar_split_clause,[],[f1591,f11804]) ).
fof(f11804,plain,
( spl0_1416
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f1591,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__appendR_0) ).
fof(f11802,plain,
spl0_1415,
inference(avatar_split_clause,[],[f1589,f11800]) ).
fof(f11800,plain,
( spl0_1415
<=> ! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f1589,axiom,
! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_1) ).
fof(f11798,plain,
spl0_1414,
inference(avatar_split_clause,[],[f1581,f11796]) ).
fof(f11796,plain,
( spl0_1414
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f1581,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__append2_0) ).
fof(f11794,plain,
spl0_1413,
inference(avatar_split_clause,[],[f1580,f11792]) ).
fof(f11792,plain,
( spl0_1413
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f1580,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__Cons__tl_0) ).
fof(f11790,plain,
spl0_1412,
inference(avatar_split_clause,[],[f1578,f11788]) ).
fof(f11788,plain,
( spl0_1412
<=> ! [X59,X43,X15] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f1578,axiom,
! [X59,X15,X43] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__upt_0) ).
fof(f11777,plain,
spl0_1411,
inference(avatar_split_clause,[],[f1576,f11775]) ).
fof(f11775,plain,
( spl0_1411
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f1576,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_1) ).
fof(f11773,plain,
spl0_1410,
inference(avatar_split_clause,[],[f1575,f11771]) ).
fof(f11771,plain,
( spl0_1410
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f1575,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__eq__Nil_0) ).
fof(f11769,plain,
spl0_1409,
inference(avatar_split_clause,[],[f1475,f11767]) ).
fof(f11767,plain,
( spl0_1409
<=> ! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f1475,axiom,
! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f11765,plain,
spl0_1408,
inference(avatar_split_clause,[],[f1416,f11763]) ).
fof(f11763,plain,
( spl0_1408
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f1416,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__minus_0) ).
fof(f11761,plain,
spl0_1407,
inference(avatar_split_clause,[],[f1305,f11759]) ).
fof(f11759,plain,
( spl0_1407
<=> ! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f1305,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f11757,plain,
spl0_1406,
inference(avatar_split_clause,[],[f1304,f11755]) ).
fof(f11755,plain,
( spl0_1406
<=> ! [X16,X21,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f1304,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f11753,plain,
spl0_1405,
inference(avatar_split_clause,[],[f1291,f11751]) ).
fof(f11751,plain,
( spl0_1405
<=> ! [X12,X1,X18] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f1291,axiom,
! [X1,X18,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__insert_0) ).
fof(f11749,plain,
spl0_1404,
inference(avatar_split_clause,[],[f1287,f11747]) ).
fof(f11747,plain,
( spl0_1404
<=> ! [X20,X1,X19] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f1287,axiom,
! [X1,X19,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_1) ).
fof(f11745,plain,
spl0_1403,
inference(avatar_split_clause,[],[f1286,f11743]) ).
fof(f11743,plain,
( spl0_1403
<=> ! [X20,X1,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f1286,axiom,
! [X1,X19,X20] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Un_0) ).
fof(f11741,plain,
spl0_1402,
inference(avatar_split_clause,[],[f1285,f11739]) ).
fof(f11739,plain,
( spl0_1402
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f1285,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f11737,plain,
spl0_1401,
inference(avatar_split_clause,[],[f1284,f11735]) ).
fof(f11735,plain,
( spl0_1401
<=> ! [X12,X1] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f1284,axiom,
! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f11733,plain,
spl0_1400,
inference(avatar_split_clause,[],[f1276,f11731]) ).
fof(f11731,plain,
( spl0_1400
<=> ! [X12,X1] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f1276,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f11729,plain,
spl0_1399,
inference(avatar_split_clause,[],[f1223,f11727]) ).
fof(f11727,plain,
( spl0_1399
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f1223,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f11725,plain,
spl0_1398,
inference(avatar_split_clause,[],[f1221,f11723]) ).
fof(f11723,plain,
( spl0_1398
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f1221,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f11721,plain,
spl0_1397,
inference(avatar_split_clause,[],[f111,f11719]) ).
fof(f11719,plain,
( spl0_1397
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f111,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f11717,plain,
spl0_1396,
inference(avatar_split_clause,[],[f108,f11715]) ).
fof(f11715,plain,
( spl0_1396
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f108,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f11713,plain,
spl0_1395,
inference(avatar_split_clause,[],[f104,f11711]) ).
fof(f11711,plain,
( spl0_1395
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f104,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetI_0) ).
fof(f11709,plain,
spl0_1394,
inference(avatar_split_clause,[],[f100,f11707]) ).
fof(f11707,plain,
( spl0_1394
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f100,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnionE_1) ).
fof(f11705,plain,
spl0_1393,
inference(avatar_split_clause,[],[f97,f11703]) ).
fof(f11703,plain,
( spl0_1393
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f97,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInterI_1) ).
fof(f11701,plain,
spl0_1392,
inference(avatar_split_clause,[],[f29,f11699]) ).
fof(f11699,plain,
( spl0_1392
<=> ! [X12,X1,X18] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f29,axiom,
! [X1,X18,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f11697,plain,
( ~ spl0_1391
| spl0_1
| ~ spl0_1377 ),
inference(avatar_split_clause,[],[f11557,f10668,f3219,f11694]) ).
fof(f11694,plain,
( spl0_1391
<=> c_lessequals(c_Message_Oanalz(v_H),v_H,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f10668,plain,
( spl0_1377
<=> ! [X20,X88] :
( ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f11557,plain,
( ~ c_lessequals(c_Message_Oanalz(v_H),v_H,tc_set(tc_Message_Omsg))
| spl0_1
| ~ spl0_1377 ),
inference(resolution,[],[f10669,f3221]) ).
fof(f10669,plain,
( ! [X88,X20] :
( c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg)) )
| ~ spl0_1377 ),
inference(avatar_component_clause,[],[f10668]) ).
fof(f11458,plain,
( spl0_1390
| ~ spl0_717
| ~ spl0_1139 ),
inference(avatar_split_clause,[],[f9404,f9111,f6985,f11456]) ).
fof(f11456,plain,
( spl0_1390
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f6985,plain,
( spl0_717
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f9111,plain,
( spl0_1139
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f9404,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_717
| ~ spl0_1139 ),
inference(superposition,[],[f9112,f6986]) ).
fof(f6986,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_717 ),
inference(avatar_component_clause,[],[f6985]) ).
fof(f9112,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1139 ),
inference(avatar_component_clause,[],[f9111]) ).
fof(f11202,plain,
( spl0_1389
| ~ spl0_644
| ~ spl0_1109 ),
inference(avatar_split_clause,[],[f9321,f8990,f5897,f11200]) ).
fof(f11200,plain,
( spl0_1389
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f5897,plain,
( spl0_644
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f8990,plain,
( spl0_1109
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f9321,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_644
| ~ spl0_1109 ),
inference(resolution,[],[f8991,f5898]) ).
fof(f5898,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_644 ),
inference(avatar_component_clause,[],[f5897]) ).
fof(f8991,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1109 ),
inference(avatar_component_clause,[],[f8990]) ).
fof(f11128,plain,
( spl0_1388
| ~ spl0_644
| ~ spl0_1106 ),
inference(avatar_split_clause,[],[f9311,f8977,f5897,f11126]) ).
fof(f11126,plain,
( spl0_1388
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f8977,plain,
( spl0_1106
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f9311,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_644
| ~ spl0_1106 ),
inference(resolution,[],[f8978,f5898]) ).
fof(f8978,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1106 ),
inference(avatar_component_clause,[],[f8977]) ).
fof(f10738,plain,
( spl0_1387
| ~ spl0_1071
| ~ spl0_1258 ),
inference(avatar_split_clause,[],[f10730,f10171,f8656,f10736]) ).
fof(f10736,plain,
( spl0_1387
<=> ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f8656,plain,
( spl0_1071
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f10171,plain,
( spl0_1258
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f10730,plain,
( ! [X0] : c_lessequals(X0,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1071
| ~ spl0_1258 ),
inference(resolution,[],[f10172,f8657]) ).
fof(f8657,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1071 ),
inference(avatar_component_clause,[],[f8656]) ).
fof(f10172,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1258 ),
inference(avatar_component_clause,[],[f10171]) ).
fof(f10706,plain,
spl0_1386,
inference(avatar_split_clause,[],[f3170,f10704]) ).
fof(f10704,plain,
( spl0_1386
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f3170,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3169,f2115]) ).
fof(f2115,axiom,
! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3169,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2970,f2797]) ).
fof(f2797,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f2126,f2129]) ).
fof(f2126,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f2970,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1338,f2129]) ).
fof(f1338,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10702,plain,
spl0_1385,
inference(avatar_split_clause,[],[f3099,f10700]) ).
fof(f10700,plain,
( spl0_1385
<=> ! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f3099,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f3098,f2156]) ).
fof(f3098,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f3097,f2154]) ).
fof(f3097,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f1878,f2156]) ).
fof(f1878,axiom,
! [X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10698,plain,
spl0_1384,
inference(avatar_split_clause,[],[f3092,f10696]) ).
fof(f10696,plain,
( spl0_1384
<=> ! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f3092,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3091,f2156]) ).
fof(f3091,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f3090,f2154]) ).
fof(f3090,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1328,f2156]) ).
fof(f1328,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10694,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2911,f10692]) ).
fof(f10692,plain,
( spl0_1383
<=> ! [X13,X12,X1] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f2911,plain,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2598,f2373]) ).
fof(f2598,axiom,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10690,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2910,f10688]) ).
fof(f10688,plain,
( spl0_1382
<=> ! [X13,X12,X1] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f2910,plain,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
inference(definition_unfolding,[],[f2599,f2373]) ).
fof(f2599,axiom,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10686,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2905,f10684]) ).
fof(f10684,plain,
( spl0_1381
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f2905,plain,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),X1) ),
inference(definition_unfolding,[],[f2346,f2544]) ).
fof(f2346,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10682,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2834,f10680]) ).
fof(f2834,plain,
! [X15] : c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1372,f2544]) ).
fof(f1372,axiom,
! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10678,plain,
spl0_1379,
inference(avatar_split_clause,[],[f2831,f10676]) ).
fof(f10676,plain,
( spl0_1379
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f2831,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X12,tc_set(X1)),X1),X12,X1,X1),
inference(definition_unfolding,[],[f2578,f2373]) ).
fof(f2578,axiom,
! [X1,X12] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10674,plain,
spl0_1378,
inference(avatar_split_clause,[],[f2830,f10672]) ).
fof(f10672,plain,
( spl0_1378
<=> ! [X12,X1] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f2830,plain,
! [X1,X12] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X12,X1),c_uminus(X12,tc_set(X1)),X1,X1),
inference(definition_unfolding,[],[f2579,f2373]) ).
fof(f2579,axiom,
! [X1,X12] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10670,plain,
spl0_1377,
inference(avatar_split_clause,[],[f2789,f10668]) ).
fof(f2789,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__mono_0) ).
fof(f10666,plain,
spl0_1376,
inference(avatar_split_clause,[],[f2779,f10664]) ).
fof(f10664,plain,
( spl0_1376
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f2779,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OBody__dest_0) ).
fof(f10662,plain,
spl0_1375,
inference(avatar_split_clause,[],[f2773,f10660]) ).
fof(f10660,plain,
( spl0_1375
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f2773,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_1) ).
fof(f10658,plain,
spl0_1374,
inference(avatar_split_clause,[],[f2772,f10656]) ).
fof(f10656,plain,
( spl0_1374
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f2772,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
fof(f10654,plain,
spl0_1373,
inference(avatar_split_clause,[],[f2771,f10652]) ).
fof(f10652,plain,
( spl0_1373
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f2771,axiom,
! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Ostrange__Un__eq_0) ).
fof(f10650,plain,
spl0_1372,
inference(avatar_split_clause,[],[f2768,f10648]) ).
fof(f10648,plain,
( spl0_1372
<=> ! [X20,X88] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f2768,axiom,
! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
fof(f10646,plain,
spl0_1371,
inference(avatar_split_clause,[],[f2742,f10644]) ).
fof(f10644,plain,
( spl0_1371
<=> ! [X93,X88] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f2742,axiom,
! [X88,X93] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
fof(f10642,plain,
spl0_1370,
inference(avatar_split_clause,[],[f2729,f10640]) ).
fof(f10640,plain,
( spl0_1370
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f2729,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_1) ).
fof(f10638,plain,
spl0_1369,
inference(avatar_split_clause,[],[f2728,f10636]) ).
fof(f10636,plain,
( spl0_1369
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f2728,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__parts_0) ).
fof(f10634,plain,
spl0_1368,
inference(avatar_split_clause,[],[f2703,f10632]) ).
fof(f10632,plain,
( spl0_1368
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f2703,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10630,plain,
spl0_1367,
inference(avatar_split_clause,[],[f2701,f10628]) ).
fof(f10628,plain,
( spl0_1367
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f2701,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10626,plain,
spl0_1366,
inference(avatar_split_clause,[],[f2692,f10624]) ).
fof(f10624,plain,
( spl0_1366
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f2692,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_0) ).
fof(f10622,plain,
spl0_1365,
inference(avatar_split_clause,[],[f2688,f10620]) ).
fof(f10620,plain,
( spl0_1365
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f2688,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10618,plain,
spl0_1364,
inference(avatar_split_clause,[],[f2676,f10616]) ).
fof(f10616,plain,
( spl0_1364
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f2676,axiom,
! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10614,plain,
spl0_1363,
inference(avatar_split_clause,[],[f2670,f10612]) ).
fof(f10612,plain,
( spl0_1363
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f2670,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10610,plain,
spl0_1362,
inference(avatar_split_clause,[],[f2653,f10608]) ).
fof(f10608,plain,
( spl0_1362
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f2653,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10606,plain,
spl0_1361,
inference(avatar_split_clause,[],[f2628,f10604]) ).
fof(f10604,plain,
( spl0_1361
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f2628,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10602,plain,
spl0_1360,
inference(avatar_split_clause,[],[f2627,f10600]) ).
fof(f10600,plain,
( spl0_1360
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f2627,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10598,plain,
spl0_1359,
inference(avatar_split_clause,[],[f2617,f10596]) ).
fof(f10596,plain,
( spl0_1359
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f2617,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10594,plain,
spl0_1358,
inference(avatar_split_clause,[],[f2614,f10592]) ).
fof(f10592,plain,
( spl0_1358
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f2614,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10590,plain,
spl0_1357,
inference(avatar_split_clause,[],[f2595,f10588]) ).
fof(f10588,plain,
( spl0_1357
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f2595,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10586,plain,
spl0_1356,
inference(avatar_split_clause,[],[f2594,f10584]) ).
fof(f10584,plain,
( spl0_1356
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f2594,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10582,plain,
spl0_1355,
inference(avatar_split_clause,[],[f2592,f10580]) ).
fof(f10580,plain,
( spl0_1355
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f2592,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10578,plain,
spl0_1354,
inference(avatar_split_clause,[],[f2591,f10576]) ).
fof(f10576,plain,
( spl0_1354
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f2591,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10574,plain,
spl0_1353,
inference(avatar_split_clause,[],[f2581,f10572]) ).
fof(f10572,plain,
( spl0_1353
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f2581,axiom,
! [X1,X12,X13] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10570,plain,
( spl0_1352
| ~ spl0_708
| ~ spl0_784
| ~ spl0_1065 ),
inference(avatar_split_clause,[],[f8839,f8611,f7271,f6946,f10567]) ).
fof(f10567,plain,
( spl0_1352
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f6946,plain,
( spl0_708
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f7271,plain,
( spl0_784
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f8611,plain,
( spl0_1065
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f8839,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_708
| ~ spl0_784
| ~ spl0_1065 ),
inference(forward_demodulation,[],[f8836,f6948]) ).
fof(f6948,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_708 ),
inference(avatar_component_clause,[],[f6946]) ).
fof(f8836,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_784
| ~ spl0_1065 ),
inference(superposition,[],[f8612,f7273]) ).
fof(f7273,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_784 ),
inference(avatar_component_clause,[],[f7271]) ).
fof(f8612,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1065 ),
inference(avatar_component_clause,[],[f8611]) ).
fof(f10565,plain,
spl0_1351,
inference(avatar_split_clause,[],[f2570,f10563]) ).
fof(f10563,plain,
( spl0_1351
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f2570,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10561,plain,
spl0_1350,
inference(avatar_split_clause,[],[f2569,f10559]) ).
fof(f10559,plain,
( spl0_1350
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f2569,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10557,plain,
spl0_1349,
inference(avatar_split_clause,[],[f2568,f10555]) ).
fof(f10555,plain,
( spl0_1349
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f2568,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10553,plain,
spl0_1348,
inference(avatar_split_clause,[],[f2559,f10551]) ).
fof(f10551,plain,
( spl0_1348
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f2559,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10549,plain,
spl0_1347,
inference(avatar_split_clause,[],[f2558,f10547]) ).
fof(f10547,plain,
( spl0_1347
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f2558,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10545,plain,
spl0_1346,
inference(avatar_split_clause,[],[f2557,f10543]) ).
fof(f10543,plain,
( spl0_1346
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f2557,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10541,plain,
spl0_1345,
inference(avatar_split_clause,[],[f2550,f10539]) ).
fof(f10539,plain,
( spl0_1345
<=> ! [X16,X1,X26] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f2550,axiom,
! [X1,X26,X16] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10537,plain,
spl0_1344,
inference(avatar_split_clause,[],[f2546,f10535]) ).
fof(f10535,plain,
( spl0_1344
<=> ! [X14,X26] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f2546,axiom,
! [X26,X14] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10533,plain,
spl0_1343,
inference(avatar_split_clause,[],[f2543,f10531]) ).
fof(f10531,plain,
( spl0_1343
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f2543,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10529,plain,
spl0_1342,
inference(avatar_split_clause,[],[f2537,f10527]) ).
fof(f10527,plain,
( spl0_1342
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f2537,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10525,plain,
spl0_1341,
inference(avatar_split_clause,[],[f2536,f10523]) ).
fof(f10523,plain,
( spl0_1341
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f2536,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10521,plain,
spl0_1340,
inference(avatar_split_clause,[],[f2535,f10519]) ).
fof(f10519,plain,
( spl0_1340
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f2535,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10517,plain,
spl0_1339,
inference(avatar_split_clause,[],[f2531,f10515]) ).
fof(f10515,plain,
( spl0_1339
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f2531,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10513,plain,
spl0_1338,
inference(avatar_split_clause,[],[f2530,f10511]) ).
fof(f10511,plain,
( spl0_1338
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f2530,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10509,plain,
spl0_1337,
inference(avatar_split_clause,[],[f2529,f10507]) ).
fof(f10507,plain,
( spl0_1337
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f2529,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10505,plain,
spl0_1336,
inference(avatar_split_clause,[],[f2523,f10503]) ).
fof(f10503,plain,
( spl0_1336
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f2523,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10501,plain,
spl0_1335,
inference(avatar_split_clause,[],[f2518,f10499]) ).
fof(f10499,plain,
( spl0_1335
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f2518,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10497,plain,
spl0_1334,
inference(avatar_split_clause,[],[f2517,f10495]) ).
fof(f10495,plain,
( spl0_1334
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f2517,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10493,plain,
spl0_1333,
inference(avatar_split_clause,[],[f2516,f10491]) ).
fof(f10491,plain,
( spl0_1333
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f2516,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10489,plain,
spl0_1332,
inference(avatar_split_clause,[],[f2515,f10487]) ).
fof(f10487,plain,
( spl0_1332
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f2515,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10485,plain,
( spl0_1330
| ~ spl0_1331
| ~ spl0_786
| ~ spl0_1034 ),
inference(avatar_split_clause,[],[f8794,f8486,f7280,f10482,f10479]) ).
fof(f10479,plain,
( spl0_1330
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f10482,plain,
( spl0_1331
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f7280,plain,
( spl0_786
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f8486,plain,
( spl0_1034
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f8794,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_786
| ~ spl0_1034 ),
inference(superposition,[],[f8487,f7281]) ).
fof(f7281,plain,
( ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat)
| ~ spl0_786 ),
inference(avatar_component_clause,[],[f7280]) ).
fof(f8487,plain,
( ! [X3,X0] :
( ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1034 ),
inference(avatar_component_clause,[],[f8486]) ).
fof(f10477,plain,
spl0_1329,
inference(avatar_split_clause,[],[f2514,f10475]) ).
fof(f10475,plain,
( spl0_1329
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f2514,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10473,plain,
spl0_1328,
inference(avatar_split_clause,[],[f2302,f10471]) ).
fof(f10471,plain,
( spl0_1328
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f2302,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10469,plain,
spl0_1327,
inference(avatar_split_clause,[],[f2301,f10467]) ).
fof(f10467,plain,
( spl0_1327
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f2301,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10465,plain,
spl0_1326,
inference(avatar_split_clause,[],[f2300,f10463]) ).
fof(f10463,plain,
( spl0_1326
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f2300,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10461,plain,
spl0_1325,
inference(avatar_split_clause,[],[f2299,f10459]) ).
fof(f10459,plain,
( spl0_1325
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f2299,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10457,plain,
spl0_1324,
inference(avatar_split_clause,[],[f2296,f10455]) ).
fof(f10455,plain,
( spl0_1324
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f2296,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10453,plain,
spl0_1323,
inference(avatar_split_clause,[],[f2289,f10451]) ).
fof(f10451,plain,
( spl0_1323
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f2289,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10449,plain,
spl0_1322,
inference(avatar_split_clause,[],[f2288,f10447]) ).
fof(f10447,plain,
( spl0_1322
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f2288,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10445,plain,
spl0_1321,
inference(avatar_split_clause,[],[f2287,f10443]) ).
fof(f10443,plain,
( spl0_1321
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f2287,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10441,plain,
spl0_1320,
inference(avatar_split_clause,[],[f2286,f10439]) ).
fof(f10439,plain,
( spl0_1320
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f2286,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10437,plain,
spl0_1319,
inference(avatar_split_clause,[],[f2283,f10435]) ).
fof(f10435,plain,
( spl0_1319
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f2283,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10433,plain,
spl0_1318,
inference(avatar_split_clause,[],[f2277,f10431]) ).
fof(f10431,plain,
( spl0_1318
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f2277,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10429,plain,
spl0_1317,
inference(avatar_split_clause,[],[f2276,f10427]) ).
fof(f10427,plain,
( spl0_1317
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f2276,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10425,plain,
spl0_1316,
inference(avatar_split_clause,[],[f2275,f10423]) ).
fof(f10423,plain,
( spl0_1316
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f2275,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10421,plain,
spl0_1315,
inference(avatar_split_clause,[],[f2274,f10419]) ).
fof(f10419,plain,
( spl0_1315
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f2274,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10417,plain,
spl0_1314,
inference(avatar_split_clause,[],[f2234,f10415]) ).
fof(f10415,plain,
( spl0_1314
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f2234,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10413,plain,
spl0_1313,
inference(avatar_split_clause,[],[f2233,f10411]) ).
fof(f10411,plain,
( spl0_1313
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f2233,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10409,plain,
spl0_1312,
inference(avatar_split_clause,[],[f2230,f10407]) ).
fof(f10407,plain,
( spl0_1312
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f2230,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10405,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2229,f10403]) ).
fof(f10403,plain,
( spl0_1311
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f2229,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10401,plain,
spl0_1310,
inference(avatar_split_clause,[],[f2227,f10399]) ).
fof(f10399,plain,
( spl0_1310
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f2227,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10397,plain,
( spl0_1309
| ~ spl0_752
| ~ spl0_999 ),
inference(avatar_split_clause,[],[f8705,f8345,f7143,f10395]) ).
fof(f10395,plain,
( spl0_1309
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f7143,plain,
( spl0_752
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f8345,plain,
( spl0_999
<=> ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f8705,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_752
| ~ spl0_999 ),
inference(superposition,[],[f8346,f7144]) ).
fof(f7144,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_752 ),
inference(avatar_component_clause,[],[f7143]) ).
fof(f8346,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_999 ),
inference(avatar_component_clause,[],[f8345]) ).
fof(f10393,plain,
spl0_1308,
inference(avatar_split_clause,[],[f2224,f10391]) ).
fof(f10391,plain,
( spl0_1308
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f2224,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10389,plain,
spl0_1307,
inference(avatar_split_clause,[],[f2223,f10387]) ).
fof(f10387,plain,
( spl0_1307
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f2223,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10385,plain,
spl0_1306,
inference(avatar_split_clause,[],[f2222,f10383]) ).
fof(f10383,plain,
( spl0_1306
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f2222,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10381,plain,
spl0_1305,
inference(avatar_split_clause,[],[f2221,f10379]) ).
fof(f2221,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10377,plain,
spl0_1304,
inference(avatar_split_clause,[],[f2167,f10375]) ).
fof(f10375,plain,
( spl0_1304
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f2167,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10373,plain,
spl0_1303,
inference(avatar_split_clause,[],[f2166,f10371]) ).
fof(f10371,plain,
( spl0_1303
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f2166,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10369,plain,
spl0_1302,
inference(avatar_split_clause,[],[f2086,f10367]) ).
fof(f10367,plain,
( spl0_1302
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f2086,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10365,plain,
spl0_1301,
inference(avatar_split_clause,[],[f2081,f10363]) ).
fof(f10363,plain,
( spl0_1301
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f2081,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10361,plain,
spl0_1300,
inference(avatar_split_clause,[],[f2065,f10359]) ).
fof(f10359,plain,
( spl0_1300
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f2065,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10357,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1850,f10355]) ).
fof(f1850,axiom,
! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10349,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1813,f10347]) ).
fof(f10347,plain,
( spl0_1298
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1813,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10345,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1807,f10343]) ).
fof(f10343,plain,
( spl0_1297
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1807,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10341,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1806,f10339]) ).
fof(f10339,plain,
( spl0_1296
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1806,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10337,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1784,f10335]) ).
fof(f10335,plain,
( spl0_1295
<=> ! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1784,axiom,
! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10333,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1743,f10331]) ).
fof(f10331,plain,
( spl0_1294
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1743,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10329,plain,
spl0_1293,
inference(avatar_split_clause,[],[f1737,f10327]) ).
fof(f10327,plain,
( spl0_1293
<=> ! [X1,X3] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f1737,axiom,
! [X3,X1] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10325,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1626,f10323]) ).
fof(f10323,plain,
( spl0_1292
<=> ! [X18,X42,X64,X63,X1] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f1626,axiom,
! [X1,X18,X63,X42,X64] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10321,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1625,f10319]) ).
fof(f10319,plain,
( spl0_1291
<=> ! [X18,X42,X64,X63,X1] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1625,axiom,
! [X18,X1,X63,X42,X64] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10317,plain,
spl0_1290,
inference(avatar_split_clause,[],[f1610,f10315]) ).
fof(f10315,plain,
( spl0_1290
<=> ! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f1610,axiom,
! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10313,plain,
spl0_1289,
inference(avatar_split_clause,[],[f1552,f10311]) ).
fof(f10311,plain,
( spl0_1289
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f1552,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10309,plain,
( spl0_1288
| ~ spl0_965
| ~ spl0_1068 ),
inference(avatar_split_clause,[],[f10266,f8623,f8080,f10306]) ).
fof(f10306,plain,
( spl0_1288
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f8080,plain,
( spl0_965
<=> ! [X12,X1] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f8623,plain,
( spl0_1068
<=> c_lessequals(c_Message_Oanalz(c_emptyset),c_emptyset,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f10266,plain,
( c_emptyset = c_Message_Oanalz(c_emptyset)
| ~ spl0_965
| ~ spl0_1068 ),
inference(resolution,[],[f8625,f8081]) ).
fof(f8081,plain,
( ! [X1,X12] :
( ~ c_lessequals(X12,c_emptyset,tc_set(X1))
| c_emptyset = X12 )
| ~ spl0_965 ),
inference(avatar_component_clause,[],[f8080]) ).
fof(f8625,plain,
( c_lessequals(c_Message_Oanalz(c_emptyset),c_emptyset,tc_set(tc_Message_Omsg))
| ~ spl0_1068 ),
inference(avatar_component_clause,[],[f8623]) ).
fof(f10304,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1530,f10302]) ).
fof(f10302,plain,
( spl0_1287
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1530,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10300,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1493,f10298]) ).
fof(f10298,plain,
( spl0_1286
<=> ! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1493,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10296,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1492,f10294]) ).
fof(f10294,plain,
( spl0_1285
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1492,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10292,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1485,f10290]) ).
fof(f10290,plain,
( spl0_1284
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1485,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10287,plain,
( spl0_1283
| ~ spl0_884
| ~ spl0_1282 ),
inference(avatar_split_clause,[],[f10283,f10280,f7739,f10285]) ).
fof(f10285,plain,
( spl0_1283
<=> ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f7739,plain,
( spl0_884
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f10280,plain,
( spl0_1282
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f10283,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_884
| ~ spl0_1282 ),
inference(forward_demodulation,[],[f10281,f7741]) ).
fof(f7741,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_884 ),
inference(avatar_component_clause,[],[f7739]) ).
fof(f10281,plain,
( ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1282 ),
inference(avatar_component_clause,[],[f10280]) ).
fof(f10282,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1484,f10280]) ).
fof(f1484,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10278,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1477,f10276]) ).
fof(f10276,plain,
( spl0_1281
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1477,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10274,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1476,f10272]) ).
fof(f10272,plain,
( spl0_1280
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1476,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10270,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1457,f10268]) ).
fof(f10268,plain,
( spl0_1279
<=> ! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1457,axiom,
! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10265,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1442,f10263]) ).
fof(f10263,plain,
( spl0_1278
<=> ! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1442,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10261,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1413,f10259]) ).
fof(f10259,plain,
( spl0_1277
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1413,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f10257,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1412,f10255]) ).
fof(f10255,plain,
( spl0_1276
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1412,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f10253,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1409,f10251]) ).
fof(f10251,plain,
( spl0_1275
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1409,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f10249,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1408,f10247]) ).
fof(f10247,plain,
( spl0_1274
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1408,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f10245,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1406,f10243]) ).
fof(f10243,plain,
( spl0_1273
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f1406,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f10241,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1400,f10239]) ).
fof(f10239,plain,
( spl0_1272
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f1400,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f10237,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1399,f10235]) ).
fof(f10235,plain,
( spl0_1271
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1399,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f10233,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1398,f10231]) ).
fof(f10231,plain,
( spl0_1270
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f1398,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f10229,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1397,f10227]) ).
fof(f1397,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f10219,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1361,f10217]) ).
fof(f10217,plain,
( spl0_1268
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1361,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f10215,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1356,f10213]) ).
fof(f10213,plain,
( spl0_1267
<=> ! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1356,axiom,
! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f10211,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1342,f10209]) ).
fof(f10209,plain,
( spl0_1266
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1342,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f10207,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1341,f10205]) ).
