TSTP Solution File: ANA042-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ANA042-1 : 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 : n020.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 10:31:27 EDT 2024
% Result : Unsatisfiable 1.29s 0.60s
% Output : Refutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1906
% Syntax : Number of formulae : 2954 (1096 unt; 0 def)
% Number of atoms : 5695 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 4543 (1802 ~;1773 |; 0 &)
% ( 968 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 1045 (1043 usr; 969 prp; 0-3 aty)
% Number of functors : 34 ( 34 usr; 19 con; 0-3 aty)
% Number of variables : 1666 (1666 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8529,plain,
$false,
inference(avatar_sat_refutation,[],[f3207,f3211,f3215,f3220,f3225,f3230,f3235,f3240,f3245,f3250,f3255,f3260,f3265,f3270,f3275,f3280,f3285,f3290,f3295,f3300,f3305,f3310,f3315,f3320,f3325,f3330,f3335,f3340,f3345,f3350,f3355,f3360,f3365,f3370,f3375,f3380,f3385,f3390,f3395,f3400,f3405,f3410,f3415,f3420,f3425,f3430,f3435,f3440,f3445,f3450,f3455,f3460,f3465,f3470,f3475,f3480,f3485,f3490,f3495,f3500,f3505,f3510,f3515,f3520,f3525,f3530,f3535,f3540,f3545,f3550,f3555,f3560,f3565,f3570,f3575,f3580,f3585,f3590,f3595,f3600,f3605,f3610,f3615,f3620,f3625,f3630,f3635,f3640,f3645,f3650,f3655,f3660,f3665,f3670,f3675,f3680,f3685,f3690,f3695,f3700,f3705,f3710,f3715,f3720,f3725,f3730,f3735,f3740,f3745,f3750,f3755,f3760,f3765,f3770,f3774,f3778,f3783,f3788,f3793,f3798,f3803,f3807,f3812,f3817,f3821,f3825,f3829,f3833,f3837,f3842,f3847,f3852,f3856,f3860,f3864,f3869,f3873,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4626,f4630,f4634,f4638,f4642,f4646,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4794,f4798,f4802,f4806,f4810,f4814,f4818,f4822,f4826,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4914,f4918,f4922,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5054,f5058,f5062,f5066,f5070,f5074,f5078,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5118,f5122,f5126,f5130,f5134,f5138,f5142,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5186,f5190,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5246,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5294,f5298,f5302,f5306,f5310,f5314,f5318,f5322,f5326,f5330,f5334,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5490,f5494,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5582,f5586,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f5622,f5626,f5630,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5718,f5722,f5726,f5730,f5734,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5778,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5890,f5894,f5898,f5902,f5906,f5910,f5914,f5918,f5922,f5926,f5930,f5934,f5938,f5942,f5946,f5950,f5954,f5958,f5962,f5966,f5970,f5974,f5978,f5982,f5986,f5990,f5994,f5998,f6002,f6006,f6010,f6014,f6018,f6022,f6026,f6030,f6034,f6038,f6042,f6046,f6050,f6054,f6058,f6062,f6066,f6070,f6074,f6078,f6082,f6086,f6090,f6094,f6098,f6102,f6106,f6110,f6114,f6118,f6122,f6126,f6130,f6134,f6138,f6142,f6146,f6150,f6154,f6158,f6162,f6166,f6170,f6174,f6178,f6182,f6186,f6190,f6194,f6198,f6202,f6206,f6210,f6214,f6218,f6222,f6226,f6230,f6234,f6238,f6242,f6246,f6250,f6254,f6258,f6262,f6266,f6270,f6274,f6278,f6282,f6286,f6290,f6294,f6298,f6302,f6306,f6310,f6314,f6318,f6322,f6326,f6330,f6334,f6338,f6342,f6346,f6350,f6354,f6358,f6362,f6366,f6370,f6374,f6378,f6382,f6386,f6390,f6394,f6398,f6402,f6406,f6410,f6414,f6418,f6422,f6426,f6430,f6434,f6438,f6442,f6446,f6450,f6454,f6458,f6462,f6466,f6470,f6474,f6478,f6482,f6486,f6490,f6494,f6498,f6502,f6506,f6510,f6514,f6518,f6522,f6526,f6530,f6534,f6538,f6542,f6546,f6550,f6554,f6558,f6562,f6566,f6570,f6574,f6578,f6582,f6586,f6590,f6594,f6598,f6602,f6606,f6610,f6614,f6618,f6622,f6626,f6630,f6634,f6638,f6642,f6646,f6650,f6654,f6658,f6662,f6666,f6670,f6674,f6678,f6682,f6686,f6690,f6694,f6698,f6702,f6706,f6710,f6714,f6718,f6722,f6726,f6730,f6734,f6738,f6742,f6746,f6750,f6754,f6758,f6762,f6766,f6770,f6774,f6778,f6782,f6786,f6790,f6794,f6798,f6802,f6806,f6810,f6814,f6818,f6822,f6826,f6830,f6834,f6838,f6842,f6846,f6850,f6854,f6858,f6862,f6866,f6870,f6874,f6878,f6882,f6886,f6890,f6894,f6898,f6902,f6906,f6910,f6914,f6918,f6922,f6926,f6930,f6934,f6938,f6942,f6946,f6950,f6954,f6958,f6962,f6966,f6970,f6974,f6978,f6982,f6986,f6990,f6994,f6998,f7002,f7006,f7010,f7014,f7018,f7022,f7026,f7030,f7034,f7038,f7042,f7046,f7051,f7056,f7060,f7065,f7072,f7077,f7734,f7808,f7833,f7858,f7883,f7905,f7920,f7935,f7950,f7971,f7996,f8060,f8085,f8110,f8135,f8160,f8185,f8210,f8255,f8271,f8286,f8307,f8328,f8343,f8358,f8373,f8398,f8451,f8482,f8507,f8522,f8526,f8528]) ).
fof(f8528,plain,
( ~ spl0_128
| ~ spl0_968 ),
inference(avatar_contradiction_clause,[],[f8527]) ).
fof(f8527,plain,
( $false
| ~ spl0_128
| ~ spl0_968 ),
inference(resolution,[],[f8525,f3832]) ).
fof(f3832,plain,
( ! [X29,X52] : c_lessequals(c_HOL_Oabs(v_f(X29,X52),t_c),c_times(v_x,v_h(X29,X52),t_c),t_c)
| ~ spl0_128 ),
inference(avatar_component_clause,[],[f3831]) ).
fof(f3831,plain,
( spl0_128
<=> ! [X29,X52] : c_lessequals(c_HOL_Oabs(v_f(X29,X52),t_c),c_times(v_x,v_h(X29,X52),t_c),t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f8525,plain,
( ! [X29] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X29),v_xb(X29)),t_c),c_times(X29,v_h(v_xa(X29),v_xb(X29)),t_c),t_c)
| ~ spl0_968 ),
inference(avatar_component_clause,[],[f8524]) ).
fof(f8524,plain,
( spl0_968
<=> ! [X29] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X29),v_xb(X29)),t_c),c_times(X29,v_h(v_xa(X29),v_xb(X29)),t_c),t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f8526,plain,
spl0_968,
inference(avatar_split_clause,[],[f2786,f8524]) ).
fof(f2786,axiom,
! [X29] : ~ c_lessequals(c_HOL_Oabs(v_f(v_xa(X29),v_xb(X29)),t_c),c_times(X29,v_h(v_xa(X29),v_xb(X29)),t_c),t_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f8522,plain,
( spl0_967
| ~ spl0_1
| ~ spl0_636 ),
inference(avatar_split_clause,[],[f7865,f5868,f3204,f8519]) ).
fof(f8519,plain,
( spl0_967
<=> class_Ring__and__Field_Opordered__ring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f3204,plain,
( spl0_1
<=> class_Ring__and__Field_Oordered__idom(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f5868,plain,
( spl0_636
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f7865,plain,
( class_Ring__and__Field_Opordered__ring(t_c)
| ~ spl0_1
| ~ spl0_636 ),
inference(resolution,[],[f5869,f3206]) ).
fof(f3206,plain,
( class_Ring__and__Field_Oordered__idom(t_c)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f3204]) ).
fof(f5869,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) )
| ~ spl0_636 ),
inference(avatar_component_clause,[],[f5868]) ).
fof(f8507,plain,
( spl0_966
| ~ spl0_1
| ~ spl0_635 ),
inference(avatar_split_clause,[],[f7863,f5864,f3204,f8504]) ).
fof(f8504,plain,
( spl0_966
<=> class_Ring__and__Field_Olordered__ring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f5864,plain,
( spl0_635
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f7863,plain,
( class_Ring__and__Field_Olordered__ring(t_c)
| ~ spl0_1
| ~ spl0_635 ),
inference(resolution,[],[f5865,f3206]) ).
fof(f5865,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) )
| ~ spl0_635 ),
inference(avatar_component_clause,[],[f5864]) ).
fof(f8482,plain,
( spl0_965
| ~ spl0_1
| ~ spl0_634 ),
inference(avatar_split_clause,[],[f7861,f5860,f3204,f8479]) ).
fof(f8479,plain,
( spl0_965
<=> class_Ring__and__Field_Oordered__ring__strict(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f5860,plain,
( spl0_634
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f7861,plain,
( class_Ring__and__Field_Oordered__ring__strict(t_c)
| ~ spl0_1
| ~ spl0_634 ),
inference(resolution,[],[f5861,f3206]) ).
fof(f5861,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) )
| ~ spl0_634 ),
inference(avatar_component_clause,[],[f5860]) ).
fof(f8451,plain,
( spl0_964
| ~ spl0_1
| ~ spl0_633 ),
inference(avatar_split_clause,[],[f7859,f5856,f3204,f8448]) ).
fof(f8448,plain,
( spl0_964
<=> class_Ring__and__Field_Oaxclass__abs__if(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f5856,plain,
( spl0_633
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f7859,plain,
( class_Ring__and__Field_Oaxclass__abs__if(t_c)
| ~ spl0_1
| ~ spl0_633 ),
inference(resolution,[],[f5857,f3206]) ).
fof(f5857,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) )
| ~ spl0_633 ),
inference(avatar_component_clause,[],[f5856]) ).
fof(f8398,plain,
( spl0_963
| ~ spl0_1
| ~ spl0_632 ),
inference(avatar_split_clause,[],[f7852,f5852,f3204,f8395]) ).
fof(f8395,plain,
( spl0_963
<=> class_Orderings_Oord(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f5852,plain,
( spl0_632
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f7852,plain,
( class_Orderings_Oord(t_c)
| ~ spl0_1
| ~ spl0_632 ),
inference(resolution,[],[f5853,f3206]) ).
fof(f5853,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) )
| ~ spl0_632 ),
inference(avatar_component_clause,[],[f5852]) ).
fof(f8373,plain,
( spl0_962
| ~ spl0_1
| ~ spl0_631 ),
inference(avatar_split_clause,[],[f7850,f5848,f3204,f8370]) ).
fof(f8370,plain,
( spl0_962
<=> class_Orderings_Oorder(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f5848,plain,
( spl0_631
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f7850,plain,
( class_Orderings_Oorder(t_c)
| ~ spl0_1
| ~ spl0_631 ),
inference(resolution,[],[f5849,f3206]) ).
fof(f5849,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) )
| ~ spl0_631 ),
inference(avatar_component_clause,[],[f5848]) ).
fof(f8358,plain,
( spl0_961
| ~ spl0_1
| ~ spl0_630 ),
inference(avatar_split_clause,[],[f7848,f5844,f3204,f8355]) ).
fof(f8355,plain,
( spl0_961
<=> class_OrderedGroup_Opordered__ab__semigroup__add(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f5844,plain,
( spl0_630
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f7848,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add(t_c)
| ~ spl0_1
| ~ spl0_630 ),
inference(resolution,[],[f5845,f3206]) ).
fof(f5845,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) )
| ~ spl0_630 ),
inference(avatar_component_clause,[],[f5844]) ).
fof(f8343,plain,
( spl0_960
| ~ spl0_1
| ~ spl0_629 ),
inference(avatar_split_clause,[],[f7846,f5840,f3204,f8340]) ).
fof(f8340,plain,
( spl0_960
<=> class_Ring__and__Field_Opordered__semiring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f5840,plain,
( spl0_629
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f7846,plain,
( class_Ring__and__Field_Opordered__semiring(t_c)
| ~ spl0_1
| ~ spl0_629 ),
inference(resolution,[],[f5841,f3206]) ).
fof(f5841,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) )
| ~ spl0_629 ),
inference(avatar_component_clause,[],[f5840]) ).
fof(f8328,plain,
( spl0_959
| ~ spl0_1
| ~ spl0_628 ),
inference(avatar_split_clause,[],[f7844,f5836,f3204,f8325]) ).
fof(f8325,plain,
( spl0_959
<=> class_Ring__and__Field_Opordered__comm__semiring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f5836,plain,
( spl0_628
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f7844,plain,
( class_Ring__and__Field_Opordered__comm__semiring(t_c)
| ~ spl0_1
| ~ spl0_628 ),
inference(resolution,[],[f5837,f3206]) ).
fof(f5837,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) )
| ~ spl0_628 ),
inference(avatar_component_clause,[],[f5836]) ).
fof(f8307,plain,
( spl0_958
| ~ spl0_1
| ~ spl0_627 ),
inference(avatar_split_clause,[],[f7842,f5832,f3204,f8304]) ).
fof(f8304,plain,
( spl0_958
<=> class_Ring__and__Field_Opordered__cancel__semiring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f5832,plain,
( spl0_627
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f7842,plain,
( class_Ring__and__Field_Opordered__cancel__semiring(t_c)
| ~ spl0_1
| ~ spl0_627 ),
inference(resolution,[],[f5833,f3206]) ).
fof(f5833,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) )
| ~ spl0_627 ),
inference(avatar_component_clause,[],[f5832]) ).
fof(f8286,plain,
( spl0_957
| ~ spl0_1
| ~ spl0_625 ),
inference(avatar_split_clause,[],[f7838,f5824,f3204,f8283]) ).
fof(f8283,plain,
( spl0_957
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f5824,plain,
( spl0_625
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f7838,plain,
( class_Ring__and__Field_Opordered__cancel__comm__semiring(t_c)
| ~ spl0_1
| ~ spl0_625 ),
inference(resolution,[],[f5825,f3206]) ).
fof(f5825,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) )
| ~ spl0_625 ),
inference(avatar_component_clause,[],[f5824]) ).
fof(f8271,plain,
( spl0_956
| ~ spl0_1
| ~ spl0_624 ),
inference(avatar_split_clause,[],[f7836,f5820,f3204,f8268]) ).
fof(f8268,plain,
( spl0_956
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f5820,plain,
( spl0_624
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f7836,plain,
( class_OrderedGroup_Opordered__cancel__ab__semigroup__add(t_c)
| ~ spl0_1
| ~ spl0_624 ),
inference(resolution,[],[f5821,f3206]) ).
fof(f5821,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) )
| ~ spl0_624 ),
inference(avatar_component_clause,[],[f5820]) ).
fof(f8255,plain,
( spl0_955
| ~ spl0_1
| ~ spl0_623 ),
inference(avatar_split_clause,[],[f7834,f5816,f3204,f8252]) ).
fof(f8252,plain,
( spl0_955
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f5816,plain,
( spl0_623
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f7834,plain,
( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(t_c)
| ~ spl0_1
| ~ spl0_623 ),
inference(resolution,[],[f5817,f3206]) ).
fof(f5817,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) )
| ~ spl0_623 ),
inference(avatar_component_clause,[],[f5816]) ).
fof(f8210,plain,
( spl0_954
| ~ spl0_1
| ~ spl0_622 ),
inference(avatar_split_clause,[],[f7827,f5812,f3204,f8207]) ).
fof(f8207,plain,
( spl0_954
<=> class_LOrder_Omeet__semilorder(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f5812,plain,
( spl0_622
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f7827,plain,
( class_LOrder_Omeet__semilorder(t_c)
| ~ spl0_1
| ~ spl0_622 ),
inference(resolution,[],[f5813,f3206]) ).
fof(f5813,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) )
| ~ spl0_622 ),
inference(avatar_component_clause,[],[f5812]) ).
fof(f8185,plain,
( spl0_953
| ~ spl0_1
| ~ spl0_621 ),
inference(avatar_split_clause,[],[f7825,f5808,f3204,f8182]) ).
fof(f8182,plain,
( spl0_953
<=> class_LOrder_Ojoin__semilorder(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f5808,plain,
( spl0_621
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f7825,plain,
( class_LOrder_Ojoin__semilorder(t_c)
| ~ spl0_1
| ~ spl0_621 ),
inference(resolution,[],[f5809,f3206]) ).
fof(f5809,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) )
| ~ spl0_621 ),
inference(avatar_component_clause,[],[f5808]) ).
fof(f8160,plain,
( spl0_952
| ~ spl0_1
| ~ spl0_620 ),
inference(avatar_split_clause,[],[f7823,f5804,f3204,f8157]) ).
fof(f8157,plain,
( spl0_952
<=> class_LOrder_Olorder(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f5804,plain,
( spl0_620
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f7823,plain,
( class_LOrder_Olorder(t_c)
| ~ spl0_1
| ~ spl0_620 ),
inference(resolution,[],[f5805,f3206]) ).
fof(f5805,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) )
| ~ spl0_620 ),
inference(avatar_component_clause,[],[f5804]) ).
fof(f8135,plain,
( spl0_951
| ~ spl0_1
| ~ spl0_619 ),
inference(avatar_split_clause,[],[f7821,f5800,f3204,f8132]) ).
fof(f8132,plain,
( spl0_951
<=> class_Orderings_Olinorder(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f5800,plain,
( spl0_619
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f7821,plain,
( class_Orderings_Olinorder(t_c)
| ~ spl0_1
| ~ spl0_619 ),
inference(resolution,[],[f5801,f3206]) ).
fof(f5801,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) )
| ~ spl0_619 ),
inference(avatar_component_clause,[],[f5800]) ).
fof(f8110,plain,
( spl0_950
| ~ spl0_1
| ~ spl0_618 ),
inference(avatar_split_clause,[],[f7819,f5796,f3204,f8107]) ).
fof(f8107,plain,
( spl0_950
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f5796,plain,
( spl0_618
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f7819,plain,
( class_OrderedGroup_Oordered__cancel__ab__semigroup__add(t_c)
| ~ spl0_1
| ~ spl0_618 ),
inference(resolution,[],[f5797,f3206]) ).
fof(f5797,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) )
| ~ spl0_618 ),
inference(avatar_component_clause,[],[f5796]) ).
fof(f8085,plain,
( spl0_949
| ~ spl0_1
| ~ spl0_617 ),
inference(avatar_split_clause,[],[f7817,f5792,f3204,f8082]) ).
fof(f8082,plain,
( spl0_949
<=> class_Ring__and__Field_Oordered__semiring__strict(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f5792,plain,
( spl0_617
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f7817,plain,
( class_Ring__and__Field_Oordered__semiring__strict(t_c)
| ~ spl0_1
| ~ spl0_617 ),
inference(resolution,[],[f5793,f3206]) ).
fof(f5793,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) )
| ~ spl0_617 ),
inference(avatar_component_clause,[],[f5792]) ).
fof(f8060,plain,
( spl0_948
| ~ spl0_1
| ~ spl0_616 ),
inference(avatar_split_clause,[],[f7815,f5788,f3204,f8057]) ).
fof(f8057,plain,
( spl0_948
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f5788,plain,
( spl0_616
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f7815,plain,
( class_Ring__and__Field_Oordered__comm__semiring__strict(t_c)
| ~ spl0_1
| ~ spl0_616 ),
inference(resolution,[],[f5789,f3206]) ).
fof(f5789,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) )
| ~ spl0_616 ),
inference(avatar_component_clause,[],[f5788]) ).
fof(f7996,plain,
( spl0_947
| ~ spl0_1
| ~ spl0_602 ),
inference(avatar_split_clause,[],[f7753,f5732,f3204,f7993]) ).
fof(f7993,plain,
( spl0_947
<=> class_Ring__and__Field_Osemiring__0__cancel(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f5732,plain,
( spl0_602
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f7753,plain,
( class_Ring__and__Field_Osemiring__0__cancel(t_c)
| ~ spl0_1
| ~ spl0_602 ),
inference(resolution,[],[f5733,f3206]) ).
fof(f5733,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) )
| ~ spl0_602 ),
inference(avatar_component_clause,[],[f5732]) ).
fof(f7971,plain,
( spl0_946
| ~ spl0_1
| ~ spl0_601 ),
inference(avatar_split_clause,[],[f7751,f5728,f3204,f7968]) ).