fof(f10205,plain,
( spl0_1265
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f1341,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f10203,plain,
spl0_1264,
inference(avatar_split_clause,[],[f1243,f10201]) ).
fof(f10201,plain,
( spl0_1264
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f1243,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f10199,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1233,f10197]) ).
fof(f10197,plain,
( spl0_1263
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f1233,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f10195,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1232,f10193]) ).
fof(f10193,plain,
( spl0_1262
<=> ! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f1232,axiom,
! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f10191,plain,
spl0_1261,
inference(avatar_split_clause,[],[f1191,f10189]) ).
fof(f10189,plain,
( spl0_1261
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f1191,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f10187,plain,
spl0_1260,
inference(avatar_split_clause,[],[f1189,f10185]) ).
fof(f10185,plain,
( spl0_1260
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f1189,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f10183,plain,
spl0_1259,
inference(avatar_split_clause,[],[f1185,f10181]) ).
fof(f10181,plain,
( spl0_1259
<=> ! [X2,X18,X27,X1] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f1185,axiom,
! [X2,X18,X1,X27] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f10173,plain,
spl0_1258,
inference(avatar_split_clause,[],[f110,f10171]) ).
fof(f110,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10169,plain,
spl0_1257,
inference(avatar_split_clause,[],[f109,f10167]) ).
fof(f10167,plain,
( spl0_1257
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f109,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10165,plain,
spl0_1256,
inference(avatar_split_clause,[],[f49,f10163]) ).
fof(f10163,plain,
( spl0_1256
<=> ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f49,axiom,
! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10161,plain,
spl0_1255,
inference(avatar_split_clause,[],[f2,f10159]) ).
fof(f10159,plain,
( spl0_1255
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10157,plain,
spl0_1254,
inference(avatar_split_clause,[],[f1,f10155]) ).
fof(f10155,plain,
( spl0_1254
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f9986,plain,
( ~ spl0_1252
| spl0_1253
| ~ spl0_774
| ~ spl0_1217 ),
inference(avatar_split_clause,[],[f9978,f9628,f7231,f9984,f9980]) ).
fof(f9980,plain,
( spl0_1252
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f9984,plain,
( spl0_1253
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f7231,plain,
( spl0_774
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f9628,plain,
( spl0_1217
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f9978,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_774
| ~ spl0_1217 ),
inference(trivial_inequality_removal,[],[f9971]) ).
fof(f9971,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_774
| ~ spl0_1217 ),
inference(superposition,[],[f9629,f7232]) ).
fof(f7232,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_774 ),
inference(avatar_component_clause,[],[f7231]) ).
fof(f9629,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1217 ),
inference(avatar_component_clause,[],[f9628]) ).
fof(f9918,plain,
( spl0_1251
| ~ spl0_53
| ~ spl0_979 ),
inference(avatar_split_clause,[],[f8269,f8138,f3479,f9915]) ).
fof(f9915,plain,
( spl0_1251
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f3479,plain,
( spl0_53
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f8138,plain,
( spl0_979
<=> ! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f8269,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_979 ),
inference(resolution,[],[f8139,f3481]) ).
fof(f3481,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f3479]) ).
fof(f8139,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_979 ),
inference(avatar_component_clause,[],[f8138]) ).
fof(f9870,plain,
( spl0_1250
| ~ spl0_873
| ~ spl0_963 ),
inference(avatar_split_clause,[],[f8251,f8071,f7633,f9867]) ).
fof(f9867,plain,
( spl0_1250
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f7633,plain,
( spl0_873
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f8071,plain,
( spl0_963
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f8251,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_873
| ~ spl0_963 ),
inference(superposition,[],[f7634,f8073]) ).
fof(f8073,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_963 ),
inference(avatar_component_clause,[],[f8071]) ).
fof(f7634,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_873 ),
inference(avatar_component_clause,[],[f7633]) ).
fof(f9817,plain,
( spl0_1249
| ~ spl0_88
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8235,f8023,f3654,f9815]) ).
fof(f9815,plain,
( spl0_1249
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f3654,plain,
( spl0_88
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f8023,plain,
( spl0_951
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f8235,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_88
| ~ spl0_951 ),
inference(resolution,[],[f8024,f3656]) ).
fof(f3656,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_88 ),
inference(avatar_component_clause,[],[f3654]) ).
fof(f8024,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_951 ),
inference(avatar_component_clause,[],[f8023]) ).
fof(f9789,plain,
( spl0_1248
| ~ spl0_53
| ~ spl0_1029
| ~ spl0_1175 ),
inference(avatar_split_clause,[],[f9462,f9459,f8466,f3479,f9787]) ).
fof(f9787,plain,
( spl0_1248
<=> ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f8466,plain,
( spl0_1029
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f9459,plain,
( spl0_1175
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f9462,plain,
( ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_53
| ~ spl0_1029
| ~ spl0_1175 ),
inference(forward_demodulation,[],[f9460,f8785]) ).
fof(f8785,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1029 ),
inference(resolution,[],[f8467,f3481]) ).
fof(f8467,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1029 ),
inference(avatar_component_clause,[],[f8466]) ).
fof(f9460,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) )
| ~ spl0_1175 ),
inference(avatar_component_clause,[],[f9459]) ).
fof(f9783,plain,
( spl0_1247
| ~ spl0_54
| ~ spl0_951 ),
inference(avatar_split_clause,[],[f8234,f8023,f3484,f9781]) ).
fof(f9781,plain,
( spl0_1247
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f3484,plain,
( spl0_54
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f8234,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_54
| ~ spl0_951 ),
inference(resolution,[],[f8024,f3486]) ).
fof(f3486,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3484]) ).
fof(f9751,plain,
spl0_1246,
inference(avatar_split_clause,[],[f3116,f9749]) ).
fof(f9749,plain,
( spl0_1246
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f3116,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ),
inference(forward_demodulation,[],[f2934,f2798]) ).
fof(f2934,plain,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2096,f2544]) ).
fof(f2096,axiom,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9747,plain,
spl0_1245,
inference(avatar_split_clause,[],[f3115,f9745]) ).
fof(f9745,plain,
( spl0_1245
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f3115,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f2933,f2798]) ).
fof(f2933,plain,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X15,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2095,f2544]) ).
fof(f2095,axiom,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9743,plain,
spl0_1244,
inference(avatar_split_clause,[],[f3105,f9741]) ).
fof(f9741,plain,
( spl0_1244
<=> ! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f3105,plain,
! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ),
inference(forward_demodulation,[],[f2918,f2798]) ).
fof(f2918,plain,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2340,f2544]) ).
fof(f2340,axiom,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9739,plain,
spl0_1243,
inference(avatar_split_clause,[],[f3046,f9737]) ).
fof(f9737,plain,
( spl0_1243
<=> ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f3046,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2849,f2798]) ).
fof(f2849,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2764,f2544]) ).
fof(f2764,axiom,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__5_0) ).
fof(f9735,plain,
spl0_1242,
inference(avatar_split_clause,[],[f3042,f9733]) ).
fof(f9733,plain,
( spl0_1242
<=> ! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f3042,plain,
! [X21,X15] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2838,f2834]) ).
fof(f2838,plain,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
inference(definition_unfolding,[],[f38,f2544]) ).
fof(f38,axiom,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9731,plain,
( spl0_1241
| ~ spl0_88
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8233,f8019,f3654,f9729]) ).
fof(f9729,plain,
( spl0_1241
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f8019,plain,
( spl0_950
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f8233,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_88
| ~ spl0_950 ),
inference(resolution,[],[f8020,f3656]) ).
fof(f8020,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_950 ),
inference(avatar_component_clause,[],[f8019]) ).
fof(f9727,plain,
spl0_1240,
inference(avatar_split_clause,[],[f3038,f9725]) ).
fof(f9725,plain,
( spl0_1240
<=> ! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f3038,plain,
! [X11] : c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2836,f2813]) ).
fof(f2836,plain,
! [X11] : c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X11,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f2131,f2113,f2113]) ).
fof(f2131,axiom,
! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9723,plain,
spl0_1239,
inference(avatar_split_clause,[],[f2837,f9721]) ).
fof(f9721,plain,
( spl0_1239
<=> ! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f2837,plain,
! [X11] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X11),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f2123,f2129,f2129]) ).
fof(f2123,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9715,plain,
( spl0_1238
| ~ spl0_1237 ),
inference(avatar_split_clause,[],[f9711,f9708,f9713]) ).
fof(f9708,plain,
( spl0_1237
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f9711,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1237 ),
inference(forward_demodulation,[],[f9709,f2834]) ).
fof(f9709,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1237 ),
inference(avatar_component_clause,[],[f9708]) ).
fof(f9710,plain,
spl0_1237,
inference(avatar_split_clause,[],[f2826,f9708]) ).
fof(f2826,plain,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1394,f2544]) ).
fof(f1394,axiom,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9706,plain,
spl0_1236,
inference(avatar_split_clause,[],[f2715,f9704]) ).
fof(f9704,plain,
( spl0_1236
<=> ! [X5,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f2715,axiom,
! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9702,plain,
spl0_1235,
inference(avatar_split_clause,[],[f2713,f9700]) ).
fof(f9700,plain,
( spl0_1235
<=> ! [X5,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f2713,axiom,
! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9698,plain,
spl0_1234,
inference(avatar_split_clause,[],[f2685,f9696]) ).
fof(f9696,plain,
( spl0_1234
<=> ! [X18,X12,X27,X1] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f2685,axiom,
! [X18,X1,X27,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9694,plain,
spl0_1233,
inference(avatar_split_clause,[],[f2642,f9692]) ).
fof(f9692,plain,
( spl0_1233
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f2642,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9690,plain,
spl0_1232,
inference(avatar_split_clause,[],[f2641,f9688]) ).
fof(f9688,plain,
( spl0_1232
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f2641,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9686,plain,
( spl0_1231
| ~ spl0_54
| ~ spl0_950 ),
inference(avatar_split_clause,[],[f8232,f8019,f3484,f9684]) ).
fof(f9684,plain,
( spl0_1231
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f8232,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_950 ),
inference(resolution,[],[f8020,f3486]) ).
fof(f9682,plain,
spl0_1230,
inference(avatar_split_clause,[],[f2583,f9680]) ).
fof(f9680,plain,
( spl0_1230
<=> ! [X12,X1,X4] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f2583,axiom,
! [X1,X4,X12] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9678,plain,
spl0_1229,
inference(avatar_split_clause,[],[f2582,f9676]) ).
fof(f9676,plain,
( spl0_1229
<=> ! [X12,X1,X4] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f2582,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9674,plain,
spl0_1228,
inference(avatar_split_clause,[],[f2545,f9672]) ).
fof(f9672,plain,
( spl0_1228
<=> ! [X14,X26] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f2545,axiom,
! [X26,X14] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9670,plain,
spl0_1227,
inference(avatar_split_clause,[],[f2542,f9668]) ).
fof(f9668,plain,
( spl0_1227
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f2542,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9666,plain,
spl0_1226,
inference(avatar_split_clause,[],[f2522,f9664]) ).
fof(f9664,plain,
( spl0_1226
<=> ! [X18,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f2522,axiom,
! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9662,plain,
spl0_1225,
inference(avatar_split_clause,[],[f2271,f9660]) ).
fof(f9660,plain,
( spl0_1225
<=> ! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f2271,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/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(f9658,plain,
spl0_1224,
inference(avatar_split_clause,[],[f2270,f9656]) ).
fof(f9656,plain,
( spl0_1224
<=> ! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f2270,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/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(f9654,plain,
spl0_1223,
inference(avatar_split_clause,[],[f2252,f9652]) ).
fof(f9652,plain,
( spl0_1223
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f2252,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9650,plain,
spl0_1222,
inference(avatar_split_clause,[],[f2245,f9648]) ).
fof(f9648,plain,
( spl0_1222
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f2245,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9646,plain,
spl0_1221,
inference(avatar_split_clause,[],[f2244,f9644]) ).
fof(f9644,plain,
( spl0_1221
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2244,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9642,plain,
( spl0_1220
| ~ spl0_92
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8225,f8007,f3674,f9640]) ).
fof(f9640,plain,
( spl0_1220
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f3674,plain,
( spl0_92
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f8007,plain,
( spl0_947
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f8225,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_92
| ~ spl0_947 ),
inference(resolution,[],[f8008,f3676]) ).
fof(f3676,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_92 ),
inference(avatar_component_clause,[],[f3674]) ).
fof(f8008,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f8007]) ).
fof(f9638,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2240,f9636]) ).
fof(f9636,plain,
( spl0_1219
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f2240,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9634,plain,
spl0_1218,
inference(avatar_split_clause,[],[f2239,f9632]) ).
fof(f9632,plain,
( spl0_1218
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f2239,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9630,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2199,f9628]) ).
fof(f2199,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9626,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2183,f9624]) ).
fof(f9624,plain,
( spl0_1216
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f2183,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9622,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2181,f9620]) ).
fof(f9620,plain,
( spl0_1215
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f2181,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9618,plain,
spl0_1214,
inference(avatar_split_clause,[],[f2179,f9616]) ).
fof(f9616,plain,
( spl0_1214
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f2179,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9614,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2178,f9612]) ).
fof(f9612,plain,
( spl0_1213
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f2178,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9610,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2147,f9608]) ).
fof(f9608,plain,
( spl0_1212
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f2147,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9606,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2127,f9604]) ).
fof(f9604,plain,
( spl0_1211
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f9602,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2104,f9600]) ).
fof(f9600,plain,
( spl0_1210
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f2104,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9598,plain,
( spl0_1209
| ~ spl0_28
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8224,f8007,f3354,f9596]) ).
fof(f9596,plain,
( spl0_1209
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f3354,plain,
( spl0_28
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f8224,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_947 ),
inference(resolution,[],[f8008,f3356]) ).
fof(f3356,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3354]) ).
fof(f9594,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2103,f9592]) ).
fof(f9592,plain,
( spl0_1208
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f2103,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9590,plain,
spl0_1207,
inference(avatar_split_clause,[],[f2079,f9588]) ).
fof(f9588,plain,
( spl0_1207
<=> ! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f2079,axiom,
! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9586,plain,
spl0_1206,
inference(avatar_split_clause,[],[f2078,f9584]) ).
fof(f9584,plain,
( spl0_1206
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f2078,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9582,plain,
spl0_1205,
inference(avatar_split_clause,[],[f2030,f9580]) ).
fof(f9580,plain,
( spl0_1205
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f2030,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9578,plain,
spl0_1204,
inference(avatar_split_clause,[],[f2029,f9576]) ).
fof(f9576,plain,
( spl0_1204
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f2029,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9574,plain,
spl0_1203,
inference(avatar_split_clause,[],[f1851,f9572]) ).
fof(f9572,plain,
( spl0_1203
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1851,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9570,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1814,f9568]) ).
fof(f9568,plain,
( spl0_1202
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1814,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9566,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1734,f9564]) ).
fof(f9564,plain,
( spl0_1201
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1734,axiom,
! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f9562,plain,
spl0_1200,
inference(avatar_split_clause,[],[f1731,f9560]) ).
fof(f9560,plain,
( spl0_1200
<=> ! [X0,X1,X21] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f1731,axiom,
! [X21,X0,X1] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9558,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1712,f9556]) ).
fof(f9556,plain,
( spl0_1199
<=> ! [X41,X0,X3,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1712,axiom,
! [X41,X3,X0,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9554,plain,
( spl0_1198
| ~ spl0_92
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8223,f8003,f3674,f9552]) ).
fof(f9552,plain,
( spl0_1198
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f8003,plain,
( spl0_946
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f8223,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_92
| ~ spl0_946 ),
inference(resolution,[],[f8004,f3676]) ).
fof(f8004,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_946 ),
inference(avatar_component_clause,[],[f8003]) ).
fof(f9550,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1613,f9548]) ).
fof(f9548,plain,
( spl0_1197
<=> ! [X43,X59] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1613,axiom,
! [X59,X43] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9546,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1609,f9544]) ).
fof(f9544,plain,
( spl0_1196
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1609,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9542,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1608,f9540]) ).
fof(f9540,plain,
( spl0_1195
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1608,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9538,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1595,f9536]) ).
fof(f9536,plain,
( spl0_1194
<=> ! [X1,X23,X3] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1595,axiom,
! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9534,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1594,f9532]) ).
fof(f9532,plain,
( spl0_1193
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1594,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9530,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1593,f9528]) ).
fof(f9528,plain,
( spl0_1192
<=> ! [X60,X1] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1593,axiom,
! [X1,X60] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9526,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1584,f9524]) ).
fof(f9524,plain,
( spl0_1191
<=> ! [X59,X3] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1584,axiom,
! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9522,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1583,f9520]) ).
fof(f9520,plain,
( spl0_1190
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1583,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9518,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1582,f9516]) ).
fof(f9516,plain,
( spl0_1189
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f1582,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9514,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1539,f9512]) ).
fof(f9512,plain,
( spl0_1188
<=> ! [X0,X1,X3] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1539,axiom,
! [X3,X0,X1] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9510,plain,
( spl0_1187
| ~ spl0_28
| ~ spl0_946 ),
inference(avatar_split_clause,[],[f8222,f8003,f3354,f9508]) ).
fof(f9508,plain,
( spl0_1187
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f8222,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_946 ),
inference(resolution,[],[f8004,f3356]) ).
fof(f9506,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1463,f9504]) ).
fof(f9504,plain,
( spl0_1186
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1463,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9502,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1462,f9500]) ).
fof(f9500,plain,
( spl0_1185
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1462,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9498,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1455,f9496]) ).
fof(f9496,plain,
( spl0_1184
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f1455,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9494,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1454,f9492]) ).
fof(f9492,plain,
( spl0_1183
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f1454,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9490,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1418,f9488]) ).
fof(f9488,plain,
( spl0_1182
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f1418,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9486,plain,
spl0_1181,
inference(avatar_split_clause,[],[f1354,f9484]) ).
fof(f9484,plain,
( spl0_1181
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f1354,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9482,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1353,f9480]) ).
fof(f9480,plain,
( spl0_1180
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1353,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9478,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1352,f9476]) ).
fof(f9476,plain,
( spl0_1179
<=> ! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1352,axiom,
! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9474,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1351,f9472]) ).
fof(f9472,plain,
( spl0_1178
<=> ! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1351,axiom,
! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9470,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1348,f9468]) ).
fof(f9468,plain,
( spl0_1177
<=> ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1348,axiom,
! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f9466,plain,
( spl0_1176
| ~ spl0_65
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8217,f7987,f3539,f9464]) ).
fof(f9464,plain,
( spl0_1176
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f3539,plain,
( spl0_65
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f7987,plain,
( spl0_942
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f8217,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_65
| ~ spl0_942 ),
inference(resolution,[],[f7988,f3541]) ).
fof(f3541,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_65 ),
inference(avatar_component_clause,[],[f3539]) ).
fof(f7988,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_942 ),
inference(avatar_component_clause,[],[f7987]) ).
fof(f9461,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1345,f9459]) ).
fof(f1345,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9457,plain,
spl0_1174,
inference(avatar_split_clause,[],[f1310,f9455]) ).
fof(f9455,plain,
( spl0_1174
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f1310,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9453,plain,
spl0_1173,
inference(avatar_split_clause,[],[f1307,f9451]) ).
fof(f9451,plain,
( spl0_1173
<=> ! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f1307,axiom,
! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9449,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1236,f9447]) ).
fof(f9447,plain,
( spl0_1172
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f1236,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9445,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1234,f9443]) ).
fof(f9443,plain,
( spl0_1171
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1234,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9441,plain,
spl0_1170,
inference(avatar_split_clause,[],[f1178,f9439]) ).
fof(f9439,plain,
( spl0_1170
<=> ! [X2,X27,X1,X18] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f1178,axiom,
! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9437,plain,
spl0_1169,
inference(avatar_split_clause,[],[f1166,f9435]) ).
fof(f9435,plain,
( spl0_1169
<=> ! [X0,X1,X40] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f1166,axiom,
! [X40,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9422,plain,
( spl0_1168
| ~ spl0_16
| ~ spl0_942 ),
inference(avatar_split_clause,[],[f8216,f7987,f3294,f9420]) ).
fof(f9420,plain,
( spl0_1168
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f3294,plain,
( spl0_16
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f8216,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_16
| ~ spl0_942 ),
inference(resolution,[],[f7988,f3296]) ).
fof(f3296,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f9411,plain,
( spl0_1167
| ~ spl0_65
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f8215,f7983,f3539,f9409]) ).
fof(f9409,plain,
( spl0_1167
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f7983,plain,
( spl0_941
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f8215,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_65
| ~ spl0_941 ),
inference(resolution,[],[f7984,f3541]) ).
fof(f7984,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_941 ),
inference(avatar_component_clause,[],[f7983]) ).
fof(f9395,plain,
( spl0_1166
| ~ spl0_16
| ~ spl0_941 ),
inference(avatar_split_clause,[],[f8214,f7983,f3294,f9393]) ).
fof(f9393,plain,
( spl0_1166
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f8214,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_16
| ~ spl0_941 ),
inference(resolution,[],[f7984,f3296]) ).
fof(f9354,plain,
( spl0_1165
| ~ spl0_10
| ~ spl0_940 ),
inference(avatar_split_clause,[],[f8213,f7979,f3264,f9352]) ).
fof(f9352,plain,
( spl0_1165
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f3264,plain,
( spl0_10
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f7979,plain,
( spl0_940
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f8213,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_10
| ~ spl0_940 ),
inference(resolution,[],[f7980,f3266]) ).
fof(f3266,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f3264]) ).
fof(f7980,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_940 ),
inference(avatar_component_clause,[],[f7979]) ).
fof(f9320,plain,
( spl0_1164
| ~ spl0_53
| ~ spl0_1029
| ~ spl0_1108 ),
inference(avatar_split_clause,[],[f8988,f8985,f8466,f3479,f9318]) ).
fof(f9318,plain,
( spl0_1164
<=> ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f8985,plain,
( spl0_1108
<=> ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f8988,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_1029
| ~ spl0_1108 ),
inference(forward_demodulation,[],[f8986,f8785]) ).
fof(f8986,plain,
( ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint)
| ~ spl0_1108 ),
inference(avatar_component_clause,[],[f8985]) ).
fof(f9275,plain,
( spl0_1163
| spl0_676
| ~ spl0_1094 ),
inference(avatar_split_clause,[],[f9257,f8929,f6799,f9272]) ).
fof(f9272,plain,
( spl0_1163
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f6799,plain,
( spl0_676
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f8929,plain,
( spl0_1094
<=> ! [X12,X1] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f9257,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_676
| ~ spl0_1094 ),
inference(resolution,[],[f8930,f6801]) ).
fof(f6801,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_676 ),
inference(avatar_component_clause,[],[f6799]) ).
fof(f8930,plain,
( ! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_0 = c_Finite__Set_Ocard(X12,X1) )
| ~ spl0_1094 ),
inference(avatar_component_clause,[],[f8929]) ).
fof(f9218,plain,
( spl0_1162
| ~ spl0_641
| ~ spl0_1134
| ~ spl0_1154 ),
inference(avatar_split_clause,[],[f9182,f9173,f9091,f5883,f9215]) ).
fof(f9215,plain,
( spl0_1162
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f9173,plain,
( spl0_1154
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f9182,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1134
| ~ spl0_1154 ),
inference(forward_demodulation,[],[f9181,f9092]) ).
fof(f9181,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_1154 ),
inference(superposition,[],[f9174,f5885]) ).
fof(f9174,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1154 ),
inference(avatar_component_clause,[],[f9173]) ).
fof(f9206,plain,
spl0_1161,
inference(avatar_split_clause,[],[f3165,f9204]) ).
fof(f9204,plain,
( spl0_1161
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f3165,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(inner_rewriting,[],[f3164]) ).
fof(f3164,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f3163,f2115]) ).
fof(f3163,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2966,f2797]) ).
fof(f2966,plain,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X1),X1) ),
inference(definition_unfolding,[],[f1337,f2129]) ).
fof(f1337,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f9202,plain,
spl0_1160,
inference(avatar_split_clause,[],[f3049,f9200]) ).
fof(f9200,plain,
( spl0_1160
<=> ! [X96,X90] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f3049,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
inference(forward_demodulation,[],[f3048,f3046]) ).
fof(f3048,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2863,f2798]) ).
fof(f2863,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f2766,f2544]) ).
fof(f2766,axiom,
! [X90,X96] : c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__7_0) ).
fof(f9198,plain,
spl0_1159,
inference(avatar_split_clause,[],[f3045,f9196]) ).
fof(f9196,plain,
( spl0_1159
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f3045,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2843,f2798]) ).
fof(f2843,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1210,f2544]) ).
fof(f1210,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f9194,plain,
spl0_1158,
inference(avatar_split_clause,[],[f3044,f9192]) ).
fof(f9192,plain,
( spl0_1158
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f3044,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f2842,f2798]) ).
fof(f2842,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(definition_unfolding,[],[f1209,f2544]) ).
fof(f1209,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f9190,plain,
spl0_1157,
inference(avatar_split_clause,[],[f2917,f9188]) ).
fof(f9188,plain,
( spl0_1157
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f2917,plain,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2279,f2544]) ).
fof(f2279,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9186,plain,
spl0_1156,
inference(avatar_split_clause,[],[f2907,f9184]) ).
fof(f9184,plain,
( spl0_1156
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f2907,plain,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2278,f2544]) ).
fof(f2278,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9179,plain,
( spl0_1155
| ~ spl0_10
| ~ spl0_939 ),
inference(avatar_split_clause,[],[f8208,f7975,f3264,f9177]) ).
fof(f9177,plain,
( spl0_1155
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f7975,plain,
( spl0_939
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f8208,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_10
| ~ spl0_939 ),
inference(resolution,[],[f7976,f3266]) ).
fof(f7976,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_939 ),
inference(avatar_component_clause,[],[f7975]) ).
fof(f9175,plain,
( spl0_1154
| ~ spl0_1153 ),
inference(avatar_split_clause,[],[f9171,f9168,f9173]) ).
fof(f9168,plain,
( spl0_1153
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f9171,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X21),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1153 ),
inference(forward_demodulation,[],[f9169,f2834]) ).
fof(f9169,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1153 ),
inference(avatar_component_clause,[],[f9168]) ).
fof(f9170,plain,
spl0_1153,
inference(avatar_split_clause,[],[f2825,f9168]) ).
fof(f2825,plain,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1388,f2544]) ).
fof(f1388,axiom,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f9166,plain,
( spl0_1152
| ~ spl0_801
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9162,f9159,f7340,f9164]) ).
fof(f9164,plain,
( spl0_1152
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f7340,plain,
( spl0_801
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f9159,plain,
( spl0_1151
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f9162,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X1)
| ~ spl0_801
| ~ spl0_1151 ),
inference(forward_demodulation,[],[f9160,f7341]) ).
fof(f7341,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_801 ),
inference(avatar_component_clause,[],[f7340]) ).
fof(f9160,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1)
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f9159]) ).
fof(f9161,plain,
spl0_1151,
inference(avatar_split_clause,[],[f2799,f9159]) ).
fof(f2799,plain,
! [X1] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X1,X1)),X1),
inference(definition_unfolding,[],[f2709,f2716]) ).
fof(f2709,axiom,
! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f9157,plain,
spl0_1150,
inference(avatar_split_clause,[],[f2759,f9155]) ).
fof(f9155,plain,
( spl0_1150
<=> ! [X89,X96,X97,X90] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f2759,axiom,
! [X90,X89,X96,X97] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_1) ).
fof(f9153,plain,
spl0_1149,
inference(avatar_split_clause,[],[f2758,f9151]) ).
fof(f9151,plain,
( spl0_1149
<=> ! [X96,X97,X90,X89] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f2758,axiom,
! [X90,X89,X96,X97] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__7_0) ).
fof(f9149,plain,
spl0_1148,
inference(avatar_split_clause,[],[f2757,f9147]) ).
fof(f9147,plain,
( spl0_1148
<=> ! [X100,X101,X98,X99] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f2757,axiom,
! [X101,X98,X99,X100] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_1) ).
fof(f9145,plain,
spl0_1147,
inference(avatar_split_clause,[],[f2756,f9143]) ).
fof(f9143,plain,
( spl0_1147
<=> ! [X101,X98,X100,X99] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f2756,axiom,
! [X101,X98,X99,X100] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__6_0) ).
fof(f9141,plain,
spl0_1146,
inference(avatar_split_clause,[],[f2748,f9139]) ).
fof(f9139,plain,
( spl0_1146
<=> ! [X87,X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f2748,axiom,
! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__MPair_0) ).
fof(f9137,plain,
( spl0_1145
| ~ spl0_5
| ~ spl0_938 ),
inference(avatar_split_clause,[],[f8206,f7971,f3239,f9135]) ).
fof(f9135,plain,
( spl0_1145
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f3239,plain,
( spl0_5
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f7971,plain,
( spl0_938
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f8206,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_5
| ~ spl0_938 ),
inference(resolution,[],[f7972,f3241]) ).
fof(f3241,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f3239]) ).
fof(f7972,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_938 ),
inference(avatar_component_clause,[],[f7971]) ).
fof(f9133,plain,
spl0_1144,
inference(avatar_split_clause,[],[f2671,f9131]) ).
fof(f9131,plain,
( spl0_1144
<=> ! [X12,X1] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f2671,axiom,
! [X1,X12] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f9129,plain,
spl0_1143,
inference(avatar_split_clause,[],[f2654,f9127]) ).
fof(f9127,plain,
( spl0_1143
<=> ! [X12,X1] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f2654,axiom,
! [X1,X12] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f9125,plain,
spl0_1142,
inference(avatar_split_clause,[],[f2618,f9123]) ).
fof(f9123,plain,
( spl0_1142
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f2618,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f9121,plain,
spl0_1141,
inference(avatar_split_clause,[],[f2615,f9119]) ).
fof(f9119,plain,
( spl0_1141
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f2615,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f9117,plain,
spl0_1140,
inference(avatar_split_clause,[],[f2388,f9115]) ).
fof(f9115,plain,
( spl0_1140
<=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f2388,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f9113,plain,
spl0_1139,
inference(avatar_split_clause,[],[f2383,f9111]) ).
fof(f2383,axiom,
! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f9109,plain,
spl0_1138,
inference(avatar_split_clause,[],[f2366,f9107]) ).
fof(f9107,plain,
( spl0_1138
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f2366,axiom,
! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f9105,plain,
spl0_1137,
inference(avatar_split_clause,[],[f2364,f9103]) ).
fof(f9103,plain,
( spl0_1137
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f2364,axiom,
! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f9101,plain,
spl0_1136,
inference(avatar_split_clause,[],[f2342,f9099]) ).
fof(f9099,plain,
( spl0_1136
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f2342,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f9097,plain,
spl0_1135,
inference(avatar_split_clause,[],[f2341,f9095]) ).