fof(f7968,plain,
( spl0_946
<=> class_OrderedGroup_Oab__semigroup__mult(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f5728,plain,
( spl0_601
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f7751,plain,
( class_OrderedGroup_Oab__semigroup__mult(t_c)
| ~ spl0_1
| ~ spl0_601 ),
inference(resolution,[],[f5729,f3206]) ).
fof(f5729,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) )
| ~ spl0_601 ),
inference(avatar_component_clause,[],[f5728]) ).
fof(f7950,plain,
( spl0_945
| ~ spl0_1
| ~ spl0_600 ),
inference(avatar_split_clause,[],[f7749,f5724,f3204,f7947]) ).
fof(f7947,plain,
( spl0_945
<=> class_Ring__and__Field_Ocomm__semiring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f5724,plain,
( spl0_600
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f7749,plain,
( class_Ring__and__Field_Ocomm__semiring(t_c)
| ~ spl0_1
| ~ spl0_600 ),
inference(resolution,[],[f5725,f3206]) ).
fof(f5725,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) )
| ~ spl0_600 ),
inference(avatar_component_clause,[],[f5724]) ).
fof(f7935,plain,
( spl0_944
| ~ spl0_1
| ~ spl0_599 ),
inference(avatar_split_clause,[],[f7747,f5720,f3204,f7932]) ).
fof(f7932,plain,
( spl0_944
<=> class_Ring__and__Field_Ocomm__semiring__0(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f5720,plain,
( spl0_599
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f7747,plain,
( class_Ring__and__Field_Ocomm__semiring__0(t_c)
| ~ spl0_1
| ~ spl0_599 ),
inference(resolution,[],[f5721,f3206]) ).
fof(f5721,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) )
| ~ spl0_599 ),
inference(avatar_component_clause,[],[f5720]) ).
fof(f7920,plain,
( spl0_943
| ~ spl0_1
| ~ spl0_598 ),
inference(avatar_split_clause,[],[f7745,f5716,f3204,f7917]) ).
fof(f7917,plain,
( spl0_943
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f5716,plain,
( spl0_598
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f7745,plain,
( class_Ring__and__Field_Ocomm__semiring__0__cancel(t_c)
| ~ spl0_1
| ~ spl0_598 ),
inference(resolution,[],[f5717,f3206]) ).
fof(f5717,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) )
| ~ spl0_598 ),
inference(avatar_component_clause,[],[f5716]) ).
fof(f7905,plain,
( spl0_942
| ~ spl0_1
| ~ spl0_597 ),
inference(avatar_split_clause,[],[f7743,f5712,f3204,f7902]) ).
fof(f7902,plain,
( spl0_942
<=> class_HOL_Oone(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f5712,plain,
( spl0_597
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f7743,plain,
( class_HOL_Oone(t_c)
| ~ spl0_1
| ~ spl0_597 ),
inference(resolution,[],[f5713,f3206]) ).
fof(f5713,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) )
| ~ spl0_597 ),
inference(avatar_component_clause,[],[f5712]) ).
fof(f7883,plain,
( spl0_941
| ~ spl0_1
| ~ spl0_596 ),
inference(avatar_split_clause,[],[f7741,f5708,f3204,f7880]) ).
fof(f7880,plain,
( spl0_941
<=> class_OrderedGroup_Omonoid__mult(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f5708,plain,
( spl0_596
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f7741,plain,
( class_OrderedGroup_Omonoid__mult(t_c)
| ~ spl0_1
| ~ spl0_596 ),
inference(resolution,[],[f5709,f3206]) ).
fof(f5709,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) )
| ~ spl0_596 ),
inference(avatar_component_clause,[],[f5708]) ).
fof(f7858,plain,
( spl0_940
| ~ spl0_1
| ~ spl0_595 ),
inference(avatar_split_clause,[],[f7739,f5704,f3204,f7855]) ).
fof(f7855,plain,
( spl0_940
<=> class_Ring__and__Field_Oaxclass__0__neq__1(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f5704,plain,
( spl0_595
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f7739,plain,
( class_Ring__and__Field_Oaxclass__0__neq__1(t_c)
| ~ spl0_1
| ~ spl0_595 ),
inference(resolution,[],[f5705,f3206]) ).
fof(f5705,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) )
| ~ spl0_595 ),
inference(avatar_component_clause,[],[f5704]) ).
fof(f7833,plain,
( spl0_939
| ~ spl0_1
| ~ spl0_594 ),
inference(avatar_split_clause,[],[f7737,f5700,f3204,f7830]) ).
fof(f7830,plain,
( spl0_939
<=> class_Ring__and__Field_Osemiring__1(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f5700,plain,
( spl0_594
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f7737,plain,
( class_Ring__and__Field_Osemiring__1(t_c)
| ~ spl0_1
| ~ spl0_594 ),
inference(resolution,[],[f5701,f3206]) ).
fof(f5701,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) )
| ~ spl0_594 ),
inference(avatar_component_clause,[],[f5700]) ).
fof(f7808,plain,
( spl0_938
| ~ spl0_1
| ~ spl0_593 ),
inference(avatar_split_clause,[],[f7735,f5696,f3204,f7805]) ).
fof(f7805,plain,
( spl0_938
<=> class_Ring__and__Field_Ocomm__ring(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f5696,plain,
( spl0_593
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f7735,plain,
( class_Ring__and__Field_Ocomm__ring(t_c)
| ~ spl0_1
| ~ spl0_593 ),
inference(resolution,[],[f5697,f3206]) ).
fof(f5697,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) )
| ~ spl0_593 ),
inference(avatar_component_clause,[],[f5696]) ).
fof(f7734,plain,
( spl0_937
| ~ spl0_1
| ~ spl0_592 ),
inference(avatar_split_clause,[],[f7728,f5692,f3204,f7731]) ).
fof(f7731,plain,
( spl0_937
<=> class_Ring__and__Field_Ocomm__ring__1(t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f5692,plain,
( spl0_592
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f7728,plain,
( class_Ring__and__Field_Ocomm__ring__1(t_c)
| ~ spl0_1
| ~ spl0_592 ),
inference(resolution,[],[f5693,f3206]) ).
fof(f5693,plain,
( ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) )
| ~ spl0_592 ),
inference(avatar_component_clause,[],[f5692]) ).
fof(f7077,plain,
( ~ spl0_936
| ~ spl0_131
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f7067,f3854,f3844,f7074]) ).
fof(f7074,plain,
( spl0_936
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f3844,plain,
( spl0_131
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f3854,plain,
( spl0_133
<=> ! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f7067,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_131
| ~ spl0_133 ),
inference(superposition,[],[f3855,f3846]) ).
fof(f3846,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_131 ),
inference(avatar_component_clause,[],[f3844]) ).
fof(f3855,plain,
( ! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint)
| ~ spl0_133 ),
inference(avatar_component_clause,[],[f3854]) ).
fof(f7072,plain,
( ~ spl0_935
| ~ spl0_130
| ~ spl0_133 ),
inference(avatar_split_clause,[],[f7066,f3854,f3839,f7069]) ).
fof(f7069,plain,
( spl0_935
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f3839,plain,
( spl0_130
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f7066,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_130
| ~ spl0_133 ),
inference(superposition,[],[f3855,f3841]) ).
fof(f3841,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_130 ),
inference(avatar_component_clause,[],[f3839]) ).
fof(f7065,plain,
spl0_934,
inference(avatar_split_clause,[],[f3031,f7062]) ).
fof(f7062,plain,
( spl0_934
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f3031,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f380,f358]) ).
fof(f358,axiom,
! [X38] : c_1 = c_Nat_Opower(X38,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f380,axiom,
! [X12] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X12,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f7060,plain,
spl0_933,
inference(avatar_split_clause,[],[f3012,f7058]) ).
fof(f7058,plain,
( spl0_933
<=> ! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f3012,plain,
! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat),
inference(forward_demodulation,[],[f2796,f2792]) ).
fof(f2792,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f910,f1438]) ).
fof(f1438,axiom,
! [X36] : c_Suc(X36) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X36,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f910,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2796,plain,
! [X9] : c_Divides_Oop_Advd(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X9,tc_nat),
inference(definition_unfolding,[],[f1645,f1438]) ).
fof(f1645,axiom,
! [X9] : c_Divides_Oop_Advd(c_Suc(c_0),X9,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__left_0) ).
fof(f7056,plain,
spl0_932,
inference(avatar_split_clause,[],[f3010,f7053]) ).
fof(f7053,plain,
( spl0_932
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f3010,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f271,f268]) ).
fof(f268,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f271,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_1) ).
fof(f7051,plain,
spl0_931,
inference(avatar_split_clause,[],[f3009,f7048]) ).
fof(f7048,plain,
( spl0_931
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f3009,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2794,f2792]) ).
fof(f2794,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f238,f1438]) ).
fof(f238,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f7046,plain,
spl0_930,
inference(avatar_split_clause,[],[f2780,f7044]) ).
fof(f7044,plain,
( spl0_930
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f2780,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f7042,plain,
spl0_929,
inference(avatar_split_clause,[],[f2779,f7040]) ).
fof(f7040,plain,
( spl0_929
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f2779,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f7038,plain,
spl0_928,
inference(avatar_split_clause,[],[f2778,f7036]) ).
fof(f7036,plain,
( spl0_928
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f2778,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f7034,plain,
spl0_927,
inference(avatar_split_clause,[],[f2777,f7032]) ).
fof(f7032,plain,
( spl0_927
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f2777,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f7030,plain,
spl0_926,
inference(avatar_split_clause,[],[f2776,f7028]) ).
fof(f7028,plain,
( spl0_926
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f2776,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f7026,plain,
spl0_925,
inference(avatar_split_clause,[],[f2775,f7024]) ).
fof(f7024,plain,
( spl0_925
<=> ! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f2775,axiom,
! [X87] :
( ~ class_Wellfounded__Recursion_Owellorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f7022,plain,
spl0_924,
inference(avatar_split_clause,[],[f2774,f7020]) ).
fof(f7020,plain,
( spl0_924
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f2774,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f7018,plain,
spl0_923,
inference(avatar_split_clause,[],[f2773,f7016]) ).
fof(f7016,plain,
( spl0_923
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f2773,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
fof(f7014,plain,
spl0_922,
inference(avatar_split_clause,[],[f2772,f7012]) ).
fof(f7012,plain,
( spl0_922
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f2772,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
fof(f7010,plain,
spl0_921,
inference(avatar_split_clause,[],[f2771,f7008]) ).
fof(f7008,plain,
( spl0_921
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f2771,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
fof(f7006,plain,
spl0_920,
inference(avatar_split_clause,[],[f2770,f7004]) ).
fof(f7004,plain,
( spl0_920
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f2770,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
fof(f7002,plain,
spl0_919,
inference(avatar_split_clause,[],[f2769,f7000]) ).
fof(f7000,plain,
( spl0_919
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f2769,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f6998,plain,
spl0_918,
inference(avatar_split_clause,[],[f2768,f6996]) ).
fof(f6996,plain,
( spl0_918
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f2768,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f6994,plain,
spl0_917,
inference(avatar_split_clause,[],[f2767,f6992]) ).
fof(f6992,plain,
( spl0_917
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f2767,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f6990,plain,
spl0_916,
inference(avatar_split_clause,[],[f2766,f6988]) ).
fof(f6988,plain,
( spl0_916
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f2766,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f6986,plain,
spl0_915,
inference(avatar_split_clause,[],[f2765,f6984]) ).
fof(f6984,plain,
( spl0_915
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f2765,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f6982,plain,
spl0_914,
inference(avatar_split_clause,[],[f2764,f6980]) ).
fof(f6980,plain,
( spl0_914
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f2764,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f6978,plain,
spl0_913,
inference(avatar_split_clause,[],[f2763,f6976]) ).
fof(f6976,plain,
( spl0_913
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f2763,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
fof(f6974,plain,
spl0_912,
inference(avatar_split_clause,[],[f2762,f6972]) ).
fof(f6972,plain,
( spl0_912
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f2762,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
fof(f6970,plain,
spl0_911,
inference(avatar_split_clause,[],[f2761,f6968]) ).
fof(f6968,plain,
( spl0_911
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f2761,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f6966,plain,
spl0_910,
inference(avatar_split_clause,[],[f2760,f6964]) ).
fof(f6964,plain,
( spl0_910
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f2760,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f6962,plain,
spl0_909,
inference(avatar_split_clause,[],[f2759,f6960]) ).
fof(f6960,plain,
( spl0_909
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f2759,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f6958,plain,
spl0_908,
inference(avatar_split_clause,[],[f2758,f6956]) ).
fof(f6956,plain,
( spl0_908
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f2758,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_9) ).
fof(f6954,plain,
spl0_907,
inference(avatar_split_clause,[],[f2757,f6952]) ).
fof(f6952,plain,
( spl0_907
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f2757,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_8) ).
fof(f6950,plain,
spl0_906,
inference(avatar_split_clause,[],[f2756,f6948]) ).
fof(f6948,plain,
( spl0_906
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f2756,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f6946,plain,
spl0_905,
inference(avatar_split_clause,[],[f2755,f6944]) ).
fof(f6944,plain,
( spl0_905
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f2755,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_6) ).
fof(f6942,plain,
spl0_904,
inference(avatar_split_clause,[],[f2754,f6940]) ).
fof(f6940,plain,
( spl0_904
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f2754,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_5) ).
fof(f6938,plain,
spl0_903,
inference(avatar_split_clause,[],[f2753,f6936]) ).
fof(f6936,plain,
( spl0_903
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f2753,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f6934,plain,
spl0_902,
inference(avatar_split_clause,[],[f2752,f6932]) ).
fof(f6932,plain,
( spl0_902
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f2752,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f6930,plain,
spl0_901,
inference(avatar_split_clause,[],[f2751,f6928]) ).
fof(f6928,plain,
( spl0_901
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f2751,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f6926,plain,
spl0_900,
inference(avatar_split_clause,[],[f2750,f6924]) ).
fof(f6924,plain,
( spl0_900
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f2750,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f6922,plain,
spl0_899,
inference(avatar_split_clause,[],[f2749,f6920]) ).
fof(f6920,plain,
( spl0_899
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f2749,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_10) ).
fof(f6918,plain,
spl0_898,
inference(avatar_split_clause,[],[f2748,f6916]) ).
fof(f6916,plain,
( spl0_898
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f2748,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_1) ).
fof(f6914,plain,
spl0_897,
inference(avatar_split_clause,[],[f2747,f6912]) ).
fof(f6912,plain,
( spl0_897
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f2747,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f6910,plain,
spl0_896,
inference(avatar_split_clause,[],[f2746,f6908]) ).
fof(f6908,plain,
( spl0_896
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f2746,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f6906,plain,
spl0_895,
inference(avatar_split_clause,[],[f2745,f6904]) ).
fof(f6904,plain,
( spl0_895
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f2745,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
fof(f6902,plain,
spl0_894,
inference(avatar_split_clause,[],[f2744,f6900]) ).
fof(f6900,plain,
( spl0_894
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f2744,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
fof(f6898,plain,
spl0_893,
inference(avatar_split_clause,[],[f2743,f6896]) ).
fof(f6896,plain,
( spl0_893
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f2743,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
fof(f6894,plain,
spl0_892,
inference(avatar_split_clause,[],[f2742,f6892]) ).
fof(f6892,plain,
( spl0_892
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f2742,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
fof(f6890,plain,
spl0_891,
inference(avatar_split_clause,[],[f2741,f6888]) ).
fof(f6888,plain,
( spl0_891
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f2741,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f6886,plain,
spl0_890,
inference(avatar_split_clause,[],[f2740,f6884]) ).
fof(f6884,plain,
( spl0_890
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f2740,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
fof(f6882,plain,
spl0_889,
inference(avatar_split_clause,[],[f2739,f6880]) ).
fof(f6880,plain,
( spl0_889
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f2739,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
fof(f6878,plain,
spl0_888,
inference(avatar_split_clause,[],[f2738,f6876]) ).
fof(f6876,plain,
( spl0_888
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f2738,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f6874,plain,
spl0_887,
inference(avatar_split_clause,[],[f2737,f6872]) ).
fof(f6872,plain,
( spl0_887
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f2737,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f6870,plain,
spl0_886,
inference(avatar_split_clause,[],[f2736,f6868]) ).
fof(f6868,plain,
( spl0_886
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f2736,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f6866,plain,
spl0_885,
inference(avatar_split_clause,[],[f2735,f6864]) ).
fof(f6864,plain,
( spl0_885
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f2735,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_7) ).
fof(f6862,plain,
spl0_884,
inference(avatar_split_clause,[],[f2734,f6860]) ).
fof(f6860,plain,
( spl0_884
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f2734,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f6858,plain,
spl0_883,
inference(avatar_split_clause,[],[f2733,f6856]) ).
fof(f6856,plain,
( spl0_883
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f2733,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_5) ).
fof(f6854,plain,
spl0_882,
inference(avatar_split_clause,[],[f2732,f6852]) ).
fof(f6852,plain,
( spl0_882
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f2732,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_4) ).
fof(f6850,plain,
spl0_881,
inference(avatar_split_clause,[],[f2731,f6848]) ).
fof(f6848,plain,
( spl0_881
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f2731,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_3) ).
fof(f6846,plain,
spl0_880,
inference(avatar_split_clause,[],[f2730,f6844]) ).
fof(f6844,plain,
( spl0_880
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f2730,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_2) ).
fof(f6842,plain,
spl0_879,
inference(avatar_split_clause,[],[f2729,f6840]) ).
fof(f6840,plain,
( spl0_879
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f2729,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_1) ).
fof(f6838,plain,
spl0_878,
inference(avatar_split_clause,[],[f2728,f6836]) ).
fof(f6836,plain,
( spl0_878
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f2728,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f6834,plain,
spl0_877,
inference(avatar_split_clause,[],[f2727,f6832]) ).
fof(f6832,plain,
( spl0_877
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f2727,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_4) ).
fof(f6830,plain,
spl0_876,
inference(avatar_split_clause,[],[f2726,f6828]) ).
fof(f6828,plain,
( spl0_876
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2726,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_3) ).
fof(f6826,plain,
spl0_875,
inference(avatar_split_clause,[],[f2725,f6824]) ).
fof(f6824,plain,
( spl0_875
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f2725,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_2) ).
fof(f6822,plain,
spl0_874,
inference(avatar_split_clause,[],[f2724,f6820]) ).
fof(f6820,plain,
( spl0_874
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f2724,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_1) ).
fof(f6818,plain,
spl0_873,
inference(avatar_split_clause,[],[f2723,f6816]) ).
fof(f6816,plain,
( spl0_873
<=> ! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f2723,axiom,
! [X87] :
( ~ class_Ring__and__Field_Osemiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring_0) ).
fof(f6814,plain,
spl0_872,
inference(avatar_split_clause,[],[f2722,f6812]) ).
fof(f6812,plain,
( spl0_872
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2722,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_9) ).
fof(f6810,plain,
spl0_871,
inference(avatar_split_clause,[],[f2721,f6808]) ).
fof(f6808,plain,
( spl0_871
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f2721,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_8) ).
fof(f6806,plain,
spl0_870,
inference(avatar_split_clause,[],[f2720,f6804]) ).
fof(f6804,plain,
( spl0_870
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f2720,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f6802,plain,
spl0_869,
inference(avatar_split_clause,[],[f2719,f6800]) ).
fof(f6800,plain,
( spl0_869
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f2719,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f6798,plain,
spl0_868,
inference(avatar_split_clause,[],[f2718,f6796]) ).
fof(f6796,plain,
( spl0_868
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f2718,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f6794,plain,
spl0_867,
inference(avatar_split_clause,[],[f2717,f6792]) ).
fof(f6792,plain,
( spl0_867
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f2717,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f6790,plain,
spl0_866,
inference(avatar_split_clause,[],[f2716,f6788]) ).
fof(f6788,plain,
( spl0_866
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f2716,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f6786,plain,
spl0_865,
inference(avatar_split_clause,[],[f2715,f6784]) ).
fof(f6784,plain,
( spl0_865
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f2715,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_2) ).
fof(f6782,plain,
spl0_864,
inference(avatar_split_clause,[],[f2714,f6780]) ).
fof(f6780,plain,
( spl0_864
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f2714,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f6778,plain,
spl0_863,
inference(avatar_split_clause,[],[f2713,f6776]) ).
fof(f6776,plain,
( spl0_863
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f2713,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f6774,plain,
spl0_862,
inference(avatar_split_clause,[],[f2712,f6772]) ).
fof(f6772,plain,
( spl0_862
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f2712,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f6770,plain,
spl0_861,
inference(avatar_split_clause,[],[f2711,f6768]) ).
fof(f6768,plain,
( spl0_861
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f2711,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f6766,plain,
spl0_860,
inference(avatar_split_clause,[],[f2710,f6764]) ).
fof(f6764,plain,
( spl0_860
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f2710,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f6762,plain,
spl0_859,
inference(avatar_split_clause,[],[f2709,f6760]) ).
fof(f6760,plain,
( spl0_859
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f2709,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_14) ).
fof(f6758,plain,
spl0_858,
inference(avatar_split_clause,[],[f2708,f6756]) ).
fof(f6756,plain,
( spl0_858
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f2708,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_13) ).
fof(f6754,plain,
spl0_857,
inference(avatar_split_clause,[],[f2707,f6752]) ).
fof(f6752,plain,
( spl0_857
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f2707,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_12) ).
fof(f6750,plain,
spl0_856,
inference(avatar_split_clause,[],[f2706,f6748]) ).
fof(f6748,plain,
( spl0_856
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f2706,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_11) ).
fof(f6746,plain,
spl0_855,
inference(avatar_split_clause,[],[f2705,f6744]) ).
fof(f6744,plain,
( spl0_855
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f2705,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f6742,plain,
spl0_854,
inference(avatar_split_clause,[],[f2704,f6740]) ).
fof(f6740,plain,
( spl0_854
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f2704,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f6738,plain,
spl0_853,
inference(avatar_split_clause,[],[f2703,f6736]) ).
fof(f6736,plain,
( spl0_853
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f2703,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring__1(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f6734,plain,
spl0_852,
inference(avatar_split_clause,[],[f2702,f6732]) ).
fof(f6732,plain,
( spl0_852
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f2702,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_9) ).
fof(f6730,plain,
spl0_851,
inference(avatar_split_clause,[],[f2701,f6728]) ).
fof(f6728,plain,
( spl0_851
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f2701,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f6726,plain,
spl0_850,
inference(avatar_split_clause,[],[f2700,f6724]) ).
fof(f6724,plain,
( spl0_850
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f2700,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_7) ).
fof(f6722,plain,
spl0_849,
inference(avatar_split_clause,[],[f2699,f6720]) ).
fof(f6720,plain,
( spl0_849
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f2699,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f6718,plain,
spl0_848,
inference(avatar_split_clause,[],[f2698,f6716]) ).
fof(f6716,plain,
( spl0_848
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f2698,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_5) ).
fof(f6714,plain,
spl0_847,
inference(avatar_split_clause,[],[f2697,f6712]) ).
fof(f6712,plain,
( spl0_847
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f2697,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_4) ).
fof(f6710,plain,
spl0_846,
inference(avatar_split_clause,[],[f2696,f6708]) ).
fof(f6708,plain,
( spl0_846
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f2696,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_3) ).
fof(f6706,plain,
spl0_845,
inference(avatar_split_clause,[],[f2695,f6704]) ).
fof(f6704,plain,
( spl0_845
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f2695,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_2) ).
fof(f6702,plain,
spl0_844,
inference(avatar_split_clause,[],[f2694,f6700]) ).
fof(f6700,plain,
( spl0_844
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f2694,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f6698,plain,
spl0_843,
inference(avatar_split_clause,[],[f2693,f6696]) ).
fof(f6696,plain,
( spl0_843
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f2693,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f6694,plain,
spl0_842,
inference(avatar_split_clause,[],[f2692,f6692]) ).
fof(f6692,plain,
( spl0_842
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f2692,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f6690,plain,
spl0_841,
inference(avatar_split_clause,[],[f2691,f6688]) ).
fof(f6688,plain,
( spl0_841
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f2691,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f6686,plain,
spl0_840,
inference(avatar_split_clause,[],[f2690,f6684]) ).
fof(f6684,plain,
( spl0_840
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f2690,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_1) ).
fof(f6682,plain,
spl0_839,
inference(avatar_split_clause,[],[f2689,f6680]) ).
fof(f6680,plain,
( spl0_839
<=> ! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f2689,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f6678,plain,
spl0_838,
inference(avatar_split_clause,[],[f2688,f6676]) ).
fof(f6676,plain,
( spl0_838
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f2688,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f6674,plain,
spl0_837,
inference(avatar_split_clause,[],[f2687,f6672]) ).
fof(f6672,plain,
( spl0_837
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f2687,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_8) ).
fof(f6670,plain,
spl0_836,
inference(avatar_split_clause,[],[f2686,f6668]) ).
fof(f6668,plain,
( spl0_836
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f2686,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_7) ).
fof(f6666,plain,
spl0_835,
inference(avatar_split_clause,[],[f2685,f6664]) ).
fof(f6664,plain,
( spl0_835
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f2685,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_6) ).
fof(f6662,plain,
spl0_834,
inference(avatar_split_clause,[],[f2684,f6660]) ).
fof(f6660,plain,
( spl0_834
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f2684,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_5) ).
fof(f6658,plain,
spl0_833,
inference(avatar_split_clause,[],[f2683,f6656]) ).
fof(f6656,plain,
( spl0_833
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f2683,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f6654,plain,
spl0_832,
inference(avatar_split_clause,[],[f2682,f6652]) ).
fof(f6652,plain,
( spl0_832
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f2682,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_3) ).
fof(f6650,plain,
spl0_831,
inference(avatar_split_clause,[],[f2681,f6648]) ).
fof(f6648,plain,
( spl0_831
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f2681,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_2) ).
fof(f6646,plain,
spl0_830,
inference(avatar_split_clause,[],[f2680,f6644]) ).
fof(f6644,plain,
( spl0_830
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f2680,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f6642,plain,
spl0_829,
inference(avatar_split_clause,[],[f2679,f6640]) ).
fof(f6640,plain,
( spl0_829
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f2679,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f6638,plain,
spl0_828,
inference(avatar_split_clause,[],[f2678,f6636]) ).
fof(f6636,plain,
( spl0_828
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f2678,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f6634,plain,
spl0_827,
inference(avatar_split_clause,[],[f2677,f6632]) ).
fof(f6632,plain,
( spl0_827
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f2677,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f6630,plain,
spl0_826,
inference(avatar_split_clause,[],[f2676,f6628]) ).
fof(f6628,plain,
( spl0_826
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f2676,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_9) ).
fof(f6626,plain,
spl0_825,
inference(avatar_split_clause,[],[f2675,f6624]) ).
fof(f6624,plain,
( spl0_825
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f2675,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_8) ).
fof(f6622,plain,
spl0_824,
inference(avatar_split_clause,[],[f2674,f6620]) ).
fof(f6620,plain,
( spl0_824
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f2674,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f6618,plain,
spl0_823,
inference(avatar_split_clause,[],[f2673,f6616]) ).
fof(f6616,plain,
( spl0_823
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f2673,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f6614,plain,
spl0_822,
inference(avatar_split_clause,[],[f2672,f6612]) ).
fof(f6612,plain,
( spl0_822
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f2672,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f6610,plain,
spl0_821,
inference(avatar_split_clause,[],[f2671,f6608]) ).
fof(f6608,plain,
( spl0_821
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f2671,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f6606,plain,
spl0_820,
inference(avatar_split_clause,[],[f2670,f6604]) ).
fof(f6604,plain,
( spl0_820
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f2670,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f6602,plain,
spl0_819,
inference(avatar_split_clause,[],[f2669,f6600]) ).
fof(f6600,plain,
( spl0_819
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f2669,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f6598,plain,
spl0_818,
inference(avatar_split_clause,[],[f2668,f6596]) ).
fof(f6596,plain,
( spl0_818
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f2668,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f6594,plain,
spl0_817,
inference(avatar_split_clause,[],[f2667,f6592]) ).
fof(f6592,plain,
( spl0_817
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f2667,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f6590,plain,
spl0_816,
inference(avatar_split_clause,[],[f2666,f6588]) ).
fof(f6588,plain,
( spl0_816
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f2666,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_2) ).
fof(f6586,plain,
spl0_815,
inference(avatar_split_clause,[],[f2665,f6584]) ).
fof(f6584,plain,
( spl0_815
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f2665,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f6582,plain,
spl0_814,
inference(avatar_split_clause,[],[f2664,f6580]) ).
fof(f6580,plain,
( spl0_814
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f2664,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f6578,plain,
spl0_813,
inference(avatar_split_clause,[],[f2663,f6576]) ).
fof(f6576,plain,
( spl0_813
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f2663,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f6574,plain,
spl0_812,
inference(avatar_split_clause,[],[f2662,f6572]) ).
fof(f6572,plain,
( spl0_812
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f2662,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f6570,plain,
spl0_811,
inference(avatar_split_clause,[],[f2661,f6568]) ).
fof(f6568,plain,
( spl0_811
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f2661,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f6566,plain,
spl0_810,
inference(avatar_split_clause,[],[f2660,f6564]) ).
fof(f6564,plain,
( spl0_810
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f2660,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_14) ).
fof(f6562,plain,
spl0_809,
inference(avatar_split_clause,[],[f2659,f6560]) ).
fof(f6560,plain,
( spl0_809
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f2659,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_13) ).
fof(f6558,plain,
spl0_808,
inference(avatar_split_clause,[],[f2658,f6556]) ).
fof(f6556,plain,
( spl0_808
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2658,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_12) ).
fof(f6554,plain,
spl0_807,
inference(avatar_split_clause,[],[f2657,f6552]) ).
fof(f6552,plain,
( spl0_807
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2657,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_11) ).
fof(f6550,plain,
spl0_806,
inference(avatar_split_clause,[],[f2656,f6548]) ).
fof(f6548,plain,
( spl0_806
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2656,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f6546,plain,
spl0_805,
inference(avatar_split_clause,[],[f2655,f6544]) ).
fof(f6544,plain,
( spl0_805
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2655,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f6542,plain,
spl0_804,
inference(avatar_split_clause,[],[f2654,f6540]) ).
fof(f6540,plain,
( spl0_804
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2654,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f6538,plain,
spl0_803,
inference(avatar_split_clause,[],[f2653,f6536]) ).
fof(f6536,plain,
( spl0_803
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2653,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
fof(f6534,plain,
spl0_802,
inference(avatar_split_clause,[],[f2652,f6532]) ).
fof(f6532,plain,
( spl0_802
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2652,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
fof(f6530,plain,
spl0_801,
inference(avatar_split_clause,[],[f2651,f6528]) ).
fof(f6528,plain,
( spl0_801
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2651,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f6526,plain,
spl0_800,
inference(avatar_split_clause,[],[f2650,f6524]) ).
fof(f6524,plain,
( spl0_800
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f2650,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
fof(f6522,plain,
spl0_799,
inference(avatar_split_clause,[],[f2649,f6520]) ).
fof(f6520,plain,
( spl0_799
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f2649,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
fof(f6518,plain,
spl0_798,
inference(avatar_split_clause,[],[f2648,f6516]) ).
fof(f6516,plain,
( spl0_798
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f2648,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f6514,plain,
spl0_797,
inference(avatar_split_clause,[],[f2647,f6512]) ).
fof(f6512,plain,
( spl0_797
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f2647,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f6510,plain,
spl0_796,
inference(avatar_split_clause,[],[f2646,f6508]) ).
fof(f6508,plain,
( spl0_796
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f2646,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
fof(f6506,plain,
spl0_795,
inference(avatar_split_clause,[],[f2645,f6504]) ).
fof(f6504,plain,
( spl0_795
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f2645,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f6502,plain,
spl0_794,
inference(avatar_split_clause,[],[f2644,f6500]) ).
fof(f6500,plain,
( spl0_794
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f2644,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f6498,plain,
spl0_793,
inference(avatar_split_clause,[],[f2643,f6496]) ).
fof(f6496,plain,
( spl0_793
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f2643,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f6494,plain,
spl0_792,
inference(avatar_split_clause,[],[f2642,f6492]) ).
fof(f6492,plain,
( spl0_792
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f2642,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f6490,plain,
spl0_791,
inference(avatar_split_clause,[],[f2641,f6488]) ).
fof(f6488,plain,
( spl0_791
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f2641,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
fof(f6486,plain,
spl0_790,
inference(avatar_split_clause,[],[f2640,f6484]) ).
fof(f6484,plain,
( spl0_790
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f2640,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
fof(f6482,plain,
spl0_789,
inference(avatar_split_clause,[],[f2639,f6480]) ).
fof(f6480,plain,
( spl0_789
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f2639,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f6478,plain,
spl0_788,
inference(avatar_split_clause,[],[f2638,f6476]) ).
fof(f6476,plain,
( spl0_788
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f2638,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f6474,plain,
spl0_787,
inference(avatar_split_clause,[],[f2612,f6472]) ).
fof(f6472,plain,
( spl0_787
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f2612,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
fof(f6470,plain,
spl0_786,
inference(avatar_split_clause,[],[f2611,f6468]) ).
fof(f6468,plain,
( spl0_786
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f2611,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
fof(f6466,plain,
spl0_785,
inference(avatar_split_clause,[],[f2610,f6464]) ).
fof(f6464,plain,
( spl0_785
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f2610,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f6462,plain,
spl0_784,
inference(avatar_split_clause,[],[f2609,f6460]) ).
fof(f6460,plain,
( spl0_784
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f2609,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
fof(f6458,plain,
spl0_783,
inference(avatar_split_clause,[],[f2608,f6456]) ).
fof(f6456,plain,
( spl0_783
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f2608,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f6454,plain,
spl0_782,
inference(avatar_split_clause,[],[f2607,f6452]) ).
fof(f6452,plain,
( spl0_782
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f2607,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
fof(f6450,plain,
spl0_781,
inference(avatar_split_clause,[],[f2606,f6448]) ).
fof(f6448,plain,
( spl0_781
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f2606,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
fof(f6446,plain,
spl0_780,
inference(avatar_split_clause,[],[f2605,f6444]) ).
fof(f6444,plain,
( spl0_780
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f2605,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f6442,plain,
spl0_779,
inference(avatar_split_clause,[],[f2604,f6440]) ).
fof(f6440,plain,
( spl0_779
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f2604,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f6438,plain,
spl0_778,
inference(avatar_split_clause,[],[f2603,f6436]) ).
fof(f6436,plain,
( spl0_778
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f2603,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f6434,plain,
spl0_777,
inference(avatar_split_clause,[],[f2602,f6432]) ).
fof(f6432,plain,
( spl0_777
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f2602,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f6430,plain,
spl0_776,
inference(avatar_split_clause,[],[f2601,f6428]) ).
fof(f6428,plain,
( spl0_776
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f2601,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f6426,plain,
spl0_775,
inference(avatar_split_clause,[],[f2600,f6424]) ).
fof(f6424,plain,
( spl0_775
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f2600,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f6422,plain,
spl0_774,
inference(avatar_split_clause,[],[f2599,f6420]) ).
fof(f6420,plain,
( spl0_774
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f2599,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
fof(f6418,plain,
spl0_773,
inference(avatar_split_clause,[],[f2598,f6416]) ).
fof(f6416,plain,
( spl0_773
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f2598,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f6414,plain,
spl0_772,
inference(avatar_split_clause,[],[f2597,f6412]) ).
fof(f6412,plain,
( spl0_772
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f2597,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f6410,plain,
spl0_771,
inference(avatar_split_clause,[],[f2596,f6408]) ).
fof(f6408,plain,
( spl0_771
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f2596,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
fof(f6406,plain,
spl0_770,
inference(avatar_split_clause,[],[f2595,f6404]) ).
fof(f6404,plain,
( spl0_770
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f2595,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f6402,plain,
spl0_769,
inference(avatar_split_clause,[],[f2594,f6400]) ).
fof(f6400,plain,
( spl0_769
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f2594,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
fof(f6398,plain,
spl0_768,
inference(avatar_split_clause,[],[f2593,f6396]) ).
fof(f6396,plain,
( spl0_768
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f2593,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
fof(f6394,plain,
spl0_767,
inference(avatar_split_clause,[],[f2592,f6392]) ).
fof(f6392,plain,
( spl0_767
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f2592,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f6390,plain,
spl0_766,
inference(avatar_split_clause,[],[f2591,f6388]) ).
fof(f6388,plain,
( spl0_766
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f2591,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f6386,plain,
spl0_765,
inference(avatar_split_clause,[],[f2590,f6384]) ).
fof(f6384,plain,
( spl0_765
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f2590,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
fof(f6382,plain,
spl0_764,
inference(avatar_split_clause,[],[f2589,f6380]) ).
fof(f6380,plain,
( spl0_764
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f2589,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f6378,plain,
spl0_763,
inference(avatar_split_clause,[],[f2588,f6376]) ).
fof(f6376,plain,
( spl0_763
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f2588,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f6374,plain,
spl0_762,
inference(avatar_split_clause,[],[f2587,f6372]) ).
fof(f6372,plain,
( spl0_762
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f2587,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f6370,plain,
spl0_761,
inference(avatar_split_clause,[],[f2586,f6368]) ).
fof(f6368,plain,
( spl0_761
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f2586,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f6366,plain,
spl0_760,
inference(avatar_split_clause,[],[f2585,f6364]) ).
fof(f6364,plain,
( spl0_760
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f2585,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f6362,plain,
spl0_759,
inference(avatar_split_clause,[],[f2584,f6360]) ).
fof(f6360,plain,
( spl0_759
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f2584,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f6358,plain,
spl0_758,
inference(avatar_split_clause,[],[f2583,f6356]) ).
fof(f6356,plain,
( spl0_758
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f2583,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f6354,plain,
spl0_757,
inference(avatar_split_clause,[],[f2582,f6352]) ).
fof(f6352,plain,
( spl0_757
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f2582,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f6350,plain,
spl0_756,
inference(avatar_split_clause,[],[f2581,f6348]) ).
fof(f6348,plain,
( spl0_756
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f2581,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
fof(f6346,plain,
spl0_755,
inference(avatar_split_clause,[],[f2580,f6344]) ).
fof(f6344,plain,
( spl0_755
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f2580,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
fof(f6342,plain,
spl0_754,
inference(avatar_split_clause,[],[f2579,f6340]) ).
fof(f6340,plain,
( spl0_754
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f2579,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
fof(f6338,plain,
spl0_753,
inference(avatar_split_clause,[],[f2578,f6336]) ).
fof(f6336,plain,
( spl0_753
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f2578,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f6334,plain,
spl0_752,
inference(avatar_split_clause,[],[f2577,f6332]) ).
fof(f6332,plain,
( spl0_752
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f2577,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f6330,plain,
spl0_751,
inference(avatar_split_clause,[],[f2576,f6328]) ).
fof(f6328,plain,
( spl0_751
<=> ! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f2576,axiom,
! [X87] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f6326,plain,
spl0_750,
inference(avatar_split_clause,[],[f2575,f6324]) ).
fof(f6324,plain,
( spl0_750
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f2575,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f6322,plain,
spl0_749,
inference(avatar_split_clause,[],[f2574,f6320]) ).
fof(f6320,plain,
( spl0_749
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f2574,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
fof(f6318,plain,
spl0_748,
inference(avatar_split_clause,[],[f2573,f6316]) ).
fof(f6316,plain,
( spl0_748
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f2573,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
fof(f6314,plain,
spl0_747,
inference(avatar_split_clause,[],[f2572,f6312]) ).
fof(f6312,plain,
( spl0_747
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f2572,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
fof(f6310,plain,
spl0_746,
inference(avatar_split_clause,[],[f2571,f6308]) ).
fof(f6308,plain,
( spl0_746
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f2571,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
fof(f6306,plain,
spl0_745,
inference(avatar_split_clause,[],[f2570,f6304]) ).
fof(f6304,plain,
( spl0_745
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f2570,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f6302,plain,
spl0_744,
inference(avatar_split_clause,[],[f2569,f6300]) ).
fof(f6300,plain,
( spl0_744
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f2569,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
fof(f6298,plain,
spl0_743,
inference(avatar_split_clause,[],[f2568,f6296]) ).
fof(f6296,plain,
( spl0_743
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f2568,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f6294,plain,
spl0_742,
inference(avatar_split_clause,[],[f2567,f6292]) ).
fof(f6292,plain,
( spl0_742
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f2567,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f6290,plain,
spl0_741,
inference(avatar_split_clause,[],[f2566,f6288]) ).
fof(f6288,plain,
( spl0_741
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f2566,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f6286,plain,
spl0_740,
inference(avatar_split_clause,[],[f2565,f6284]) ).
fof(f6284,plain,
( spl0_740
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f2565,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f6282,plain,
spl0_739,
inference(avatar_split_clause,[],[f2564,f6280]) ).