fof(f9095,plain,
( spl0_1135
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f2341,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f9093,plain,
( spl0_1134
| ~ spl0_5
| ~ spl0_937 ),
inference(avatar_split_clause,[],[f8204,f7967,f3239,f9091]) ).
fof(f7967,plain,
( spl0_937
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f8204,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_5
| ~ spl0_937 ),
inference(resolution,[],[f7968,f3241]) ).
fof(f7968,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_937 ),
inference(avatar_component_clause,[],[f7967]) ).
fof(f9089,plain,
spl0_1133,
inference(avatar_split_clause,[],[f2294,f9087]) ).
fof(f9087,plain,
( spl0_1133
<=> ! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f2294,axiom,
! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f9085,plain,
spl0_1132,
inference(avatar_split_clause,[],[f2281,f9083]) ).
fof(f9083,plain,
( spl0_1132
<=> ! [X0,X3] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f2281,axiom,
! [X3,X0] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f9081,plain,
spl0_1131,
inference(avatar_split_clause,[],[f2247,f9079]) ).
fof(f9079,plain,
( spl0_1131
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2247,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f9077,plain,
spl0_1130,
inference(avatar_split_clause,[],[f2219,f9075]) ).
fof(f9075,plain,
( spl0_1130
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f2219,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_0) ).
fof(f9073,plain,
spl0_1129,
inference(avatar_split_clause,[],[f2213,f9071]) ).
fof(f9071,plain,
( spl0_1129
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f2213,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f9069,plain,
spl0_1128,
inference(avatar_split_clause,[],[f2211,f9067]) ).
fof(f9067,plain,
( spl0_1128
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f2211,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f9065,plain,
spl0_1127,
inference(avatar_split_clause,[],[f2197,f9063]) ).
fof(f9063,plain,
( spl0_1127
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f2197,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f9061,plain,
spl0_1126,
inference(avatar_split_clause,[],[f2172,f9059]) ).
fof(f9059,plain,
( spl0_1126
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f2172,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__0__eq_0) ).
fof(f9057,plain,
spl0_1125,
inference(avatar_split_clause,[],[f2171,f9055]) ).
fof(f9055,plain,
( spl0_1125
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f2171,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f9053,plain,
spl0_1124,
inference(avatar_split_clause,[],[f2039,f9051]) ).
fof(f9051,plain,
( spl0_1124
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f2039,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f9049,plain,
( spl0_1123
| ~ spl0_707
| ~ spl0_878
| ~ spl0_933 ),
inference(avatar_split_clause,[],[f8193,f7951,f7654,f6941,f9046]) ).
fof(f9046,plain,
( spl0_1123
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f6941,plain,
( spl0_707
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f7654,plain,
( spl0_878
<=> 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_878])]) ).
fof(f7951,plain,
( spl0_933
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f8193,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_707
| ~ spl0_878
| ~ spl0_933 ),
inference(forward_demodulation,[],[f8191,f6943]) ).
fof(f6943,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_707 ),
inference(avatar_component_clause,[],[f6941]) ).
fof(f8191,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_878
| ~ spl0_933 ),
inference(superposition,[],[f7952,f7656]) ).
fof(f7656,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f7654]) ).
fof(f7952,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_933 ),
inference(avatar_component_clause,[],[f7951]) ).
fof(f9044,plain,
spl0_1122,
inference(avatar_split_clause,[],[f2038,f9042]) ).
fof(f9042,plain,
( spl0_1122
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f2038,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f9040,plain,
spl0_1121,
inference(avatar_split_clause,[],[f1849,f9038]) ).
fof(f9038,plain,
( spl0_1121
<=> ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f1849,axiom,
! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_2) ).
fof(f9036,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1832,f9034]) ).
fof(f9034,plain,
( spl0_1120
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1832,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_1) ).
fof(f9032,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1803,f9030]) ).
fof(f9030,plain,
( spl0_1119
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1803,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X21
| c_0 != c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_0) ).
fof(f9028,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1759,f9026]) ).
fof(f9026,plain,
( spl0_1118
<=> ! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1759,axiom,
! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f9024,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1730,f9022]) ).
fof(f9022,plain,
( spl0_1117
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1730,axiom,
! [X1,X25,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f9020,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1603,f9018]) ).
fof(f9018,plain,
( spl0_1116
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1603,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f9016,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1548,f9014]) ).
fof(f9014,plain,
( spl0_1115
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1548,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f9012,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1541,f9010]) ).
fof(f9010,plain,
( spl0_1114
<=> ! [X54,X57,X55,X56] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1541,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f9008,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1540,f9006]) ).
fof(f9006,plain,
( spl0_1113
<=> ! [X55,X54,X56,X57] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1540,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f9004,plain,
( spl0_1112
| ~ spl0_83
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8171,f7874,f3629,f9002]) ).
fof(f9002,plain,
( spl0_1112
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f3629,plain,
( spl0_83
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f7874,plain,
( spl0_914
<=> ! [X1,X3] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f8171,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_83
| ~ spl0_914 ),
inference(resolution,[],[f7875,f3631]) ).
fof(f3631,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_83 ),
inference(avatar_component_clause,[],[f3629]) ).
fof(f7875,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_914 ),
inference(avatar_component_clause,[],[f7874]) ).
fof(f9000,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1509,f8998]) ).
fof(f8998,plain,
( spl0_1111
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f1509,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f8996,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1488,f8994]) ).
fof(f8994,plain,
( spl0_1110
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1488,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f8992,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1487,f8990]) ).
fof(f1487,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f8987,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1467,f8985]) ).
fof(f1467,axiom,
! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f8983,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1440,f8981]) ).
fof(f8981,plain,
( spl0_1107
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1440,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f8979,plain,
spl0_1106,
inference(avatar_split_clause,[],[f1439,f8977]) ).
fof(f1439,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f8975,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1430,f8973]) ).
fof(f8973,plain,
( spl0_1105
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1430,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f8971,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1429,f8969]) ).
fof(f8969,plain,
( spl0_1104
<=> ! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1429,axiom,
! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f8967,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1428,f8965]) ).
fof(f8965,plain,
( spl0_1103
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1428,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f8963,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1427,f8961]) ).
fof(f8961,plain,
( spl0_1102
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1427,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f8959,plain,
( spl0_1101
| ~ spl0_25
| ~ spl0_914 ),
inference(avatar_split_clause,[],[f8170,f7874,f3339,f8957]) ).
fof(f8957,plain,
( spl0_1101
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f3339,plain,
( spl0_25
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f8170,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_25
| ~ spl0_914 ),
inference(resolution,[],[f7875,f3341]) ).
fof(f3341,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f3339]) ).
fof(f8955,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1426,f8953]) ).
fof(f8953,plain,
( spl0_1100
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1426,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f8951,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1425,f8949]) ).
fof(f8949,plain,
( spl0_1099
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1425,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f8947,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1407,f8945]) ).
fof(f8945,plain,
( spl0_1098
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1407,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f8943,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1395,f8941]) ).
fof(f8941,plain,
( spl0_1097
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X48
| c_0 != c_IntDef_Oof__int(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f1395,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X48
| c_0 != c_IntDef_Oof__int(X48,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_0) ).
fof(f8939,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1390,f8937]) ).
fof(f8937,plain,
( spl0_1096
<=> ! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1390,axiom,
! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f8935,plain,
spl0_1095,
inference(avatar_split_clause,[],[f1389,f8933]) ).
fof(f8933,plain,
( spl0_1095
<=> ! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f1389,axiom,
! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8931,plain,
spl0_1094,
inference(avatar_split_clause,[],[f1279,f8929]) ).
fof(f1279,axiom,
! [X1,X12] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8927,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1275,f8925]) ).
fof(f8925,plain,
( spl0_1093
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1275,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8923,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1265,f8921]) ).
fof(f8921,plain,
( spl0_1092
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f1265,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8919,plain,
spl0_1091,
inference(avatar_split_clause,[],[f1235,f8917]) ).
fof(f8917,plain,
( spl0_1091
<=> ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f1235,axiom,
! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8915,plain,
( spl0_1090
| ~ spl0_90
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f8169,f7865,f3664,f8913]) ).
fof(f8913,plain,
( spl0_1090
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f3664,plain,
( spl0_90
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f7865,plain,
( spl0_912
<=> ! [X1,X3] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f8169,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_90
| ~ spl0_912 ),
inference(resolution,[],[f7866,f3666]) ).
fof(f3666,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_90 ),
inference(avatar_component_clause,[],[f3664]) ).
fof(f7866,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_912 ),
inference(avatar_component_clause,[],[f7865]) ).
fof(f8911,plain,
spl0_1089,
inference(avatar_split_clause,[],[f1224,f8909]) ).
fof(f8909,plain,
( spl0_1089
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1224,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8907,plain,
spl0_1088,
inference(avatar_split_clause,[],[f1216,f8905]) ).
fof(f8905,plain,
( spl0_1088
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f1216,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8903,plain,
spl0_1087,
inference(avatar_split_clause,[],[f1201,f8901]) ).
fof(f8901,plain,
( spl0_1087
<=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f1201,axiom,
! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Numb_0) ).
fof(f8899,plain,
spl0_1086,
inference(avatar_split_clause,[],[f1200,f8897]) ).
fof(f8897,plain,
( spl0_1086
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f1200,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OScons__not__Leaf_0) ).
fof(f8895,plain,
spl0_1085,
inference(avatar_split_clause,[],[f1186,f8893]) ).
fof(f8893,plain,
( spl0_1085
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f1186,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f8891,plain,
spl0_1084,
inference(avatar_split_clause,[],[f1180,f8889]) ).
fof(f8889,plain,
( spl0_1084
<=> ! [X2,X27,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f1180,axiom,
! [X2,X1,X27] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8887,plain,
spl0_1083,
inference(avatar_split_clause,[],[f1179,f8885]) ).
fof(f8885,plain,
( spl0_1083
<=> ! [X2,X1,X18] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f1179,axiom,
! [X2,X18,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8883,plain,
spl0_1082,
inference(avatar_split_clause,[],[f1175,f8881]) ).
fof(f8881,plain,
( spl0_1082
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f1175,axiom,
! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8879,plain,
spl0_1081,
inference(avatar_split_clause,[],[f1170,f8877]) ).
fof(f8877,plain,
( spl0_1081
<=> ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f1170,axiom,
! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8875,plain,
spl0_1080,
inference(avatar_split_clause,[],[f1169,f8873]) ).
fof(f8873,plain,
( spl0_1080
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f1169,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8870,plain,
spl0_1079,
inference(avatar_split_clause,[],[f1168,f8868]) ).
fof(f8868,plain,
( spl0_1079
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f1168,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8866,plain,
spl0_1078,
inference(avatar_split_clause,[],[f105,f8864]) ).
fof(f8864,plain,
( spl0_1078
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f105,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8862,plain,
spl0_1077,
inference(avatar_split_clause,[],[f103,f8860]) ).
fof(f8860,plain,
( spl0_1077
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f103,axiom,
! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8858,plain,
spl0_1076,
inference(avatar_split_clause,[],[f102,f8856]) ).
fof(f8856,plain,
( spl0_1076
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f102,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8829,plain,
( spl0_1075
| ~ spl0_803
| ~ spl0_1044 ),
inference(avatar_split_clause,[],[f8807,f8527,f7348,f8827]) ).
fof(f8827,plain,
( spl0_1075
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f7348,plain,
( spl0_803
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f8527,plain,
( spl0_1044
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f8807,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_803
| ~ spl0_1044 ),
inference(superposition,[],[f7349,f8528]) ).
fof(f8528,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1044 ),
inference(avatar_component_clause,[],[f8527]) ).
fof(f7349,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_803 ),
inference(avatar_component_clause,[],[f7348]) ).
fof(f8804,plain,
( spl0_1074
| ~ spl0_882
| ~ spl0_1026 ),
inference(avatar_split_clause,[],[f8768,f8454,f7695,f8802]) ).
fof(f8802,plain,
( spl0_1074
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f7695,plain,
( spl0_882
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f8454,plain,
( spl0_1026
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f8768,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_882
| ~ spl0_1026 ),
inference(resolution,[],[f8455,f7696]) ).
fof(f7696,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_882 ),
inference(avatar_component_clause,[],[f7695]) ).
fof(f8455,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1026 ),
inference(avatar_component_clause,[],[f8454]) ).
fof(f8757,plain,
( spl0_1073
| ~ spl0_803
| ~ spl0_1018 ),
inference(avatar_split_clause,[],[f8752,f8422,f7348,f8755]) ).
fof(f8755,plain,
( spl0_1073
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f8422,plain,
( spl0_1018
<=> ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f8752,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_803
| ~ spl0_1018 ),
inference(superposition,[],[f7349,f8423]) ).
fof(f8423,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1018 ),
inference(avatar_component_clause,[],[f8422]) ).
fof(f8738,plain,
( spl0_1072
| ~ spl0_26
| ~ spl0_912 ),
inference(avatar_split_clause,[],[f8168,f7865,f3344,f8736]) ).
fof(f8736,plain,
( spl0_1072
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f3344,plain,
( spl0_26
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f8168,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_26
| ~ spl0_912 ),
inference(resolution,[],[f7866,f3346]) ).
fof(f3346,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3344]) ).
fof(f8658,plain,
( ~ spl0_75
| spl0_1071
| ~ spl0_674
| ~ spl0_910 ),
inference(avatar_split_clause,[],[f8167,f7857,f6791,f8656,f3589]) ).
fof(f3589,plain,
( spl0_75
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f6791,plain,
( spl0_674
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f7857,plain,
( spl0_910
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f8167,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_674
| ~ spl0_910 ),
inference(superposition,[],[f7858,f6792]) ).
fof(f6792,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_674 ),
inference(avatar_component_clause,[],[f6791]) ).
fof(f7858,plain,
( ! [X21,X1] :
( c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) )
| ~ spl0_910 ),
inference(avatar_component_clause,[],[f7857]) ).
fof(f8634,plain,
spl0_1070,
inference(avatar_split_clause,[],[f3117,f8632]) ).
fof(f8632,plain,
( spl0_1070
<=> ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f3117,plain,
! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2936,f2798]) ).
fof(f2936,plain,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1346,f2544]) ).
fof(f1346,axiom,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8630,plain,
spl0_1069,
inference(avatar_split_clause,[],[f3106,f8628]) ).
fof(f8628,plain,
( spl0_1069
<=> ! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f3106,plain,
! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2921,f2798]) ).
fof(f2921,plain,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X48),tc_nat) ),
inference(definition_unfolding,[],[f1347,f2544]) ).
fof(f1347,axiom,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8626,plain,
( spl0_1068
| ~ spl0_653
| ~ spl0_875 ),
inference(avatar_split_clause,[],[f7745,f7641,f5936,f8623]) ).
fof(f5936,plain,
( spl0_653
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f7745,plain,
( c_lessequals(c_Message_Oanalz(c_emptyset),c_emptyset,tc_set(tc_Message_Omsg))
| ~ spl0_653
| ~ spl0_875 ),
inference(superposition,[],[f7642,f5938]) ).
fof(f5938,plain,
( c_emptyset = c_Message_Oparts(c_emptyset)
| ~ spl0_653 ),
inference(avatar_component_clause,[],[f5936]) ).
fof(f8621,plain,
spl0_1067,
inference(avatar_split_clause,[],[f3101,f8619]) ).
fof(f8619,plain,
( spl0_1067
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f3101,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ),
inference(forward_demodulation,[],[f2913,f2798]) ).
fof(f2913,plain,
! [X21,X15] :
( c_1 = X21
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2093,f2544]) ).
fof(f2093,axiom,
! [X21,X15] :
( c_1 = X21
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
fof(f8617,plain,
spl0_1066,
inference(avatar_split_clause,[],[f3100,f8615]) ).
fof(f8615,plain,
( spl0_1066
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f3100,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f2912,f2798]) ).
fof(f2912,plain,
! [X21,X15] :
( c_1 = X15
| c_times(X15,X21,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f2062,f2544]) ).
fof(f2062,axiom,
! [X21,X15] :
( c_1 = X15
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
fof(f8613,plain,
spl0_1065,
inference(avatar_split_clause,[],[f2829,f8611]) ).
fof(f2829,plain,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f2132,f2113]) ).
fof(f2132,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8609,plain,
spl0_1064,
inference(avatar_split_clause,[],[f2818,f8607]) ).
fof(f8607,plain,
( spl0_1064
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f2818,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2603,f2373]) ).
fof(f2603,axiom,
! [X3,X1] : c_inter(X3,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8605,plain,
spl0_1063,
inference(avatar_split_clause,[],[f2817,f8603]) ).
fof(f8603,plain,
( spl0_1063
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f2817,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X1),X3,X1,X1) = X3,
inference(definition_unfolding,[],[f2601,f2373]) ).
fof(f2601,axiom,
! [X3,X1] : c_inter(c_UNIV,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8601,plain,
spl0_1062,
inference(avatar_split_clause,[],[f2816,f8599]) ).
fof(f8599,plain,
( spl0_1062
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f2816,plain,
! [X3,X1] : c_Relation_OImage(c_Relation_Odiag(X3,X1),c_UNIV,X1,X1) = X3,
inference(definition_unfolding,[],[f2602,f2373]) ).
fof(f2602,axiom,
! [X3,X1] : c_inter(X3,c_UNIV,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8597,plain,
spl0_1061,
inference(avatar_split_clause,[],[f2810,f8595]) ).
fof(f8595,plain,
( spl0_1061
<=> ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f2810,plain,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X16,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f1160,f2544]) ).
fof(f1160,axiom,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8593,plain,
spl0_1060,
inference(avatar_split_clause,[],[f2775,f8591]) ).
fof(f8591,plain,
( spl0_1060
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f2775,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz_OInj_0) ).
fof(f8589,plain,
spl0_1059,
inference(avatar_split_clause,[],[f2767,f8587]) ).
fof(f8587,plain,
( spl0_1059
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f2767,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts_OInj_0) ).
fof(f8585,plain,
spl0_1058,
inference(avatar_split_clause,[],[f2750,f8583]) ).
fof(f8583,plain,
( spl0_1058
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f2750,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Number_0) ).
fof(f8581,plain,
( spl0_1057
| ~ spl0_820
| ~ spl0_838 ),
inference(avatar_split_clause,[],[f7702,f7493,f7421,f8579]) ).
fof(f8579,plain,
( spl0_1057
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f7421,plain,
( spl0_820
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f7493,plain,
( spl0_838
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f7702,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_820
| ~ spl0_838 ),
inference(resolution,[],[f7494,f7422]) ).
fof(f7422,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_820 ),
inference(avatar_component_clause,[],[f7421]) ).
fof(f7494,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_838 ),
inference(avatar_component_clause,[],[f7493]) ).
fof(f8577,plain,
spl0_1056,
inference(avatar_split_clause,[],[f2749,f8575]) ).
fof(f8575,plain,
( spl0_1056
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f2749,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Nonce_0) ).
fof(f8573,plain,
spl0_1055,
inference(avatar_split_clause,[],[f2747,f8571]) ).
fof(f8571,plain,
( spl0_1055
<=> ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f2747,axiom,
! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Key_0) ).
fof(f8569,plain,
spl0_1054,
inference(avatar_split_clause,[],[f2746,f8567]) ).
fof(f8567,plain,
( spl0_1054
<=> ! [X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f2746,axiom,
! [X88,X86] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Hash_0) ).
fof(f8565,plain,
spl0_1053,
inference(avatar_split_clause,[],[f2744,f8563]) ).
fof(f8563,plain,
( spl0_1053
<=> ! [X12,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f2744,axiom,
! [X88,X12] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__insert__Agent_0) ).
fof(f8561,plain,
spl0_1052,
inference(avatar_split_clause,[],[f2718,f8559]) ).
fof(f8559,plain,
( spl0_1052
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f2718,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8557,plain,
spl0_1051,
inference(avatar_split_clause,[],[f2717,f8555]) ).
fof(f8555,plain,
( spl0_1051
<=> ! [X5,X1] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f2717,axiom,
! [X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8553,plain,
spl0_1050,
inference(avatar_split_clause,[],[f2704,f8551]) ).
fof(f8551,plain,
( spl0_1050
<=> ! [X2,X27,X1,X18] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f2704,axiom,
! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl_0) ).
fof(f8549,plain,
spl0_1049,
inference(avatar_split_clause,[],[f2667,f8547]) ).
fof(f8547,plain,
( spl0_1049
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f2667,axiom,
! [X3,X1] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8545,plain,
spl0_1048,
inference(avatar_split_clause,[],[f2659,f8543]) ).
fof(f8543,plain,
( spl0_1048
<=> ! [X12,X1] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f2659,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8541,plain,
spl0_1047,
inference(avatar_split_clause,[],[f2636,f8539]) ).
fof(f8539,plain,
( spl0_1047
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f2636,axiom,
! [X1,X12,X13] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8537,plain,
( spl0_1046
| ~ spl0_819
| ~ spl0_838 ),
inference(avatar_split_clause,[],[f7701,f7493,f7417,f8535]) ).
fof(f8535,plain,
( spl0_1046
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f7417,plain,
( spl0_819
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f7701,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_819
| ~ spl0_838 ),
inference(resolution,[],[f7494,f7418]) ).
fof(f7418,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7417]) ).
fof(f8533,plain,
spl0_1045,
inference(avatar_split_clause,[],[f2635,f8531]) ).
fof(f8531,plain,
( spl0_1045
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f2635,axiom,
! [X1,X12,X13] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8529,plain,
spl0_1044,
inference(avatar_split_clause,[],[f2626,f8527]) ).
fof(f2626,axiom,
! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8525,plain,
spl0_1043,
inference(avatar_split_clause,[],[f2390,f8523]) ).
fof(f8523,plain,
( spl0_1043
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f2390,axiom,
! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8521,plain,
spl0_1042,
inference(avatar_split_clause,[],[f2389,f8519]) ).
fof(f8519,plain,
( spl0_1042
<=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f2389,axiom,
! [X3,X1] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8517,plain,
spl0_1041,
inference(avatar_split_clause,[],[f2382,f8515]) ).
fof(f8515,plain,
( spl0_1041
<=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f2382,axiom,
! [X2,X3,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8513,plain,
spl0_1040,
inference(avatar_split_clause,[],[f2298,f8511]) ).
fof(f8511,plain,
( spl0_1040
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f2298,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8509,plain,
spl0_1039,
inference(avatar_split_clause,[],[f2297,f8507]) ).
fof(f8507,plain,
( spl0_1039
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f2297,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8505,plain,
spl0_1038,
inference(avatar_split_clause,[],[f2293,f8503]) ).
fof(f8503,plain,
( spl0_1038
<=> ! [X0,X21] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f2293,axiom,
! [X21,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8501,plain,
spl0_1037,
inference(avatar_split_clause,[],[f2285,f8499]) ).
fof(f8499,plain,
( spl0_1037
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f2285,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8497,plain,
spl0_1036,
inference(avatar_split_clause,[],[f2284,f8495]) ).
fof(f8495,plain,
( spl0_1036
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f2284,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8493,plain,
( spl0_1035
| ~ spl0_640
| ~ spl0_835 ),
inference(avatar_split_clause,[],[f7690,f7481,f5878,f8490]) ).
fof(f8490,plain,
( spl0_1035
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f7481,plain,
( spl0_835
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f7690,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_640
| ~ spl0_835 ),
inference(superposition,[],[f7482,f5880]) ).
fof(f7482,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_835 ),
inference(avatar_component_clause,[],[f7481]) ).
fof(f8488,plain,
spl0_1034,
inference(avatar_split_clause,[],[f2280,f8486]) ).
fof(f2280,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8484,plain,
spl0_1033,
inference(avatar_split_clause,[],[f2216,f8482]) ).
fof(f8482,plain,
( spl0_1033
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f2216,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8480,plain,
spl0_1032,
inference(avatar_split_clause,[],[f2154,f8478]) ).
fof(f8478,plain,
( spl0_1032
<=> ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f8476,plain,
spl0_1031,
inference(avatar_split_clause,[],[f2150,f8474]) ).
fof(f8474,plain,
( spl0_1031
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f2150,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8472,plain,
spl0_1030,
inference(avatar_split_clause,[],[f2136,f8470]) ).
fof(f8470,plain,
( spl0_1030
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f2136,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8468,plain,
spl0_1029,
inference(avatar_split_clause,[],[f2118,f8466]) ).
fof(f2118,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8464,plain,
spl0_1028,
inference(avatar_split_clause,[],[f2032,f8462]) ).
fof(f8462,plain,
( spl0_1028
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f2032,axiom,
! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8460,plain,
spl0_1027,
inference(avatar_split_clause,[],[f2031,f8458]) ).
fof(f8458,plain,
( spl0_1027
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f2031,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8456,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1786,f8454]) ).
fof(f1786,axiom,
! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8452,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1758,f8450]) ).
fof(f8450,plain,
( spl0_1025
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1758,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8448,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1757,f8446]) ).
fof(f8446,plain,
( spl0_1024
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1757,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8444,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1754,f8442]) ).
fof(f8442,plain,
( spl0_1023
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1754,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8440,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1744,f8438]) ).
fof(f8438,plain,
( spl0_1022
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1744,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8436,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1740,f8434]) ).
fof(f8434,plain,
( spl0_1021
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1740,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8432,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1720,f8430]) ).
fof(f8430,plain,
( spl0_1020
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1720,axiom,
! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8428,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1692,f8426]) ).
fof(f8426,plain,
( spl0_1019
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1692,axiom,
! [X3,X1,X23] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8424,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1639,f8422]) ).
fof(f1639,axiom,
! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f8420,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1607,f8418]) ).
fof(f8418,plain,
( spl0_1017
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1607,axiom,
! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8416,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1597,f8414]) ).
fof(f8414,plain,
( spl0_1016
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1597,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8412,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1565,f8410]) ).
fof(f8410,plain,
( spl0_1015
<=> ! [X1,X23,X58] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1565,axiom,
! [X58,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8408,plain,
( ~ spl0_53
| spl0_1014
| ~ spl0_853
| ~ spl0_966 ),
inference(avatar_split_clause,[],[f8244,f8084,f7553,f8405,f3479]) ).
fof(f8405,plain,
( spl0_1014
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f7553,plain,
( spl0_853
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f8084,plain,
( spl0_966
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f8244,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_853
| ~ spl0_966 ),
inference(superposition,[],[f7554,f8086]) ).
fof(f8086,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_966 ),
inference(avatar_component_clause,[],[f8084]) ).
fof(f7554,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_853 ),
inference(avatar_component_clause,[],[f7553]) ).
fof(f8403,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1564,f8401]) ).
fof(f8401,plain,
( spl0_1013
<=> ! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1564,axiom,
! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8399,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1563,f8397]) ).
fof(f8397,plain,
( spl0_1012
<=> ! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1563,axiom,
! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8395,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1560,f8393]) ).
fof(f8393,plain,
( spl0_1011
<=> ! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1560,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8391,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1559,f8389]) ).
fof(f8389,plain,
( spl0_1010
<=> ! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f1559,axiom,
! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8387,plain,
spl0_1009,
inference(avatar_split_clause,[],[f1556,f8385]) ).
fof(f8385,plain,
( spl0_1009
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f1556,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8383,plain,
spl0_1008,
inference(avatar_split_clause,[],[f1555,f8381]) ).
fof(f8381,plain,
( spl0_1008
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1555,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8379,plain,
spl0_1007,
inference(avatar_split_clause,[],[f1553,f8377]) ).
fof(f8377,plain,
( spl0_1007
<=> ! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1553,axiom,
! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8375,plain,
spl0_1006,
inference(avatar_split_clause,[],[f1533,f8373]) ).
fof(f8373,plain,
( spl0_1006
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f1533,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8371,plain,
spl0_1005,
inference(avatar_split_clause,[],[f1528,f8369]) ).
fof(f8369,plain,
( spl0_1005
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1528,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_1) ).
fof(f8367,plain,
spl0_1004,
inference(avatar_split_clause,[],[f1527,f8365]) ).
fof(f8365,plain,
( spl0_1004
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1527,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__is__Nil__conv_0) ).
fof(f8363,plain,
spl0_1003,
inference(avatar_split_clause,[],[f1497,f8361]) ).
fof(f8361,plain,
( spl0_1003
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1497,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8359,plain,
spl0_1002,
inference(avatar_split_clause,[],[f1496,f8357]) ).
fof(f8357,plain,
( spl0_1002
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1496,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8355,plain,
spl0_1001,
inference(avatar_split_clause,[],[f1483,f8353]) ).
fof(f8353,plain,
( spl0_1001
<=> ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f1483,axiom,
! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8351,plain,
spl0_1000,
inference(avatar_split_clause,[],[f1471,f8349]) ).
fof(f8349,plain,
( spl0_1000
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1471,axiom,
! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8347,plain,
spl0_999,
inference(avatar_split_clause,[],[f1441,f8345]) ).
fof(f1441,axiom,
! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8343,plain,
spl0_998,
inference(avatar_split_clause,[],[f1423,f8341]) ).
fof(f8341,plain,
( spl0_998
<=> ! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f1423,axiom,
! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8339,plain,
spl0_997,
inference(avatar_split_clause,[],[f1422,f8337]) ).
fof(f8337,plain,
( spl0_997
<=> ! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f1422,axiom,
! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8335,plain,
spl0_996,
inference(avatar_split_clause,[],[f1421,f8333]) ).
fof(f8333,plain,
( spl0_996
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1421,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8331,plain,
spl0_995,
inference(avatar_split_clause,[],[f1420,f8329]) ).
fof(f8329,plain,
( spl0_995
<=> ! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1420,axiom,
! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8327,plain,
spl0_994,
inference(avatar_split_clause,[],[f1380,f8325]) ).
fof(f8325,plain,
( spl0_994
<=> ! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f1380,axiom,
! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8323,plain,
( ~ spl0_993
| ~ spl0_803
| ~ spl0_963 ),
inference(avatar_split_clause,[],[f8252,f8071,f7348,f8320]) ).
fof(f8320,plain,
( spl0_993
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f8252,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_803
| ~ spl0_963 ),
inference(superposition,[],[f7349,f8073]) ).
fof(f8318,plain,
spl0_992,
inference(avatar_split_clause,[],[f1379,f8316]) ).
fof(f8316,plain,
( spl0_992
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f1379,axiom,
! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8314,plain,
spl0_991,
inference(avatar_split_clause,[],[f1349,f8312]) ).
fof(f8312,plain,
( spl0_991
<=> ! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f1349,axiom,
! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8310,plain,
spl0_990,
inference(avatar_split_clause,[],[f1246,f8308]) ).
fof(f8308,plain,
( spl0_990
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f1246,axiom,
! [X1,X5,X12] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f8306,plain,
spl0_989,
inference(avatar_split_clause,[],[f1242,f8304]) ).
fof(f8304,plain,
( spl0_989
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f1242,axiom,
! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8302,plain,
spl0_988,
inference(avatar_split_clause,[],[f1240,f8300]) ).
fof(f8300,plain,
( spl0_988
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f1240,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8298,plain,
spl0_987,
inference(avatar_split_clause,[],[f1238,f8296]) ).
fof(f8296,plain,
( spl0_987
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f1238,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8294,plain,
spl0_986,
inference(avatar_split_clause,[],[f1195,f8292]) ).
fof(f8292,plain,
( spl0_986
<=> ! [X2,X16,X1,X18] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f1195,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f8290,plain,
spl0_985,
inference(avatar_split_clause,[],[f1190,f8288]) ).
fof(f8288,plain,
( spl0_985
<=> ! [X2,X1,X7,X9] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f1190,axiom,
! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f8286,plain,
spl0_984,
inference(avatar_split_clause,[],[f63,f8284]) ).
fof(f8284,plain,
( spl0_984
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f63,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8282,plain,
spl0_983,
inference(avatar_split_clause,[],[f62,f8280]) ).
fof(f8280,plain,
( spl0_983
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f62,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8277,plain,
spl0_982,
inference(avatar_split_clause,[],[f35,f8275]) ).
fof(f8275,plain,
( spl0_982
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f35,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8273,plain,
spl0_981,
inference(avatar_split_clause,[],[f34,f8271]) ).
fof(f8271,plain,
( spl0_981
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f34,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8150,plain,
( spl0_980
| ~ spl0_41
| ~ spl0_863 ),
inference(avatar_split_clause,[],[f7736,f7593,f3419,f8147]) ).
fof(f8147,plain,
( spl0_980
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f3419,plain,
( spl0_41
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f7593,plain,
( spl0_863
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f7736,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_41
| ~ spl0_863 ),
inference(resolution,[],[f7594,f3421]) ).
fof(f3421,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_41 ),
inference(avatar_component_clause,[],[f3419]) ).
fof(f7594,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_863 ),
inference(avatar_component_clause,[],[f7593]) ).
fof(f8140,plain,
spl0_979,
inference(avatar_split_clause,[],[f3089,f8138]) ).
fof(f3089,plain,
! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2170,f2156]) ).
fof(f2170,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f8136,plain,
spl0_978,
inference(avatar_split_clause,[],[f3037,f8134]) ).
fof(f8134,plain,
( spl0_978
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f3037,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2833,f2798]) ).
fof(f2833,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X15,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1300,f2544]) ).
fof(f1300,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X15,tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f8132,plain,
( spl0_977
| ~ spl0_41
| ~ spl0_862 ),
inference(avatar_split_clause,[],[f7735,f7589,f3419,f8129]) ).
fof(f8129,plain,
( spl0_977
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f7589,plain,
( spl0_862
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f7735,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_41
| ~ spl0_862 ),
inference(resolution,[],[f7590,f3421]) ).
fof(f7590,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f7589]) ).
fof(f8127,plain,
spl0_976,
inference(avatar_split_clause,[],[f3036,f8125]) ).
fof(f8125,plain,
( spl0_976
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f3036,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2832,f2798]) ).
fof(f2832,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f1299,f2544]) ).
fof(f1299,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f8123,plain,
spl0_975,
inference(avatar_split_clause,[],[f2804,f8121]) ).
fof(f8121,plain,
( spl0_975
<=> ! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f2804,plain,
! [X21] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f67,f2544]) ).
fof(f67,axiom,
! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f8119,plain,
spl0_974,
inference(avatar_split_clause,[],[f2803,f8117]) ).
fof(f8117,plain,
( spl0_974
<=> ! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f2803,plain,
! [X21] : c_less(X21,c_Finite__Set_Ocard(c_SetInterval_OatMost(X21,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f65,f2544]) ).
fof(f65,axiom,
! [X21] : c_less(X21,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f8115,plain,
spl0_973,
inference(avatar_split_clause,[],[f2755,f8113]) ).
fof(f8113,plain,
( spl0_973
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f2755,axiom,
! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__5_0) ).
fof(f8111,plain,
spl0_972,
inference(avatar_split_clause,[],[f2754,f8109]) ).
fof(f8109,plain,
( spl0_972
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f2754,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__4_0) ).
fof(f8107,plain,
spl0_971,
inference(avatar_split_clause,[],[f2753,f8105]) ).
fof(f8105,plain,
( spl0_971
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f2753,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__3_0) ).
fof(f8103,plain,
spl0_970,
inference(avatar_split_clause,[],[f2752,f8101]) ).
fof(f8101,plain,
( spl0_970
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f2752,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__2_0) ).
fof(f8099,plain,
spl0_969,
inference(avatar_split_clause,[],[f2751,f8097]) ).
fof(f8097,plain,
( spl0_969
<=> ! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f2751,axiom,
! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Oinject__1_0) ).
fof(f8095,plain,
spl0_968,
inference(avatar_split_clause,[],[f2741,f8093]) ).
fof(f8093,plain,
( spl0_968
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f2741,axiom,
! [X91,X92] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey__eq_0) ).
fof(f8091,plain,
spl0_967,
inference(avatar_split_clause,[],[f2736,f8089]) ).
fof(f8089,plain,
( spl0_967
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f2736,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Oinject_0) ).
fof(f8087,plain,
( spl0_966
| ~ spl0_53
| ~ spl0_859 ),
inference(avatar_split_clause,[],[f7732,f7577,f3479,f8084]) ).
fof(f7577,plain,
( spl0_859
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f7732,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_53
| ~ spl0_859 ),
inference(resolution,[],[f7578,f3481]) ).
fof(f7578,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_859 ),
inference(avatar_component_clause,[],[f7577]) ).
fof(f8082,plain,
spl0_965,
inference(avatar_split_clause,[],[f2699,f8080]) ).
fof(f2699,axiom,
! [X1,X12] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f8078,plain,
spl0_964,
inference(avatar_split_clause,[],[f2660,f8076]) ).
fof(f8076,plain,
( spl0_964
<=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2660,axiom,
! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f8074,plain,
spl0_963,
inference(avatar_split_clause,[],[f2534,f8071]) ).
fof(f2534,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(f8069,plain,
spl0_962,
inference(avatar_split_clause,[],[f2492,f8067]) ).
fof(f8067,plain,
( spl0_962
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f2492,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f8065,plain,
spl0_961,
inference(avatar_split_clause,[],[f2491,f8063]) ).
fof(f8063,plain,
( spl0_961
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f2491,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f8061,plain,
spl0_960,
inference(avatar_split_clause,[],[f2474,f8059]) ).
fof(f8059,plain,
( spl0_960
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f2474,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f8057,plain,
spl0_959,
inference(avatar_split_clause,[],[f2473,f8055]) ).
fof(f8055,plain,
( spl0_959
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f2473,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f8053,plain,
spl0_958,
inference(avatar_split_clause,[],[f2470,f8051]) ).
fof(f8051,plain,
( spl0_958
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f2470,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f8049,plain,
spl0_957,
inference(avatar_split_clause,[],[f2469,f8047]) ).
fof(f8047,plain,
( spl0_957
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f2469,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f8045,plain,
spl0_956,
inference(avatar_split_clause,[],[f2379,f8043]) ).
fof(f8043,plain,
( spl0_956
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f2379,axiom,
! [X3,X1] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f8041,plain,
spl0_955,
inference(avatar_split_clause,[],[f2377,f8039]) ).
fof(f8039,plain,
( spl0_955
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f2377,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f8037,plain,
spl0_954,
inference(avatar_split_clause,[],[f2371,f8035]) ).
fof(f8035,plain,
( spl0_954
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f2371,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f8033,plain,
spl0_953,
inference(avatar_split_clause,[],[f2369,f8031]) ).
fof(f8031,plain,
( spl0_953
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f2369,axiom,
! [X3,X1] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f8029,plain,
spl0_952,
inference(avatar_split_clause,[],[f2357,f8027]) ).
fof(f8027,plain,
( spl0_952
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f2357,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f8025,plain,
spl0_951,
inference(avatar_split_clause,[],[f2354,f8023]) ).
fof(f2354,axiom,
! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f8021,plain,
spl0_950,
inference(avatar_split_clause,[],[f2353,f8019]) ).
fof(f2353,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f8017,plain,
spl0_949,
inference(avatar_split_clause,[],[f2292,f8015]) ).
fof(f8015,plain,
( spl0_949
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f2292,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f8013,plain,
spl0_948,
inference(avatar_split_clause,[],[f2291,f8011]) ).
fof(f8011,plain,
( spl0_948
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f2291,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f8009,plain,
spl0_947,
inference(avatar_split_clause,[],[f2267,f8007]) ).
fof(f2267,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f8005,plain,
spl0_946,
inference(avatar_split_clause,[],[f2262,f8003]) ).
fof(f2262,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f8001,plain,
spl0_945,
inference(avatar_split_clause,[],[f2251,f7999]) ).
fof(f7999,plain,
( spl0_945
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f2251,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f7997,plain,
spl0_944,
inference(avatar_split_clause,[],[f2250,f7995]) ).
fof(f7995,plain,
( spl0_944
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f2250,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f7993,plain,
spl0_943,
inference(avatar_split_clause,[],[f2241,f7991]) ).
fof(f7991,plain,
( spl0_943
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f2241,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f7989,plain,
spl0_942,
inference(avatar_split_clause,[],[f2218,f7987]) ).
fof(f2218,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f7985,plain,
spl0_941,
inference(avatar_split_clause,[],[f2217,f7983]) ).
fof(f2217,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f7981,plain,
spl0_940,
inference(avatar_split_clause,[],[f2205,f7979]) ).
fof(f2205,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f7977,plain,
spl0_939,
inference(avatar_split_clause,[],[f2198,f7975]) ).
fof(f2198,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f7973,plain,
spl0_938,
inference(avatar_split_clause,[],[f2196,f7971]) ).
fof(f2196,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f7969,plain,
spl0_937,
inference(avatar_split_clause,[],[f2185,f7967]) ).
fof(f2185,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f7965,plain,
spl0_936,
inference(avatar_split_clause,[],[f2182,f7963]) ).
fof(f7963,plain,
( spl0_936
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f2182,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f7961,plain,
spl0_935,
inference(avatar_split_clause,[],[f2180,f7959]) ).
fof(f7959,plain,
( spl0_935
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f2180,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f7957,plain,
spl0_934,
inference(avatar_split_clause,[],[f2177,f7955]) ).
fof(f7955,plain,
( spl0_934
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f2177,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7953,plain,
spl0_933,
inference(avatar_split_clause,[],[f2153,f7951]) ).
fof(f2153,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f7949,plain,
spl0_932,
inference(avatar_split_clause,[],[f1865,f7947]) ).
fof(f7947,plain,
( spl0_932
<=> ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1865,axiom,
! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f7945,plain,
spl0_931,
inference(avatar_split_clause,[],[f1818,f7943]) ).
fof(f7943,plain,
( spl0_931
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1818,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f7941,plain,
spl0_930,
inference(avatar_split_clause,[],[f1815,f7939]) ).
fof(f7939,plain,
( spl0_930
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1815,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7937,plain,
spl0_929,
inference(avatar_split_clause,[],[f1805,f7935]) ).
fof(f7935,plain,
( spl0_929
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1805,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7933,plain,
spl0_928,
inference(avatar_split_clause,[],[f1779,f7931]) ).
fof(f7931,plain,
( spl0_928
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1779,axiom,
! [X3,X41,X0] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7929,plain,
spl0_927,
inference(avatar_split_clause,[],[f1750,f7927]) ).
fof(f7927,plain,
( spl0_927
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1750,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
fof(f7925,plain,
spl0_926,
inference(avatar_split_clause,[],[f1735,f7923]) ).
fof(f7923,plain,
( spl0_926
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1735,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7921,plain,
( ~ spl0_924
| spl0_925
| ~ spl0_706
| ~ spl0_853 ),
inference(avatar_split_clause,[],[f7726,f7553,f6936,f7918,f7914]) ).
fof(f7914,plain,
( spl0_924
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f7918,plain,
( spl0_925
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f6936,plain,
( spl0_706
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f7726,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_706
| ~ spl0_853 ),
inference(superposition,[],[f7554,f6938]) ).
fof(f6938,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_706 ),
inference(avatar_component_clause,[],[f6936]) ).
fof(f7912,plain,
spl0_923,
inference(avatar_split_clause,[],[f1717,f7910]) ).
fof(f7910,plain,
( spl0_923
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1717,axiom,
! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f7908,plain,
spl0_922,
inference(avatar_split_clause,[],[f1588,f7906]) ).
fof(f7906,plain,
( spl0_922
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f1588,axiom,
! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7904,plain,
spl0_921,
inference(avatar_split_clause,[],[f1579,f7902]) ).
fof(f7902,plain,
( spl0_921
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f1579,axiom,
! [X3,X1,X23] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7900,plain,
spl0_920,
inference(avatar_split_clause,[],[f1562,f7898]) ).
fof(f7898,plain,
( spl0_920
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1562,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7896,plain,
spl0_919,
inference(avatar_split_clause,[],[f1561,f7894]) ).
fof(f7894,plain,
( spl0_919
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f1561,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7892,plain,
spl0_918,
inference(avatar_split_clause,[],[f1550,f7890]) ).
fof(f7890,plain,
( spl0_918
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f1550,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7888,plain,
spl0_917,
inference(avatar_split_clause,[],[f1549,f7886]) ).
fof(f7886,plain,
( spl0_917
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1549,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7884,plain,
spl0_916,
inference(avatar_split_clause,[],[f1537,f7882]) ).
fof(f7882,plain,
( spl0_916
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1537,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7880,plain,
spl0_915,
inference(avatar_split_clause,[],[f1513,f7878]) ).
fof(f7878,plain,
( spl0_915
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1513,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7876,plain,
spl0_914,
inference(avatar_split_clause,[],[f1499,f7874]) ).
fof(f1499,axiom,
! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7872,plain,
( spl0_913
| ~ spl0_22
| ~ spl0_846 ),
inference(avatar_split_clause,[],[f7706,f7525,f3324,f7869]) ).
fof(f7869,plain,
( spl0_913
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f3324,plain,
( spl0_22
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f7525,plain,
( spl0_846
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f7706,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_22
| ~ spl0_846 ),
inference(resolution,[],[f7526,f3326]) ).
fof(f3326,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f3324]) ).
fof(f7526,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_846 ),
inference(avatar_component_clause,[],[f7525]) ).
fof(f7867,plain,
spl0_912,
inference(avatar_split_clause,[],[f1498,f7865]) ).
fof(f1498,axiom,
! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7863,plain,
spl0_911,
inference(avatar_split_clause,[],[f1490,f7861]) ).
fof(f7861,plain,
( spl0_911
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1490,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f7859,plain,
spl0_910,
inference(avatar_split_clause,[],[f1419,f7857]) ).
fof(f1419,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7855,plain,
spl0_909,
inference(avatar_split_clause,[],[f1392,f7853]) ).
fof(f7853,plain,
( spl0_909
<=> ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1392,axiom,
! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7851,plain,
spl0_908,
inference(avatar_split_clause,[],[f1385,f7849]) ).
fof(f7849,plain,
( spl0_908
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1385,axiom,
! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7847,plain,
spl0_907,
inference(avatar_split_clause,[],[f1376,f7845]) ).
fof(f7845,plain,
( spl0_907
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1376,axiom,
! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7843,plain,
spl0_906,
inference(avatar_split_clause,[],[f1375,f7841]) ).
fof(f7841,plain,
( spl0_906
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1375,axiom,
! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7839,plain,
spl0_905,
inference(avatar_split_clause,[],[f1308,f7837]) ).
fof(f7837,plain,
( spl0_905
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f1308,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7835,plain,
spl0_904,
inference(avatar_split_clause,[],[f1298,f7833]) ).
fof(f7833,plain,
( spl0_904
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f1298,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7831,plain,
spl0_903,
inference(avatar_split_clause,[],[f1297,f7829]) ).
fof(f7829,plain,
( spl0_903
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1297,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7827,plain,
( spl0_902
| ~ spl0_49
| ~ spl0_845 ),
inference(avatar_split_clause,[],[f7704,f7521,f3459,f7824]) ).
fof(f7824,plain,
( spl0_902
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f3459,plain,
( spl0_49
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f7521,plain,
( spl0_845
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f7704,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_49
| ~ spl0_845 ),
inference(resolution,[],[f7522,f3461]) ).
fof(f3461,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_49 ),
inference(avatar_component_clause,[],[f3459]) ).
fof(f7522,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_845 ),
inference(avatar_component_clause,[],[f7521]) ).
fof(f7822,plain,
spl0_901,
inference(avatar_split_clause,[],[f1177,f7820]) ).
fof(f7820,plain,
( spl0_901
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f1177,axiom,
! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7818,plain,
spl0_900,
inference(avatar_split_clause,[],[f1171,f7816]) ).
fof(f7816,plain,
( spl0_900
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f1171,axiom,
! [X40,X1] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7813,plain,
spl0_899,
inference(avatar_split_clause,[],[f1167,f7811]) ).
fof(f7811,plain,
( spl0_899
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1167,axiom,
! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7809,plain,
spl0_898,
inference(avatar_split_clause,[],[f252,f7807]) ).
fof(f7807,plain,
( spl0_898
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f252,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f7805,plain,
spl0_897,
inference(avatar_split_clause,[],[f246,f7803]) ).
fof(f7803,plain,
( spl0_897
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f246,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f7801,plain,
spl0_896,
inference(avatar_split_clause,[],[f196,f7799]) ).
fof(f7799,plain,
( spl0_896
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f196,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f7797,plain,
spl0_895,
inference(avatar_split_clause,[],[f94,f7795]) ).
fof(f7795,plain,
( spl0_895
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f94,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f7793,plain,
spl0_894,
inference(avatar_split_clause,[],[f93,f7791]) ).
fof(f7791,plain,
( spl0_894
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f93,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f7789,plain,
spl0_893,
inference(avatar_split_clause,[],[f92,f7787]) ).
fof(f7787,plain,
( spl0_893
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f92,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f7785,plain,
spl0_892,
inference(avatar_split_clause,[],[f91,f7783]) ).
fof(f7783,plain,
( spl0_892
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f91,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7781,plain,
( spl0_891
| ~ spl0_51
| ~ spl0_837 ),
inference(avatar_split_clause,[],[f7698,f7489,f3469,f7778]) ).
fof(f7778,plain,
( spl0_891
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f3469,plain,
( spl0_51
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f7489,plain,
( spl0_837
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f7698,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_51
| ~ spl0_837 ),
inference(resolution,[],[f7490,f3471]) ).
fof(f3471,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_51 ),
inference(avatar_component_clause,[],[f3469]) ).
fof(f7490,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_837 ),
inference(avatar_component_clause,[],[f7489]) ).
fof(f7776,plain,
spl0_890,
inference(avatar_split_clause,[],[f89,f7774]) ).
fof(f7774,plain,
( spl0_890
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f89,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f7772,plain,
spl0_889,
inference(avatar_split_clause,[],[f88,f7770]) ).
fof(f7770,plain,
( spl0_889
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f88,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7768,plain,
spl0_888,
inference(avatar_split_clause,[],[f87,f7766]) ).
fof(f7766,plain,
( spl0_888
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f87,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f7764,plain,
spl0_887,
inference(avatar_split_clause,[],[f86,f7762]) ).
fof(f7762,plain,
( spl0_887
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f86,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7760,plain,
spl0_886,
inference(avatar_split_clause,[],[f37,f7758]) ).
fof(f7758,plain,
( spl0_886
<=> ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f37,axiom,
! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7751,plain,
( spl0_885
| ~ spl0_23
| ~ spl0_836 ),
inference(avatar_split_clause,[],[f7693,f7485,f3329,f7748]) ).
fof(f7748,plain,
( spl0_885
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f3329,plain,
( spl0_23
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f7485,plain,
( spl0_836
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f7693,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_836 ),
inference(resolution,[],[f7486,f3331]) ).
fof(f3331,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f3329]) ).
fof(f7486,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_836 ),
inference(avatar_component_clause,[],[f7485]) ).
fof(f7742,plain,
( spl0_884
| ~ spl0_641
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f7687,f7473,f5883,f7739]) ).
fof(f7473,plain,
( spl0_833
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f7687,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_833 ),
inference(superposition,[],[f7474,f5885]) ).
fof(f7474,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f7473]) ).
fof(f7731,plain,
( spl0_883
| ~ spl0_640
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f7686,f7473,f5878,f7728]) ).
fof(f7728,plain,
( spl0_883
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f7686,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_833 ),
inference(superposition,[],[f7474,f5880]) ).
fof(f7697,plain,
( spl0_882
| ~ spl0_816
| ~ spl0_827 ),
inference(avatar_split_clause,[],[f7680,f7449,f7403,f7695]) ).
fof(f7403,plain,
( spl0_816
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f7449,plain,
( spl0_827
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f7680,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_816
| ~ spl0_827 ),
inference(superposition,[],[f7450,f7404]) ).
fof(f7404,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_816 ),
inference(avatar_component_clause,[],[f7403]) ).
fof(f7450,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_827 ),
inference(avatar_component_clause,[],[f7449]) ).
fof(f7669,plain,
spl0_881,
inference(avatar_split_clause,[],[f3114,f7667]) ).
fof(f7667,plain,
( spl0_881
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f3114,plain,
! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f3113,f2798]) ).
fof(f3113,plain,
! [X15] :
( c_1 = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2932,f2798]) ).
fof(f2932,plain,
! [X15] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X15
| ~ c_Divides_Oop_Advd(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1227,f2544,f2544]) ).
fof(f1227,axiom,
! [X15] :
( c_Suc(c_0) = X15
| ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7665,plain,
spl0_880,
inference(avatar_split_clause,[],[f3024,f7663]) ).
fof(f7663,plain,
( spl0_880
<=> ! [X13,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f3024,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_emptyset,X13,X1,X1),
inference(forward_demodulation,[],[f2809,f2386]) ).
fof(f2386,axiom,
! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2809,plain,
! [X1,X13] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X1),X13,X1,X1),
inference(definition_unfolding,[],[f2604,f2373]) ).
fof(f2604,axiom,
! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7661,plain,
spl0_879,
inference(avatar_split_clause,[],[f2813,f7659]) ).
fof(f7659,plain,
( spl0_879
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f7657,plain,
spl0_878,
inference(avatar_split_clause,[],[f2811,f7654]) ).
fof(f2811,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2133,f2113]) ).
fof(f2133,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7652,plain,
spl0_877,
inference(avatar_split_clause,[],[f2798,f7649]) ).
fof(f7649,plain,
( spl0_877
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f7647,plain,
spl0_876,
inference(avatar_split_clause,[],[f2794,f7645]) ).
fof(f7645,plain,
( spl0_876
<=> ! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2794,plain,
! [X15] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X15,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2023,f2544]) ).
fof(f2023,axiom,
! [X15] : c_0 != c_Suc(X15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
fof(f7643,plain,
spl0_875,
inference(avatar_split_clause,[],[f2777,f7641]) ).
fof(f2777,axiom,
! [X88] : c_lessequals(c_Message_Oanalz(X88),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
fof(f7639,plain,
spl0_874,
inference(avatar_split_clause,[],[f2705,f7637]) ).
fof(f7637,plain,
( spl0_874
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2705,axiom,
! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7635,plain,
spl0_873,
inference(avatar_split_clause,[],[f2684,f7633]) ).
fof(f2684,axiom,
! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7631,plain,
spl0_872,
inference(avatar_split_clause,[],[f2668,f7629]) ).
fof(f7629,plain,
( spl0_872
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2668,axiom,
! [X1,X12] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7627,plain,
spl0_871,
inference(avatar_split_clause,[],[f2648,f7625]) ).
fof(f7625,plain,
( spl0_871
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2648,axiom,
! [X3,X1] : c_Union(c_Pow(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7623,plain,
spl0_870,
inference(avatar_split_clause,[],[f2590,f7621]) ).
fof(f7621,plain,
( spl0_870
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2590,axiom,
! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7619,plain,
spl0_869,
inference(avatar_split_clause,[],[f2588,f7617]) ).
fof(f7617,plain,
( spl0_869
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2588,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7615,plain,
spl0_868,
inference(avatar_split_clause,[],[f2587,f7613]) ).
fof(f7613,plain,
( spl0_868
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2587,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7611,plain,
spl0_867,
inference(avatar_split_clause,[],[f2549,f7609]) ).
fof(f7609,plain,
( spl0_867
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2549,axiom,
! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7607,plain,
spl0_866,
inference(avatar_split_clause,[],[f2394,f7605]) ).
fof(f7605,plain,
( spl0_866
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2394,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7603,plain,
spl0_865,
inference(avatar_split_clause,[],[f2374,f7601]) ).
fof(f7601,plain,
( spl0_865
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2374,axiom,
! [X2,X1,X85] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7599,plain,
spl0_864,
inference(avatar_split_clause,[],[f2372,f7597]) ).
fof(f7597,plain,
( spl0_864
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2372,axiom,
! [X3,X1] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7595,plain,
spl0_863,
inference(avatar_split_clause,[],[f2243,f7593]) ).
fof(f2243,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7591,plain,
spl0_862,
inference(avatar_split_clause,[],[f2238,f7589]) ).
fof(f2238,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7587,plain,
spl0_861,
inference(avatar_split_clause,[],[f2220,f7585]) ).
fof(f7585,plain,
( spl0_861
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2220,axiom,
! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
fof(f7583,plain,
spl0_860,
inference(avatar_split_clause,[],[f2176,f7581]) ).
fof(f7581,plain,
( spl0_860
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2176,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7579,plain,
spl0_859,
inference(avatar_split_clause,[],[f2169,f7577]) ).
fof(f2169,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7575,plain,
spl0_858,
inference(avatar_split_clause,[],[f2162,f7573]) ).
fof(f7573,plain,
( spl0_858
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f2162,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7571,plain,
spl0_857,
inference(avatar_split_clause,[],[f2161,f7569]) ).
fof(f7569,plain,
( spl0_857
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2161,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7567,plain,
spl0_856,
inference(avatar_split_clause,[],[f2158,f7565]) ).
fof(f7565,plain,
( spl0_856
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2158,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7563,plain,
spl0_855,
inference(avatar_split_clause,[],[f2157,f7561]) ).
fof(f7561,plain,
( spl0_855
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2157,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7559,plain,
spl0_854,
inference(avatar_split_clause,[],[f2144,f7557]) ).
fof(f7557,plain,
( spl0_854
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2144,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7555,plain,
spl0_853,
inference(avatar_split_clause,[],[f2143,f7553]) ).
fof(f2143,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7551,plain,
spl0_852,
inference(avatar_split_clause,[],[f2089,f7549]) ).
fof(f7549,plain,
( spl0_852
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f2089,axiom,
! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7547,plain,
spl0_851,
inference(avatar_split_clause,[],[f2088,f7545]) ).
fof(f7545,plain,
( spl0_851
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f2088,axiom,
! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7543,plain,
spl0_850,
inference(avatar_split_clause,[],[f2087,f7541]) ).
fof(f7541,plain,
( spl0_850
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f2087,axiom,
! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7539,plain,
spl0_849,
inference(avatar_split_clause,[],[f2048,f7537]) ).
fof(f7537,plain,
( spl0_849
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f2048,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7535,plain,
spl0_848,
inference(avatar_split_clause,[],[f2042,f7533]) ).
fof(f7533,plain,
( spl0_848
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f2042,axiom,
! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7531,plain,
spl0_847,
inference(avatar_split_clause,[],[f2040,f7529]) ).
fof(f7529,plain,
( spl0_847
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f2040,axiom,
! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7527,plain,
spl0_846,
inference(avatar_split_clause,[],[f1808,f7525]) ).
fof(f1808,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7523,plain,
spl0_845,
inference(avatar_split_clause,[],[f1804,f7521]) ).
fof(f1804,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__eq__iff_1) ).
fof(f7519,plain,
spl0_844,
inference(avatar_split_clause,[],[f1790,f7517]) ).
fof(f7517,plain,
( spl0_844
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1790,axiom,
! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7515,plain,
spl0_843,
inference(avatar_split_clause,[],[f1788,f7513]) ).
fof(f7513,plain,
( spl0_843
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f1788,axiom,
! [X82,X41,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7511,plain,
spl0_842,
inference(avatar_split_clause,[],[f1732,f7509]) ).
fof(f7509,plain,
( spl0_842
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f1732,axiom,
! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7507,plain,
spl0_841,
inference(avatar_split_clause,[],[f1711,f7505]) ).
fof(f7505,plain,
( spl0_841
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f1711,axiom,
! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7503,plain,
spl0_840,
inference(avatar_split_clause,[],[f1631,f7501]) ).
fof(f7501,plain,
( spl0_840
<=> ! [X41,X43,X47] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f1631,axiom,
! [X41,X47,X43] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7499,plain,
spl0_839,
inference(avatar_split_clause,[],[f1542,f7497]) ).
fof(f7497,plain,
( spl0_839
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f1542,axiom,
! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7495,plain,
spl0_838,
inference(avatar_split_clause,[],[f1478,f7493]) ).
fof(f1478,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7491,plain,
spl0_837,
inference(avatar_split_clause,[],[f1405,f7489]) ).
fof(f1405,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_1) ).
fof(f7487,plain,
spl0_836,
inference(avatar_split_clause,[],[f1401,f7485]) ).
fof(f1401,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7483,plain,
spl0_835,
inference(avatar_split_clause,[],[f1387,f7481]) ).
fof(f1387,axiom,
! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7479,plain,
spl0_834,
inference(avatar_split_clause,[],[f1373,f7477]) ).
fof(f7477,plain,
( spl0_834
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f1373,axiom,
! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7475,plain,
spl0_833,
inference(avatar_split_clause,[],[f1367,f7473]) ).
fof(f1367,axiom,
! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7471,plain,
spl0_832,
inference(avatar_split_clause,[],[f1253,f7469]) ).
fof(f7469,plain,
( spl0_832
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f1253,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7467,plain,
spl0_831,
inference(avatar_split_clause,[],[f1252,f7465]) ).
fof(f7465,plain,
( spl0_831
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f1252,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7463,plain,
spl0_830,
inference(avatar_split_clause,[],[f1249,f7461]) ).
fof(f7461,plain,
( spl0_830
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f1249,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7459,plain,
spl0_829,
inference(avatar_split_clause,[],[f1248,f7457]) ).
fof(f7457,plain,
( spl0_829
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f1248,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7455,plain,
spl0_828,
inference(avatar_split_clause,[],[f1225,f7453]) ).
fof(f7453,plain,
( spl0_828
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f1225,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7451,plain,
spl0_827,
inference(avatar_split_clause,[],[f1215,f7449]) ).
fof(f1215,axiom,
! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7447,plain,
spl0_826,
inference(avatar_split_clause,[],[f1202,f7445]) ).
fof(f7445,plain,
( spl0_826
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f1202,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7443,plain,
spl0_825,
inference(avatar_split_clause,[],[f1181,f7441]) ).