fof(f6280,plain,
( spl0_739
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f2564,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
fof(f6278,plain,
spl0_738,
inference(avatar_split_clause,[],[f2563,f6276]) ).
fof(f6276,plain,
( spl0_738
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f2563,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f6274,plain,
spl0_737,
inference(avatar_split_clause,[],[f2562,f6272]) ).
fof(f6272,plain,
( spl0_737
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f2562,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f6270,plain,
spl0_736,
inference(avatar_split_clause,[],[f2561,f6268]) ).
fof(f6268,plain,
( spl0_736
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f2561,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f6266,plain,
spl0_735,
inference(avatar_split_clause,[],[f2560,f6264]) ).
fof(f6264,plain,
( spl0_735
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f2560,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f6262,plain,
spl0_734,
inference(avatar_split_clause,[],[f2559,f6260]) ).
fof(f6260,plain,
( spl0_734
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f2559,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f6258,plain,
spl0_733,
inference(avatar_split_clause,[],[f2558,f6256]) ).
fof(f6256,plain,
( spl0_733
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f2558,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f6254,plain,
spl0_732,
inference(avatar_split_clause,[],[f2557,f6252]) ).
fof(f6252,plain,
( spl0_732
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f2557,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f6250,plain,
spl0_731,
inference(avatar_split_clause,[],[f2556,f6248]) ).
fof(f6248,plain,
( spl0_731
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f2556,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f6246,plain,
spl0_730,
inference(avatar_split_clause,[],[f2555,f6244]) ).
fof(f6244,plain,
( spl0_730
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2555,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f6242,plain,
spl0_729,
inference(avatar_split_clause,[],[f2554,f6240]) ).
fof(f6240,plain,
( spl0_729
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2554,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f6238,plain,
spl0_728,
inference(avatar_split_clause,[],[f2553,f6236]) ).
fof(f6236,plain,
( spl0_728
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f2553,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f6234,plain,
spl0_727,
inference(avatar_split_clause,[],[f2552,f6232]) ).
fof(f6232,plain,
( spl0_727
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f2552,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f6230,plain,
spl0_726,
inference(avatar_split_clause,[],[f2551,f6228]) ).
fof(f6228,plain,
( spl0_726
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f2551,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f6226,plain,
spl0_725,
inference(avatar_split_clause,[],[f2550,f6224]) ).
fof(f6224,plain,
( spl0_725
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f2550,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f6222,plain,
spl0_724,
inference(avatar_split_clause,[],[f2549,f6220]) ).
fof(f6220,plain,
( spl0_724
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f2549,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f6218,plain,
spl0_723,
inference(avatar_split_clause,[],[f2548,f6216]) ).
fof(f6216,plain,
( spl0_723
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f2548,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f6214,plain,
spl0_722,
inference(avatar_split_clause,[],[f2547,f6212]) ).
fof(f6212,plain,
( spl0_722
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f2547,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f6210,plain,
spl0_721,
inference(avatar_split_clause,[],[f2546,f6208]) ).
fof(f6208,plain,
( spl0_721
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f2546,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f6206,plain,
spl0_720,
inference(avatar_split_clause,[],[f2545,f6204]) ).
fof(f6204,plain,
( spl0_720
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f2545,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f6202,plain,
spl0_719,
inference(avatar_split_clause,[],[f2544,f6200]) ).
fof(f6200,plain,
( spl0_719
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f2544,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f6198,plain,
spl0_718,
inference(avatar_split_clause,[],[f2543,f6196]) ).
fof(f6196,plain,
( spl0_718
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f2543,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f6194,plain,
spl0_717,
inference(avatar_split_clause,[],[f2542,f6192]) ).
fof(f6192,plain,
( spl0_717
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f2542,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f6190,plain,
spl0_716,
inference(avatar_split_clause,[],[f2541,f6188]) ).
fof(f6188,plain,
( spl0_716
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f2541,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f6186,plain,
spl0_715,
inference(avatar_split_clause,[],[f2540,f6184]) ).
fof(f6184,plain,
( spl0_715
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f2540,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f6182,plain,
spl0_714,
inference(avatar_split_clause,[],[f2539,f6180]) ).
fof(f6180,plain,
( spl0_714
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f2539,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f6178,plain,
spl0_713,
inference(avatar_split_clause,[],[f2538,f6176]) ).
fof(f6176,plain,
( spl0_713
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f2538,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f6174,plain,
spl0_712,
inference(avatar_split_clause,[],[f2537,f6172]) ).
fof(f6172,plain,
( spl0_712
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f2537,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f6170,plain,
spl0_711,
inference(avatar_split_clause,[],[f2536,f6168]) ).
fof(f6168,plain,
( spl0_711
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f2536,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f6166,plain,
spl0_710,
inference(avatar_split_clause,[],[f2535,f6164]) ).
fof(f6164,plain,
( spl0_710
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f2535,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f6162,plain,
spl0_709,
inference(avatar_split_clause,[],[f2534,f6160]) ).
fof(f6160,plain,
( spl0_709
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f2534,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f6158,plain,
spl0_708,
inference(avatar_split_clause,[],[f2533,f6156]) ).
fof(f6156,plain,
( spl0_708
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f2533,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f6154,plain,
spl0_707,
inference(avatar_split_clause,[],[f2532,f6152]) ).
fof(f6152,plain,
( spl0_707
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f2532,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f6150,plain,
spl0_706,
inference(avatar_split_clause,[],[f2531,f6148]) ).
fof(f6148,plain,
( spl0_706
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f2531,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f6146,plain,
spl0_705,
inference(avatar_split_clause,[],[f2530,f6144]) ).
fof(f6144,plain,
( spl0_705
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f2530,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f6142,plain,
spl0_704,
inference(avatar_split_clause,[],[f2529,f6140]) ).
fof(f6140,plain,
( spl0_704
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f2529,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f6138,plain,
spl0_703,
inference(avatar_split_clause,[],[f2528,f6136]) ).
fof(f6136,plain,
( spl0_703
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f2528,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_23) ).
fof(f6134,plain,
spl0_702,
inference(avatar_split_clause,[],[f2527,f6132]) ).
fof(f6132,plain,
( spl0_702
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f2527,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_22) ).
fof(f6130,plain,
spl0_701,
inference(avatar_split_clause,[],[f2526,f6128]) ).
fof(f6128,plain,
( spl0_701
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f2526,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f6126,plain,
spl0_700,
inference(avatar_split_clause,[],[f2525,f6124]) ).
fof(f6124,plain,
( spl0_700
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f2525,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_20) ).
fof(f6122,plain,
spl0_699,
inference(avatar_split_clause,[],[f2524,f6120]) ).
fof(f6120,plain,
( spl0_699
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f2524,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f6118,plain,
spl0_698,
inference(avatar_split_clause,[],[f2523,f6116]) ).
fof(f6116,plain,
( spl0_698
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f2523,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f6114,plain,
spl0_697,
inference(avatar_split_clause,[],[f2522,f6112]) ).
fof(f6112,plain,
( spl0_697
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f2522,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_18) ).
fof(f6110,plain,
spl0_696,
inference(avatar_split_clause,[],[f2521,f6108]) ).
fof(f6108,plain,
( spl0_696
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f2521,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f6106,plain,
spl0_695,
inference(avatar_split_clause,[],[f2520,f6104]) ).
fof(f6104,plain,
( spl0_695
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f2520,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_16) ).
fof(f6102,plain,
spl0_694,
inference(avatar_split_clause,[],[f2519,f6100]) ).
fof(f6100,plain,
( spl0_694
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f2519,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_15) ).
fof(f6098,plain,
spl0_693,
inference(avatar_split_clause,[],[f2518,f6096]) ).
fof(f6096,plain,
( spl0_693
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f2518,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f6094,plain,
spl0_692,
inference(avatar_split_clause,[],[f2517,f6092]) ).
fof(f6092,plain,
( spl0_692
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f2517,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f6090,plain,
spl0_691,
inference(avatar_split_clause,[],[f2516,f6088]) ).
fof(f6088,plain,
( spl0_691
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f2516,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f6086,plain,
spl0_690,
inference(avatar_split_clause,[],[f2515,f6084]) ).
fof(f6084,plain,
( spl0_690
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f2515,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_11) ).
fof(f6082,plain,
spl0_689,
inference(avatar_split_clause,[],[f2514,f6080]) ).
fof(f6080,plain,
( spl0_689
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f2514,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f6078,plain,
spl0_688,
inference(avatar_split_clause,[],[f2513,f6076]) ).
fof(f6076,plain,
( spl0_688
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f2513,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f6074,plain,
spl0_687,
inference(avatar_split_clause,[],[f2512,f6072]) ).
fof(f6072,plain,
( spl0_687
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f2512,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__semidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f6070,plain,
spl0_686,
inference(avatar_split_clause,[],[f2511,f6068]) ).
fof(f6068,plain,
( spl0_686
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f2511,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
fof(f6066,plain,
spl0_685,
inference(avatar_split_clause,[],[f2510,f6064]) ).
fof(f6064,plain,
( spl0_685
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f2510,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
fof(f6062,plain,
spl0_684,
inference(avatar_split_clause,[],[f2509,f6060]) ).
fof(f6060,plain,
( spl0_684
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f2509,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f6058,plain,
spl0_683,
inference(avatar_split_clause,[],[f2508,f6056]) ).
fof(f6056,plain,
( spl0_683
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f2508,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f6054,plain,
spl0_682,
inference(avatar_split_clause,[],[f2507,f6052]) ).
fof(f6052,plain,
( spl0_682
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f2507,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f6050,plain,
spl0_681,
inference(avatar_split_clause,[],[f2506,f6048]) ).
fof(f6048,plain,
( spl0_681
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f2506,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f6046,plain,
spl0_680,
inference(avatar_split_clause,[],[f2505,f6044]) ).
fof(f6044,plain,
( spl0_680
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f2505,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
fof(f6042,plain,
spl0_679,
inference(avatar_split_clause,[],[f2504,f6040]) ).
fof(f6040,plain,
( spl0_679
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f2504,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f6038,plain,
spl0_678,
inference(avatar_split_clause,[],[f2503,f6036]) ).
fof(f6036,plain,
( spl0_678
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f2503,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f6034,plain,
spl0_677,
inference(avatar_split_clause,[],[f2502,f6032]) ).
fof(f6032,plain,
( spl0_677
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f2502,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f6030,plain,
spl0_676,
inference(avatar_split_clause,[],[f2501,f6028]) ).
fof(f6028,plain,
( spl0_676
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f2501,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f6026,plain,
spl0_675,
inference(avatar_split_clause,[],[f2500,f6024]) ).
fof(f6024,plain,
( spl0_675
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Olordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f2500,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f6022,plain,
spl0_674,
inference(avatar_split_clause,[],[f2499,f6020]) ).
fof(f6020,plain,
( spl0_674
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f2499,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f6018,plain,
spl0_673,
inference(avatar_split_clause,[],[f2498,f6016]) ).
fof(f6016,plain,
( spl0_673
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f2498,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f6014,plain,
spl0_672,
inference(avatar_split_clause,[],[f2497,f6012]) ).
fof(f6012,plain,
( spl0_672
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f2497,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f6010,plain,
spl0_671,
inference(avatar_split_clause,[],[f2496,f6008]) ).
fof(f6008,plain,
( spl0_671
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f2496,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f6006,plain,
spl0_670,
inference(avatar_split_clause,[],[f2495,f6004]) ).
fof(f6004,plain,
( spl0_670
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f2495,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f6002,plain,
spl0_669,
inference(avatar_split_clause,[],[f2494,f6000]) ).
fof(f6000,plain,
( spl0_669
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f2494,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5998,plain,
spl0_668,
inference(avatar_split_clause,[],[f2493,f5996]) ).
fof(f5996,plain,
( spl0_668
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f2493,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5994,plain,
spl0_667,
inference(avatar_split_clause,[],[f2492,f5992]) ).
fof(f5992,plain,
( spl0_667
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f2492,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5990,plain,
spl0_666,
inference(avatar_split_clause,[],[f2491,f5988]) ).
fof(f5988,plain,
( spl0_666
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f2491,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5986,plain,
spl0_665,
inference(avatar_split_clause,[],[f2490,f5984]) ).
fof(f5984,plain,
( spl0_665
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f2490,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5982,plain,
spl0_664,
inference(avatar_split_clause,[],[f2489,f5980]) ).
fof(f5980,plain,
( spl0_664
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f2489,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5978,plain,
spl0_663,
inference(avatar_split_clause,[],[f2488,f5976]) ).
fof(f5976,plain,
( spl0_663
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f2488,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5974,plain,
spl0_662,
inference(avatar_split_clause,[],[f2487,f5972]) ).
fof(f5972,plain,
( spl0_662
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f2487,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
fof(f5970,plain,
spl0_661,
inference(avatar_split_clause,[],[f2486,f5968]) ).
fof(f5968,plain,
( spl0_661
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f2486,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5966,plain,
spl0_660,
inference(avatar_split_clause,[],[f2485,f5964]) ).
fof(f5964,plain,
( spl0_660
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f2485,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5962,plain,
spl0_659,
inference(avatar_split_clause,[],[f2484,f5960]) ).
fof(f5960,plain,
( spl0_659
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f2484,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5958,plain,
spl0_658,
inference(avatar_split_clause,[],[f2483,f5956]) ).
fof(f5956,plain,
( spl0_658
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f2483,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5954,plain,
spl0_657,
inference(avatar_split_clause,[],[f2482,f5952]) ).
fof(f5952,plain,
( spl0_657
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f2482,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5950,plain,
spl0_656,
inference(avatar_split_clause,[],[f2481,f5948]) ).
fof(f5948,plain,
( spl0_656
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2481,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
fof(f5946,plain,
spl0_655,
inference(avatar_split_clause,[],[f2480,f5944]) ).
fof(f5944,plain,
( spl0_655
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2480,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
fof(f5942,plain,
spl0_654,
inference(avatar_split_clause,[],[f2479,f5940]) ).
fof(f5940,plain,
( spl0_654
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2479,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
fof(f5938,plain,
spl0_653,
inference(avatar_split_clause,[],[f2478,f5936]) ).
fof(f5936,plain,
( spl0_653
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2478,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
fof(f5934,plain,
spl0_652,
inference(avatar_split_clause,[],[f2477,f5932]) ).
fof(f5932,plain,
( spl0_652
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2477,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5930,plain,
spl0_651,
inference(avatar_split_clause,[],[f2476,f5928]) ).
fof(f5928,plain,
( spl0_651
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2476,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5926,plain,
spl0_650,
inference(avatar_split_clause,[],[f2475,f5924]) ).
fof(f5924,plain,
( spl0_650
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2475,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5922,plain,
spl0_649,
inference(avatar_split_clause,[],[f2474,f5920]) ).
fof(f5920,plain,
( spl0_649
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2474,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5918,plain,
spl0_648,
inference(avatar_split_clause,[],[f2473,f5916]) ).
fof(f5916,plain,
( spl0_648
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2473,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5914,plain,
spl0_647,
inference(avatar_split_clause,[],[f2472,f5912]) ).
fof(f5912,plain,
( spl0_647
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2472,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5910,plain,
spl0_646,
inference(avatar_split_clause,[],[f2471,f5908]) ).
fof(f5908,plain,
( spl0_646
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2471,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5906,plain,
spl0_645,
inference(avatar_split_clause,[],[f2470,f5904]) ).
fof(f5904,plain,
( spl0_645
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f2470,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5902,plain,
spl0_644,
inference(avatar_split_clause,[],[f2469,f5900]) ).
fof(f5900,plain,
( spl0_644
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f2469,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_56) ).
fof(f5898,plain,
spl0_643,
inference(avatar_split_clause,[],[f2468,f5896]) ).
fof(f5896,plain,
( spl0_643
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2468,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semidom(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5894,plain,
spl0_642,
inference(avatar_split_clause,[],[f2467,f5892]) ).
fof(f5892,plain,
( spl0_642
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f2467,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5890,plain,
spl0_641,
inference(avatar_split_clause,[],[f2466,f5888]) ).
fof(f5888,plain,
( spl0_641
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f2466,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5886,plain,
spl0_640,
inference(avatar_split_clause,[],[f2465,f5884]) ).
fof(f5884,plain,
( spl0_640
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f2465,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5882,plain,
spl0_639,
inference(avatar_split_clause,[],[f2464,f5880]) ).
fof(f5880,plain,
( spl0_639
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f2464,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5878,plain,
spl0_638,
inference(avatar_split_clause,[],[f2463,f5876]) ).
fof(f5876,plain,
( spl0_638
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f2463,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5874,plain,
spl0_637,
inference(avatar_split_clause,[],[f2462,f5872]) ).
fof(f5872,plain,
( spl0_637
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2462,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_5) ).
fof(f5870,plain,
spl0_636,
inference(avatar_split_clause,[],[f2461,f5868]) ).
fof(f2461,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5866,plain,
spl0_635,
inference(avatar_split_clause,[],[f2460,f5864]) ).
fof(f2460,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Olordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5862,plain,
spl0_634,
inference(avatar_split_clause,[],[f2459,f5860]) ).
fof(f2459,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__ring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5858,plain,
spl0_633,
inference(avatar_split_clause,[],[f2458,f5856]) ).
fof(f2458,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__abs__if(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5854,plain,
spl0_632,
inference(avatar_split_clause,[],[f2457,f5852]) ).
fof(f2457,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5850,plain,
spl0_631,
inference(avatar_split_clause,[],[f2456,f5848]) ).
fof(f2456,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5846,plain,
spl0_630,
inference(avatar_split_clause,[],[f2455,f5844]) ).
fof(f2455,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5842,plain,
spl0_629,
inference(avatar_split_clause,[],[f2454,f5840]) ).
fof(f2454,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5838,plain,
spl0_628,
inference(avatar_split_clause,[],[f2453,f5836]) ).
fof(f2453,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5834,plain,
spl0_627,
inference(avatar_split_clause,[],[f2452,f5832]) ).
fof(f2452,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5830,plain,
spl0_626,
inference(avatar_split_clause,[],[f2451,f5828]) ).
fof(f5828,plain,
( spl0_626
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2451,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5826,plain,
spl0_625,
inference(avatar_split_clause,[],[f2450,f5824]) ).
fof(f2450,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5822,plain,
spl0_624,
inference(avatar_split_clause,[],[f2449,f5820]) ).
fof(f2449,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5818,plain,
spl0_623,
inference(avatar_split_clause,[],[f2448,f5816]) ).
fof(f2448,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5814,plain,
spl0_622,
inference(avatar_split_clause,[],[f2447,f5812]) ).
fof(f2447,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5810,plain,
spl0_621,
inference(avatar_split_clause,[],[f2446,f5808]) ).
fof(f2446,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5806,plain,
spl0_620,
inference(avatar_split_clause,[],[f2445,f5804]) ).
fof(f2445,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5802,plain,
spl0_619,
inference(avatar_split_clause,[],[f2444,f5800]) ).
fof(f2444,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5798,plain,
spl0_618,
inference(avatar_split_clause,[],[f2443,f5796]) ).
fof(f2443,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5794,plain,
spl0_617,
inference(avatar_split_clause,[],[f2442,f5792]) ).
fof(f2442,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5790,plain,
spl0_616,
inference(avatar_split_clause,[],[f2441,f5788]) ).
fof(f2441,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5786,plain,
spl0_615,
inference(avatar_split_clause,[],[f2440,f5784]) ).
fof(f5784,plain,
( spl0_615
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2440,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5782,plain,
spl0_614,
inference(avatar_split_clause,[],[f2439,f5780]) ).
fof(f5780,plain,
( spl0_614
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2439,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_29) ).
fof(f5778,plain,
spl0_613,
inference(avatar_split_clause,[],[f2438,f5776]) ).
fof(f5776,plain,
( spl0_613
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2438,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_28) ).
fof(f5774,plain,
spl0_612,
inference(avatar_split_clause,[],[f2437,f5772]) ).
fof(f5772,plain,
( spl0_612
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2437,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5770,plain,
spl0_611,
inference(avatar_split_clause,[],[f2436,f5768]) ).
fof(f5768,plain,
( spl0_611
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2436,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_26) ).
fof(f5766,plain,
spl0_610,
inference(avatar_split_clause,[],[f2435,f5764]) ).
fof(f5764,plain,
( spl0_610
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2435,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5762,plain,
spl0_609,
inference(avatar_split_clause,[],[f2434,f5760]) ).
fof(f5760,plain,
( spl0_609
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2434,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_24) ).
fof(f5758,plain,
spl0_608,
inference(avatar_split_clause,[],[f2433,f5756]) ).
fof(f5756,plain,
( spl0_608
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2433,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5754,plain,
spl0_607,
inference(avatar_split_clause,[],[f2432,f5752]) ).
fof(f5752,plain,
( spl0_607
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2432,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_22) ).
fof(f5750,plain,
spl0_606,
inference(avatar_split_clause,[],[f2431,f5748]) ).
fof(f5748,plain,
( spl0_606
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2431,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f5746,plain,
spl0_605,
inference(avatar_split_clause,[],[f2430,f5744]) ).
fof(f5744,plain,
( spl0_605
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2430,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5742,plain,
spl0_604,
inference(avatar_split_clause,[],[f2429,f5740]) ).
fof(f5740,plain,
( spl0_604
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2429,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5738,plain,
spl0_603,
inference(avatar_split_clause,[],[f2428,f5736]) ).
fof(f5736,plain,
( spl0_603
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2428,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5734,plain,
spl0_602,
inference(avatar_split_clause,[],[f2427,f5732]) ).
fof(f2427,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5730,plain,
spl0_601,
inference(avatar_split_clause,[],[f2426,f5728]) ).
fof(f2426,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f5726,plain,
spl0_600,
inference(avatar_split_clause,[],[f2425,f5724]) ).
fof(f2425,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5722,plain,
spl0_599,
inference(avatar_split_clause,[],[f2424,f5720]) ).
fof(f2424,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f5718,plain,
spl0_598,
inference(avatar_split_clause,[],[f2423,f5716]) ).
fof(f2423,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f5714,plain,
spl0_597,
inference(avatar_split_clause,[],[f2422,f5712]) ).
fof(f2422,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f5710,plain,
spl0_596,
inference(avatar_split_clause,[],[f2421,f5708]) ).
fof(f2421,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f5706,plain,
spl0_595,
inference(avatar_split_clause,[],[f2420,f5704]) ).
fof(f2420,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f5702,plain,
spl0_594,
inference(avatar_split_clause,[],[f2419,f5700]) ).
fof(f2419,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f5698,plain,
spl0_593,
inference(avatar_split_clause,[],[f2418,f5696]) ).
fof(f2418,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f5694,plain,
spl0_592,
inference(avatar_split_clause,[],[f2417,f5692]) ).
fof(f2417,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__idom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f5690,plain,
spl0_591,
inference(avatar_split_clause,[],[f2355,f5688]) ).
fof(f5688,plain,
( spl0_591
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2355,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
fof(f5686,plain,
spl0_590,
inference(avatar_split_clause,[],[f2354,f5684]) ).
fof(f5684,plain,
( spl0_590
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2354,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
fof(f5682,plain,
spl0_589,
inference(avatar_split_clause,[],[f2353,f5680]) ).
fof(f5680,plain,
( spl0_589
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2353,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f5678,plain,
spl0_588,
inference(avatar_split_clause,[],[f2352,f5676]) ).
fof(f5676,plain,
( spl0_588
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2352,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
fof(f5674,plain,
spl0_587,
inference(avatar_split_clause,[],[f2351,f5672]) ).
fof(f5672,plain,
( spl0_587
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2351,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
fof(f5670,plain,
spl0_586,
inference(avatar_split_clause,[],[f2350,f5668]) ).
fof(f5668,plain,
( spl0_586
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2350,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f5666,plain,
spl0_585,
inference(avatar_split_clause,[],[f2349,f5664]) ).
fof(f5664,plain,
( spl0_585
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2349,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f5662,plain,
spl0_584,
inference(avatar_split_clause,[],[f2348,f5660]) ).
fof(f5660,plain,
( spl0_584
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2348,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f5658,plain,
spl0_583,
inference(avatar_split_clause,[],[f2347,f5656]) ).
fof(f5656,plain,
( spl0_583
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2347,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f5654,plain,
spl0_582,
inference(avatar_split_clause,[],[f2346,f5652]) ).
fof(f5652,plain,
( spl0_582
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2346,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f5650,plain,
spl0_581,
inference(avatar_split_clause,[],[f2345,f5648]) ).
fof(f5648,plain,
( spl0_581
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2345,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f5646,plain,
spl0_580,
inference(avatar_split_clause,[],[f2344,f5644]) ).
fof(f5644,plain,
( spl0_580
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2344,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f5642,plain,
spl0_579,
inference(avatar_split_clause,[],[f2343,f5640]) ).
fof(f5640,plain,
( spl0_579
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2343,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Oordered__semiring__strict(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f5638,plain,
spl0_578,
inference(avatar_split_clause,[],[f2342,f5636]) ).
fof(f5636,plain,
( spl0_578
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2342,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f5634,plain,
spl0_577,
inference(avatar_split_clause,[],[f2341,f5632]) ).
fof(f5632,plain,
( spl0_577
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2341,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f5630,plain,
spl0_576,
inference(avatar_split_clause,[],[f2340,f5628]) ).
fof(f5628,plain,
( spl0_576
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2340,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f5626,plain,
spl0_575,
inference(avatar_split_clause,[],[f2339,f5624]) ).
fof(f5624,plain,
( spl0_575
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2339,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f5622,plain,
spl0_574,
inference(avatar_split_clause,[],[f2338,f5620]) ).
fof(f5620,plain,
( spl0_574
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2338,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
fof(f5618,plain,
spl0_573,
inference(avatar_split_clause,[],[f2337,f5616]) ).
fof(f5616,plain,
( spl0_573
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2337,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f5614,plain,
spl0_572,
inference(avatar_split_clause,[],[f2336,f5612]) ).
fof(f5612,plain,
( spl0_572
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2336,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f5610,plain,
spl0_571,
inference(avatar_split_clause,[],[f2335,f5608]) ).
fof(f5608,plain,
( spl0_571
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2335,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f5606,plain,
spl0_570,
inference(avatar_split_clause,[],[f2334,f5604]) ).
fof(f5604,plain,
( spl0_570
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2334,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f5602,plain,
spl0_569,
inference(avatar_split_clause,[],[f2333,f5600]) ).
fof(f5600,plain,
( spl0_569
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2333,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f5598,plain,
spl0_568,
inference(avatar_split_clause,[],[f2332,f5596]) ).
fof(f5596,plain,
( spl0_568
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2332,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f5594,plain,
spl0_567,
inference(avatar_split_clause,[],[f2331,f5592]) ).
fof(f5592,plain,
( spl0_567
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2331,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f5590,plain,
spl0_566,
inference(avatar_split_clause,[],[f2330,f5588]) ).
fof(f5588,plain,
( spl0_566
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2330,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f5586,plain,
spl0_565,
inference(avatar_split_clause,[],[f2329,f5584]) ).
fof(f5584,plain,
( spl0_565
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2329,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
fof(f5582,plain,
spl0_564,
inference(avatar_split_clause,[],[f2328,f5580]) ).
fof(f5580,plain,
( spl0_564
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2328,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
fof(f5578,plain,
spl0_563,
inference(avatar_split_clause,[],[f2327,f5576]) ).
fof(f5576,plain,
( spl0_563
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2327,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f5574,plain,
spl0_562,
inference(avatar_split_clause,[],[f2326,f5572]) ).
fof(f5572,plain,
( spl0_562
<=> ! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2326,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f5570,plain,
spl0_561,
inference(avatar_split_clause,[],[f2325,f5568]) ).
fof(f5568,plain,
( spl0_561
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2325,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f5566,plain,
spl0_560,
inference(avatar_split_clause,[],[f2324,f5564]) ).
fof(f5564,plain,
( spl0_560
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2324,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f5562,plain,
spl0_559,
inference(avatar_split_clause,[],[f2323,f5560]) ).
fof(f5560,plain,
( spl0_559
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2323,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__cancel__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f5558,plain,
spl0_558,
inference(avatar_split_clause,[],[f2322,f5556]) ).
fof(f5556,plain,
( spl0_558
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2322,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f5554,plain,
spl0_557,
inference(avatar_split_clause,[],[f2321,f5552]) ).
fof(f5552,plain,
( spl0_557
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2321,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f5550,plain,
spl0_556,
inference(avatar_split_clause,[],[f2320,f5548]) ).
fof(f5548,plain,
( spl0_556
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2320,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_4) ).
fof(f5546,plain,
spl0_555,
inference(avatar_split_clause,[],[f2319,f5544]) ).
fof(f5544,plain,
( spl0_555
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2319,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__join(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f5542,plain,
spl0_554,
inference(avatar_split_clause,[],[f2318,f5540]) ).
fof(f5540,plain,
( spl0_554
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2318,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f5538,plain,
spl0_553,
inference(avatar_split_clause,[],[f2317,f5536]) ).
fof(f5536,plain,
( spl0_553
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2317,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__meet(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f5534,plain,
spl0_552,
inference(avatar_split_clause,[],[f2316,f5532]) ).
fof(f5532,plain,
( spl0_552
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2316,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f5530,plain,
spl0_551,
inference(avatar_split_clause,[],[f2315,f5528]) ).
fof(f5528,plain,
( spl0_551
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2315,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f5526,plain,
spl0_550,
inference(avatar_split_clause,[],[f2314,f5524]) ).
fof(f5524,plain,
( spl0_550
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2314,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f5522,plain,
spl0_549,
inference(avatar_split_clause,[],[f2313,f5520]) ).
fof(f5520,plain,
( spl0_549
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2313,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f5518,plain,
spl0_548,
inference(avatar_split_clause,[],[f2312,f5516]) ).
fof(f5516,plain,
( spl0_548
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2312,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Olordered__ab__group__abs(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f5514,plain,
spl0_547,
inference(avatar_split_clause,[],[f2311,f5512]) ).
fof(f5512,plain,
( spl0_547
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2311,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_23) ).
fof(f5510,plain,
spl0_546,
inference(avatar_split_clause,[],[f2310,f5508]) ).
fof(f5508,plain,
( spl0_546
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2310,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_22) ).
fof(f5506,plain,
spl0_545,
inference(avatar_split_clause,[],[f2309,f5504]) ).
fof(f5504,plain,
( spl0_545
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2309,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f5502,plain,
spl0_544,
inference(avatar_split_clause,[],[f2308,f5500]) ).
fof(f5500,plain,
( spl0_544
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2308,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_20) ).
fof(f5498,plain,
spl0_543,
inference(avatar_split_clause,[],[f2307,f5496]) ).
fof(f5496,plain,
( spl0_543
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2307,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f5494,plain,
spl0_542,
inference(avatar_split_clause,[],[f2306,f5492]) ).
fof(f5492,plain,
( spl0_542
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2306,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f5490,plain,
spl0_541,
inference(avatar_split_clause,[],[f2305,f5488]) ).
fof(f5488,plain,
( spl0_541
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2305,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_18) ).
fof(f5486,plain,
spl0_540,
inference(avatar_split_clause,[],[f2304,f5484]) ).
fof(f5484,plain,
( spl0_540
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2304,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f5482,plain,
spl0_539,
inference(avatar_split_clause,[],[f2303,f5480]) ).
fof(f5480,plain,
( spl0_539
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2303,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_16) ).
fof(f5478,plain,
spl0_538,
inference(avatar_split_clause,[],[f2302,f5476]) ).
fof(f5476,plain,
( spl0_538
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2302,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_15) ).
fof(f5474,plain,
spl0_537,
inference(avatar_split_clause,[],[f2301,f5472]) ).
fof(f5472,plain,
( spl0_537
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2301,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f5470,plain,
spl0_536,
inference(avatar_split_clause,[],[f2300,f5468]) ).
fof(f5468,plain,
( spl0_536
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2300,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f5466,plain,
spl0_535,
inference(avatar_split_clause,[],[f2299,f5464]) ).
fof(f5464,plain,
( spl0_535
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2299,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f5462,plain,
spl0_534,
inference(avatar_split_clause,[],[f2298,f5460]) ).
fof(f5460,plain,
( spl0_534
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2298,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f5458,plain,
spl0_533,
inference(avatar_split_clause,[],[f2297,f5456]) ).
fof(f5456,plain,
( spl0_533
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2297,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f5454,plain,
spl0_532,
inference(avatar_split_clause,[],[f2296,f5452]) ).
fof(f5452,plain,
( spl0_532
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2296,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f5450,plain,
spl0_531,
inference(avatar_split_clause,[],[f2295,f5448]) ).
fof(f5448,plain,
( spl0_531
<=> ! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2295,axiom,
! [X87] :
( ~ class_Ring__and__Field_Olordered__ring(X87)
| class_Ring__and__Field_Opordered__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f5446,plain,
spl0_530,
inference(avatar_split_clause,[],[f2294,f5444]) ).
fof(f5444,plain,
( spl0_530
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2294,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f5442,plain,
spl0_529,
inference(avatar_split_clause,[],[f2293,f5440]) ).
fof(f5440,plain,
( spl0_529
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2293,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f5438,plain,
spl0_528,
inference(avatar_split_clause,[],[f2292,f5436]) ).
fof(f5436,plain,
( spl0_528
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2292,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f5434,plain,
spl0_527,
inference(avatar_split_clause,[],[f2291,f5432]) ).
fof(f5432,plain,
( spl0_527
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2291,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f5430,plain,
spl0_526,
inference(avatar_split_clause,[],[f2290,f5428]) ).
fof(f5428,plain,
( spl0_526
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2290,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_5) ).
fof(f5426,plain,
spl0_525,
inference(avatar_split_clause,[],[f2289,f5424]) ).
fof(f5424,plain,
( spl0_525
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2289,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f5422,plain,
spl0_524,
inference(avatar_split_clause,[],[f2288,f5420]) ).
fof(f5420,plain,
( spl0_524
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2288,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_30) ).
fof(f5418,plain,
spl0_523,
inference(avatar_split_clause,[],[f2287,f5416]) ).
fof(f5416,plain,
( spl0_523
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2287,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f5414,plain,
spl0_522,
inference(avatar_split_clause,[],[f2286,f5412]) ).
fof(f5412,plain,
( spl0_522
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2286,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_29) ).
fof(f5410,plain,
spl0_521,
inference(avatar_split_clause,[],[f2285,f5408]) ).
fof(f5408,plain,
( spl0_521
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2285,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_28) ).
fof(f5406,plain,
spl0_520,
inference(avatar_split_clause,[],[f2284,f5404]) ).
fof(f5404,plain,
( spl0_520
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2284,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f5402,plain,
spl0_519,
inference(avatar_split_clause,[],[f2283,f5400]) ).
fof(f5400,plain,
( spl0_519
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2283,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_26) ).
fof(f5398,plain,
spl0_518,
inference(avatar_split_clause,[],[f2282,f5396]) ).
fof(f5396,plain,
( spl0_518
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2282,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f5394,plain,
spl0_517,
inference(avatar_split_clause,[],[f2281,f5392]) ).
fof(f5392,plain,
( spl0_517
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2281,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_24) ).
fof(f5390,plain,
spl0_516,
inference(avatar_split_clause,[],[f2280,f5388]) ).
fof(f5388,plain,
( spl0_516
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2280,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f5386,plain,
spl0_515,
inference(avatar_split_clause,[],[f2279,f5384]) ).
fof(f5384,plain,
( spl0_515
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2279,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_22) ).
fof(f5382,plain,
spl0_514,
inference(avatar_split_clause,[],[f2278,f5380]) ).
fof(f5380,plain,
( spl0_514
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2278,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_21) ).
fof(f5378,plain,
spl0_513,
inference(avatar_split_clause,[],[f2277,f5376]) ).
fof(f5376,plain,
( spl0_513
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2277,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f5374,plain,
spl0_512,
inference(avatar_split_clause,[],[f2276,f5372]) ).
fof(f5372,plain,
( spl0_512
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2276,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f5370,plain,
spl0_511,
inference(avatar_split_clause,[],[f2275,f5368]) ).
fof(f5368,plain,
( spl0_511
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2275,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f5366,plain,
spl0_510,
inference(avatar_split_clause,[],[f2274,f5364]) ).
fof(f5364,plain,
( spl0_510
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2274,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f5362,plain,
spl0_509,
inference(avatar_split_clause,[],[f2273,f5360]) ).
fof(f5360,plain,
( spl0_509
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2273,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_17) ).
fof(f5358,plain,
spl0_508,
inference(avatar_split_clause,[],[f2272,f5356]) ).
fof(f5356,plain,
( spl0_508
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2272,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f5354,plain,
spl0_507,
inference(avatar_split_clause,[],[f2271,f5352]) ).
fof(f5352,plain,
( spl0_507
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2271,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f5350,plain,
spl0_506,
inference(avatar_split_clause,[],[f2270,f5348]) ).
fof(f5348,plain,
( spl0_506
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2270,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f5346,plain,
spl0_505,
inference(avatar_split_clause,[],[f2269,f5344]) ).
fof(f5344,plain,
( spl0_505
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2269,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f5342,plain,
spl0_504,
inference(avatar_split_clause,[],[f2268,f5340]) ).
fof(f5340,plain,
( spl0_504
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2268,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f5338,plain,
spl0_503,
inference(avatar_split_clause,[],[f2267,f5336]) ).
fof(f5336,plain,
( spl0_503
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2267,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f5334,plain,
spl0_502,
inference(avatar_split_clause,[],[f2266,f5332]) ).
fof(f5332,plain,
( spl0_502
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2266,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f5330,plain,
spl0_501,
inference(avatar_split_clause,[],[f2265,f5328]) ).
fof(f5328,plain,
( spl0_501
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2265,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f5326,plain,
spl0_500,
inference(avatar_split_clause,[],[f2264,f5324]) ).
fof(f5324,plain,
( spl0_500
<=> ! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2264,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oidom(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f5322,plain,
spl0_499,
inference(avatar_split_clause,[],[f2228,f5320]) ).
fof(f5320,plain,
( spl0_499
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2228,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f5318,plain,
spl0_498,
inference(avatar_split_clause,[],[f2227,f5316]) ).
fof(f5316,plain,
( spl0_498
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2227,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f5314,plain,
spl0_497,
inference(avatar_split_clause,[],[f2226,f5312]) ).
fof(f5312,plain,
( spl0_497
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2226,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f5310,plain,
spl0_496,
inference(avatar_split_clause,[],[f2225,f5308]) ).
fof(f5308,plain,
( spl0_496
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2225,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f5306,plain,
spl0_495,
inference(avatar_split_clause,[],[f2224,f5304]) ).
fof(f5304,plain,
( spl0_495
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2224,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f5302,plain,
spl0_494,
inference(avatar_split_clause,[],[f2223,f5300]) ).
fof(f5300,plain,
( spl0_494
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2223,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
fof(f5298,plain,
spl0_493,
inference(avatar_split_clause,[],[f2222,f5296]) ).
fof(f5296,plain,
( spl0_493
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2222,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f5294,plain,
spl0_492,
inference(avatar_split_clause,[],[f2221,f5292]) ).
fof(f5292,plain,
( spl0_492
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2221,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f5290,plain,
spl0_491,
inference(avatar_split_clause,[],[f2220,f5288]) ).
fof(f5288,plain,
( spl0_491
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2220,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f5286,plain,
spl0_490,
inference(avatar_split_clause,[],[f2219,f5284]) ).
fof(f5284,plain,
( spl0_490
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2219,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f5282,plain,
spl0_489,
inference(avatar_split_clause,[],[f2218,f5280]) ).
fof(f5280,plain,
( spl0_489
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2218,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f5278,plain,
spl0_488,
inference(avatar_split_clause,[],[f2217,f5276]) ).
fof(f5276,plain,
( spl0_488
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2217,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f5274,plain,
spl0_487,
inference(avatar_split_clause,[],[f2216,f5272]) ).
fof(f5272,plain,
( spl0_487
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2216,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f5270,plain,
spl0_486,
inference(avatar_split_clause,[],[f2215,f5268]) ).
fof(f5268,plain,
( spl0_486
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2215,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
fof(f5266,plain,
spl0_485,
inference(avatar_split_clause,[],[f2214,f5264]) ).
fof(f5264,plain,
( spl0_485
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2214,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
fof(f5262,plain,
spl0_484,
inference(avatar_split_clause,[],[f2213,f5260]) ).
fof(f5260,plain,
( spl0_484
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2213,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f5258,plain,
spl0_483,
inference(avatar_split_clause,[],[f2212,f5256]) ).
fof(f5256,plain,
( spl0_483
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2212,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f5254,plain,
spl0_482,
inference(avatar_split_clause,[],[f2211,f5252]) ).
fof(f5252,plain,
( spl0_482
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2211,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
fof(f5250,plain,
spl0_481,
inference(avatar_split_clause,[],[f2210,f5248]) ).
fof(f5248,plain,
( spl0_481
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2210,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
fof(f5246,plain,
spl0_480,
inference(avatar_split_clause,[],[f2209,f5244]) ).