fof(f7441,plain,
( spl0_825
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f1181,axiom,
! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7439,plain,
spl0_824,
inference(avatar_split_clause,[],[f95,f7437]) ).
fof(f7437,plain,
( spl0_824
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f95,axiom,
! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7435,plain,
spl0_823,
inference(avatar_split_clause,[],[f90,f7433]) ).
fof(f7433,plain,
( spl0_823
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f90,axiom,
! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7431,plain,
spl0_822,
inference(avatar_split_clause,[],[f61,f7429]) ).
fof(f7429,plain,
( spl0_822
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f61,axiom,
! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7427,plain,
spl0_821,
inference(avatar_split_clause,[],[f45,f7425]) ).
fof(f7425,plain,
( spl0_821
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f45,axiom,
! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7423,plain,
spl0_820,
inference(avatar_split_clause,[],[f42,f7421]) ).
fof(f42,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7419,plain,
spl0_819,
inference(avatar_split_clause,[],[f41,f7417]) ).
fof(f41,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7415,plain,
spl0_818,
inference(avatar_split_clause,[],[f26,f7413]) ).
fof(f7413,plain,
( spl0_818
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f26,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7411,plain,
spl0_817,
inference(avatar_split_clause,[],[f25,f7409]) ).
fof(f7409,plain,
( spl0_817
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f25,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7405,plain,
spl0_816,
inference(avatar_split_clause,[],[f3034,f7403]) ).
fof(f3034,plain,
! [X3] : c_div(X3,c_1,tc_nat) = X3,
inference(forward_demodulation,[],[f2824,f2798]) ).
fof(f2824,plain,
! [X3] : c_div(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X3,
inference(definition_unfolding,[],[f1214,f2544]) ).
fof(f1214,axiom,
! [X3] : c_div(X3,c_Suc(c_0),tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7401,plain,
spl0_815,
inference(avatar_split_clause,[],[f3032,f7398]) ).
fof(f7398,plain,
( spl0_815
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f3032,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2821,f2798]) ).
fof(f2821,plain,
c_times(c_1,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f2094,f2544]) ).
fof(f2094,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_2) ).
fof(f7396,plain,
spl0_814,
inference(avatar_split_clause,[],[f3030,f7394]) ).
fof(f7394,plain,
( spl0_814
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f3030,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
inference(forward_demodulation,[],[f2820,f2798]) ).
fof(f2820,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1231,f2544]) ).
fof(f1231,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7392,plain,
spl0_813,
inference(avatar_split_clause,[],[f3029,f7389]) ).
fof(f7389,plain,
( spl0_813
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f3029,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f1867,f2156]) ).
fof(f1867,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7387,plain,
spl0_812,
inference(avatar_split_clause,[],[f3027,f7385]) ).
fof(f7385,plain,
( spl0_812
<=> ! [X41,X3] : c_append(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f3027,plain,
! [X3,X41] : c_append(c_List_Olist_ONil,X3,X41) = X3,
inference(forward_demodulation,[],[f2815,f1729]) ).
fof(f1729,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orev__is__Nil__conv_1) ).
fof(f2815,plain,
! [X41,X3] : c_append(c_List_Orev(c_List_Olist_ONil,X41),X3,X41) = X3,
inference(definition_unfolding,[],[f1586,f1585]) ).
fof(f1585,axiom,
! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f1586,axiom,
! [X3,X41] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7383,plain,
spl0_811,
inference(avatar_split_clause,[],[f3025,f7380]) ).
fof(f7380,plain,
( spl0_811
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f3025,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2812,f2156]) ).
fof(f2812,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f2125,f2129]) ).
fof(f2125,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7378,plain,
spl0_810,
inference(avatar_split_clause,[],[f2781,f7376]) ).
fof(f7376,plain,
( spl0_810
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f2781,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__idem_0) ).
fof(f7374,plain,
spl0_809,
inference(avatar_split_clause,[],[f2776,f7372]) ).
fof(f7372,plain,
( spl0_809
<=> ! [X88] : c_lessequals(X88,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f2776,axiom,
! [X88] : c_lessequals(X88,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__increasing_0) ).
fof(f7370,plain,
spl0_808,
inference(avatar_split_clause,[],[f2763,f7368]) ).
fof(f7368,plain,
( spl0_808
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2763,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__4_0) ).
fof(f7366,plain,
spl0_807,
inference(avatar_split_clause,[],[f2762,f7364]) ).
fof(f7364,plain,
( spl0_807
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2762,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__3_0) ).
fof(f7362,plain,
spl0_806,
inference(avatar_split_clause,[],[f2761,f7360]) ).
fof(f7360,plain,
( spl0_806
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2761,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__2_0) ).
fof(f7358,plain,
spl0_805,
inference(avatar_split_clause,[],[f2760,f7356]) ).
fof(f7356,plain,
( spl0_805
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2760,axiom,
! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Omsg_Osize__1_0) ).
fof(f7354,plain,
spl0_804,
inference(avatar_split_clause,[],[f2738,f7352]) ).
fof(f7352,plain,
( spl0_804
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2738,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__2_0) ).
fof(f7350,plain,
spl0_803,
inference(avatar_split_clause,[],[f2687,f7348]) ).
fof(f2687,axiom,
! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
fof(f7346,plain,
spl0_802,
inference(avatar_split_clause,[],[f2639,f7344]) ).
fof(f7344,plain,
( spl0_802
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2639,axiom,
! [X3,X1] : c_union(X3,c_emptyset,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7342,plain,
spl0_801,
inference(avatar_split_clause,[],[f2638,f7340]) ).
fof(f2638,axiom,
! [X3,X1] : c_union(c_emptyset,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7338,plain,
spl0_800,
inference(avatar_split_clause,[],[f2634,f7336]) ).
fof(f7336,plain,
( spl0_800
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7334,plain,
spl0_799,
inference(avatar_split_clause,[],[f2633,f7332]) ).
fof(f7332,plain,
( spl0_799
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f2633,axiom,
! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7330,plain,
spl0_798,
inference(avatar_split_clause,[],[f2632,f7328]) ).
fof(f7328,plain,
( spl0_798
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2632,axiom,
! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7326,plain,
spl0_797,
inference(avatar_split_clause,[],[f2580,f7324]) ).
fof(f7324,plain,
( spl0_797
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2580,axiom,
! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7322,plain,
spl0_796,
inference(avatar_split_clause,[],[f2576,f7320]) ).
fof(f7320,plain,
( spl0_796
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2576,axiom,
! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7318,plain,
spl0_795,
inference(avatar_split_clause,[],[f2511,f7316]) ).
fof(f7316,plain,
( spl0_795
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2511,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7314,plain,
spl0_794,
inference(avatar_split_clause,[],[f2499,f7312]) ).
fof(f7312,plain,
( spl0_794
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2499,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7310,plain,
spl0_793,
inference(avatar_split_clause,[],[f2494,f7308]) ).
fof(f7308,plain,
( spl0_793
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2494,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7306,plain,
spl0_792,
inference(avatar_split_clause,[],[f2493,f7304]) ).
fof(f7304,plain,
( spl0_792
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2493,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7302,plain,
spl0_791,
inference(avatar_split_clause,[],[f2381,f7300]) ).
fof(f7300,plain,
( spl0_791
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2381,axiom,
! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7298,plain,
spl0_790,
inference(avatar_split_clause,[],[f2380,f7296]) ).
fof(f7296,plain,
( spl0_790
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2380,axiom,
! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7294,plain,
spl0_789,
inference(avatar_split_clause,[],[f2378,f7292]) ).
fof(f7292,plain,
( spl0_789
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2378,axiom,
! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7290,plain,
spl0_788,
inference(avatar_split_clause,[],[f2370,f7288]) ).
fof(f7288,plain,
( spl0_788
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2370,axiom,
! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7286,plain,
spl0_787,
inference(avatar_split_clause,[],[f2368,f7284]) ).
fof(f7284,plain,
( spl0_787
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f2368,axiom,
! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7282,plain,
spl0_786,
inference(avatar_split_clause,[],[f2344,f7280]) ).
fof(f2344,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7278,plain,
spl0_785,
inference(avatar_split_clause,[],[f2269,f7276]) ).
fof(f7276,plain,
( spl0_785
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f2269,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7274,plain,
spl0_784,
inference(avatar_split_clause,[],[f2156,f7271]) ).
fof(f7269,plain,
spl0_783,
inference(avatar_split_clause,[],[f2102,f7267]) ).
fof(f7267,plain,
( spl0_783
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f2102,axiom,
! [X3] : c_minus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7265,plain,
spl0_782,
inference(avatar_split_clause,[],[f2100,f7263]) ).
fof(f7263,plain,
( spl0_782
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f2100,axiom,
! [X3] : c_plus(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7261,plain,
spl0_781,
inference(avatar_split_clause,[],[f2098,f7259]) ).
fof(f7259,plain,
( spl0_781
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f2098,axiom,
! [X21] : c_0 = c_times(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7257,plain,
spl0_780,
inference(avatar_split_clause,[],[f2056,f7255]) ).
fof(f7255,plain,
( spl0_780
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f2056,axiom,
! [X15] : c_0 = c_times(X15,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7253,plain,
spl0_779,
inference(avatar_split_clause,[],[f2054,f7251]) ).
fof(f7251,plain,
( spl0_779
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f2054,axiom,
! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7249,plain,
spl0_778,
inference(avatar_split_clause,[],[f2053,f7247]) ).
fof(f7247,plain,
( spl0_778
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2053,axiom,
! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7245,plain,
spl0_777,
inference(avatar_split_clause,[],[f2051,f7243]) ).
fof(f7243,plain,
( spl0_777
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2051,axiom,
! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7241,plain,
spl0_776,
inference(avatar_split_clause,[],[f2050,f7239]) ).
fof(f7239,plain,
( spl0_776
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f2050,axiom,
! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7237,plain,
spl0_775,
inference(avatar_split_clause,[],[f2041,f7235]) ).
fof(f7235,plain,
( spl0_775
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f2041,axiom,
! [X15] : c_0 = c_minus(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7233,plain,
spl0_774,
inference(avatar_split_clause,[],[f2034,f7231]) ).
fof(f2034,axiom,
! [X21] : c_0 = c_minus(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7229,plain,
spl0_773,
inference(avatar_split_clause,[],[f2026,f7227]) ).
fof(f7227,plain,
( spl0_773
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f2026,axiom,
! [X3] : c_plus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7225,plain,
spl0_772,
inference(avatar_split_clause,[],[f1787,f7223]) ).
fof(f7223,plain,
( spl0_772
<=> ! [X0,X81,X1] : c_List_Olist_OCons(X0,X81,X1) != X81 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f1787,axiom,
! [X0,X1,X81] : c_List_Olist_OCons(X0,X81,X1) != X81,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
fof(f7221,plain,
spl0_771,
inference(avatar_split_clause,[],[f1763,f7219]) ).
fof(f7219,plain,
( spl0_771
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f1763,axiom,
! [X1,X12] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7217,plain,
spl0_770,
inference(avatar_split_clause,[],[f1762,f7215]) ).
fof(f7215,plain,
( spl0_770
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f1762,axiom,
! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7213,plain,
spl0_769,
inference(avatar_split_clause,[],[f1741,f7211]) ).
fof(f7211,plain,
( spl0_769
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f1741,axiom,
! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7209,plain,
spl0_768,
inference(avatar_split_clause,[],[f1722,f7207]) ).
fof(f7207,plain,
( spl0_768
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f1722,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7205,plain,
spl0_767,
inference(avatar_split_clause,[],[f1719,f7203]) ).
fof(f7203,plain,
( spl0_767
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f1719,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7201,plain,
spl0_766,
inference(avatar_split_clause,[],[f1707,f7199]) ).
fof(f7199,plain,
( spl0_766
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f1707,axiom,
! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7197,plain,
spl0_765,
inference(avatar_split_clause,[],[f1628,f7195]) ).
fof(f7195,plain,
( spl0_765
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f1628,axiom,
! [X65,X41] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7193,plain,
spl0_764,
inference(avatar_split_clause,[],[f1623,f7191]) ).
fof(f7191,plain,
( spl0_764
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f1623,axiom,
! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_0) ).
fof(f7189,plain,
spl0_763,
inference(avatar_split_clause,[],[f1615,f7187]) ).
fof(f7187,plain,
( spl0_763
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f1615,axiom,
! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7185,plain,
spl0_762,
inference(avatar_split_clause,[],[f1598,f7183]) ).
fof(f7183,plain,
( spl0_762
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f1598,axiom,
! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7181,plain,
spl0_761,
inference(avatar_split_clause,[],[f1569,f7179]) ).
fof(f7179,plain,
( spl0_761
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f1569,axiom,
! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7177,plain,
spl0_760,
inference(avatar_split_clause,[],[f1568,f7175]) ).
fof(f7175,plain,
( spl0_760
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f1568,axiom,
! [X21,X41] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7173,plain,
spl0_759,
inference(avatar_split_clause,[],[f1534,f7171]) ).
fof(f7171,plain,
( spl0_759
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f1534,axiom,
! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
fof(f7169,plain,
spl0_758,
inference(avatar_split_clause,[],[f1494,f7167]) ).
fof(f7167,plain,
( spl0_758
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f1494,axiom,
! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7165,plain,
spl0_757,
inference(avatar_split_clause,[],[f1491,f7163]) ).
fof(f7163,plain,
( spl0_757
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f1491,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7161,plain,
spl0_756,
inference(avatar_split_clause,[],[f1489,f7159]) ).
fof(f7159,plain,
( spl0_756
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f1489,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7157,plain,
spl0_755,
inference(avatar_split_clause,[],[f1474,f7155]) ).
fof(f7155,plain,
( spl0_755
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f1474,axiom,
! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7153,plain,
spl0_754,
inference(avatar_split_clause,[],[f1466,f7151]) ).
fof(f7151,plain,
( spl0_754
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f1466,axiom,
! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7149,plain,
spl0_753,
inference(avatar_split_clause,[],[f1464,f7147]) ).
fof(f7147,plain,
( spl0_753
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f1464,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7145,plain,
spl0_752,
inference(avatar_split_clause,[],[f1432,f7143]) ).
fof(f1432,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7141,plain,
spl0_751,
inference(avatar_split_clause,[],[f1364,f7139]) ).
fof(f7139,plain,
( spl0_751
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f1364,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7137,plain,
spl0_750,
inference(avatar_split_clause,[],[f1363,f7135]) ).
fof(f7135,plain,
( spl0_750
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f1363,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7133,plain,
spl0_749,
inference(avatar_split_clause,[],[f1358,f7131]) ).
fof(f7131,plain,
( spl0_749
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f1358,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7129,plain,
spl0_748,
inference(avatar_split_clause,[],[f1357,f7127]) ).
fof(f7127,plain,
( spl0_748
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f1357,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7125,plain,
spl0_747,
inference(avatar_split_clause,[],[f1350,f7122]) ).
fof(f7122,plain,
( spl0_747
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f1350,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(f7120,plain,
spl0_746,
inference(avatar_split_clause,[],[f1245,f7118]) ).
fof(f7118,plain,
( spl0_746
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f1245,axiom,
! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
fof(f7116,plain,
spl0_745,
inference(avatar_split_clause,[],[f1241,f7114]) ).
fof(f7114,plain,
( spl0_745
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f1241,axiom,
! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7112,plain,
spl0_744,
inference(avatar_split_clause,[],[f1230,f7110]) ).
fof(f7110,plain,
( spl0_744
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f1230,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7108,plain,
spl0_743,
inference(avatar_split_clause,[],[f1213,f7106]) ).
fof(f7106,plain,
( spl0_743
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f1213,axiom,
! [X15] : c_0 = c_div(c_0,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7104,plain,
spl0_742,
inference(avatar_split_clause,[],[f1212,f7102]) ).
fof(f7102,plain,
( spl0_742
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f1212,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7100,plain,
spl0_741,
inference(avatar_split_clause,[],[f1211,f7098]) ).
fof(f7098,plain,
( spl0_741
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f1211,axiom,
! [X18] : c_0 = c_div(X18,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7096,plain,
spl0_740,
inference(avatar_split_clause,[],[f1183,f7094]) ).
fof(f7094,plain,
( spl0_740
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f1183,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7092,plain,
spl0_739,
inference(avatar_split_clause,[],[f1182,f7090]) ).
fof(f7090,plain,
( spl0_739
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f1182,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7088,plain,
spl0_738,
inference(avatar_split_clause,[],[f1176,f7086]) ).
fof(f7086,plain,
( spl0_738
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f1176,axiom,
! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f7084,plain,
spl0_737,
inference(avatar_split_clause,[],[f68,f7082]) ).
fof(f7082,plain,
( spl0_737
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7080,plain,
( spl0_736
| ~ spl0_640
| ~ spl0_679 ),
inference(avatar_split_clause,[],[f7062,f6812,f5878,f7077]) ).
fof(f7077,plain,
( spl0_736
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f6812,plain,
( spl0_679
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f7062,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_679 ),
inference(superposition,[],[f6813,f5880]) ).
fof(f6813,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_679 ),
inference(avatar_component_clause,[],[f6812]) ).
fof(f7073,plain,
( ~ spl0_735
| ~ spl0_641
| ~ spl0_677 ),
inference(avatar_split_clause,[],[f7059,f6804,f5883,f7070]) ).
fof(f7070,plain,
( spl0_735
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f6804,plain,
( spl0_677
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f7059,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_677 ),
inference(superposition,[],[f6805,f5885]) ).
fof(f6805,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_677 ),
inference(avatar_component_clause,[],[f6804]) ).
fof(f7068,plain,
( ~ spl0_734
| ~ spl0_640
| ~ spl0_677 ),
inference(avatar_split_clause,[],[f7058,f6804,f5878,f7065]) ).
fof(f7065,plain,
( spl0_734
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f7058,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_677 ),
inference(superposition,[],[f6805,f5880]) ).
fof(f7057,plain,
spl0_733,
inference(avatar_split_clause,[],[f3031,f7054]) ).
fof(f7054,plain,
( spl0_733
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f3031,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1391,f1374]) ).
fof(f1374,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f1391,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f7052,plain,
spl0_732,
inference(avatar_split_clause,[],[f3026,f7050]) ).
fof(f7050,plain,
( spl0_732
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f3026,plain,
! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
inference(forward_demodulation,[],[f2814,f2798]) ).
fof(f2814,plain,
! [X3] : c_Binomial_Obinomial(X3,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X3,
inference(definition_unfolding,[],[f1161,f2544]) ).
fof(f1161,axiom,
! [X3] : c_Binomial_Obinomial(X3,c_Suc(c_0)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f7048,plain,
spl0_731,
inference(avatar_split_clause,[],[f2797,f7045]) ).
fof(f7045,plain,
( spl0_731
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f7043,plain,
spl0_730,
inference(avatar_split_clause,[],[f2740,f7041]) ).
fof(f7041,plain,
( spl0_730
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2740,axiom,
! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
fof(f7039,plain,
spl0_729,
inference(avatar_split_clause,[],[f2739,f7036]) ).
fof(f7036,plain,
( spl0_729
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2739,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__3_0) ).
fof(f7034,plain,
spl0_728,
inference(avatar_split_clause,[],[f2737,f7031]) ).
fof(f7031,plain,
( spl0_728
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2737,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Osize__1_0) ).
fof(f7029,plain,
spl0_727,
inference(avatar_split_clause,[],[f2714,f7027]) ).
fof(f7027,plain,
( spl0_727
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f2714,axiom,
! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f7025,plain,
spl0_726,
inference(avatar_split_clause,[],[f2698,f7023]) ).
fof(f7023,plain,
( spl0_726
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2698,axiom,
! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f7021,plain,
spl0_725,
inference(avatar_split_clause,[],[f2691,f7019]) ).
fof(f7019,plain,
( spl0_725
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2691,axiom,
! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f7017,plain,
spl0_724,
inference(avatar_split_clause,[],[f2651,f7015]) ).
fof(f7015,plain,
( spl0_724
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f7013,plain,
spl0_723,
inference(avatar_split_clause,[],[f2649,f7011]) ).
fof(f7011,plain,
( spl0_723
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f7009,plain,
spl0_722,
inference(avatar_split_clause,[],[f2625,f7007]) ).
fof(f7007,plain,
( spl0_722
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f7005,plain,
spl0_721,
inference(avatar_split_clause,[],[f2619,f7003]) ).
fof(f7003,plain,
( spl0_721
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f7001,plain,
spl0_720,
inference(avatar_split_clause,[],[f2612,f6999]) ).
fof(f6999,plain,
( spl0_720
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f6997,plain,
spl0_719,
inference(avatar_split_clause,[],[f2567,f6994]) ).
fof(f6994,plain,
( spl0_719
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2567,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f6992,plain,
spl0_718,
inference(avatar_split_clause,[],[f2528,f6989]) ).
fof(f6989,plain,
( spl0_718
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f2528,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f6987,plain,
spl0_717,
inference(avatar_split_clause,[],[f2386,f6985]) ).
fof(f6983,plain,
spl0_716,
inference(avatar_split_clause,[],[f2164,f6980]) ).
fof(f6980,plain,
( spl0_716
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2164,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(f6978,plain,
spl0_715,
inference(avatar_split_clause,[],[f2163,f6975]) ).
fof(f6975,plain,
( spl0_715
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f2163,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(f6973,plain,
spl0_714,
inference(avatar_split_clause,[],[f2152,f6971]) ).
fof(f6971,plain,
( spl0_714
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f2152,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f6969,plain,
spl0_713,
inference(avatar_split_clause,[],[f2151,f6967]) ).
fof(f6967,plain,
( spl0_713
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f2151,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f6965,plain,
spl0_712,
inference(avatar_split_clause,[],[f2135,f6963]) ).
fof(f6963,plain,
( spl0_712
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f2135,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f6961,plain,
spl0_711,
inference(avatar_split_clause,[],[f2130,f6959]) ).
fof(f6959,plain,
( spl0_711
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f2130,axiom,
! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6957,plain,
spl0_710,
inference(avatar_split_clause,[],[f2115,f6955]) ).
fof(f6955,plain,
( spl0_710
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f6953,plain,
spl0_709,
inference(avatar_split_clause,[],[f2114,f6951]) ).
fof(f6951,plain,
( spl0_709
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f2114,axiom,
! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f6949,plain,
spl0_708,
inference(avatar_split_clause,[],[f2106,f6946]) ).
fof(f2106,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(f6944,plain,
spl0_707,
inference(avatar_split_clause,[],[f2105,f6941]) ).
fof(f2105,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(f6939,plain,
spl0_706,
inference(avatar_split_clause,[],[f1866,f6936]) ).
fof(f1866,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(f6934,plain,
spl0_705,
inference(avatar_split_clause,[],[f1785,f6932]) ).
fof(f6932,plain,
( spl0_705
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f1785,axiom,
! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6930,plain,
spl0_704,
inference(avatar_split_clause,[],[f1778,f6928]) ).
fof(f6928,plain,
( spl0_704
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f1778,axiom,
! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6926,plain,
spl0_703,
inference(avatar_split_clause,[],[f1751,f6924]) ).
fof(f6924,plain,
( spl0_703
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f1751,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oset__empty2_1) ).
fof(f6922,plain,
spl0_702,
inference(avatar_split_clause,[],[f1736,f6920]) ).
fof(f6920,plain,
( spl0_702
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f1736,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6918,plain,
spl0_701,
inference(avatar_split_clause,[],[f1729,f6916]) ).
fof(f6916,plain,
( spl0_701
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f6914,plain,
spl0_700,
inference(avatar_split_clause,[],[f1718,f6912]) ).
fof(f6912,plain,
( spl0_700
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f1718,axiom,
! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_1) ).
fof(f6910,plain,
spl0_699,
inference(avatar_split_clause,[],[f1688,f6907]) ).
fof(f6907,plain,
( spl0_699
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f1688,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(f6905,plain,
spl0_698,
inference(avatar_split_clause,[],[f1687,f6902]) ).
fof(f6902,plain,
( spl0_698
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f1687,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(f6900,plain,
spl0_697,
inference(avatar_split_clause,[],[f1686,f6897]) ).
fof(f6897,plain,
( spl0_697
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f1686,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(f6895,plain,
spl0_696,
inference(avatar_split_clause,[],[f1685,f6892]) ).
fof(f6892,plain,
( spl0_696
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f1685,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(f6890,plain,
spl0_695,
inference(avatar_split_clause,[],[f1684,f6887]) ).
fof(f6887,plain,
( spl0_695
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f1684,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(f6885,plain,
spl0_694,
inference(avatar_split_clause,[],[f1683,f6882]) ).
fof(f6882,plain,
( spl0_694
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f1683,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(f6880,plain,
spl0_693,
inference(avatar_split_clause,[],[f1682,f6877]) ).
fof(f6877,plain,
( spl0_693
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f1682,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(f6875,plain,
spl0_692,
inference(avatar_split_clause,[],[f1681,f6872]) ).
fof(f6872,plain,
( spl0_692
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f1681,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(f6870,plain,
spl0_691,
inference(avatar_split_clause,[],[f1680,f6867]) ).
fof(f6867,plain,
( spl0_691
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f1680,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(f6865,plain,
spl0_690,
inference(avatar_split_clause,[],[f1679,f6862]) ).
fof(f6862,plain,
( spl0_690
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f1679,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(f6860,plain,
spl0_689,
inference(avatar_split_clause,[],[f1678,f6857]) ).
fof(f6857,plain,
( spl0_689
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f1678,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(f6855,plain,
spl0_688,
inference(avatar_split_clause,[],[f1677,f6852]) ).
fof(f6852,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f1677,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(f6850,plain,
spl0_687,
inference(avatar_split_clause,[],[f1676,f6847]) ).
fof(f6847,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f1676,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(f6845,plain,
spl0_686,
inference(avatar_split_clause,[],[f1675,f6842]) ).
fof(f6842,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f1675,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(f6840,plain,
spl0_685,
inference(avatar_split_clause,[],[f1674,f6837]) ).
fof(f6837,plain,
( spl0_685
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f1674,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(f6835,plain,
spl0_684,
inference(avatar_split_clause,[],[f1673,f6832]) ).
fof(f6832,plain,
( spl0_684
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f1673,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(f6830,plain,
spl0_683,
inference(avatar_split_clause,[],[f1638,f6828]) ).
fof(f6828,plain,
( spl0_683
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f1638,axiom,
! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6826,plain,
spl0_682,
inference(avatar_split_clause,[],[f1567,f6824]) ).
fof(f6824,plain,
( spl0_682
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f1567,axiom,
! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6822,plain,
spl0_681,
inference(avatar_split_clause,[],[f1543,f6820]) ).
fof(f6820,plain,
( spl0_681
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f1543,axiom,
! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6818,plain,
spl0_680,
inference(avatar_split_clause,[],[f1536,f6816]) ).
fof(f6816,plain,
( spl0_680
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f1536,axiom,
! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6814,plain,
spl0_679,
inference(avatar_split_clause,[],[f1424,f6812]) ).
fof(f1424,axiom,
! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6810,plain,
spl0_678,
inference(avatar_split_clause,[],[f1384,f6808]) ).
fof(f1384,axiom,
! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6806,plain,
spl0_677,
inference(avatar_split_clause,[],[f1378,f6804]) ).
fof(f1378,axiom,
! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6802,plain,
~ spl0_676,
inference(avatar_split_clause,[],[f1309,f6799]) ).
fof(f1309,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(f6797,plain,
spl0_675,
inference(avatar_split_clause,[],[f1296,f6795]) ).
fof(f6795,plain,
( spl0_675
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6793,plain,
spl0_674,
inference(avatar_split_clause,[],[f1295,f6791]) ).
fof(f1295,axiom,
! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6789,plain,
spl0_673,
inference(avatar_split_clause,[],[f1278,f6787]) ).
fof(f6787,plain,
( spl0_673
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f1278,axiom,
! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6785,plain,
spl0_672,
inference(avatar_split_clause,[],[f1255,f6782]) ).
fof(f6782,plain,
( spl0_672
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f1255,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(f6780,plain,
spl0_671,
inference(avatar_split_clause,[],[f1254,f6777]) ).
fof(f6777,plain,
( spl0_671
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f1254,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(f6775,plain,
spl0_670,
inference(avatar_split_clause,[],[f1184,f6772]) ).
fof(f6772,plain,
( spl0_670
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f1184,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(f6770,plain,
spl0_669,
inference(avatar_split_clause,[],[f1174,f6768]) ).
fof(f6768,plain,
( spl0_669
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f1174,axiom,
! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__2_0) ).
fof(f6766,plain,
spl0_668,
inference(avatar_split_clause,[],[f1172,f6764]) ).
fof(f6764,plain,
( spl0_668
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f1172,axiom,
! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6762,plain,
spl0_667,
inference(avatar_split_clause,[],[f1165,f6760]) ).
fof(f6760,plain,
( spl0_667
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f1165,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,X21),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6758,plain,
spl0_666,
inference(avatar_split_clause,[],[f1164,f6756]) ).
fof(f6756,plain,
( spl0_666
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f1164,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f6754,plain,
( ~ spl0_665
| ~ spl0_641
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f6720,f5893,f5883,f6751]) ).
fof(f6751,plain,
( spl0_665
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f5893,plain,
( spl0_643
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f6720,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_641
| ~ spl0_643 ),
inference(superposition,[],[f5894,f5885]) ).
fof(f5894,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_643 ),
inference(avatar_component_clause,[],[f5893]) ).
fof(f6749,plain,
spl0_664,
inference(avatar_split_clause,[],[f250,f6747]) ).
fof(f6747,plain,
( spl0_664
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f250,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6745,plain,
spl0_663,
inference(avatar_split_clause,[],[f128,f6743]) ).
fof(f6743,plain,
( spl0_663
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f128,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6741,plain,
spl0_662,
inference(avatar_split_clause,[],[f112,f6739]) ).
fof(f6739,plain,
( spl0_662
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f112,axiom,
! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6737,plain,
spl0_661,
inference(avatar_split_clause,[],[f101,f6735]) ).
fof(f6735,plain,
( spl0_661
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f101,axiom,
! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6733,plain,
spl0_660,
inference(avatar_split_clause,[],[f44,f6731]) ).
fof(f6731,plain,
( spl0_660
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f44,axiom,
! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6729,plain,
spl0_659,
inference(avatar_split_clause,[],[f28,f6727]) ).
fof(f6727,plain,
( spl0_659
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f28,axiom,
! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6725,plain,
( ~ spl0_658
| ~ spl0_640
| ~ spl0_643 ),
inference(avatar_split_clause,[],[f6719,f5893,f5878,f6722]) ).
fof(f6722,plain,
( spl0_658
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f6719,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_640
| ~ spl0_643 ),
inference(superposition,[],[f5894,f5880]) ).