fof(f5244,plain,
( spl0_480
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2209,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
fof(f5242,plain,
spl0_479,
inference(avatar_split_clause,[],[f2208,f5240]) ).
fof(f5240,plain,
( spl0_479
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2208,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
fof(f5238,plain,
spl0_478,
inference(avatar_split_clause,[],[f2207,f5236]) ).
fof(f5236,plain,
( spl0_478
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2207,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f5234,plain,
spl0_477,
inference(avatar_split_clause,[],[f2206,f5232]) ).
fof(f5232,plain,
( spl0_477
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2206,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f5230,plain,
spl0_476,
inference(avatar_split_clause,[],[f2205,f5228]) ).
fof(f5228,plain,
( spl0_476
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2205,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
fof(f5226,plain,
spl0_475,
inference(avatar_split_clause,[],[f2204,f5224]) ).
fof(f5224,plain,
( spl0_475
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2204,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
fof(f5222,plain,
spl0_474,
inference(avatar_split_clause,[],[f2203,f5220]) ).
fof(f5220,plain,
( spl0_474
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2203,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f5218,plain,
spl0_473,
inference(avatar_split_clause,[],[f2202,f5216]) ).
fof(f5216,plain,
( spl0_473
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2202,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f5214,plain,
spl0_472,
inference(avatar_split_clause,[],[f2201,f5212]) ).
fof(f5212,plain,
( spl0_472
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2201,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
fof(f5210,plain,
spl0_471,
inference(avatar_split_clause,[],[f2200,f5208]) ).
fof(f5208,plain,
( spl0_471
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2200,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f5206,plain,
spl0_470,
inference(avatar_split_clause,[],[f2199,f5204]) ).
fof(f5204,plain,
( spl0_470
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2199,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f5202,plain,
spl0_469,
inference(avatar_split_clause,[],[f2198,f5200]) ).
fof(f5200,plain,
( spl0_469
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2198,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f5198,plain,
spl0_468,
inference(avatar_split_clause,[],[f2197,f5196]) ).
fof(f5196,plain,
( spl0_468
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2197,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f5194,plain,
spl0_467,
inference(avatar_split_clause,[],[f2196,f5192]) ).
fof(f5192,plain,
( spl0_467
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2196,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f5190,plain,
spl0_466,
inference(avatar_split_clause,[],[f2195,f5188]) ).
fof(f5188,plain,
( spl0_466
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2195,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f5186,plain,
spl0_465,
inference(avatar_split_clause,[],[f2194,f5184]) ).
fof(f5184,plain,
( spl0_465
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2194,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
fof(f5182,plain,
spl0_464,
inference(avatar_split_clause,[],[f2193,f5180]) ).
fof(f5180,plain,
( spl0_464
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2193,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
fof(f5178,plain,
spl0_463,
inference(avatar_split_clause,[],[f2192,f5176]) ).
fof(f5176,plain,
( spl0_463
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2192,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
fof(f5174,plain,
spl0_462,
inference(avatar_split_clause,[],[f2191,f5172]) ).
fof(f5172,plain,
( spl0_462
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2191,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f5170,plain,
spl0_461,
inference(avatar_split_clause,[],[f2190,f5168]) ).
fof(f5168,plain,
( spl0_461
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2190,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
fof(f5166,plain,
spl0_460,
inference(avatar_split_clause,[],[f2189,f5164]) ).
fof(f5164,plain,
( spl0_460
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2189,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f5162,plain,
spl0_459,
inference(avatar_split_clause,[],[f2188,f5160]) ).
fof(f5160,plain,
( spl0_459
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2188,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
fof(f5158,plain,
spl0_458,
inference(avatar_split_clause,[],[f2187,f5156]) ).
fof(f5156,plain,
( spl0_458
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2187,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
fof(f5154,plain,
spl0_457,
inference(avatar_split_clause,[],[f2186,f5152]) ).
fof(f5152,plain,
( spl0_457
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2186,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f5150,plain,
spl0_456,
inference(avatar_split_clause,[],[f2185,f5148]) ).
fof(f5148,plain,
( spl0_456
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2185,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
fof(f5146,plain,
spl0_455,
inference(avatar_split_clause,[],[f2184,f5144]) ).
fof(f5144,plain,
( spl0_455
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2184,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
fof(f5142,plain,
spl0_454,
inference(avatar_split_clause,[],[f2183,f5140]) ).
fof(f5140,plain,
( spl0_454
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2183,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f5138,plain,
spl0_453,
inference(avatar_split_clause,[],[f2182,f5136]) ).
fof(f5136,plain,
( spl0_453
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2182,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f5134,plain,
spl0_452,
inference(avatar_split_clause,[],[f2181,f5132]) ).
fof(f5132,plain,
( spl0_452
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2181,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
fof(f5130,plain,
spl0_451,
inference(avatar_split_clause,[],[f2180,f5128]) ).
fof(f5128,plain,
( spl0_451
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2180,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f5126,plain,
spl0_450,
inference(avatar_split_clause,[],[f2179,f5124]) ).
fof(f5124,plain,
( spl0_450
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2179,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f5122,plain,
spl0_449,
inference(avatar_split_clause,[],[f2178,f5120]) ).
fof(f5120,plain,
( spl0_449
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2178,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f5118,plain,
spl0_448,
inference(avatar_split_clause,[],[f2177,f5116]) ).
fof(f5116,plain,
( spl0_448
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2177,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
fof(f5114,plain,
spl0_447,
inference(avatar_split_clause,[],[f2176,f5112]) ).
fof(f5112,plain,
( spl0_447
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2176,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
fof(f5110,plain,
spl0_446,
inference(avatar_split_clause,[],[f2175,f5108]) ).
fof(f5108,plain,
( spl0_446
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2175,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f5106,plain,
spl0_445,
inference(avatar_split_clause,[],[f2174,f5104]) ).
fof(f5104,plain,
( spl0_445
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2174,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f5102,plain,
spl0_444,
inference(avatar_split_clause,[],[f2173,f5100]) ).
fof(f5100,plain,
( spl0_444
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2173,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
fof(f5098,plain,
spl0_443,
inference(avatar_split_clause,[],[f2172,f5096]) ).
fof(f5096,plain,
( spl0_443
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2172,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f5094,plain,
spl0_442,
inference(avatar_split_clause,[],[f2171,f5092]) ).
fof(f5092,plain,
( spl0_442
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2171,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
fof(f5090,plain,
spl0_441,
inference(avatar_split_clause,[],[f2170,f5088]) ).
fof(f5088,plain,
( spl0_441
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2170,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
fof(f5086,plain,
spl0_440,
inference(avatar_split_clause,[],[f2169,f5084]) ).
fof(f5084,plain,
( spl0_440
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2169,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
fof(f5082,plain,
spl0_439,
inference(avatar_split_clause,[],[f2168,f5080]) ).
fof(f5080,plain,
( spl0_439
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2168,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
fof(f5078,plain,
spl0_438,
inference(avatar_split_clause,[],[f2167,f5076]) ).
fof(f5076,plain,
( spl0_438
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2167,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
fof(f5074,plain,
spl0_437,
inference(avatar_split_clause,[],[f2166,f5072]) ).
fof(f5072,plain,
( spl0_437
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2166,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f5070,plain,
spl0_436,
inference(avatar_split_clause,[],[f2165,f5068]) ).
fof(f5068,plain,
( spl0_436
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2165,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f5066,plain,
spl0_435,
inference(avatar_split_clause,[],[f2164,f5064]) ).
fof(f5064,plain,
( spl0_435
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2164,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
fof(f5062,plain,
spl0_434,
inference(avatar_split_clause,[],[f2163,f5060]) ).
fof(f5060,plain,
( spl0_434
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2163,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f5058,plain,
spl0_433,
inference(avatar_split_clause,[],[f2162,f5056]) ).
fof(f5056,plain,
( spl0_433
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2162,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f5054,plain,
spl0_432,
inference(avatar_split_clause,[],[f2161,f5052]) ).
fof(f5052,plain,
( spl0_432
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2161,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
fof(f5050,plain,
spl0_431,
inference(avatar_split_clause,[],[f2160,f5048]) ).
fof(f5048,plain,
( spl0_431
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2160,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
fof(f5046,plain,
spl0_430,
inference(avatar_split_clause,[],[f2159,f5044]) ).
fof(f5044,plain,
( spl0_430
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2159,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
fof(f5042,plain,
spl0_429,
inference(avatar_split_clause,[],[f2158,f5040]) ).
fof(f5040,plain,
( spl0_429
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2158,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
fof(f5038,plain,
spl0_428,
inference(avatar_split_clause,[],[f2157,f5036]) ).
fof(f5036,plain,
( spl0_428
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2157,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
fof(f5034,plain,
spl0_427,
inference(avatar_split_clause,[],[f2156,f5032]) ).
fof(f5032,plain,
( spl0_427
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2156,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__semiring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
fof(f5030,plain,
spl0_426,
inference(avatar_split_clause,[],[f2155,f5028]) ).
fof(f5028,plain,
( spl0_426
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2155,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f5026,plain,
spl0_425,
inference(avatar_split_clause,[],[f2154,f5024]) ).
fof(f5024,plain,
( spl0_425
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2154,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f5022,plain,
spl0_424,
inference(avatar_split_clause,[],[f2153,f5020]) ).
fof(f5020,plain,
( spl0_424
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2153,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
fof(f5018,plain,
spl0_423,
inference(avatar_split_clause,[],[f2152,f5016]) ).
fof(f5016,plain,
( spl0_423
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2152,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f5014,plain,
spl0_422,
inference(avatar_split_clause,[],[f2151,f5012]) ).
fof(f5012,plain,
( spl0_422
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2151,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f5010,plain,
spl0_421,
inference(avatar_split_clause,[],[f2150,f5008]) ).
fof(f5008,plain,
( spl0_421
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2150,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f5006,plain,
spl0_420,
inference(avatar_split_clause,[],[f2149,f5004]) ).
fof(f5004,plain,
( spl0_420
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2149,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
fof(f5002,plain,
spl0_419,
inference(avatar_split_clause,[],[f2148,f5000]) ).
fof(f5000,plain,
( spl0_419
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2148,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4998,plain,
spl0_418,
inference(avatar_split_clause,[],[f2147,f4996]) ).
fof(f4996,plain,
( spl0_418
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2147,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4994,plain,
spl0_417,
inference(avatar_split_clause,[],[f2146,f4992]) ).
fof(f4992,plain,
( spl0_417
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2146,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4990,plain,
spl0_416,
inference(avatar_split_clause,[],[f2145,f4988]) ).
fof(f4988,plain,
( spl0_416
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2145,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4986,plain,
spl0_415,
inference(avatar_split_clause,[],[f2144,f4984]) ).
fof(f4984,plain,
( spl0_415
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2144,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4982,plain,
spl0_414,
inference(avatar_split_clause,[],[f2143,f4980]) ).
fof(f4980,plain,
( spl0_414
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2143,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4978,plain,
spl0_413,
inference(avatar_split_clause,[],[f2142,f4976]) ).
fof(f4976,plain,
( spl0_413
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2142,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4974,plain,
spl0_412,
inference(avatar_split_clause,[],[f2141,f4972]) ).
fof(f4972,plain,
( spl0_412
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2141,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4970,plain,
spl0_411,
inference(avatar_split_clause,[],[f2140,f4968]) ).
fof(f4968,plain,
( spl0_411
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2140,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4966,plain,
spl0_410,
inference(avatar_split_clause,[],[f2139,f4964]) ).
fof(f4964,plain,
( spl0_410
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2139,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4962,plain,
spl0_409,
inference(avatar_split_clause,[],[f2138,f4960]) ).
fof(f4960,plain,
( spl0_409
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2138,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
fof(f4958,plain,
spl0_408,
inference(avatar_split_clause,[],[f2137,f4956]) ).
fof(f4956,plain,
( spl0_408
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2137,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
fof(f4954,plain,
spl0_407,
inference(avatar_split_clause,[],[f2136,f4952]) ).
fof(f4952,plain,
( spl0_407
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2136,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4950,plain,
spl0_406,
inference(avatar_split_clause,[],[f2135,f4948]) ).
fof(f4948,plain,
( spl0_406
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2135,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
fof(f4946,plain,
spl0_405,
inference(avatar_split_clause,[],[f2134,f4944]) ).
fof(f4944,plain,
( spl0_405
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2134,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4942,plain,
spl0_404,
inference(avatar_split_clause,[],[f2133,f4940]) ).
fof(f4940,plain,
( spl0_404
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2133,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
fof(f4938,plain,
spl0_403,
inference(avatar_split_clause,[],[f2132,f4936]) ).
fof(f4936,plain,
( spl0_403
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2132,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4934,plain,
spl0_402,
inference(avatar_split_clause,[],[f2131,f4932]) ).
fof(f4932,plain,
( spl0_402
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2131,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
fof(f4930,plain,
spl0_401,
inference(avatar_split_clause,[],[f2130,f4928]) ).
fof(f4928,plain,
( spl0_401
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2130,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
fof(f4926,plain,
spl0_400,
inference(avatar_split_clause,[],[f2129,f4924]) ).
fof(f4924,plain,
( spl0_400
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2129,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4922,plain,
spl0_399,
inference(avatar_split_clause,[],[f2128,f4920]) ).
fof(f4920,plain,
( spl0_399
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2128,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4918,plain,
spl0_398,
inference(avatar_split_clause,[],[f2127,f4916]) ).
fof(f4916,plain,
( spl0_398
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2127,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4914,plain,
spl0_397,
inference(avatar_split_clause,[],[f2126,f4912]) ).
fof(f4912,plain,
( spl0_397
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2126,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_9) ).
fof(f4910,plain,
spl0_396,
inference(avatar_split_clause,[],[f2125,f4908]) ).
fof(f4908,plain,
( spl0_396
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2125,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_8) ).
fof(f4906,plain,
spl0_395,
inference(avatar_split_clause,[],[f2124,f4904]) ).
fof(f4904,plain,
( spl0_395
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2124,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4902,plain,
spl0_394,
inference(avatar_split_clause,[],[f2123,f4900]) ).
fof(f4900,plain,
( spl0_394
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2123,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_6) ).
fof(f4898,plain,
spl0_393,
inference(avatar_split_clause,[],[f2122,f4896]) ).
fof(f4896,plain,
( spl0_393
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2122,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_5) ).
fof(f4894,plain,
spl0_392,
inference(avatar_split_clause,[],[f2121,f4892]) ).
fof(f4892,plain,
( spl0_392
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2121,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4890,plain,
spl0_391,
inference(avatar_split_clause,[],[f2120,f4888]) ).
fof(f4888,plain,
( spl0_391
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2120,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4886,plain,
spl0_390,
inference(avatar_split_clause,[],[f2119,f4884]) ).
fof(f4884,plain,
( spl0_390
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2119,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_2) ).
fof(f4882,plain,
spl0_389,
inference(avatar_split_clause,[],[f2118,f4880]) ).
fof(f4880,plain,
( spl0_389
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2118,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4878,plain,
spl0_388,
inference(avatar_split_clause,[],[f2117,f4876]) ).
fof(f4876,plain,
( spl0_388
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2117,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4874,plain,
spl0_387,
inference(avatar_split_clause,[],[f2116,f4872]) ).
fof(f4872,plain,
( spl0_387
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2116,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4870,plain,
spl0_386,
inference(avatar_split_clause,[],[f2115,f4868]) ).
fof(f4868,plain,
( spl0_386
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2115,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4866,plain,
spl0_385,
inference(avatar_split_clause,[],[f2114,f4864]) ).
fof(f4864,plain,
( spl0_385
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2114,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4862,plain,
spl0_384,
inference(avatar_split_clause,[],[f2113,f4860]) ).
fof(f4860,plain,
( spl0_384
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2113,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_13) ).
fof(f4858,plain,
spl0_383,
inference(avatar_split_clause,[],[f2112,f4856]) ).
fof(f4856,plain,
( spl0_383
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2112,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4854,plain,
spl0_382,
inference(avatar_split_clause,[],[f2111,f4852]) ).
fof(f4852,plain,
( spl0_382
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2111,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_11) ).
fof(f4850,plain,
spl0_381,
inference(avatar_split_clause,[],[f2110,f4848]) ).
fof(f4848,plain,
( spl0_381
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2110,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_10) ).
fof(f4846,plain,
spl0_380,
inference(avatar_split_clause,[],[f2109,f4844]) ).
fof(f4844,plain,
( spl0_380
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2109,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4842,plain,
spl0_379,
inference(avatar_split_clause,[],[f2108,f4840]) ).
fof(f4840,plain,
( spl0_379
<=> ! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2108,axiom,
! [X87] :
( ~ class_Ring__and__Field_Ocomm__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4838,plain,
spl0_378,
inference(avatar_split_clause,[],[f2107,f4836]) ).
fof(f4836,plain,
( spl0_378
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2107,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
fof(f4834,plain,
spl0_377,
inference(avatar_split_clause,[],[f2106,f4832]) ).
fof(f4832,plain,
( spl0_377
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2106,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
fof(f4830,plain,
spl0_376,
inference(avatar_split_clause,[],[f2105,f4828]) ).
fof(f4828,plain,
( spl0_376
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2105,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
fof(f4826,plain,
spl0_375,
inference(avatar_split_clause,[],[f2104,f4824]) ).
fof(f4824,plain,
( spl0_375
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2104,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4822,plain,
spl0_374,
inference(avatar_split_clause,[],[f2103,f4820]) ).
fof(f4820,plain,
( spl0_374
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f2103,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
fof(f4818,plain,
spl0_373,
inference(avatar_split_clause,[],[f2102,f4816]) ).
fof(f4816,plain,
( spl0_373
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2102,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4814,plain,
spl0_372,
inference(avatar_split_clause,[],[f2101,f4812]) ).
fof(f4812,plain,
( spl0_372
<=> ! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2101,axiom,
! [X87] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
fof(f4810,plain,
spl0_371,
inference(avatar_split_clause,[],[f2100,f4808]) ).
fof(f4808,plain,
( spl0_371
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2100,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_9) ).
fof(f4806,plain,
spl0_370,
inference(avatar_split_clause,[],[f2099,f4804]) ).
fof(f4804,plain,
( spl0_370
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2099,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_8) ).
fof(f4802,plain,
spl0_369,
inference(avatar_split_clause,[],[f2098,f4800]) ).
fof(f4800,plain,
( spl0_369
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2098,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_7) ).
fof(f4798,plain,
spl0_368,
inference(avatar_split_clause,[],[f2097,f4796]) ).
fof(f4796,plain,
( spl0_368
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2097,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_6) ).
fof(f4794,plain,
spl0_367,
inference(avatar_split_clause,[],[f2096,f4792]) ).
fof(f4792,plain,
( spl0_367
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2096,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_5) ).
fof(f4790,plain,
spl0_366,
inference(avatar_split_clause,[],[f2095,f4788]) ).
fof(f4788,plain,
( spl0_366
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2095,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_4) ).
fof(f4786,plain,
spl0_365,
inference(avatar_split_clause,[],[f2094,f4784]) ).
fof(f4784,plain,
( spl0_365
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2094,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4782,plain,
spl0_364,
inference(avatar_split_clause,[],[f2093,f4780]) ).
fof(f4780,plain,
( spl0_364
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2093,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4778,plain,
spl0_363,
inference(avatar_split_clause,[],[f2092,f4776]) ).
fof(f4776,plain,
( spl0_363
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2092,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4774,plain,
spl0_362,
inference(avatar_split_clause,[],[f2091,f4772]) ).
fof(f4772,plain,
( spl0_362
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2091,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4770,plain,
spl0_361,
inference(avatar_split_clause,[],[f2090,f4768]) ).
fof(f4768,plain,
( spl0_361
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2090,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4766,plain,
spl0_360,
inference(avatar_split_clause,[],[f2089,f4764]) ).
fof(f4764,plain,
( spl0_360
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2089,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4762,plain,
spl0_359,
inference(avatar_split_clause,[],[f2088,f4760]) ).
fof(f4760,plain,
( spl0_359
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2088,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4758,plain,
spl0_358,
inference(avatar_split_clause,[],[f2087,f4756]) ).
fof(f4756,plain,
( spl0_358
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2087,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4754,plain,
spl0_357,
inference(avatar_split_clause,[],[f2086,f4752]) ).
fof(f4752,plain,
( spl0_357
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2086,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4750,plain,
spl0_356,
inference(avatar_split_clause,[],[f2085,f4748]) ).
fof(f4748,plain,
( spl0_356
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2085,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4746,plain,
spl0_355,
inference(avatar_split_clause,[],[f2084,f4744]) ).