fof(f5958,plain,
spl0_657,
inference(avatar_split_clause,[],[f3041,f5955]) ).
fof(f5955,plain,
( spl0_657
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f3041,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1486,f1464]) ).
fof(f1486,axiom,
! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f5953,plain,
spl0_656,
inference(avatar_split_clause,[],[f3022,f5951]) ).
fof(f5951,plain,
( spl0_656
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f3022,plain,
! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
inference(forward_demodulation,[],[f2802,f2798]) ).
fof(f2802,plain,
! [X16] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X16,tc_nat),
inference(definition_unfolding,[],[f24,f2544]) ).
fof(f24,axiom,
! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f5949,plain,
spl0_655,
inference(avatar_split_clause,[],[f3020,f5946]) ).
fof(f5946,plain,
( spl0_655
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f3020,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1377,f1374]) ).
fof(f1377,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f5944,plain,
spl0_654,
inference(avatar_split_clause,[],[f3019,f5941]) ).
fof(f5941,plain,
( spl0_654
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f3019,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2800,f2798]) ).
fof(f2800,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f1344,f2544]) ).
fof(f1344,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5939,plain,
spl0_653,
inference(avatar_split_clause,[],[f2770,f5936]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__empty_0) ).
fof(f5934,plain,
spl0_652,
inference(avatar_split_clause,[],[f2743,f5931]) ).
fof(f5931,plain,
( spl0_652
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__empty_0) ).
fof(f5929,plain,
spl0_651,
inference(avatar_split_clause,[],[f2735,f5927]) ).
fof(f5927,plain,
( spl0_651
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2735,axiom,
! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__6_0) ).
fof(f5925,plain,
spl0_650,
inference(avatar_split_clause,[],[f2730,f5923]) ).
fof(f5923,plain,
( spl0_650
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2730,axiom,
! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__1_0) ).
fof(f5921,plain,
spl0_649,
inference(avatar_split_clause,[],[f2672,f5919]) ).
fof(f5919,plain,
( spl0_649
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f5917,plain,
spl0_648,
inference(avatar_split_clause,[],[f2155,f5914]) ).
fof(f5914,plain,
( spl0_648
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2155,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f5912,plain,
spl0_647,
inference(avatar_split_clause,[],[f2091,f5910]) ).
fof(f5910,plain,
( spl0_647
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f5908,plain,
spl0_646,
inference(avatar_split_clause,[],[f2049,f5905]) ).
fof(f5905,plain,
( spl0_646
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f5903,plain,
spl0_645,
inference(avatar_split_clause,[],[f1709,f5901]) ).
fof(f5901,plain,
( spl0_645
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f1709,axiom,
! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f5899,plain,
spl0_644,
inference(avatar_split_clause,[],[f1482,f5897]) ).
fof(f1482,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f5895,plain,
spl0_643,
inference(avatar_split_clause,[],[f1393,f5893]) ).
fof(f1393,axiom,
! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f5891,plain,
spl0_642,
inference(avatar_split_clause,[],[f1386,f5888]) ).
fof(f5888,plain,
( spl0_642
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f5886,plain,
spl0_641,
inference(avatar_split_clause,[],[f1374,f5883]) ).
fof(f5881,plain,
spl0_640,
inference(avatar_split_clause,[],[f1371,f5878]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f5876,plain,
spl0_639,
inference(avatar_split_clause,[],[f1229,f5874]) ).
fof(f5874,plain,
( spl0_639
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f1229,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f5872,plain,
spl0_638,
inference(avatar_split_clause,[],[f1159,f5870]) ).
fof(f5870,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f1159,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5868,plain,
spl0_637,
inference(avatar_split_clause,[],[f1158,f5866]) ).
fof(f5866,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f1158,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5864,plain,
spl0_636,
inference(avatar_split_clause,[],[f1157,f5862]) ).
fof(f5862,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f1157,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5860,plain,
spl0_635,
inference(avatar_split_clause,[],[f1156,f5858]) ).
fof(f5858,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f1156,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5856,plain,
spl0_634,
inference(avatar_split_clause,[],[f1155,f5854]) ).
fof(f5854,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f1155,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5852,plain,
spl0_633,
inference(avatar_split_clause,[],[f1154,f5850]) ).
fof(f5850,plain,
( spl0_633
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f1154,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5848,plain,
spl0_632,
inference(avatar_split_clause,[],[f1153,f5846]) ).
fof(f5846,plain,
( spl0_632
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f1153,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5844,plain,
spl0_631,
inference(avatar_split_clause,[],[f1148,f5842]) ).
fof(f5842,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f1148,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5840,plain,
spl0_630,
inference(avatar_split_clause,[],[f1147,f5838]) ).
fof(f5838,plain,
( spl0_630
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f1147,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5836,plain,
spl0_629,
inference(avatar_split_clause,[],[f1146,f5834]) ).
fof(f5834,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f1146,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5832,plain,
spl0_628,
inference(avatar_split_clause,[],[f1145,f5830]) ).
fof(f5830,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f1145,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5828,plain,
spl0_627,
inference(avatar_split_clause,[],[f1144,f5826]) ).
fof(f5826,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f1144,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5824,plain,
spl0_626,
inference(avatar_split_clause,[],[f1143,f5822]) ).
fof(f5822,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f1143,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5820,plain,
spl0_625,
inference(avatar_split_clause,[],[f1140,f5818]) ).
fof(f5818,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f1140,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5816,plain,
spl0_624,
inference(avatar_split_clause,[],[f1139,f5814]) ).
fof(f5814,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f1139,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5812,plain,
spl0_623,
inference(avatar_split_clause,[],[f1138,f5810]) ).
fof(f5810,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f1138,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5808,plain,
spl0_622,
inference(avatar_split_clause,[],[f1135,f5806]) ).
fof(f5806,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f1135,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5804,plain,
spl0_621,
inference(avatar_split_clause,[],[f1132,f5802]) ).
fof(f5802,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f1132,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5800,plain,
spl0_620,
inference(avatar_split_clause,[],[f1131,f5798]) ).
fof(f5798,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f1131,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5796,plain,
spl0_619,
inference(avatar_split_clause,[],[f1130,f5794]) ).
fof(f5794,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f1130,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5792,plain,
spl0_618,
inference(avatar_split_clause,[],[f1129,f5790]) ).
fof(f5790,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f1129,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5788,plain,
spl0_617,
inference(avatar_split_clause,[],[f1126,f5786]) ).
fof(f5786,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f1126,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5784,plain,
spl0_616,
inference(avatar_split_clause,[],[f1125,f5782]) ).
fof(f5782,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f1125,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5780,plain,
spl0_615,
inference(avatar_split_clause,[],[f1120,f5778]) ).
fof(f5778,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f1120,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5776,plain,
spl0_614,
inference(avatar_split_clause,[],[f1117,f5774]) ).
fof(f5774,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f1117,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5772,plain,
spl0_613,
inference(avatar_split_clause,[],[f1116,f5770]) ).
fof(f5770,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f1116,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5768,plain,
spl0_612,
inference(avatar_split_clause,[],[f1115,f5766]) ).
fof(f5766,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f1115,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5764,plain,
spl0_611,
inference(avatar_split_clause,[],[f1113,f5762]) ).
fof(f5762,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f1113,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5760,plain,
spl0_610,
inference(avatar_split_clause,[],[f1107,f5758]) ).
fof(f5758,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f1107,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5756,plain,
spl0_609,
inference(avatar_split_clause,[],[f1099,f5754]) ).
fof(f5754,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f1099,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5752,plain,
spl0_608,
inference(avatar_split_clause,[],[f1098,f5750]) ).
fof(f5750,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f1098,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5748,plain,
spl0_607,
inference(avatar_split_clause,[],[f1097,f5746]) ).
fof(f5746,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f1097,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5744,plain,
spl0_606,
inference(avatar_split_clause,[],[f1096,f5742]) ).
fof(f5742,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f1096,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5740,plain,
spl0_605,
inference(avatar_split_clause,[],[f1095,f5738]) ).
fof(f5738,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f1095,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5736,plain,
spl0_604,
inference(avatar_split_clause,[],[f1093,f5734]) ).
fof(f5734,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f1093,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5732,plain,
spl0_603,
inference(avatar_split_clause,[],[f1092,f5730]) ).
fof(f5730,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f1092,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5728,plain,
spl0_602,
inference(avatar_split_clause,[],[f1091,f5726]) ).
fof(f5726,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f1091,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5724,plain,
spl0_601,
inference(avatar_split_clause,[],[f1090,f5722]) ).
fof(f5722,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f1090,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5720,plain,
spl0_600,
inference(avatar_split_clause,[],[f1089,f5718]) ).
fof(f5718,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f1089,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5716,plain,
spl0_599,
inference(avatar_split_clause,[],[f1084,f5714]) ).
fof(f5714,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f1084,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5712,plain,
spl0_598,
inference(avatar_split_clause,[],[f1083,f5710]) ).
fof(f5710,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f1083,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5708,plain,
spl0_597,
inference(avatar_split_clause,[],[f1082,f5706]) ).
fof(f5706,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f1082,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5704,plain,
spl0_596,
inference(avatar_split_clause,[],[f1080,f5702]) ).
fof(f5702,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f1080,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5700,plain,
spl0_595,
inference(avatar_split_clause,[],[f1078,f5698]) ).
fof(f5698,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f1078,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5696,plain,
spl0_594,
inference(avatar_split_clause,[],[f1073,f5694]) ).
fof(f5694,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f1073,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5692,plain,
spl0_593,
inference(avatar_split_clause,[],[f1072,f5690]) ).
fof(f5690,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f1072,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5688,plain,
spl0_592,
inference(avatar_split_clause,[],[f1071,f5686]) ).
fof(f5686,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f1071,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5684,plain,
spl0_591,
inference(avatar_split_clause,[],[f1070,f5682]) ).
fof(f5682,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f1070,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5680,plain,
spl0_590,
inference(avatar_split_clause,[],[f1068,f5678]) ).
fof(f5678,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f1068,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5676,plain,
spl0_589,
inference(avatar_split_clause,[],[f1067,f5674]) ).
fof(f5674,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f1067,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5672,plain,
spl0_588,
inference(avatar_split_clause,[],[f1062,f5670]) ).
fof(f5670,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f1062,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5668,plain,
spl0_587,
inference(avatar_split_clause,[],[f1059,f5666]) ).
fof(f5666,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f1059,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5664,plain,
spl0_586,
inference(avatar_split_clause,[],[f1058,f5662]) ).
fof(f5662,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f1058,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5660,plain,
spl0_585,
inference(avatar_split_clause,[],[f1057,f5658]) ).
fof(f5658,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f1057,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5656,plain,
spl0_584,
inference(avatar_split_clause,[],[f1056,f5654]) ).
fof(f5654,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f1056,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5652,plain,
spl0_583,
inference(avatar_split_clause,[],[f1053,f5650]) ).
fof(f5650,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f1053,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5648,plain,
spl0_582,
inference(avatar_split_clause,[],[f1052,f5646]) ).
fof(f5646,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f1052,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5644,plain,
spl0_581,
inference(avatar_split_clause,[],[f1051,f5642]) ).
fof(f5642,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f1051,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5640,plain,
spl0_580,
inference(avatar_split_clause,[],[f1050,f5638]) ).
fof(f5638,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f1050,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5636,plain,
spl0_579,
inference(avatar_split_clause,[],[f1049,f5634]) ).
fof(f5634,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f1049,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5632,plain,
spl0_578,
inference(avatar_split_clause,[],[f1048,f5630]) ).
fof(f5630,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f1048,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5628,plain,
spl0_577,
inference(avatar_split_clause,[],[f1047,f5626]) ).
fof(f5626,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f1047,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5624,plain,
spl0_576,
inference(avatar_split_clause,[],[f1046,f5622]) ).
fof(f5622,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f1046,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5620,plain,
spl0_575,
inference(avatar_split_clause,[],[f1044,f5618]) ).
fof(f5618,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f1044,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5616,plain,
spl0_574,
inference(avatar_split_clause,[],[f1043,f5614]) ).
fof(f5614,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f1043,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5612,plain,
spl0_573,
inference(avatar_split_clause,[],[f1042,f5610]) ).
fof(f5610,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f1042,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5608,plain,
spl0_572,
inference(avatar_split_clause,[],[f1041,f5606]) ).
fof(f5606,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f1041,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5604,plain,
spl0_571,
inference(avatar_split_clause,[],[f1040,f5602]) ).
fof(f5602,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f1040,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5600,plain,
spl0_570,
inference(avatar_split_clause,[],[f1035,f5598]) ).
fof(f5598,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f1035,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5596,plain,
spl0_569,
inference(avatar_split_clause,[],[f1034,f5594]) ).
fof(f5594,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f1034,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5592,plain,
spl0_568,
inference(avatar_split_clause,[],[f1033,f5590]) ).
fof(f5590,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f1033,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5588,plain,
spl0_567,
inference(avatar_split_clause,[],[f1030,f5586]) ).
fof(f5586,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f1030,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5584,plain,
spl0_566,
inference(avatar_split_clause,[],[f1027,f5582]) ).
fof(f5582,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f1027,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5580,plain,
spl0_565,
inference(avatar_split_clause,[],[f1026,f5578]) ).
fof(f5578,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f1026,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5576,plain,
spl0_564,
inference(avatar_split_clause,[],[f1024,f5574]) ).
fof(f5574,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f1024,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5572,plain,
spl0_563,
inference(avatar_split_clause,[],[f1023,f5570]) ).
fof(f5570,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f1023,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5568,plain,
spl0_562,
inference(avatar_split_clause,[],[f1022,f5566]) ).
fof(f5566,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f1022,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5564,plain,
spl0_561,
inference(avatar_split_clause,[],[f1021,f5562]) ).
fof(f5562,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f1021,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5560,plain,
spl0_560,
inference(avatar_split_clause,[],[f1018,f5558]) ).
fof(f5558,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f1018,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5556,plain,
spl0_559,
inference(avatar_split_clause,[],[f1017,f5554]) ).
fof(f5554,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f1017,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5552,plain,
spl0_558,
inference(avatar_split_clause,[],[f989,f5550]) ).
fof(f5550,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f989,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5548,plain,
spl0_557,
inference(avatar_split_clause,[],[f987,f5546]) ).
fof(f5546,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f987,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5544,plain,
spl0_556,
inference(avatar_split_clause,[],[f984,f5542]) ).
fof(f5542,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f984,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5540,plain,
spl0_555,
inference(avatar_split_clause,[],[f983,f5538]) ).
fof(f5538,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f983,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5536,plain,
spl0_554,
inference(avatar_split_clause,[],[f982,f5534]) ).
fof(f5534,plain,
( spl0_554
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f982,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5532,plain,
spl0_553,
inference(avatar_split_clause,[],[f981,f5530]) ).
fof(f5530,plain,
( spl0_553
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f981,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5528,plain,
spl0_552,
inference(avatar_split_clause,[],[f980,f5526]) ).
fof(f5526,plain,
( spl0_552
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f980,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5524,plain,
spl0_551,
inference(avatar_split_clause,[],[f979,f5522]) ).
fof(f5522,plain,
( spl0_551
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f979,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5520,plain,
spl0_550,
inference(avatar_split_clause,[],[f977,f5518]) ).
fof(f5518,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f977,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5516,plain,
spl0_549,
inference(avatar_split_clause,[],[f976,f5514]) ).
fof(f5514,plain,
( spl0_549
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f976,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5512,plain,
spl0_548,
inference(avatar_split_clause,[],[f974,f5510]) ).
fof(f5510,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f974,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5508,plain,
spl0_547,
inference(avatar_split_clause,[],[f971,f5506]) ).
fof(f5506,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f971,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5504,plain,
spl0_546,
inference(avatar_split_clause,[],[f970,f5502]) ).
fof(f5502,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f970,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5500,plain,
spl0_545,
inference(avatar_split_clause,[],[f968,f5498]) ).
fof(f5498,plain,
( spl0_545
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f968,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5496,plain,
spl0_544,
inference(avatar_split_clause,[],[f967,f5494]) ).
fof(f5494,plain,
( spl0_544
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f967,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5492,plain,
spl0_543,
inference(avatar_split_clause,[],[f966,f5490]) ).
fof(f5490,plain,
( spl0_543
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f966,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5488,plain,
spl0_542,
inference(avatar_split_clause,[],[f965,f5486]) ).
fof(f5486,plain,
( spl0_542
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f965,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5484,plain,
spl0_541,
inference(avatar_split_clause,[],[f964,f5482]) ).
fof(f5482,plain,
( spl0_541
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f964,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5480,plain,
spl0_540,
inference(avatar_split_clause,[],[f963,f5478]) ).
fof(f5478,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f963,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5476,plain,
spl0_539,
inference(avatar_split_clause,[],[f962,f5474]) ).
fof(f5474,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f962,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5472,plain,
spl0_538,
inference(avatar_split_clause,[],[f961,f5470]) ).
fof(f5470,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f961,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5468,plain,
spl0_537,
inference(avatar_split_clause,[],[f957,f5466]) ).
fof(f5466,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f957,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5464,plain,
spl0_536,
inference(avatar_split_clause,[],[f956,f5462]) ).
fof(f5462,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f956,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5460,plain,
spl0_535,
inference(avatar_split_clause,[],[f955,f5458]) ).
fof(f5458,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f955,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5456,plain,
spl0_534,
inference(avatar_split_clause,[],[f954,f5454]) ).
fof(f5454,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f954,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5452,plain,
spl0_533,
inference(avatar_split_clause,[],[f949,f5450]) ).
fof(f5450,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f949,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5448,plain,
spl0_532,
inference(avatar_split_clause,[],[f947,f5446]) ).
fof(f5446,plain,
( spl0_532
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f947,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5444,plain,
spl0_531,
inference(avatar_split_clause,[],[f946,f5442]) ).
fof(f5442,plain,
( spl0_531
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f946,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5440,plain,
spl0_530,
inference(avatar_split_clause,[],[f945,f5438]) ).
fof(f5438,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f945,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5436,plain,
spl0_529,
inference(avatar_split_clause,[],[f944,f5434]) ).
fof(f5434,plain,
( spl0_529
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f944,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5432,plain,
spl0_528,
inference(avatar_split_clause,[],[f942,f5430]) ).
fof(f5430,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f942,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5428,plain,
spl0_527,
inference(avatar_split_clause,[],[f941,f5426]) ).
fof(f5426,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f941,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5424,plain,
spl0_526,
inference(avatar_split_clause,[],[f940,f5422]) ).
fof(f5422,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f940,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5420,plain,
spl0_525,
inference(avatar_split_clause,[],[f939,f5418]) ).
fof(f5418,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f939,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5416,plain,
spl0_524,
inference(avatar_split_clause,[],[f938,f5414]) ).
fof(f5414,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f938,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5412,plain,
spl0_523,
inference(avatar_split_clause,[],[f937,f5410]) ).
fof(f5410,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f937,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5408,plain,
spl0_522,
inference(avatar_split_clause,[],[f936,f5406]) ).
fof(f5406,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f936,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5404,plain,
spl0_521,
inference(avatar_split_clause,[],[f935,f5402]) ).
fof(f5402,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f935,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5400,plain,
spl0_520,
inference(avatar_split_clause,[],[f934,f5398]) ).
fof(f5398,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f934,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5396,plain,
spl0_519,
inference(avatar_split_clause,[],[f933,f5394]) ).
fof(f5394,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f933,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5392,plain,
spl0_518,
inference(avatar_split_clause,[],[f932,f5390]) ).
fof(f5390,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f932,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5388,plain,
spl0_517,
inference(avatar_split_clause,[],[f931,f5386]) ).
fof(f5386,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f931,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5384,plain,
spl0_516,
inference(avatar_split_clause,[],[f930,f5382]) ).
fof(f5382,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f930,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5380,plain,
spl0_515,
inference(avatar_split_clause,[],[f929,f5378]) ).
fof(f5378,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f929,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5376,plain,
spl0_514,
inference(avatar_split_clause,[],[f928,f5374]) ).
fof(f5374,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f928,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5372,plain,
spl0_513,
inference(avatar_split_clause,[],[f927,f5370]) ).
fof(f5370,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f927,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5368,plain,
spl0_512,
inference(avatar_split_clause,[],[f926,f5366]) ).
fof(f5366,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f926,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5364,plain,
spl0_511,
inference(avatar_split_clause,[],[f925,f5362]) ).
fof(f5362,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f925,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5360,plain,
spl0_510,
inference(avatar_split_clause,[],[f924,f5358]) ).
fof(f5358,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f924,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5356,plain,
spl0_509,
inference(avatar_split_clause,[],[f923,f5354]) ).
fof(f5354,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f923,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5352,plain,
spl0_508,
inference(avatar_split_clause,[],[f922,f5350]) ).
fof(f5350,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f922,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5348,plain,
spl0_507,
inference(avatar_split_clause,[],[f921,f5346]) ).
fof(f5346,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f921,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5344,plain,
spl0_506,
inference(avatar_split_clause,[],[f920,f5342]) ).
fof(f5342,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f920,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5340,plain,
spl0_505,
inference(avatar_split_clause,[],[f919,f5338]) ).
fof(f5338,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f919,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5336,plain,
spl0_504,
inference(avatar_split_clause,[],[f918,f5334]) ).
fof(f5334,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f918,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5332,plain,
spl0_503,
inference(avatar_split_clause,[],[f917,f5330]) ).
fof(f5330,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f917,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5328,plain,
spl0_502,
inference(avatar_split_clause,[],[f916,f5326]) ).
fof(f5326,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f916,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5324,plain,
spl0_501,
inference(avatar_split_clause,[],[f915,f5322]) ).
fof(f5322,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f915,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5320,plain,
spl0_500,
inference(avatar_split_clause,[],[f914,f5318]) ).
fof(f5318,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f914,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5316,plain,
spl0_499,
inference(avatar_split_clause,[],[f913,f5314]) ).
fof(f5314,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f913,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5312,plain,
spl0_498,
inference(avatar_split_clause,[],[f912,f5310]) ).
fof(f5310,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f912,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5308,plain,
spl0_497,
inference(avatar_split_clause,[],[f911,f5306]) ).
fof(f5306,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f911,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5304,plain,
spl0_496,
inference(avatar_split_clause,[],[f910,f5302]) ).
fof(f5302,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f910,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5300,plain,
spl0_495,
inference(avatar_split_clause,[],[f909,f5298]) ).
fof(f5298,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f909,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5296,plain,
spl0_494,
inference(avatar_split_clause,[],[f908,f5294]) ).
fof(f5294,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f908,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5292,plain,
spl0_493,
inference(avatar_split_clause,[],[f905,f5290]) ).
fof(f5290,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f905,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5288,plain,
spl0_492,
inference(avatar_split_clause,[],[f903,f5286]) ).
fof(f5286,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f903,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5284,plain,
spl0_491,
inference(avatar_split_clause,[],[f902,f5282]) ).
fof(f5282,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f902,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5280,plain,
spl0_490,
inference(avatar_split_clause,[],[f900,f5278]) ).
fof(f5278,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f900,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5276,plain,
spl0_489,
inference(avatar_split_clause,[],[f897,f5274]) ).
fof(f5274,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f897,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5272,plain,
spl0_488,
inference(avatar_split_clause,[],[f896,f5270]) ).
fof(f5270,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f896,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5268,plain,
spl0_487,
inference(avatar_split_clause,[],[f895,f5266]) ).
fof(f5266,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f895,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5264,plain,
spl0_486,
inference(avatar_split_clause,[],[f893,f5262]) ).
fof(f5262,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f893,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5260,plain,
spl0_485,
inference(avatar_split_clause,[],[f892,f5258]) ).
fof(f5258,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f892,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5256,plain,
spl0_484,
inference(avatar_split_clause,[],[f891,f5254]) ).
fof(f5254,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f891,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5252,plain,
spl0_483,
inference(avatar_split_clause,[],[f888,f5250]) ).
fof(f5250,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f888,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5248,plain,
spl0_482,
inference(avatar_split_clause,[],[f887,f5246]) ).
fof(f5246,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f887,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5244,plain,
spl0_481,
inference(avatar_split_clause,[],[f886,f5242]) ).
fof(f5242,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f886,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5240,plain,
spl0_480,
inference(avatar_split_clause,[],[f885,f5238]) ).
fof(f5238,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f885,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5236,plain,
spl0_479,
inference(avatar_split_clause,[],[f883,f5234]) ).
fof(f5234,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f883,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5232,plain,
spl0_478,
inference(avatar_split_clause,[],[f882,f5230]) ).
fof(f5230,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f882,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5228,plain,
spl0_477,
inference(avatar_split_clause,[],[f881,f5226]) ).
fof(f5226,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f881,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5224,plain,
spl0_476,
inference(avatar_split_clause,[],[f880,f5222]) ).
fof(f5222,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f880,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5220,plain,
spl0_475,
inference(avatar_split_clause,[],[f879,f5218]) ).
fof(f5218,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f879,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5216,plain,
spl0_474,
inference(avatar_split_clause,[],[f878,f5214]) ).
fof(f5214,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f878,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5212,plain,
spl0_473,
inference(avatar_split_clause,[],[f877,f5210]) ).
fof(f5210,plain,
( spl0_473
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f877,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5208,plain,
spl0_472,
inference(avatar_split_clause,[],[f876,f5206]) ).
fof(f5206,plain,
( spl0_472
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f876,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5204,plain,
spl0_471,
inference(avatar_split_clause,[],[f875,f5202]) ).
fof(f5202,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f875,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5200,plain,
spl0_470,
inference(avatar_split_clause,[],[f874,f5198]) ).
fof(f5198,plain,
( spl0_470
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f874,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5196,plain,
spl0_469,
inference(avatar_split_clause,[],[f873,f5194]) ).
fof(f5194,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f873,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5192,plain,
spl0_468,
inference(avatar_split_clause,[],[f872,f5190]) ).
fof(f5190,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f872,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5188,plain,
spl0_467,
inference(avatar_split_clause,[],[f871,f5186]) ).
fof(f5186,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f871,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5184,plain,
spl0_466,
inference(avatar_split_clause,[],[f870,f5182]) ).
fof(f5182,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f870,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5180,plain,
spl0_465,
inference(avatar_split_clause,[],[f869,f5178]) ).
fof(f5178,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f869,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5176,plain,
spl0_464,
inference(avatar_split_clause,[],[f868,f5174]) ).
fof(f5174,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f868,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5172,plain,
spl0_463,
inference(avatar_split_clause,[],[f867,f5170]) ).
fof(f5170,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f867,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5168,plain,
spl0_462,
inference(avatar_split_clause,[],[f865,f5166]) ).
fof(f5166,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f865,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5164,plain,
spl0_461,
inference(avatar_split_clause,[],[f864,f5162]) ).
fof(f5162,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f864,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5160,plain,
spl0_460,
inference(avatar_split_clause,[],[f863,f5158]) ).
fof(f5158,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f863,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5156,plain,
spl0_459,
inference(avatar_split_clause,[],[f862,f5154]) ).
fof(f5154,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f862,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5152,plain,
spl0_458,
inference(avatar_split_clause,[],[f861,f5150]) ).
fof(f5150,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f861,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5148,plain,
spl0_457,
inference(avatar_split_clause,[],[f856,f5146]) ).
fof(f5146,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f856,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5144,plain,
spl0_456,
inference(avatar_split_clause,[],[f855,f5142]) ).
fof(f5142,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f855,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5140,plain,
spl0_455,
inference(avatar_split_clause,[],[f854,f5138]) ).
fof(f5138,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f854,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5136,plain,
spl0_454,
inference(avatar_split_clause,[],[f853,f5134]) ).
fof(f5134,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f853,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5132,plain,
spl0_453,
inference(avatar_split_clause,[],[f852,f5130]) ).
fof(f5130,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f852,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5128,plain,
spl0_452,
inference(avatar_split_clause,[],[f851,f5126]) ).
fof(f5126,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f851,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5124,plain,
spl0_451,
inference(avatar_split_clause,[],[f850,f5122]) ).
fof(f5122,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f850,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5120,plain,
spl0_450,
inference(avatar_split_clause,[],[f849,f5118]) ).
fof(f5118,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f849,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5116,plain,
spl0_449,
inference(avatar_split_clause,[],[f847,f5114]) ).
fof(f5114,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f847,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5112,plain,
spl0_448,
inference(avatar_split_clause,[],[f846,f5110]) ).
fof(f5110,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f846,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5108,plain,
spl0_447,
inference(avatar_split_clause,[],[f845,f5106]) ).
fof(f5106,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f845,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5104,plain,
spl0_446,
inference(avatar_split_clause,[],[f844,f5102]) ).
fof(f5102,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f844,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5100,plain,
spl0_445,
inference(avatar_split_clause,[],[f843,f5098]) ).
fof(f5098,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f843,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5096,plain,
spl0_444,
inference(avatar_split_clause,[],[f842,f5094]) ).
fof(f5094,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f842,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5092,plain,
spl0_443,
inference(avatar_split_clause,[],[f840,f5090]) ).
fof(f5090,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f840,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5088,plain,
spl0_442,
inference(avatar_split_clause,[],[f839,f5086]) ).
fof(f5086,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f839,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5084,plain,
spl0_441,
inference(avatar_split_clause,[],[f838,f5082]) ).
fof(f5082,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f838,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5080,plain,
spl0_440,
inference(avatar_split_clause,[],[f837,f5078]) ).
fof(f5078,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f837,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5076,plain,
spl0_439,
inference(avatar_split_clause,[],[f836,f5074]) ).
fof(f5074,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f836,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5072,plain,
spl0_438,
inference(avatar_split_clause,[],[f835,f5070]) ).
fof(f5070,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f835,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5068,plain,
spl0_437,
inference(avatar_split_clause,[],[f834,f5066]) ).
fof(f5066,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f834,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5064,plain,
spl0_436,
inference(avatar_split_clause,[],[f833,f5062]) ).
fof(f5062,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f833,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5060,plain,
spl0_435,
inference(avatar_split_clause,[],[f832,f5058]) ).
fof(f5058,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f832,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5056,plain,
spl0_434,
inference(avatar_split_clause,[],[f831,f5054]) ).
fof(f5054,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f831,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5052,plain,
spl0_433,
inference(avatar_split_clause,[],[f830,f5050]) ).
fof(f5050,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f830,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5048,plain,
spl0_432,
inference(avatar_split_clause,[],[f829,f5046]) ).
fof(f5046,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f829,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5044,plain,
spl0_431,
inference(avatar_split_clause,[],[f828,f5042]) ).
fof(f5042,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f828,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5040,plain,
spl0_430,
inference(avatar_split_clause,[],[f827,f5038]) ).
fof(f5038,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f827,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5036,plain,
spl0_429,
inference(avatar_split_clause,[],[f826,f5034]) ).
fof(f5034,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f826,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5032,plain,
spl0_428,
inference(avatar_split_clause,[],[f825,f5030]) ).
fof(f5030,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f825,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5028,plain,
spl0_427,
inference(avatar_split_clause,[],[f824,f5026]) ).
fof(f5026,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f824,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5024,plain,
spl0_426,
inference(avatar_split_clause,[],[f823,f5022]) ).
fof(f5022,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f823,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5020,plain,
spl0_425,
inference(avatar_split_clause,[],[f822,f5018]) ).
fof(f5018,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f822,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5016,plain,
spl0_424,
inference(avatar_split_clause,[],[f821,f5014]) ).
fof(f5014,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f821,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5012,plain,
spl0_423,
inference(avatar_split_clause,[],[f820,f5010]) ).
fof(f5010,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f820,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5008,plain,
spl0_422,
inference(avatar_split_clause,[],[f819,f5006]) ).
fof(f5006,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f819,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5004,plain,
spl0_421,
inference(avatar_split_clause,[],[f816,f5002]) ).
fof(f5002,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f816,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5000,plain,
spl0_420,
inference(avatar_split_clause,[],[f814,f4998]) ).
fof(f4998,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f814,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f4996,plain,
spl0_419,
inference(avatar_split_clause,[],[f812,f4994]) ).
fof(f4994,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f812,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f4992,plain,
spl0_418,
inference(avatar_split_clause,[],[f809,f4990]) ).
fof(f4990,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f809,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f4988,plain,
spl0_417,
inference(avatar_split_clause,[],[f808,f4986]) ).
fof(f4986,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f808,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f4984,plain,
spl0_416,
inference(avatar_split_clause,[],[f807,f4982]) ).
fof(f4982,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f807,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f4980,plain,
spl0_415,
inference(avatar_split_clause,[],[f806,f4978]) ).
fof(f4978,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f806,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f4976,plain,
spl0_414,
inference(avatar_split_clause,[],[f804,f4974]) ).
fof(f4974,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f804,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f4972,plain,
spl0_413,
inference(avatar_split_clause,[],[f803,f4970]) ).
fof(f4970,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f803,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f4968,plain,
spl0_412,
inference(avatar_split_clause,[],[f802,f4966]) ).
fof(f4966,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f802,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4964,plain,
spl0_411,
inference(avatar_split_clause,[],[f801,f4962]) ).
fof(f4962,plain,
( spl0_411
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f801,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4960,plain,
spl0_410,
inference(avatar_split_clause,[],[f800,f4958]) ).
fof(f4958,plain,
( spl0_410
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f800,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4956,plain,
spl0_409,
inference(avatar_split_clause,[],[f799,f4954]) ).
fof(f4954,plain,
( spl0_409
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f799,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4952,plain,
spl0_408,
inference(avatar_split_clause,[],[f798,f4950]) ).
fof(f4950,plain,
( spl0_408
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f798,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4948,plain,
spl0_407,
inference(avatar_split_clause,[],[f797,f4946]) ).
fof(f4946,plain,
( spl0_407
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f797,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4944,plain,
spl0_406,
inference(avatar_split_clause,[],[f796,f4942]) ).
fof(f4942,plain,
( spl0_406
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f796,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4940,plain,
spl0_405,
inference(avatar_split_clause,[],[f732,f4938]) ).
fof(f4938,plain,
( spl0_405
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f732,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4936,plain,
spl0_404,
inference(avatar_split_clause,[],[f729,f4934]) ).
fof(f4934,plain,
( spl0_404
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f729,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4932,plain,
spl0_403,
inference(avatar_split_clause,[],[f728,f4930]) ).
fof(f4930,plain,
( spl0_403
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f728,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4928,plain,
spl0_402,
inference(avatar_split_clause,[],[f727,f4926]) ).
fof(f4926,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f727,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4924,plain,
spl0_401,
inference(avatar_split_clause,[],[f726,f4922]) ).
fof(f4922,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f726,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4920,plain,
spl0_400,
inference(avatar_split_clause,[],[f725,f4918]) ).
fof(f4918,plain,
( spl0_400
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f725,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4916,plain,
spl0_399,
inference(avatar_split_clause,[],[f724,f4914]) ).
fof(f4914,plain,
( spl0_399
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f724,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4912,plain,
spl0_398,
inference(avatar_split_clause,[],[f723,f4910]) ).
fof(f4910,plain,
( spl0_398
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f723,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4908,plain,
spl0_397,
inference(avatar_split_clause,[],[f722,f4906]) ).
fof(f4906,plain,
( spl0_397
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f722,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4904,plain,
spl0_396,
inference(avatar_split_clause,[],[f721,f4902]) ).
fof(f4902,plain,
( spl0_396
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f721,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4900,plain,
spl0_395,
inference(avatar_split_clause,[],[f720,f4898]) ).
fof(f4898,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f720,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4896,plain,
spl0_394,
inference(avatar_split_clause,[],[f719,f4894]) ).
fof(f4894,plain,
( spl0_394
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f719,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4892,plain,
spl0_393,
inference(avatar_split_clause,[],[f718,f4890]) ).
fof(f4890,plain,
( spl0_393
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f718,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4888,plain,
spl0_392,
inference(avatar_split_clause,[],[f716,f4886]) ).
fof(f4886,plain,
( spl0_392
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f716,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4884,plain,
spl0_391,
inference(avatar_split_clause,[],[f715,f4882]) ).
fof(f4882,plain,
( spl0_391
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f715,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4880,plain,
spl0_390,
inference(avatar_split_clause,[],[f714,f4878]) ).
fof(f4878,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f714,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4876,plain,
spl0_389,
inference(avatar_split_clause,[],[f713,f4874]) ).
fof(f4874,plain,
( spl0_389
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f713,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4872,plain,
spl0_388,
inference(avatar_split_clause,[],[f712,f4870]) ).
fof(f4870,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f712,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4868,plain,
spl0_387,
inference(avatar_split_clause,[],[f711,f4866]) ).
fof(f4866,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f711,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4864,plain,
spl0_386,
inference(avatar_split_clause,[],[f710,f4862]) ).
fof(f4862,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f710,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4860,plain,
spl0_385,
inference(avatar_split_clause,[],[f709,f4858]) ).
fof(f4858,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f709,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4856,plain,
spl0_384,
inference(avatar_split_clause,[],[f706,f4854]) ).
fof(f4854,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f706,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4852,plain,
spl0_383,
inference(avatar_split_clause,[],[f705,f4850]) ).
fof(f4850,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f705,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4848,plain,
spl0_382,
inference(avatar_split_clause,[],[f704,f4846]) ).
fof(f4846,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f704,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4844,plain,
spl0_381,
inference(avatar_split_clause,[],[f703,f4842]) ).
fof(f4842,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f703,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4840,plain,
spl0_380,
inference(avatar_split_clause,[],[f702,f4838]) ).
fof(f4838,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f702,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4836,plain,
spl0_379,
inference(avatar_split_clause,[],[f701,f4834]) ).
fof(f4834,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f701,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4832,plain,
spl0_378,
inference(avatar_split_clause,[],[f700,f4830]) ).
fof(f4830,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f700,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4828,plain,
spl0_377,
inference(avatar_split_clause,[],[f698,f4826]) ).
fof(f4826,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f698,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4824,plain,
spl0_376,
inference(avatar_split_clause,[],[f697,f4822]) ).
fof(f4822,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f697,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4820,plain,
spl0_375,
inference(avatar_split_clause,[],[f696,f4818]) ).
fof(f4818,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f696,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4816,plain,
spl0_374,
inference(avatar_split_clause,[],[f695,f4814]) ).
fof(f4814,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f695,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4812,plain,
spl0_373,
inference(avatar_split_clause,[],[f694,f4810]) ).
fof(f4810,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f694,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4808,plain,
spl0_372,
inference(avatar_split_clause,[],[f693,f4806]) ).
fof(f4806,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f693,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4804,plain,
spl0_371,
inference(avatar_split_clause,[],[f692,f4802]) ).
fof(f4802,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f692,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4800,plain,
spl0_370,
inference(avatar_split_clause,[],[f691,f4798]) ).
fof(f4798,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f691,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4796,plain,
spl0_369,
inference(avatar_split_clause,[],[f688,f4794]) ).
fof(f4794,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f688,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4792,plain,
spl0_368,
inference(avatar_split_clause,[],[f686,f4790]) ).
fof(f4790,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f686,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4788,plain,
spl0_367,
inference(avatar_split_clause,[],[f685,f4786]) ).
fof(f4786,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f685,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4784,plain,
spl0_366,
inference(avatar_split_clause,[],[f683,f4782]) ).
fof(f4782,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f683,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4780,plain,
spl0_365,
inference(avatar_split_clause,[],[f680,f4778]) ).
fof(f4778,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f680,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4776,plain,
spl0_364,
inference(avatar_split_clause,[],[f679,f4774]) ).
fof(f4774,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f679,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4772,plain,
spl0_363,
inference(avatar_split_clause,[],[f678,f4770]) ).
fof(f4770,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f678,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4768,plain,
spl0_362,
inference(avatar_split_clause,[],[f677,f4766]) ).
fof(f4766,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f677,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4764,plain,
spl0_361,
inference(avatar_split_clause,[],[f676,f4762]) ).
fof(f4762,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f676,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4760,plain,
spl0_360,
inference(avatar_split_clause,[],[f675,f4758]) ).
fof(f4758,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f675,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4756,plain,
spl0_359,
inference(avatar_split_clause,[],[f674,f4754]) ).
fof(f4754,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f674,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4752,plain,
spl0_358,
inference(avatar_split_clause,[],[f673,f4750]) ).
fof(f4750,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f673,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4748,plain,
spl0_357,
inference(avatar_split_clause,[],[f672,f4746]) ).
fof(f4746,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f672,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4744,plain,
spl0_356,
inference(avatar_split_clause,[],[f671,f4742]) ).
fof(f4742,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f671,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4740,plain,
spl0_355,
inference(avatar_split_clause,[],[f670,f4738]) ).
fof(f4738,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f670,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4736,plain,
spl0_354,
inference(avatar_split_clause,[],[f668,f4734]) ).
fof(f4734,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f668,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4732,plain,
spl0_353,
inference(avatar_split_clause,[],[f666,f4730]) ).
fof(f4730,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f666,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4728,plain,
spl0_352,
inference(avatar_split_clause,[],[f663,f4726]) ).
fof(f4726,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f663,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4724,plain,
spl0_351,
inference(avatar_split_clause,[],[f661,f4722]) ).
fof(f4722,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f661,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4720,plain,
spl0_350,
inference(avatar_split_clause,[],[f659,f4718]) ).
fof(f4718,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f659,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4716,plain,
spl0_349,
inference(avatar_split_clause,[],[f656,f4714]) ).
fof(f4714,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f656,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4712,plain,
spl0_348,
inference(avatar_split_clause,[],[f655,f4710]) ).
fof(f4710,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f655,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4708,plain,
spl0_347,
inference(avatar_split_clause,[],[f654,f4706]) ).
fof(f4706,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f654,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4704,plain,
spl0_346,
inference(avatar_split_clause,[],[f653,f4702]) ).
fof(f4702,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f653,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4700,plain,
spl0_345,
inference(avatar_split_clause,[],[f651,f4698]) ).
fof(f4698,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f651,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4696,plain,
spl0_344,
inference(avatar_split_clause,[],[f650,f4694]) ).
fof(f4694,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f650,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4692,plain,
spl0_343,
inference(avatar_split_clause,[],[f649,f4690]) ).
fof(f4690,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f649,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4688,plain,
spl0_342,
inference(avatar_split_clause,[],[f648,f4686]) ).
fof(f4686,plain,
( spl0_342
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f648,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4684,plain,
spl0_341,
inference(avatar_split_clause,[],[f647,f4682]) ).
fof(f4682,plain,
( spl0_341
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f647,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4680,plain,
spl0_340,
inference(avatar_split_clause,[],[f646,f4678]) ).
fof(f4678,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f646,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4676,plain,
spl0_339,
inference(avatar_split_clause,[],[f645,f4674]) ).
fof(f4674,plain,
( spl0_339
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f645,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4672,plain,
spl0_338,
inference(avatar_split_clause,[],[f644,f4670]) ).
fof(f4670,plain,
( spl0_338
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f644,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4668,plain,
spl0_337,
inference(avatar_split_clause,[],[f643,f4666]) ).
fof(f4666,plain,
( spl0_337
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f643,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4664,plain,
spl0_336,
inference(avatar_split_clause,[],[f607,f4662]) ).
fof(f4662,plain,
( spl0_336
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f607,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4660,plain,
spl0_335,
inference(avatar_split_clause,[],[f606,f4658]) ).
fof(f4658,plain,
( spl0_335
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f606,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4656,plain,
spl0_334,
inference(avatar_split_clause,[],[f605,f4654]) ).
fof(f4654,plain,
( spl0_334
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f605,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4652,plain,
spl0_333,
inference(avatar_split_clause,[],[f604,f4650]) ).
fof(f4650,plain,
( spl0_333
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f604,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4648,plain,
spl0_332,
inference(avatar_split_clause,[],[f603,f4646]) ).
fof(f4646,plain,
( spl0_332
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f603,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4644,plain,
spl0_331,
inference(avatar_split_clause,[],[f601,f4642]) ).
fof(f4642,plain,
( spl0_331
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f601,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4640,plain,
spl0_330,
inference(avatar_split_clause,[],[f600,f4638]) ).
fof(f4638,plain,
( spl0_330
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f600,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4636,plain,
spl0_329,
inference(avatar_split_clause,[],[f599,f4634]) ).
fof(f4634,plain,
( spl0_329
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f599,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4632,plain,
spl0_328,
inference(avatar_split_clause,[],[f598,f4630]) ).
fof(f4630,plain,
( spl0_328
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f598,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4628,plain,
spl0_327,
inference(avatar_split_clause,[],[f597,f4626]) ).
fof(f4626,plain,
( spl0_327
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f597,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4624,plain,
spl0_326,
inference(avatar_split_clause,[],[f596,f4622]) ).
fof(f4622,plain,
( spl0_326
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f596,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4620,plain,
spl0_325,
inference(avatar_split_clause,[],[f595,f4618]) ).
fof(f4618,plain,
( spl0_325
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f595,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4616,plain,
spl0_324,
inference(avatar_split_clause,[],[f592,f4614]) ).
fof(f4614,plain,
( spl0_324
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f592,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4612,plain,
spl0_323,
inference(avatar_split_clause,[],[f591,f4610]) ).
fof(f4610,plain,
( spl0_323
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f591,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4608,plain,
spl0_322,
inference(avatar_split_clause,[],[f586,f4606]) ).
fof(f4606,plain,
( spl0_322
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f586,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4604,plain,
spl0_321,
inference(avatar_split_clause,[],[f585,f4602]) ).
fof(f4602,plain,
( spl0_321
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f585,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4600,plain,
spl0_320,
inference(avatar_split_clause,[],[f582,f4598]) ).
fof(f4598,plain,
( spl0_320
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f582,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4596,plain,
spl0_319,
inference(avatar_split_clause,[],[f581,f4594]) ).
fof(f4594,plain,
( spl0_319
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f581,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4592,plain,
spl0_318,
inference(avatar_split_clause,[],[f579,f4590]) ).
fof(f4590,plain,
( spl0_318
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f579,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4588,plain,
spl0_317,
inference(avatar_split_clause,[],[f578,f4586]) ).
fof(f4586,plain,
( spl0_317
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f578,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4584,plain,
spl0_316,
inference(avatar_split_clause,[],[f577,f4582]) ).
fof(f4582,plain,
( spl0_316
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f577,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4580,plain,
spl0_315,
inference(avatar_split_clause,[],[f576,f4578]) ).
fof(f4578,plain,
( spl0_315
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f576,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4576,plain,
spl0_314,
inference(avatar_split_clause,[],[f575,f4574]) ).
fof(f4574,plain,
( spl0_314
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f575,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4572,plain,
spl0_313,
inference(avatar_split_clause,[],[f574,f4570]) ).
fof(f4570,plain,
( spl0_313
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f574,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4568,plain,
spl0_312,
inference(avatar_split_clause,[],[f570,f4566]) ).
fof(f4566,plain,
( spl0_312
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f570,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4564,plain,
spl0_311,
inference(avatar_split_clause,[],[f568,f4562]) ).
fof(f4562,plain,
( spl0_311
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f568,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4560,plain,
spl0_310,
inference(avatar_split_clause,[],[f565,f4558]) ).
fof(f4558,plain,
( spl0_310
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f565,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4556,plain,
spl0_309,
inference(avatar_split_clause,[],[f562,f4554]) ).
fof(f4554,plain,
( spl0_309
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f562,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4552,plain,
spl0_308,
inference(avatar_split_clause,[],[f561,f4550]) ).
fof(f4550,plain,
( spl0_308
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f561,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4548,plain,
spl0_307,
inference(avatar_split_clause,[],[f559,f4546]) ).
fof(f4546,plain,
( spl0_307
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f559,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4544,plain,
spl0_306,
inference(avatar_split_clause,[],[f558,f4542]) ).
fof(f4542,plain,
( spl0_306
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f558,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4540,plain,
spl0_305,
inference(avatar_split_clause,[],[f557,f4538]) ).
fof(f4538,plain,
( spl0_305
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f557,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4536,plain,
spl0_304,
inference(avatar_split_clause,[],[f554,f4534]) ).
fof(f4534,plain,
( spl0_304
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f554,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4532,plain,
spl0_303,
inference(avatar_split_clause,[],[f553,f4530]) ).
fof(f4530,plain,
( spl0_303
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f553,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4528,plain,
spl0_302,
inference(avatar_split_clause,[],[f551,f4526]) ).
fof(f4526,plain,
( spl0_302
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f551,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4524,plain,
spl0_301,
inference(avatar_split_clause,[],[f545,f4522]) ).
fof(f4522,plain,
( spl0_301
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f545,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4520,plain,
spl0_300,
inference(avatar_split_clause,[],[f544,f4518]) ).
fof(f4518,plain,
( spl0_300
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f544,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4516,plain,
spl0_299,
inference(avatar_split_clause,[],[f542,f4514]) ).
fof(f4514,plain,
( spl0_299
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f542,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4512,plain,
spl0_298,
inference(avatar_split_clause,[],[f541,f4510]) ).
fof(f4510,plain,
( spl0_298
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f541,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4508,plain,
spl0_297,
inference(avatar_split_clause,[],[f534,f4506]) ).
fof(f4506,plain,
( spl0_297
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f534,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4504,plain,
spl0_296,
inference(avatar_split_clause,[],[f533,f4502]) ).
fof(f4502,plain,
( spl0_296
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f533,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4500,plain,
spl0_295,
inference(avatar_split_clause,[],[f531,f4498]) ).
fof(f4498,plain,
( spl0_295
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f531,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4496,plain,
spl0_294,
inference(avatar_split_clause,[],[f530,f4494]) ).
fof(f4494,plain,
( spl0_294
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f530,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4492,plain,
spl0_293,
inference(avatar_split_clause,[],[f529,f4490]) ).
fof(f4490,plain,
( spl0_293
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f529,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4488,plain,
spl0_292,
inference(avatar_split_clause,[],[f527,f4486]) ).
fof(f4486,plain,
( spl0_292
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f527,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4484,plain,
spl0_291,
inference(avatar_split_clause,[],[f526,f4482]) ).
fof(f4482,plain,
( spl0_291
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f526,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4480,plain,
spl0_290,
inference(avatar_split_clause,[],[f525,f4478]) ).
fof(f4478,plain,
( spl0_290
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f525,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4476,plain,
spl0_289,
inference(avatar_split_clause,[],[f524,f4474]) ).
fof(f4474,plain,
( spl0_289
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f524,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4472,plain,
spl0_288,
inference(avatar_split_clause,[],[f523,f4470]) ).
fof(f4470,plain,
( spl0_288
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f523,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4468,plain,
spl0_287,
inference(avatar_split_clause,[],[f522,f4466]) ).
fof(f4466,plain,
( spl0_287
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f522,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4464,plain,
spl0_286,
inference(avatar_split_clause,[],[f521,f4462]) ).
fof(f4462,plain,
( spl0_286
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f521,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4460,plain,
spl0_285,
inference(avatar_split_clause,[],[f520,f4458]) ).
fof(f4458,plain,
( spl0_285
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f520,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4456,plain,
spl0_284,
inference(avatar_split_clause,[],[f519,f4454]) ).
fof(f4454,plain,
( spl0_284
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f519,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4452,plain,
spl0_283,
inference(avatar_split_clause,[],[f518,f4450]) ).
fof(f4450,plain,
( spl0_283
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f518,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4448,plain,
spl0_282,
inference(avatar_split_clause,[],[f515,f4446]) ).
fof(f4446,plain,
( spl0_282
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f515,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4444,plain,
spl0_281,
inference(avatar_split_clause,[],[f513,f4442]) ).
fof(f4442,plain,
( spl0_281
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f513,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4440,plain,
spl0_280,
inference(avatar_split_clause,[],[f511,f4438]) ).
fof(f4438,plain,
( spl0_280
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f511,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4436,plain,
spl0_279,
inference(avatar_split_clause,[],[f508,f4434]) ).
fof(f4434,plain,
( spl0_279
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f508,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4432,plain,
spl0_278,
inference(avatar_split_clause,[],[f507,f4430]) ).
fof(f4430,plain,
( spl0_278
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f507,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4428,plain,
spl0_277,
inference(avatar_split_clause,[],[f506,f4426]) ).
fof(f4426,plain,
( spl0_277
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f506,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4424,plain,
spl0_276,
inference(avatar_split_clause,[],[f503,f4422]) ).
fof(f4422,plain,
( spl0_276
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f503,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4420,plain,
spl0_275,
inference(avatar_split_clause,[],[f500,f4418]) ).
fof(f4418,plain,
( spl0_275
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f500,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4416,plain,
spl0_274,
inference(avatar_split_clause,[],[f499,f4414]) ).
fof(f4414,plain,
( spl0_274
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f499,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4412,plain,
spl0_273,
inference(avatar_split_clause,[],[f497,f4410]) ).
fof(f4410,plain,
( spl0_273
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f497,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4408,plain,
spl0_272,
inference(avatar_split_clause,[],[f496,f4406]) ).
fof(f4406,plain,
( spl0_272
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f496,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4404,plain,
spl0_271,
inference(avatar_split_clause,[],[f495,f4402]) ).
fof(f4402,plain,
( spl0_271
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f495,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4400,plain,
spl0_270,
inference(avatar_split_clause,[],[f494,f4398]) ).
fof(f4398,plain,
( spl0_270
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f494,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4396,plain,
spl0_269,
inference(avatar_split_clause,[],[f493,f4394]) ).
fof(f4394,plain,
( spl0_269
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f493,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4392,plain,
spl0_268,
inference(avatar_split_clause,[],[f491,f4390]) ).
fof(f4390,plain,
( spl0_268
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f491,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4388,plain,
spl0_267,
inference(avatar_split_clause,[],[f488,f4386]) ).
fof(f4386,plain,
( spl0_267
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f488,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4384,plain,
spl0_266,
inference(avatar_split_clause,[],[f487,f4382]) ).
fof(f4382,plain,
( spl0_266
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f487,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4380,plain,
spl0_265,
inference(avatar_split_clause,[],[f483,f4378]) ).
fof(f4378,plain,
( spl0_265
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f483,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4376,plain,
spl0_264,
inference(avatar_split_clause,[],[f481,f4374]) ).
fof(f4374,plain,
( spl0_264
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f481,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4372,plain,
spl0_263,
inference(avatar_split_clause,[],[f473,f4370]) ).
fof(f4370,plain,
( spl0_263
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f473,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4368,plain,
spl0_262,
inference(avatar_split_clause,[],[f472,f4366]) ).
fof(f4366,plain,
( spl0_262
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f472,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4364,plain,
spl0_261,
inference(avatar_split_clause,[],[f471,f4362]) ).
fof(f4362,plain,
( spl0_261
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f471,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4360,plain,
spl0_260,
inference(avatar_split_clause,[],[f470,f4358]) ).
fof(f4358,plain,
( spl0_260
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f470,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4356,plain,
spl0_259,
inference(avatar_split_clause,[],[f469,f4354]) ).
fof(f4354,plain,
( spl0_259
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f469,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4352,plain,
spl0_258,
inference(avatar_split_clause,[],[f468,f4350]) ).
fof(f4350,plain,
( spl0_258
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f468,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4348,plain,
spl0_257,
inference(avatar_split_clause,[],[f467,f4346]) ).
fof(f4346,plain,
( spl0_257
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4344,plain,
spl0_256,
inference(avatar_split_clause,[],[f466,f4342]) ).
fof(f4342,plain,
( spl0_256
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f466,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4340,plain,
spl0_255,
inference(avatar_split_clause,[],[f465,f4338]) ).
fof(f4338,plain,
( spl0_255
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f465,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4336,plain,
spl0_254,
inference(avatar_split_clause,[],[f464,f4334]) ).
fof(f4334,plain,
( spl0_254
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f464,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4332,plain,
spl0_253,
inference(avatar_split_clause,[],[f463,f4330]) ).
fof(f4330,plain,
( spl0_253
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f463,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4328,plain,
spl0_252,
inference(avatar_split_clause,[],[f462,f4326]) ).
fof(f4326,plain,
( spl0_252
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f462,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4324,plain,
spl0_251,
inference(avatar_split_clause,[],[f461,f4322]) ).
fof(f4322,plain,
( spl0_251
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f461,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4320,plain,
spl0_250,
inference(avatar_split_clause,[],[f460,f4318]) ).
fof(f4318,plain,
( spl0_250
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f460,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4316,plain,
spl0_249,
inference(avatar_split_clause,[],[f459,f4314]) ).
fof(f4314,plain,
( spl0_249
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f459,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4312,plain,
spl0_248,
inference(avatar_split_clause,[],[f458,f4310]) ).
fof(f4310,plain,
( spl0_248
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f458,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4308,plain,
spl0_247,
inference(avatar_split_clause,[],[f457,f4306]) ).
fof(f4306,plain,
( spl0_247
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f457,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4304,plain,
spl0_246,
inference(avatar_split_clause,[],[f454,f4302]) ).
fof(f4302,plain,
( spl0_246
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4300,plain,
spl0_245,
inference(avatar_split_clause,[],[f453,f4298]) ).
fof(f4298,plain,
( spl0_245
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4296,plain,
spl0_244,
inference(avatar_split_clause,[],[f452,f4294]) ).
fof(f4294,plain,
( spl0_244
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4292,plain,
spl0_243,
inference(avatar_split_clause,[],[f451,f4290]) ).
fof(f4290,plain,
( spl0_243
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f451,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4288,plain,
spl0_242,
inference(avatar_split_clause,[],[f450,f4286]) ).
fof(f4286,plain,
( spl0_242
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f450,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4284,plain,
spl0_241,
inference(avatar_split_clause,[],[f449,f4282]) ).
fof(f4282,plain,
( spl0_241
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4280,plain,
spl0_240,
inference(avatar_split_clause,[],[f446,f4278]) ).
fof(f4278,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f446,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4276,plain,
spl0_239,
inference(avatar_split_clause,[],[f445,f4274]) ).
fof(f4274,plain,
( spl0_239
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f445,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4272,plain,
spl0_238,
inference(avatar_split_clause,[],[f441,f4270]) ).
fof(f4270,plain,
( spl0_238
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f441,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4268,plain,
spl0_237,
inference(avatar_split_clause,[],[f440,f4266]) ).
fof(f4266,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f440,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4264,plain,
spl0_236,
inference(avatar_split_clause,[],[f439,f4262]) ).
fof(f4262,plain,
( spl0_236
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f439,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4260,plain,
spl0_235,
inference(avatar_split_clause,[],[f436,f4258]) ).
fof(f4258,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f436,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4256,plain,
spl0_234,
inference(avatar_split_clause,[],[f434,f4254]) ).
fof(f4254,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f434,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4252,plain,
spl0_233,
inference(avatar_split_clause,[],[f433,f4250]) ).
fof(f4250,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f433,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4248,plain,
spl0_232,
inference(avatar_split_clause,[],[f432,f4246]) ).
fof(f4246,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f432,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4244,plain,
spl0_231,
inference(avatar_split_clause,[],[f431,f4242]) ).
fof(f4242,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f431,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4240,plain,
spl0_230,
inference(avatar_split_clause,[],[f430,f4238]) ).
fof(f4238,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f430,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4236,plain,
spl0_229,
inference(avatar_split_clause,[],[f426,f4234]) ).
fof(f4234,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f426,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4232,plain,
spl0_228,
inference(avatar_split_clause,[],[f425,f4230]) ).
fof(f4230,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f425,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4228,plain,
spl0_227,
inference(avatar_split_clause,[],[f424,f4226]) ).
fof(f4226,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f424,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4224,plain,
spl0_226,
inference(avatar_split_clause,[],[f421,f4222]) ).
fof(f4222,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f421,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4220,plain,
spl0_225,
inference(avatar_split_clause,[],[f419,f4218]) ).
fof(f4218,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f419,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4216,plain,
spl0_224,
inference(avatar_split_clause,[],[f417,f4214]) ).
fof(f4214,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f417,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4212,plain,
spl0_223,
inference(avatar_split_clause,[],[f416,f4210]) ).
fof(f4210,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f416,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4208,plain,
spl0_222,
inference(avatar_split_clause,[],[f415,f4206]) ).
fof(f4206,plain,
( spl0_222
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f415,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4204,plain,
spl0_221,
inference(avatar_split_clause,[],[f414,f4202]) ).
fof(f4202,plain,
( spl0_221
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f414,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4200,plain,
spl0_220,
inference(avatar_split_clause,[],[f413,f4198]) ).
fof(f4198,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f413,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4196,plain,
spl0_219,
inference(avatar_split_clause,[],[f411,f4194]) ).
fof(f4194,plain,
( spl0_219
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f411,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4192,plain,
spl0_218,
inference(avatar_split_clause,[],[f410,f4190]) ).
fof(f4190,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f410,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4188,plain,
spl0_217,
inference(avatar_split_clause,[],[f407,f4186]) ).
fof(f4186,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f407,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4184,plain,
spl0_216,
inference(avatar_split_clause,[],[f405,f4182]) ).
fof(f4182,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f405,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4180,plain,
spl0_215,
inference(avatar_split_clause,[],[f404,f4178]) ).
fof(f4178,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f404,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4176,plain,
spl0_214,
inference(avatar_split_clause,[],[f403,f4174]) ).
fof(f4174,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f403,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4172,plain,
spl0_213,
inference(avatar_split_clause,[],[f402,f4170]) ).
fof(f4170,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f402,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4168,plain,
spl0_212,
inference(avatar_split_clause,[],[f401,f4166]) ).
fof(f4166,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f401,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4164,plain,
spl0_211,
inference(avatar_split_clause,[],[f400,f4162]) ).