fof(f4744,plain,
( spl0_355
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2084,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4742,plain,
spl0_354,
inference(avatar_split_clause,[],[f2083,f4740]) ).
fof(f4740,plain,
( spl0_354
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2083,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4738,plain,
spl0_353,
inference(avatar_split_clause,[],[f2082,f4736]) ).
fof(f4736,plain,
( spl0_353
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2082,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4734,plain,
spl0_352,
inference(avatar_split_clause,[],[f2081,f4732]) ).
fof(f4732,plain,
( spl0_352
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2081,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4730,plain,
spl0_351,
inference(avatar_split_clause,[],[f2080,f4728]) ).
fof(f4728,plain,
( spl0_351
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2080,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4726,plain,
spl0_350,
inference(avatar_split_clause,[],[f2079,f4724]) ).
fof(f4724,plain,
( spl0_350
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2079,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4722,plain,
spl0_349,
inference(avatar_split_clause,[],[f2078,f4720]) ).
fof(f4720,plain,
( spl0_349
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2078,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4718,plain,
spl0_348,
inference(avatar_split_clause,[],[f2077,f4716]) ).
fof(f4716,plain,
( spl0_348
<=> ! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2077,axiom,
! [X87] :
( ~ class_Power_Orecpower(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_1) ).
fof(f4714,plain,
spl0_347,
inference(avatar_split_clause,[],[f2075,f4712]) ).
fof(f4712,plain,
( spl0_347
<=> ! [X87] :
( ~ class_Orderings_Oorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2075,axiom,
! [X87] :
( ~ class_Orderings_Oorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4710,plain,
spl0_346,
inference(avatar_split_clause,[],[f2074,f4708]) ).
fof(f4708,plain,
( spl0_346
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2074,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4706,plain,
spl0_345,
inference(avatar_split_clause,[],[f2073,f4704]) ).
fof(f4704,plain,
( spl0_345
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2073,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4702,plain,
spl0_344,
inference(avatar_split_clause,[],[f2072,f4700]) ).
fof(f4700,plain,
( spl0_344
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2072,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4698,plain,
spl0_343,
inference(avatar_split_clause,[],[f2071,f4696]) ).
fof(f4696,plain,
( spl0_343
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2071,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4694,plain,
spl0_342,
inference(avatar_split_clause,[],[f2070,f4692]) ).
fof(f4692,plain,
( spl0_342
<=> ! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2070,axiom,
! [X87] :
( ~ class_Orderings_Olinorder(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4690,plain,
spl0_341,
inference(avatar_split_clause,[],[f2069,f4688]) ).
fof(f4688,plain,
( spl0_341
<=> ! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2069,axiom,
! [X87] :
( ~ class_OrderedGroup_Osemigroup__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__mult_0) ).
fof(f4686,plain,
spl0_340,
inference(avatar_split_clause,[],[f2068,f4684]) ).
fof(f4684,plain,
( spl0_340
<=> ! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2068,axiom,
! [X87] :
( ~ class_OrderedGroup_Osemigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Osemigroup__add_0) ).
fof(f4682,plain,
spl0_339,
inference(avatar_split_clause,[],[f2067,f4680]) ).
fof(f4680,plain,
( spl0_339
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2067,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4678,plain,
spl0_338,
inference(avatar_split_clause,[],[f2066,f4676]) ).
fof(f4676,plain,
( spl0_338
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2066,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4674,plain,
spl0_337,
inference(avatar_split_clause,[],[f2065,f4672]) ).
fof(f4672,plain,
( spl0_337
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2065,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
fof(f4670,plain,
spl0_336,
inference(avatar_split_clause,[],[f2064,f4668]) ).
fof(f4668,plain,
( spl0_336
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2064,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
fof(f4666,plain,
spl0_335,
inference(avatar_split_clause,[],[f2063,f4664]) ).
fof(f4664,plain,
( spl0_335
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2063,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
fof(f4662,plain,
spl0_334,
inference(avatar_split_clause,[],[f2062,f4660]) ).
fof(f4660,plain,
( spl0_334
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2062,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4658,plain,
spl0_333,
inference(avatar_split_clause,[],[f2061,f4656]) ).
fof(f4656,plain,
( spl0_333
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2061,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4654,plain,
spl0_332,
inference(avatar_split_clause,[],[f2060,f4652]) ).
fof(f4652,plain,
( spl0_332
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2060,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4650,plain,
spl0_331,
inference(avatar_split_clause,[],[f2059,f4648]) ).
fof(f4648,plain,
( spl0_331
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2059,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
fof(f4646,plain,
spl0_330,
inference(avatar_split_clause,[],[f2058,f4644]) ).
fof(f4644,plain,
( spl0_330
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2058,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
fof(f4642,plain,
spl0_329,
inference(avatar_split_clause,[],[f2057,f4640]) ).
fof(f4640,plain,
( spl0_329
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2057,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4638,plain,
spl0_328,
inference(avatar_split_clause,[],[f2056,f4636]) ).
fof(f4636,plain,
( spl0_328
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2056,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
fof(f4634,plain,
spl0_327,
inference(avatar_split_clause,[],[f2055,f4632]) ).
fof(f4632,plain,
( spl0_327
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2055,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4630,plain,
spl0_326,
inference(avatar_split_clause,[],[f2054,f4628]) ).
fof(f4628,plain,
( spl0_326
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2054,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4626,plain,
spl0_325,
inference(avatar_split_clause,[],[f2053,f4624]) ).
fof(f4624,plain,
( spl0_325
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2053,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4622,plain,
spl0_324,
inference(avatar_split_clause,[],[f2052,f4620]) ).
fof(f4620,plain,
( spl0_324
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2052,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4618,plain,
spl0_323,
inference(avatar_split_clause,[],[f2051,f4616]) ).
fof(f4616,plain,
( spl0_323
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2051,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4614,plain,
spl0_322,
inference(avatar_split_clause,[],[f2050,f4612]) ).
fof(f4612,plain,
( spl0_322
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2050,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
fof(f4610,plain,
spl0_321,
inference(avatar_split_clause,[],[f2049,f4608]) ).
fof(f4608,plain,
( spl0_321
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2049,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
fof(f4606,plain,
spl0_320,
inference(avatar_split_clause,[],[f2048,f4604]) ).
fof(f4604,plain,
( spl0_320
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2048,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
fof(f4602,plain,
spl0_319,
inference(avatar_split_clause,[],[f2047,f4600]) ).
fof(f4600,plain,
( spl0_319
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2047,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4598,plain,
spl0_318,
inference(avatar_split_clause,[],[f2046,f4596]) ).
fof(f4596,plain,
( spl0_318
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2046,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4594,plain,
spl0_317,
inference(avatar_split_clause,[],[f2045,f4592]) ).
fof(f4592,plain,
( spl0_317
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2045,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4590,plain,
spl0_316,
inference(avatar_split_clause,[],[f2044,f4588]) ).
fof(f4588,plain,
( spl0_316
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2044,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
fof(f4586,plain,
spl0_315,
inference(avatar_split_clause,[],[f2043,f4584]) ).
fof(f4584,plain,
( spl0_315
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2043,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
fof(f4582,plain,
spl0_314,
inference(avatar_split_clause,[],[f2042,f4580]) ).
fof(f4580,plain,
( spl0_314
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2042,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4578,plain,
spl0_313,
inference(avatar_split_clause,[],[f2041,f4576]) ).
fof(f4576,plain,
( spl0_313
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2041,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
fof(f4574,plain,
spl0_312,
inference(avatar_split_clause,[],[f2040,f4572]) ).
fof(f4572,plain,
( spl0_312
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2040,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4570,plain,
spl0_311,
inference(avatar_split_clause,[],[f2039,f4568]) ).
fof(f4568,plain,
( spl0_311
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2039,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
fof(f4566,plain,
spl0_310,
inference(avatar_split_clause,[],[f2038,f4564]) ).
fof(f4564,plain,
( spl0_310
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2038,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4562,plain,
spl0_309,
inference(avatar_split_clause,[],[f2037,f4560]) ).
fof(f4560,plain,
( spl0_309
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2037,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4558,plain,
spl0_308,
inference(avatar_split_clause,[],[f2036,f4556]) ).
fof(f4556,plain,
( spl0_308
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2036,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4554,plain,
spl0_307,
inference(avatar_split_clause,[],[f2035,f4552]) ).
fof(f4552,plain,
( spl0_307
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2035,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4550,plain,
spl0_306,
inference(avatar_split_clause,[],[f2034,f4548]) ).
fof(f4548,plain,
( spl0_306
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2034,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4546,plain,
spl0_305,
inference(avatar_split_clause,[],[f2033,f4544]) ).
fof(f4544,plain,
( spl0_305
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2033,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
fof(f4542,plain,
spl0_304,
inference(avatar_split_clause,[],[f2032,f4540]) ).
fof(f4540,plain,
( spl0_304
<=> ! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2032,axiom,
! [X87] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4538,plain,
spl0_303,
inference(avatar_split_clause,[],[f2031,f4536]) ).
fof(f4536,plain,
( spl0_303
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Olinorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2031,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Olinorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4534,plain,
spl0_302,
inference(avatar_split_clause,[],[f2030,f4532]) ).
fof(f4532,plain,
( spl0_302
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2030,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
fof(f4530,plain,
spl0_301,
inference(avatar_split_clause,[],[f2029,f4528]) ).
fof(f4528,plain,
( spl0_301
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2029,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
fof(f4526,plain,
spl0_300,
inference(avatar_split_clause,[],[f2028,f4524]) ).
fof(f4524,plain,
( spl0_300
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2028,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4522,plain,
spl0_299,
inference(avatar_split_clause,[],[f2027,f4520]) ).
fof(f4520,plain,
( spl0_299
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2027,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
fof(f4518,plain,
spl0_298,
inference(avatar_split_clause,[],[f2026,f4516]) ).
fof(f4516,plain,
( spl0_298
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2026,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4514,plain,
spl0_297,
inference(avatar_split_clause,[],[f2025,f4512]) ).
fof(f4512,plain,
( spl0_297
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2025,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4510,plain,
spl0_296,
inference(avatar_split_clause,[],[f2024,f4508]) ).
fof(f4508,plain,
( spl0_296
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2024,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4506,plain,
spl0_295,
inference(avatar_split_clause,[],[f2023,f4504]) ).
fof(f4504,plain,
( spl0_295
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2023,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4502,plain,
spl0_294,
inference(avatar_split_clause,[],[f2022,f4500]) ).
fof(f4500,plain,
( spl0_294
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2022,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4498,plain,
spl0_293,
inference(avatar_split_clause,[],[f2021,f4496]) ).
fof(f4496,plain,
( spl0_293
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2021,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4494,plain,
spl0_292,
inference(avatar_split_clause,[],[f2020,f4492]) ).
fof(f4492,plain,
( spl0_292
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2020,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4490,plain,
spl0_291,
inference(avatar_split_clause,[],[f2019,f4488]) ).
fof(f4488,plain,
( spl0_291
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2019,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4486,plain,
spl0_290,
inference(avatar_split_clause,[],[f2018,f4484]) ).
fof(f4484,plain,
( spl0_290
<=> ! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2018,axiom,
! [X87] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4482,plain,
spl0_289,
inference(avatar_split_clause,[],[f2017,f4480]) ).
fof(f4480,plain,
( spl0_289
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2017,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_2) ).
fof(f4478,plain,
spl0_288,
inference(avatar_split_clause,[],[f2016,f4476]) ).
fof(f4476,plain,
( spl0_288
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2016,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_1) ).
fof(f4474,plain,
spl0_287,
inference(avatar_split_clause,[],[f2015,f4472]) ).
fof(f4472,plain,
( spl0_287
<=> ! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2015,axiom,
! [X87] :
( ~ class_OrderedGroup_Omonoid__mult(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4470,plain,
spl0_286,
inference(avatar_split_clause,[],[f2014,f4468]) ).
fof(f4468,plain,
( spl0_286
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2014,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4466,plain,
spl0_285,
inference(avatar_split_clause,[],[f2013,f4464]) ).
fof(f4464,plain,
( spl0_285
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2013,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4462,plain,
spl0_284,
inference(avatar_split_clause,[],[f2012,f4460]) ).
fof(f4460,plain,
( spl0_284
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2012,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4458,plain,
spl0_283,
inference(avatar_split_clause,[],[f2011,f4456]) ).
fof(f4456,plain,
( spl0_283
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2011,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4454,plain,
spl0_282,
inference(avatar_split_clause,[],[f2010,f4452]) ).
fof(f4452,plain,
( spl0_282
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2010,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4450,plain,
spl0_281,
inference(avatar_split_clause,[],[f2009,f4448]) ).
fof(f4448,plain,
( spl0_281
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2009,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
fof(f4446,plain,
spl0_280,
inference(avatar_split_clause,[],[f2008,f4444]) ).
fof(f4444,plain,
( spl0_280
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2008,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4442,plain,
spl0_279,
inference(avatar_split_clause,[],[f2007,f4440]) ).
fof(f4440,plain,
( spl0_279
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2007,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
fof(f4438,plain,
spl0_278,
inference(avatar_split_clause,[],[f2006,f4436]) ).
fof(f4436,plain,
( spl0_278
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2006,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4434,plain,
spl0_277,
inference(avatar_split_clause,[],[f2005,f4432]) ).
fof(f4432,plain,
( spl0_277
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2005,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4430,plain,
spl0_276,
inference(avatar_split_clause,[],[f2004,f4428]) ).
fof(f4428,plain,
( spl0_276
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2004,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4426,plain,
spl0_275,
inference(avatar_split_clause,[],[f2003,f4424]) ).
fof(f4424,plain,
( spl0_275
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2003,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4422,plain,
spl0_274,
inference(avatar_split_clause,[],[f2002,f4420]) ).
fof(f4420,plain,
( spl0_274
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2002,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
fof(f4418,plain,
spl0_273,
inference(avatar_split_clause,[],[f2001,f4416]) ).
fof(f4416,plain,
( spl0_273
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2001,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
fof(f4414,plain,
spl0_272,
inference(avatar_split_clause,[],[f2000,f4412]) ).
fof(f4412,plain,
( spl0_272
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2000,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4410,plain,
spl0_271,
inference(avatar_split_clause,[],[f1999,f4408]) ).
fof(f4408,plain,
( spl0_271
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f1999,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
fof(f4406,plain,
spl0_270,
inference(avatar_split_clause,[],[f1998,f4404]) ).
fof(f4404,plain,
( spl0_270
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f1998,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4402,plain,
spl0_269,
inference(avatar_split_clause,[],[f1997,f4400]) ).
fof(f4400,plain,
( spl0_269
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f1997,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4398,plain,
spl0_268,
inference(avatar_split_clause,[],[f1996,f4396]) ).
fof(f4396,plain,
( spl0_268
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f1996,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4394,plain,
spl0_267,
inference(avatar_split_clause,[],[f1995,f4392]) ).
fof(f4392,plain,
( spl0_267
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f1995,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4390,plain,
spl0_266,
inference(avatar_split_clause,[],[f1994,f4388]) ).
fof(f4388,plain,
( spl0_266
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f1994,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4386,plain,
spl0_265,
inference(avatar_split_clause,[],[f1993,f4384]) ).
fof(f4384,plain,
( spl0_265
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f1993,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4382,plain,
spl0_264,
inference(avatar_split_clause,[],[f1992,f4380]) ).
fof(f4380,plain,
( spl0_264
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f1992,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4378,plain,
spl0_263,
inference(avatar_split_clause,[],[f1991,f4376]) ).
fof(f4376,plain,
( spl0_263
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f1991,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4374,plain,
spl0_262,
inference(avatar_split_clause,[],[f1990,f4372]) ).
fof(f4372,plain,
( spl0_262
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f1990,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
fof(f4370,plain,
spl0_261,
inference(avatar_split_clause,[],[f1989,f4368]) ).
fof(f4368,plain,
( spl0_261
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f1989,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4366,plain,
spl0_260,
inference(avatar_split_clause,[],[f1988,f4364]) ).
fof(f4364,plain,
( spl0_260
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f1988,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
fof(f4362,plain,
spl0_259,
inference(avatar_split_clause,[],[f1987,f4360]) ).
fof(f4360,plain,
( spl0_259
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f1987,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4358,plain,
spl0_258,
inference(avatar_split_clause,[],[f1986,f4356]) ).
fof(f4356,plain,
( spl0_258
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f1986,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4354,plain,
spl0_257,
inference(avatar_split_clause,[],[f1985,f4352]) ).
fof(f4352,plain,
( spl0_257
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f1985,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4350,plain,
spl0_256,
inference(avatar_split_clause,[],[f1984,f4348]) ).
fof(f4348,plain,
( spl0_256
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f1984,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4346,plain,
spl0_255,
inference(avatar_split_clause,[],[f1983,f4344]) ).
fof(f4344,plain,
( spl0_255
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f1983,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
fof(f4342,plain,
spl0_254,
inference(avatar_split_clause,[],[f1982,f4340]) ).
fof(f4340,plain,
( spl0_254
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f1982,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
fof(f4338,plain,
spl0_253,
inference(avatar_split_clause,[],[f1981,f4336]) ).
fof(f4336,plain,
( spl0_253
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f1981,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4334,plain,
spl0_252,
inference(avatar_split_clause,[],[f1980,f4332]) ).
fof(f4332,plain,
( spl0_252
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f1980,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
fof(f4330,plain,
spl0_251,
inference(avatar_split_clause,[],[f1979,f4328]) ).
fof(f4328,plain,
( spl0_251
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f1979,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4326,plain,
spl0_250,
inference(avatar_split_clause,[],[f1978,f4324]) ).
fof(f4324,plain,
( spl0_250
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f1978,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4322,plain,
spl0_249,
inference(avatar_split_clause,[],[f1977,f4320]) ).
fof(f4320,plain,
( spl0_249
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f1977,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4318,plain,
spl0_248,
inference(avatar_split_clause,[],[f1976,f4316]) ).
fof(f4316,plain,
( spl0_248
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f1976,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4314,plain,
spl0_247,
inference(avatar_split_clause,[],[f1975,f4312]) ).
fof(f4312,plain,
( spl0_247
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f1975,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4310,plain,
spl0_246,
inference(avatar_split_clause,[],[f1974,f4308]) ).
fof(f4308,plain,
( spl0_246
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f1974,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4306,plain,
spl0_245,
inference(avatar_split_clause,[],[f1973,f4304]) ).
fof(f4304,plain,
( spl0_245
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f1973,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4302,plain,
spl0_244,
inference(avatar_split_clause,[],[f1972,f4300]) ).
fof(f4300,plain,
( spl0_244
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f1972,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
fof(f4298,plain,
spl0_243,
inference(avatar_split_clause,[],[f1971,f4296]) ).
fof(f4296,plain,
( spl0_243
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f1971,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4294,plain,
spl0_242,
inference(avatar_split_clause,[],[f1970,f4292]) ).
fof(f4292,plain,
( spl0_242
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f1970,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
fof(f4290,plain,
spl0_241,
inference(avatar_split_clause,[],[f1969,f4288]) ).
fof(f4288,plain,
( spl0_241
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f1969,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4286,plain,
spl0_240,
inference(avatar_split_clause,[],[f1968,f4284]) ).
fof(f4284,plain,
( spl0_240
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1968,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4282,plain,
spl0_239,
inference(avatar_split_clause,[],[f1967,f4280]) ).
fof(f4280,plain,
( spl0_239
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1967,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4278,plain,
spl0_238,
inference(avatar_split_clause,[],[f1966,f4276]) ).
fof(f4276,plain,
( spl0_238
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1966,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4274,plain,
spl0_237,
inference(avatar_split_clause,[],[f1965,f4272]) ).
fof(f4272,plain,
( spl0_237
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1965,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4270,plain,
spl0_236,
inference(avatar_split_clause,[],[f1964,f4268]) ).
fof(f4268,plain,
( spl0_236
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1964,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4266,plain,
spl0_235,
inference(avatar_split_clause,[],[f1963,f4264]) ).
fof(f4264,plain,
( spl0_235
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1963,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
fof(f4262,plain,
spl0_234,
inference(avatar_split_clause,[],[f1962,f4260]) ).
fof(f4260,plain,
( spl0_234
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1962,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
fof(f4258,plain,
spl0_233,
inference(avatar_split_clause,[],[f1961,f4256]) ).
fof(f4256,plain,
( spl0_233
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1961,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4254,plain,
spl0_232,
inference(avatar_split_clause,[],[f1960,f4252]) ).
fof(f4252,plain,
( spl0_232
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1960,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
fof(f4250,plain,
spl0_231,
inference(avatar_split_clause,[],[f1959,f4248]) ).