fof(f4162,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f400,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4160,plain,
spl0_210,
inference(avatar_split_clause,[],[f399,f4158]) ).
fof(f4158,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f399,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4156,plain,
spl0_209,
inference(avatar_split_clause,[],[f398,f4154]) ).
fof(f4154,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f398,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4152,plain,
spl0_208,
inference(avatar_split_clause,[],[f397,f4150]) ).
fof(f4150,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f397,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4148,plain,
spl0_207,
inference(avatar_split_clause,[],[f394,f4146]) ).
fof(f4146,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f394,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4144,plain,
spl0_206,
inference(avatar_split_clause,[],[f393,f4142]) ).
fof(f4142,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f393,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4140,plain,
spl0_205,
inference(avatar_split_clause,[],[f392,f4138]) ).
fof(f4138,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f392,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4136,plain,
spl0_204,
inference(avatar_split_clause,[],[f391,f4134]) ).
fof(f4134,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f391,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4132,plain,
spl0_203,
inference(avatar_split_clause,[],[f390,f4130]) ).
fof(f4130,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f390,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4128,plain,
spl0_202,
inference(avatar_split_clause,[],[f389,f4126]) ).
fof(f4126,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f389,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4124,plain,
spl0_201,
inference(avatar_split_clause,[],[f387,f4122]) ).
fof(f4122,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f387,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4120,plain,
spl0_200,
inference(avatar_split_clause,[],[f385,f4118]) ).
fof(f4118,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f385,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4116,plain,
spl0_199,
inference(avatar_split_clause,[],[f384,f4114]) ).
fof(f4114,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f384,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4112,plain,
spl0_198,
inference(avatar_split_clause,[],[f383,f4110]) ).
fof(f4110,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f383,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4108,plain,
spl0_197,
inference(avatar_split_clause,[],[f382,f4106]) ).
fof(f4106,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f382,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4104,plain,
spl0_196,
inference(avatar_split_clause,[],[f379,f4102]) ).
fof(f4102,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f379,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4100,plain,
spl0_195,
inference(avatar_split_clause,[],[f377,f4098]) ).
fof(f4098,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f377,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4096,plain,
spl0_194,
inference(avatar_split_clause,[],[f376,f4094]) ).
fof(f4094,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f376,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4092,plain,
spl0_193,
inference(avatar_split_clause,[],[f375,f4090]) ).
fof(f4090,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f375,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4088,plain,
spl0_192,
inference(avatar_split_clause,[],[f374,f4086]) ).
fof(f4086,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f374,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4084,plain,
spl0_191,
inference(avatar_split_clause,[],[f373,f4082]) ).
fof(f4082,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f373,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4080,plain,
spl0_190,
inference(avatar_split_clause,[],[f372,f4078]) ).
fof(f4078,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f372,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4076,plain,
spl0_189,
inference(avatar_split_clause,[],[f371,f4074]) ).
fof(f4074,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f371,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4072,plain,
spl0_188,
inference(avatar_split_clause,[],[f370,f4070]) ).
fof(f4070,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f370,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4068,plain,
spl0_187,
inference(avatar_split_clause,[],[f368,f4066]) ).
fof(f4066,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f368,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4064,plain,
spl0_186,
inference(avatar_split_clause,[],[f366,f4062]) ).
fof(f4062,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f366,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4060,plain,
spl0_185,
inference(avatar_split_clause,[],[f365,f4058]) ).
fof(f4058,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f365,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4056,plain,
spl0_184,
inference(avatar_split_clause,[],[f364,f4054]) ).
fof(f4054,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f364,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4052,plain,
spl0_183,
inference(avatar_split_clause,[],[f363,f4050]) ).
fof(f4050,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f363,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4048,plain,
spl0_182,
inference(avatar_split_clause,[],[f360,f4046]) ).
fof(f4046,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f360,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4044,plain,
spl0_181,
inference(avatar_split_clause,[],[f358,f4042]) ).
fof(f4042,plain,
( spl0_181
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f358,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4040,plain,
spl0_180,
inference(avatar_split_clause,[],[f357,f4038]) ).
fof(f4038,plain,
( spl0_180
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f357,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4036,plain,
spl0_179,
inference(avatar_split_clause,[],[f356,f4034]) ).
fof(f4034,plain,
( spl0_179
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f356,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4032,plain,
spl0_178,
inference(avatar_split_clause,[],[f355,f4030]) ).
fof(f4030,plain,
( spl0_178
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f355,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4028,plain,
spl0_177,
inference(avatar_split_clause,[],[f354,f4026]) ).
fof(f4026,plain,
( spl0_177
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f354,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4024,plain,
spl0_176,
inference(avatar_split_clause,[],[f353,f4022]) ).
fof(f4022,plain,
( spl0_176
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f353,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4020,plain,
spl0_175,
inference(avatar_split_clause,[],[f352,f4018]) ).
fof(f4018,plain,
( spl0_175
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f352,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4016,plain,
spl0_174,
inference(avatar_split_clause,[],[f350,f4014]) ).
fof(f4014,plain,
( spl0_174
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f350,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4012,plain,
spl0_173,
inference(avatar_split_clause,[],[f348,f4010]) ).
fof(f4010,plain,
( spl0_173
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f348,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4008,plain,
spl0_172,
inference(avatar_split_clause,[],[f347,f4006]) ).
fof(f4006,plain,
( spl0_172
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f347,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4004,plain,
spl0_171,
inference(avatar_split_clause,[],[f346,f4002]) ).
fof(f4002,plain,
( spl0_171
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f346,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4000,plain,
spl0_170,
inference(avatar_split_clause,[],[f345,f3998]) ).
fof(f3998,plain,
( spl0_170
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f345,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f3996,plain,
spl0_169,
inference(avatar_split_clause,[],[f344,f3994]) ).
fof(f3994,plain,
( spl0_169
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f344,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f3992,plain,
spl0_168,
inference(avatar_split_clause,[],[f343,f3990]) ).
fof(f3990,plain,
( spl0_168
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f343,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f3988,plain,
spl0_167,
inference(avatar_split_clause,[],[f340,f3986]) ).
fof(f3986,plain,
( spl0_167
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f340,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f3984,plain,
spl0_166,
inference(avatar_split_clause,[],[f338,f3982]) ).
fof(f3982,plain,
( spl0_166
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f338,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f3980,plain,
spl0_165,
inference(avatar_split_clause,[],[f337,f3978]) ).
fof(f3978,plain,
( spl0_165
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f337,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f3976,plain,
spl0_164,
inference(avatar_split_clause,[],[f336,f3974]) ).
fof(f3974,plain,
( spl0_164
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f336,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f3972,plain,
spl0_163,
inference(avatar_split_clause,[],[f335,f3970]) ).
fof(f3970,plain,
( spl0_163
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f335,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f3968,plain,
spl0_162,
inference(avatar_split_clause,[],[f334,f3966]) ).
fof(f3966,plain,
( spl0_162
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f334,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3964,plain,
spl0_161,
inference(avatar_split_clause,[],[f333,f3962]) ).
fof(f3962,plain,
( spl0_161
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f333,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3960,plain,
spl0_160,
inference(avatar_split_clause,[],[f332,f3958]) ).
fof(f3958,plain,
( spl0_160
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f332,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3956,plain,
spl0_159,
inference(avatar_split_clause,[],[f330,f3954]) ).
fof(f3954,plain,
( spl0_159
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f330,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3952,plain,
spl0_158,
inference(avatar_split_clause,[],[f328,f3950]) ).
fof(f3950,plain,
( spl0_158
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f328,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3948,plain,
spl0_157,
inference(avatar_split_clause,[],[f327,f3946]) ).
fof(f3946,plain,
( spl0_157
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f327,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3944,plain,
spl0_156,
inference(avatar_split_clause,[],[f326,f3942]) ).
fof(f3942,plain,
( spl0_156
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f326,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3940,plain,
spl0_155,
inference(avatar_split_clause,[],[f323,f3938]) ).
fof(f3938,plain,
( spl0_155
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f323,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3936,plain,
spl0_154,
inference(avatar_split_clause,[],[f321,f3934]) ).
fof(f3934,plain,
( spl0_154
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f321,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3932,plain,
spl0_153,
inference(avatar_split_clause,[],[f320,f3930]) ).
fof(f3930,plain,
( spl0_153
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f320,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3928,plain,
spl0_152,
inference(avatar_split_clause,[],[f319,f3926]) ).
fof(f3926,plain,
( spl0_152
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f319,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3924,plain,
spl0_151,
inference(avatar_split_clause,[],[f318,f3922]) ).
fof(f3922,plain,
( spl0_151
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f318,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3920,plain,
spl0_150,
inference(avatar_split_clause,[],[f314,f3918]) ).
fof(f3918,plain,
( spl0_150
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f314,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3916,plain,
spl0_149,
inference(avatar_split_clause,[],[f307,f3914]) ).
fof(f3914,plain,
( spl0_149
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f307,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3912,plain,
spl0_148,
inference(avatar_split_clause,[],[f299,f3910]) ).
fof(f3910,plain,
( spl0_148
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f299,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3908,plain,
spl0_147,
inference(avatar_split_clause,[],[f298,f3906]) ).
fof(f3906,plain,
( spl0_147
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f298,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3904,plain,
spl0_146,
inference(avatar_split_clause,[],[f293,f3902]) ).
fof(f3902,plain,
( spl0_146
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f293,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3900,plain,
spl0_145,
inference(avatar_split_clause,[],[f291,f3898]) ).
fof(f3898,plain,
( spl0_145
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f291,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3896,plain,
spl0_144,
inference(avatar_split_clause,[],[f289,f3894]) ).
fof(f3894,plain,
( spl0_144
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f289,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3892,plain,
spl0_143,
inference(avatar_split_clause,[],[f288,f3890]) ).
fof(f3890,plain,
( spl0_143
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f288,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3888,plain,
spl0_142,
inference(avatar_split_clause,[],[f285,f3886]) ).
fof(f3886,plain,
( spl0_142
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f285,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3884,plain,
spl0_141,
inference(avatar_split_clause,[],[f283,f3882]) ).
fof(f3882,plain,
( spl0_141
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f283,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3880,plain,
spl0_140,
inference(avatar_split_clause,[],[f282,f3878]) ).
fof(f3878,plain,
( spl0_140
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f282,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3876,plain,
spl0_139,
inference(avatar_split_clause,[],[f281,f3874]) ).
fof(f3874,plain,
( spl0_139
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f281,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3872,plain,
spl0_138,
inference(avatar_split_clause,[],[f280,f3870]) ).
fof(f3870,plain,
( spl0_138
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f280,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3868,plain,
spl0_137,
inference(avatar_split_clause,[],[f279,f3866]) ).
fof(f3866,plain,
( spl0_137
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f279,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3864,plain,
spl0_136,
inference(avatar_split_clause,[],[f278,f3862]) ).
fof(f3862,plain,
( spl0_136
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f278,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3860,plain,
spl0_135,
inference(avatar_split_clause,[],[f277,f3858]) ).
fof(f3858,plain,
( spl0_135
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f277,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3856,plain,
spl0_134,
inference(avatar_split_clause,[],[f276,f3854]) ).
fof(f3854,plain,
( spl0_134
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f276,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3852,plain,
spl0_133,
inference(avatar_split_clause,[],[f275,f3850]) ).
fof(f3850,plain,
( spl0_133
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f275,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3848,plain,
spl0_132,
inference(avatar_split_clause,[],[f274,f3846]) ).
fof(f3846,plain,
( spl0_132
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f274,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3844,plain,
spl0_131,
inference(avatar_split_clause,[],[f272,f3842]) ).
fof(f3842,plain,
( spl0_131
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f272,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3840,plain,
spl0_130,
inference(avatar_split_clause,[],[f271,f3838]) ).
fof(f3838,plain,
( spl0_130
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f271,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3836,plain,
spl0_129,
inference(avatar_split_clause,[],[f270,f3834]) ).
fof(f3834,plain,
( spl0_129
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f270,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3832,plain,
spl0_128,
inference(avatar_split_clause,[],[f269,f3830]) ).
fof(f3830,plain,
( spl0_128
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f269,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3828,plain,
spl0_127,
inference(avatar_split_clause,[],[f268,f3826]) ).
fof(f3826,plain,
( spl0_127
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f268,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3824,plain,
spl0_126,
inference(avatar_split_clause,[],[f267,f3822]) ).
fof(f3822,plain,
( spl0_126
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f267,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3820,plain,
spl0_125,
inference(avatar_split_clause,[],[f266,f3818]) ).
fof(f3818,plain,
( spl0_125
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f266,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3816,plain,
spl0_124,
inference(avatar_split_clause,[],[f264,f3814]) ).
fof(f3814,plain,
( spl0_124
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f264,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3812,plain,
spl0_123,
inference(avatar_split_clause,[],[f263,f3810]) ).
fof(f3810,plain,
( spl0_123
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f263,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3808,plain,
spl0_122,
inference(avatar_split_clause,[],[f260,f3806]) ).
fof(f3806,plain,
( spl0_122
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f260,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3804,plain,
spl0_121,
inference(avatar_split_clause,[],[f259,f3802]) ).
fof(f3802,plain,
( spl0_121
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f259,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3800,plain,
spl0_120,
inference(avatar_split_clause,[],[f258,f3798]) ).
fof(f3798,plain,
( spl0_120
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f258,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3796,plain,
spl0_119,
inference(avatar_split_clause,[],[f257,f3794]) ).
fof(f3794,plain,
( spl0_119
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3792,plain,
spl0_118,
inference(avatar_split_clause,[],[f256,f3790]) ).
fof(f3790,plain,
( spl0_118
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3788,plain,
spl0_117,
inference(avatar_split_clause,[],[f255,f3786]) ).
fof(f3786,plain,
( spl0_117
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f255,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3784,plain,
spl0_116,
inference(avatar_split_clause,[],[f254,f3782]) ).
fof(f3782,plain,
( spl0_116
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f254,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3780,plain,
spl0_115,
inference(avatar_split_clause,[],[f253,f3778]) ).
fof(f3778,plain,
( spl0_115
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f253,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3776,plain,
spl0_114,
inference(avatar_split_clause,[],[f98,f3774]) ).
fof(f3774,plain,
( spl0_114
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3772,plain,
spl0_113,
inference(avatar_split_clause,[],[f66,f3770]) ).
fof(f3770,plain,
( spl0_113
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3768,plain,
spl0_112,
inference(avatar_split_clause,[],[f64,f3766]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3764,plain,
spl0_111,
inference(avatar_split_clause,[],[f40,f3762]) ).
fof(f3762,plain,
( spl0_111
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f40,axiom,
! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3760,plain,
spl0_110,
inference(avatar_split_clause,[],[f39,f3758]) ).
fof(f3758,plain,
( spl0_110
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f39,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3756,plain,
spl0_109,
inference(avatar_split_clause,[],[f23,f3754]) ).
fof(f3754,plain,
( spl0_109
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f23,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3752,plain,
~ spl0_108,
inference(avatar_split_clause,[],[f2732,f3749]) ).
fof(f3749,plain,
( spl0_108
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f2732,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oagent_Odistinct__3_0) ).
fof(f3747,plain,
~ spl0_107,
inference(avatar_split_clause,[],[f2629,f3744]) ).
fof(f3744,plain,
( spl0_107
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3742,plain,
~ spl0_106,
inference(avatar_split_clause,[],[f2310,f3739]) ).
fof(f3739,plain,
( spl0_106
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3737,plain,
spl0_105,
inference(avatar_split_clause,[],[f2303,f3734]) ).
fof(f3734,plain,
( spl0_105
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3732,plain,
spl0_104,
inference(avatar_split_clause,[],[f2290,f3729]) ).
fof(f3729,plain,
( spl0_104
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3727,plain,
~ spl0_103,
inference(avatar_split_clause,[],[f2159,f3724]) ).
fof(f3724,plain,
( spl0_103
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f2159,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3722,plain,
spl0_102,
inference(avatar_split_clause,[],[f1706,f3720]) ).
fof(f3720,plain,
( spl0_102
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1706,axiom,
! [X41] : c_List_Onull(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3718,plain,
spl0_101,
inference(avatar_split_clause,[],[f1551,f3716]) ).
fof(f3716,plain,
( spl0_101
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1551,axiom,
! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3714,plain,
~ spl0_100,
inference(avatar_split_clause,[],[f1370,f3711]) ).
fof(f3711,plain,
( spl0_100
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3709,plain,
~ spl0_99,
inference(avatar_split_clause,[],[f1251,f3706]) ).
fof(f3706,plain,
( spl0_99
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1251,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2_0) ).
fof(f3704,plain,
spl0_98,
inference(avatar_split_clause,[],[f249,f3702]) ).
fof(f3702,plain,
( spl0_98
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3700,plain,
spl0_97,
inference(avatar_split_clause,[],[f248,f3698]) ).
fof(f3698,plain,
( spl0_97
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3696,plain,
spl0_96,
inference(avatar_split_clause,[],[f126,f3693]) ).
fof(f3693,plain,
( spl0_96
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f126,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3691,plain,
spl0_95,
inference(avatar_split_clause,[],[f124,f3688]) ).
fof(f3688,plain,
( spl0_95
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f124,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3686,plain,
spl0_94,
inference(avatar_split_clause,[],[f123,f3684]) ).
fof(f3684,plain,
( spl0_94
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f123,axiom,
! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3682,plain,
spl0_93,
inference(avatar_split_clause,[],[f244,f3679]) ).
fof(f3679,plain,
( spl0_93
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3677,plain,
spl0_92,
inference(avatar_split_clause,[],[f243,f3674]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3672,plain,
spl0_91,
inference(avatar_split_clause,[],[f242,f3669]) ).
fof(f3669,plain,
( spl0_91
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3667,plain,
spl0_90,
inference(avatar_split_clause,[],[f241,f3664]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3662,plain,
spl0_89,
inference(avatar_split_clause,[],[f239,f3659]) ).
fof(f3659,plain,
( spl0_89
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3657,plain,
spl0_88,
inference(avatar_split_clause,[],[f238,f3654]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3652,plain,
spl0_87,
inference(avatar_split_clause,[],[f236,f3649]) ).
fof(f3649,plain,
( spl0_87
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3647,plain,
spl0_86,
inference(avatar_split_clause,[],[f235,f3644]) ).
fof(f3644,plain,
( spl0_86
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3642,plain,
spl0_85,
inference(avatar_split_clause,[],[f234,f3639]) ).
fof(f3639,plain,
( spl0_85
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3637,plain,
spl0_84,
inference(avatar_split_clause,[],[f233,f3634]) ).
fof(f3634,plain,
( spl0_84
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3632,plain,
spl0_83,
inference(avatar_split_clause,[],[f232,f3629]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3627,plain,
spl0_82,
inference(avatar_split_clause,[],[f231,f3624]) ).
fof(f3624,plain,
( spl0_82
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3622,plain,
spl0_81,
inference(avatar_split_clause,[],[f230,f3619]) ).
fof(f3619,plain,
( spl0_81
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3617,plain,
spl0_80,
inference(avatar_split_clause,[],[f229,f3614]) ).
fof(f3614,plain,
( spl0_80
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3612,plain,
spl0_79,
inference(avatar_split_clause,[],[f228,f3609]) ).
fof(f3609,plain,
( spl0_79
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3607,plain,
spl0_78,
inference(avatar_split_clause,[],[f227,f3604]) ).
fof(f3604,plain,
( spl0_78
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3602,plain,
spl0_77,
inference(avatar_split_clause,[],[f226,f3599]) ).
fof(f3599,plain,
( spl0_77
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3597,plain,
spl0_76,
inference(avatar_split_clause,[],[f225,f3594]) ).
fof(f3594,plain,
( spl0_76
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3592,plain,
spl0_75,
inference(avatar_split_clause,[],[f224,f3589]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3587,plain,
spl0_74,
inference(avatar_split_clause,[],[f223,f3584]) ).
fof(f3584,plain,
( spl0_74
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3582,plain,
spl0_73,
inference(avatar_split_clause,[],[f222,f3579]) ).
fof(f3579,plain,
( spl0_73
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3577,plain,
spl0_72,
inference(avatar_split_clause,[],[f221,f3574]) ).
fof(f3574,plain,
( spl0_72
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3572,plain,
spl0_71,
inference(avatar_split_clause,[],[f220,f3569]) ).
fof(f3569,plain,
( spl0_71
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3567,plain,
spl0_70,
inference(avatar_split_clause,[],[f219,f3564]) ).
fof(f3564,plain,
( spl0_70
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3562,plain,
spl0_69,
inference(avatar_split_clause,[],[f218,f3559]) ).
fof(f3559,plain,
( spl0_69
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3557,plain,
spl0_68,
inference(avatar_split_clause,[],[f217,f3554]) ).
fof(f3554,plain,
( spl0_68
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3552,plain,
spl0_67,
inference(avatar_split_clause,[],[f216,f3549]) ).
fof(f3549,plain,
( spl0_67
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3547,plain,
spl0_66,
inference(avatar_split_clause,[],[f215,f3544]) ).
fof(f3544,plain,
( spl0_66
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3542,plain,
spl0_65,
inference(avatar_split_clause,[],[f214,f3539]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3537,plain,
spl0_64,
inference(avatar_split_clause,[],[f213,f3534]) ).
fof(f3534,plain,
( spl0_64
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3532,plain,
spl0_63,
inference(avatar_split_clause,[],[f212,f3529]) ).
fof(f3529,plain,
( spl0_63
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3527,plain,
spl0_62,
inference(avatar_split_clause,[],[f211,f3524]) ).
fof(f3524,plain,
( spl0_62
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3522,plain,
spl0_61,
inference(avatar_split_clause,[],[f210,f3519]) ).
fof(f3519,plain,
( spl0_61
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3517,plain,
spl0_60,
inference(avatar_split_clause,[],[f209,f3514]) ).
fof(f3514,plain,
( spl0_60
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3512,plain,
spl0_59,
inference(avatar_split_clause,[],[f208,f3509]) ).
fof(f3509,plain,
( spl0_59
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3507,plain,
spl0_58,
inference(avatar_split_clause,[],[f203,f3504]) ).
fof(f3504,plain,
( spl0_58
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3502,plain,
spl0_57,
inference(avatar_split_clause,[],[f198,f3499]) ).
fof(f3499,plain,
( spl0_57
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3497,plain,
spl0_56,
inference(avatar_split_clause,[],[f195,f3494]) ).
fof(f3494,plain,
( spl0_56
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3492,plain,
spl0_55,
inference(avatar_split_clause,[],[f194,f3489]) ).
fof(f3489,plain,
( spl0_55
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3487,plain,
spl0_54,
inference(avatar_split_clause,[],[f189,f3484]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3482,plain,
spl0_53,
inference(avatar_split_clause,[],[f186,f3479]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3477,plain,
spl0_52,
inference(avatar_split_clause,[],[f184,f3474]) ).
fof(f3474,plain,
( spl0_52
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3472,plain,
spl0_51,
inference(avatar_split_clause,[],[f183,f3469]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3467,plain,
spl0_50,
inference(avatar_split_clause,[],[f182,f3464]) ).
fof(f3464,plain,
( spl0_50
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3462,plain,
spl0_49,
inference(avatar_split_clause,[],[f181,f3459]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3457,plain,
spl0_48,
inference(avatar_split_clause,[],[f180,f3454]) ).
fof(f3454,plain,
( spl0_48
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f180,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3452,plain,
spl0_47,
inference(avatar_split_clause,[],[f178,f3449]) ).
fof(f3449,plain,
( spl0_47
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f178,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3447,plain,
spl0_46,
inference(avatar_split_clause,[],[f177,f3444]) ).
fof(f3444,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f177,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3442,plain,
spl0_45,
inference(avatar_split_clause,[],[f176,f3439]) ).
fof(f3439,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f176,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3437,plain,
spl0_44,
inference(avatar_split_clause,[],[f175,f3434]) ).
fof(f3434,plain,
( spl0_44
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3432,plain,
spl0_43,
inference(avatar_split_clause,[],[f174,f3429]) ).
fof(f3429,plain,
( spl0_43
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f174,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3427,plain,
spl0_42,
inference(avatar_split_clause,[],[f173,f3424]) ).
fof(f3424,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f173,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3422,plain,
spl0_41,
inference(avatar_split_clause,[],[f172,f3419]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3417,plain,
spl0_40,
inference(avatar_split_clause,[],[f171,f3414]) ).
fof(f3414,plain,
( spl0_40
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3412,plain,
spl0_39,
inference(avatar_split_clause,[],[f170,f3409]) ).
fof(f3409,plain,
( spl0_39
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f170,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3407,plain,
spl0_38,
inference(avatar_split_clause,[],[f169,f3404]) ).
fof(f3404,plain,
( spl0_38
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f169,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3402,plain,
spl0_37,
inference(avatar_split_clause,[],[f168,f3399]) ).
fof(f3399,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f168,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3397,plain,
spl0_36,
inference(avatar_split_clause,[],[f167,f3394]) ).
fof(f3394,plain,
( spl0_36
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f167,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3392,plain,
spl0_35,
inference(avatar_split_clause,[],[f166,f3389]) ).
fof(f3389,plain,
( spl0_35
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f166,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3387,plain,
spl0_34,
inference(avatar_split_clause,[],[f165,f3384]) ).
fof(f3384,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f165,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3382,plain,
spl0_33,
inference(avatar_split_clause,[],[f164,f3379]) ).
fof(f3379,plain,
( spl0_33
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f164,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3377,plain,
spl0_32,
inference(avatar_split_clause,[],[f162,f3374]) ).
fof(f3374,plain,
( spl0_32
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f162,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3372,plain,
spl0_31,
inference(avatar_split_clause,[],[f161,f3369]) ).
fof(f3369,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3367,plain,
spl0_30,
inference(avatar_split_clause,[],[f160,f3364]) ).
fof(f3364,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f160,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3362,plain,
spl0_29,
inference(avatar_split_clause,[],[f159,f3359]) ).
fof(f3359,plain,
( spl0_29
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3357,plain,
spl0_28,
inference(avatar_split_clause,[],[f158,f3354]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3352,plain,
spl0_27,
inference(avatar_split_clause,[],[f157,f3349]) ).
fof(f3349,plain,
( spl0_27
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3347,plain,
spl0_26,
inference(avatar_split_clause,[],[f156,f3344]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3342,plain,
spl0_25,
inference(avatar_split_clause,[],[f155,f3339]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3337,plain,
spl0_24,
inference(avatar_split_clause,[],[f154,f3334]) ).
fof(f3334,plain,
( spl0_24
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3332,plain,
spl0_23,
inference(avatar_split_clause,[],[f153,f3329]) ).
fof(f153,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3327,plain,
spl0_22,
inference(avatar_split_clause,[],[f151,f3324]) ).
fof(f151,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3322,plain,
spl0_21,
inference(avatar_split_clause,[],[f150,f3319]) ).
fof(f3319,plain,
( spl0_21
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3317,plain,
spl0_20,
inference(avatar_split_clause,[],[f149,f3314]) ).
fof(f3314,plain,
( spl0_20
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f149,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3312,plain,
spl0_19,
inference(avatar_split_clause,[],[f148,f3309]) ).
fof(f3309,plain,
( spl0_19
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f148,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3307,plain,
spl0_18,
inference(avatar_split_clause,[],[f147,f3304]) ).
fof(f3304,plain,
( spl0_18
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3302,plain,
spl0_17,
inference(avatar_split_clause,[],[f146,f3299]) ).
fof(f3299,plain,
( spl0_17
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3297,plain,
spl0_16,
inference(avatar_split_clause,[],[f145,f3294]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3292,plain,
spl0_15,
inference(avatar_split_clause,[],[f144,f3289]) ).
fof(f3289,plain,
( spl0_15
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f144,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3287,plain,
spl0_14,
inference(avatar_split_clause,[],[f143,f3284]) ).
fof(f3284,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3282,plain,
spl0_13,
inference(avatar_split_clause,[],[f142,f3279]) ).
fof(f3279,plain,
( spl0_13
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f142,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3277,plain,
spl0_12,
inference(avatar_split_clause,[],[f140,f3274]) ).
fof(f3274,plain,
( spl0_12
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3272,plain,
spl0_11,
inference(avatar_split_clause,[],[f139,f3269]) ).
fof(f3269,plain,
( spl0_11
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f139,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3267,plain,
spl0_10,
inference(avatar_split_clause,[],[f138,f3264]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3262,plain,
spl0_9,
inference(avatar_split_clause,[],[f137,f3259]) ).
fof(f3259,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3257,plain,
spl0_8,
inference(avatar_split_clause,[],[f136,f3254]) ).
fof(f3254,plain,
( spl0_8
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3252,plain,
spl0_7,
inference(avatar_split_clause,[],[f135,f3249]) ).
fof(f3249,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f135,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3247,plain,
spl0_6,
inference(avatar_split_clause,[],[f134,f3244]) ).
fof(f3244,plain,
( spl0_6
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3242,plain,
spl0_5,
inference(avatar_split_clause,[],[f133,f3239]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3237,plain,
spl0_4,
inference(avatar_split_clause,[],[f132,f3234]) ).
fof(f3234,plain,
( spl0_4
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3232,plain,
spl0_3,
inference(avatar_split_clause,[],[f131,f3229]) ).
fof(f3229,plain,
( spl0_3
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3227,plain,
spl0_2,
inference(avatar_split_clause,[],[f130,f3224]) ).
fof(f3224,plain,
( spl0_2
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3222,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f2793,f3219]) ).
fof(f2793,axiom,
~ c_lessequals(c_Message_Oparts(c_Message_Oanalz(v_H)),c_Message_Oparts(v_H),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV256-1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n031.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Apr 30 05:22:13 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (18063)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.45 % (18069)WARNING: value z3 for option sas not known
% 0.20/0.45 % (18069)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)
% 0.20/0.46 % (18068)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.46 % (18067)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.46 % (18070)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.46 % (18071)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)
% 0.20/0.46 % (18072)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.20/0.46 % (18073)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)
% 1.84/0.68 TRYING [1]
% 1.84/0.69 % (18071)First to succeed.
% 1.84/0.72 % (18071)Refutation found. Thanks to Tanya!
% 1.84/0.72 % SZS status Unsatisfiable for theBenchmark
% 1.84/0.72 % SZS output start Proof for theBenchmark
% See solution above
% 2.18/0.75 % (18071)------------------------------
% 2.18/0.75 % (18071)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.18/0.75 % (18071)Termination reason: Refutation
% 2.18/0.75
% 2.18/0.75 % (18071)Memory used [KB]: 7586
% 2.18/0.75 % (18071)Time elapsed: 0.263 s
% 2.18/0.75 % (18071)Instructions burned: 657 (million)
% 2.18/0.75 % (18071)------------------------------
% 2.18/0.75 % (18071)------------------------------
% 2.18/0.75 % (18063)Success in time 0.377 s
%------------------------------------------------------------------------------