fof(f4248,plain,
( spl0_231
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1959,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4246,plain,
spl0_230,
inference(avatar_split_clause,[],[f1958,f4244]) ).
fof(f4244,plain,
( spl0_230
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1958,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X87)
| class_OrderedGroup_Olordered__ab__group(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4242,plain,
spl0_229,
inference(avatar_split_clause,[],[f1957,f4240]) ).
fof(f4240,plain,
( spl0_229
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1957,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4238,plain,
spl0_228,
inference(avatar_split_clause,[],[f1956,f4236]) ).
fof(f4236,plain,
( spl0_228
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1956,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4234,plain,
spl0_227,
inference(avatar_split_clause,[],[f1955,f4232]) ).
fof(f4232,plain,
( spl0_227
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1955,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f4230,plain,
spl0_226,
inference(avatar_split_clause,[],[f1954,f4228]) ).
fof(f4228,plain,
( spl0_226
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1954,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f4226,plain,
spl0_225,
inference(avatar_split_clause,[],[f1953,f4224]) ).
fof(f4224,plain,
( spl0_225
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1953,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f4222,plain,
spl0_224,
inference(avatar_split_clause,[],[f1952,f4220]) ).
fof(f4220,plain,
( spl0_224
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1952,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_4) ).
fof(f4218,plain,
spl0_223,
inference(avatar_split_clause,[],[f1951,f4216]) ).
fof(f4216,plain,
( spl0_223
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1951,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f4214,plain,
spl0_222,
inference(avatar_split_clause,[],[f1950,f4212]) ).
fof(f4212,plain,
( spl0_222
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1950,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_2) ).
fof(f4210,plain,
spl0_221,
inference(avatar_split_clause,[],[f1949,f4208]) ).
fof(f4208,plain,
( spl0_221
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1949,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f4206,plain,
spl0_220,
inference(avatar_split_clause,[],[f1948,f4204]) ).
fof(f4204,plain,
( spl0_220
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1948,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f4202,plain,
spl0_219,
inference(avatar_split_clause,[],[f1947,f4200]) ).
fof(f4200,plain,
( spl0_219
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Olorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1947,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_LOrder_Olorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f4198,plain,
spl0_218,
inference(avatar_split_clause,[],[f1946,f4196]) ).
fof(f4196,plain,
( spl0_218
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1946,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_14) ).
fof(f4194,plain,
spl0_217,
inference(avatar_split_clause,[],[f1945,f4192]) ).
fof(f4192,plain,
( spl0_217
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1945,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_13) ).
fof(f4190,plain,
spl0_216,
inference(avatar_split_clause,[],[f1944,f4188]) ).
fof(f4188,plain,
( spl0_216
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1944,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f4186,plain,
spl0_215,
inference(avatar_split_clause,[],[f1943,f4184]) ).
fof(f4184,plain,
( spl0_215
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1943,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_11) ).
fof(f4182,plain,
spl0_214,
inference(avatar_split_clause,[],[f1942,f4180]) ).
fof(f4180,plain,
( spl0_214
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1942,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f4178,plain,
spl0_213,
inference(avatar_split_clause,[],[f1941,f4176]) ).
fof(f4176,plain,
( spl0_213
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1941,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f4174,plain,
spl0_212,
inference(avatar_split_clause,[],[f1940,f4172]) ).
fof(f4172,plain,
( spl0_212
<=> ! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1940,axiom,
! [X87] :
( ~ class_OrderedGroup_Olordered__ab__group(X87)
| class_OrderedGroup_Opordered__ab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f4170,plain,
spl0_211,
inference(avatar_split_clause,[],[f1939,f4168]) ).
fof(f4168,plain,
( spl0_211
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1939,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f4166,plain,
spl0_210,
inference(avatar_split_clause,[],[f1938,f4164]) ).
fof(f4164,plain,
( spl0_210
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1938,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
fof(f4162,plain,
spl0_209,
inference(avatar_split_clause,[],[f1937,f4160]) ).
fof(f4160,plain,
( spl0_209
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1937,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
fof(f4158,plain,
spl0_208,
inference(avatar_split_clause,[],[f1936,f4156]) ).
fof(f4156,plain,
( spl0_208
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1936,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
fof(f4154,plain,
spl0_207,
inference(avatar_split_clause,[],[f1935,f4152]) ).
fof(f4152,plain,
( spl0_207
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1935,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f4150,plain,
spl0_206,
inference(avatar_split_clause,[],[f1934,f4148]) ).
fof(f4148,plain,
( spl0_206
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1934,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
fof(f4146,plain,
spl0_205,
inference(avatar_split_clause,[],[f1933,f4144]) ).
fof(f4144,plain,
( spl0_205
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1933,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
fof(f4142,plain,
spl0_204,
inference(avatar_split_clause,[],[f1932,f4140]) ).
fof(f4140,plain,
( spl0_204
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1932,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
fof(f4138,plain,
spl0_203,
inference(avatar_split_clause,[],[f1931,f4136]) ).
fof(f4136,plain,
( spl0_203
<=> ! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1931,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
fof(f4134,plain,
spl0_202,
inference(avatar_split_clause,[],[f1930,f4132]) ).
fof(f4132,plain,
( spl0_202
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1930,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
fof(f4130,plain,
spl0_201,
inference(avatar_split_clause,[],[f1929,f4128]) ).
fof(f4128,plain,
( spl0_201
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1929,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
fof(f4126,plain,
spl0_200,
inference(avatar_split_clause,[],[f1928,f4124]) ).
fof(f4124,plain,
( spl0_200
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1928,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f4122,plain,
spl0_199,
inference(avatar_split_clause,[],[f1927,f4120]) ).
fof(f4120,plain,
( spl0_199
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1927,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
fof(f4118,plain,
spl0_198,
inference(avatar_split_clause,[],[f1926,f4116]) ).
fof(f4116,plain,
( spl0_198
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1926,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
fof(f4114,plain,
spl0_197,
inference(avatar_split_clause,[],[f1925,f4112]) ).
fof(f4112,plain,
( spl0_197
<=> ! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1925,axiom,
! [X87] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
fof(f4110,plain,
spl0_196,
inference(avatar_split_clause,[],[f1924,f4108]) ).
fof(f4108,plain,
( spl0_196
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1924,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
fof(f4106,plain,
spl0_195,
inference(avatar_split_clause,[],[f1923,f4104]) ).
fof(f4104,plain,
( spl0_195
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1923,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
fof(f4102,plain,
spl0_194,
inference(avatar_split_clause,[],[f1922,f4100]) ).
fof(f4100,plain,
( spl0_194
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1922,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
fof(f4098,plain,
spl0_193,
inference(avatar_split_clause,[],[f1921,f4096]) ).
fof(f4096,plain,
( spl0_193
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1921,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__semigroup__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
fof(f4094,plain,
spl0_192,
inference(avatar_split_clause,[],[f1920,f4092]) ).
fof(f4092,plain,
( spl0_192
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1920,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f4090,plain,
spl0_191,
inference(avatar_split_clause,[],[f1919,f4088]) ).
fof(f4088,plain,
( spl0_191
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1919,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f4086,plain,
spl0_190,
inference(avatar_split_clause,[],[f1918,f4084]) ).
fof(f4084,plain,
( spl0_190
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1918,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_5) ).
fof(f4082,plain,
spl0_189,
inference(avatar_split_clause,[],[f1917,f4080]) ).
fof(f4080,plain,
( spl0_189
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1917,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_4) ).
fof(f4078,plain,
spl0_188,
inference(avatar_split_clause,[],[f1916,f4076]) ).
fof(f4076,plain,
( spl0_188
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1916,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_3) ).
fof(f4074,plain,
spl0_187,
inference(avatar_split_clause,[],[f1915,f4072]) ).
fof(f4072,plain,
( spl0_187
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1915,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_2) ).
fof(f4070,plain,
spl0_186,
inference(avatar_split_clause,[],[f1914,f4068]) ).
fof(f4068,plain,
( spl0_186
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1914,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f4066,plain,
spl0_185,
inference(avatar_split_clause,[],[f1913,f4064]) ).
fof(f4064,plain,
( spl0_185
<=> ! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1913,axiom,
! [X87] :
( ~ class_OrderedGroup_Oab__group__add(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_0) ).
fof(f4062,plain,
spl0_184,
inference(avatar_split_clause,[],[f1912,f4060]) ).
fof(f4060,plain,
( spl0_184
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1912,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f4058,plain,
spl0_183,
inference(avatar_split_clause,[],[f1911,f4056]) ).
fof(f4056,plain,
( spl0_183
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ozero(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1911,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ozero(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_8) ).
fof(f4054,plain,
spl0_182,
inference(avatar_split_clause,[],[f1910,f4052]) ).
fof(f4052,plain,
( spl0_182
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1910,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f4050,plain,
spl0_181,
inference(avatar_split_clause,[],[f1909,f4048]) ).
fof(f4048,plain,
( spl0_181
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1909,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f4046,plain,
spl0_180,
inference(avatar_split_clause,[],[f1908,f4044]) ).
fof(f4044,plain,
( spl0_180
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1908,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_5) ).
fof(f4042,plain,
spl0_179,
inference(avatar_split_clause,[],[f1907,f4040]) ).
fof(f4040,plain,
( spl0_179
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1907,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_4) ).
fof(f4038,plain,
spl0_178,
inference(avatar_split_clause,[],[f1906,f4036]) ).
fof(f4036,plain,
( spl0_178
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Numeral_Onumber(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1906,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Numeral_Onumber(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f4034,plain,
spl0_177,
inference(avatar_split_clause,[],[f1905,f4032]) ).
fof(f4032,plain,
( spl0_177
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Otimes(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1905,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Otimes(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_3) ).
fof(f4030,plain,
spl0_176,
inference(avatar_split_clause,[],[f1904,f4028]) ).
fof(f4028,plain,
( spl0_176
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1904,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f4026,plain,
spl0_175,
inference(avatar_split_clause,[],[f1903,f4024]) ).
fof(f4024,plain,
( spl0_175
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1903,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f4022,plain,
spl0_174,
inference(avatar_split_clause,[],[f1902,f4020]) ).
fof(f4020,plain,
( spl0_174
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1902,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f4018,plain,
spl0_173,
inference(avatar_split_clause,[],[f1901,f4016]) ).
fof(f4016,plain,
( spl0_173
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1901,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f4014,plain,
spl0_172,
inference(avatar_split_clause,[],[f1900,f4012]) ).
fof(f4012,plain,
( spl0_172
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1900,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f4010,plain,
spl0_171,
inference(avatar_split_clause,[],[f1899,f4008]) ).
fof(f4008,plain,
( spl0_171
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1899,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f4006,plain,
spl0_170,
inference(avatar_split_clause,[],[f1898,f4004]) ).
fof(f4004,plain,
( spl0_170
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1898,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocomm__monoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f4002,plain,
spl0_169,
inference(avatar_split_clause,[],[f1897,f4000]) ).
fof(f4000,plain,
( spl0_169
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Omonoid__mult(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1897,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Omonoid__mult(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3998,plain,
spl0_168,
inference(avatar_split_clause,[],[f1896,f3996]) ).
fof(f3996,plain,
( spl0_168
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1896,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oaxclass__0__neq__1(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3994,plain,
spl0_167,
inference(avatar_split_clause,[],[f1895,f3992]) ).
fof(f3992,plain,
( spl0_167
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oone(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1895,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oone(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3990,plain,
spl0_166,
inference(avatar_split_clause,[],[f1894,f3988]) ).
fof(f3988,plain,
( spl0_166
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1894,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_2) ).
fof(f3986,plain,
spl0_165,
inference(avatar_split_clause,[],[f1893,f3984]) ).
fof(f3984,plain,
( spl0_165
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1893,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__ring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3982,plain,
spl0_164,
inference(avatar_split_clause,[],[f1892,f3980]) ).
fof(f3980,plain,
( spl0_164
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1892,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3978,plain,
spl0_163,
inference(avatar_split_clause,[],[f1891,f3976]) ).
fof(f3976,plain,
( spl0_163
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1891,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Oring(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3974,plain,
spl0_162,
inference(avatar_split_clause,[],[f1890,f3972]) ).
fof(f3972,plain,
( spl0_162
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1890,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0__cancel(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3970,plain,
spl0_161,
inference(avatar_split_clause,[],[f1889,f3968]) ).
fof(f3968,plain,
( spl0_161
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1889,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Oab__group__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3966,plain,
spl0_160,
inference(avatar_split_clause,[],[f1888,f3964]) ).
fof(f3964,plain,
( spl0_160
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1888,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3962,plain,
spl0_159,
inference(avatar_split_clause,[],[f1887,f3960]) ).
fof(f3960,plain,
( spl0_159
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1887,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Ocancel__semigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3958,plain,
spl0_158,
inference(avatar_split_clause,[],[f1886,f3956]) ).
fof(f3956,plain,
( spl0_158
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ominus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1886,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Ominus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_12) ).
fof(f3954,plain,
spl0_157,
inference(avatar_split_clause,[],[f1885,f3952]) ).
fof(f3952,plain,
( spl0_157
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1885,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Ocomm__semiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3950,plain,
spl0_156,
inference(avatar_split_clause,[],[f1884,f3948]) ).
fof(f3948,plain,
( spl0_156
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1884,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_Ring__and__Field_Osemiring__0(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3946,plain,
spl0_155,
inference(avatar_split_clause,[],[f1883,f3944]) ).
fof(f3944,plain,
( spl0_155
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1883,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_OrderedGroup_Osemigroup__add(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_1) ).
fof(f3942,plain,
spl0_154,
inference(avatar_split_clause,[],[f1882,f3940]) ).
fof(f3940,plain,
( spl0_154
<=> ! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oplus(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1882,axiom,
! [X87] :
( ~ class_Numeral_Onumber__ring(X87)
| class_HOL_Oplus(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_0) ).
fof(f3938,plain,
spl0_153,
inference(avatar_split_clause,[],[f1881,f3936]) ).
fof(f3936,plain,
( spl0_153
<=> ! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1881,axiom,
! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3934,plain,
spl0_152,
inference(avatar_split_clause,[],[f1880,f3932]) ).
fof(f3932,plain,
( spl0_152
<=> ! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1880,axiom,
! [X87] :
( ~ class_LOrder_Omeet__semilorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3930,plain,
spl0_151,
inference(avatar_split_clause,[],[f1879,f3928]) ).
fof(f3928,plain,
( spl0_151
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1879,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Ojoin__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3926,plain,
spl0_150,
inference(avatar_split_clause,[],[f1878,f3924]) ).
fof(f3924,plain,
( spl0_150
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1878,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3922,plain,
spl0_149,
inference(avatar_split_clause,[],[f1877,f3920]) ).
fof(f3920,plain,
( spl0_149
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1877,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3918,plain,
spl0_148,
inference(avatar_split_clause,[],[f1876,f3916]) ).
fof(f3916,plain,
( spl0_148
<=> ! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Omeet__semilorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1876,axiom,
! [X87] :
( ~ class_LOrder_Olorder(X87)
| class_LOrder_Omeet__semilorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3914,plain,
spl0_147,
inference(avatar_split_clause,[],[f1875,f3912]) ).
fof(f3912,plain,
( spl0_147
<=> ! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oorder(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1875,axiom,
! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oorder(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3910,plain,
spl0_146,
inference(avatar_split_clause,[],[f1874,f3908]) ).
fof(f3908,plain,
( spl0_146
<=> ! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oord(X87) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1874,axiom,
! [X87] :
( ~ class_LOrder_Ojoin__semilorder(X87)
| class_Orderings_Oord(X87) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3906,plain,
spl0_145,
inference(avatar_split_clause,[],[f1719,f3904]) ).
fof(f3904,plain,
( spl0_145
<=> ! [X0,X12] : c_in(X12,c_UNIV,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1719,axiom,
! [X0,X12] : c_in(X12,c_UNIV,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3902,plain,
spl0_144,
inference(avatar_split_clause,[],[f1687,f3900]) ).
fof(f3900,plain,
( spl0_144
<=> ! [X11] : ~ c_less(X11,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1687,axiom,
! [X11] : ~ c_less(X11,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3898,plain,
spl0_143,
inference(avatar_split_clause,[],[f1685,f3896]) ).
fof(f3896,plain,
( spl0_143
<=> ! [X11] : c_lessequals(c_0,X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1685,axiom,
! [X11] : c_lessequals(c_0,X11,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3894,plain,
spl0_142,
inference(avatar_split_clause,[],[f1661,f3892]) ).
fof(f3892,plain,
( spl0_142
<=> ! [X24] : c_Divides_Oop_Advd(c_1,X24,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1661,axiom,
! [X24] : c_Divides_Oop_Advd(c_1,X24,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3890,plain,
spl0_141,
inference(avatar_split_clause,[],[f1660,f3888]) ).
fof(f3888,plain,
( spl0_141
<=> ! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1660,axiom,
! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3886,plain,
spl0_140,
inference(avatar_split_clause,[],[f1644,f3884]) ).
fof(f3884,plain,
( spl0_140
<=> ! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1644,axiom,
! [X24] : c_Divides_Oop_Advd(X24,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3882,plain,
spl0_139,
inference(avatar_split_clause,[],[f1566,f3880]) ).
fof(f3880,plain,
( spl0_139
<=> ! [X25,X0] : ~ c_in(X25,c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1566,axiom,
! [X0,X25] : ~ c_in(X25,c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3878,plain,
spl0_138,
inference(avatar_split_clause,[],[f1049,f3875]) ).
fof(f3875,plain,
( spl0_138
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1049,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Min_0) ).
fof(f3873,plain,
spl0_137,
inference(avatar_split_clause,[],[f985,f3871]) ).
fof(f3871,plain,
( spl0_137
<=> ! [X11] : ~ c_less(X11,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f985,axiom,
! [X11] : ~ c_less(X11,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3869,plain,
spl0_136,
inference(avatar_split_clause,[],[f943,f3866]) ).
fof(f3866,plain,
( spl0_136
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f943,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3864,plain,
spl0_135,
inference(avatar_split_clause,[],[f603,f3862]) ).
fof(f3862,plain,
( spl0_135
<=> ! [X12,X14] : ~ c_List_Oop_Amem(X12,c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f603,axiom,
! [X14,X12] : ~ c_List_Oop_Amem(X12,c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3860,plain,
spl0_134,
inference(avatar_split_clause,[],[f376,f3858]) ).
fof(f3858,plain,
( spl0_134
<=> ! [X24] : c_Divides_Oop_Advd(X24,X24,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f376,axiom,
! [X24] : c_Divides_Oop_Advd(X24,X24,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3856,plain,
spl0_133,
inference(avatar_split_clause,[],[f287,f3854]) ).
fof(f287,axiom,
! [X11] : ~ c_IntDef_Oneg(c_IntDef_Oint(X11),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3852,plain,
spl0_132,
inference(avatar_split_clause,[],[f280,f3849]) ).
fof(f3849,plain,
( spl0_132
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f280,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3847,plain,
spl0_131,
inference(avatar_split_clause,[],[f268,f3844]) ).
fof(f3842,plain,
spl0_130,
inference(avatar_split_clause,[],[f265,f3839]) ).
fof(f265,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3837,plain,
spl0_129,
inference(avatar_split_clause,[],[f123,f3835]) ).
fof(f3835,plain,
( spl0_129
<=> ! [X24] : c_Divides_Oop_Advd(X24,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f123,axiom,
! [X24] : c_Divides_Oop_Advd(X24,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3833,plain,
spl0_128,
inference(avatar_split_clause,[],[f2784,f3831]) ).
fof(f2784,axiom,
! [X29,X52] : c_lessequals(c_HOL_Oabs(v_f(X29,X52),t_c),c_times(v_x,v_h(X29,X52),t_c),t_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3829,plain,
spl0_127,
inference(avatar_split_clause,[],[f1870,f3827]) ).
fof(f3827,plain,
( spl0_127
<=> ! [X8] : class_Orderings_Oorder(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1870,axiom,
! [X8] : class_Orderings_Oorder(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3825,plain,
spl0_126,
inference(avatar_split_clause,[],[f1869,f3823]) ).
fof(f3823,plain,
( spl0_126
<=> ! [X8] : class_Orderings_Oord(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1869,axiom,
! [X8] : class_Orderings_Oord(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3821,plain,
spl0_125,
inference(avatar_split_clause,[],[f1868,f3819]) ).
fof(f3819,plain,
( spl0_125
<=> ! [X8] : class_HOL_Ominus(tc_set(X8)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1868,axiom,
! [X8] : class_HOL_Ominus(tc_set(X8)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_0) ).
fof(f3817,plain,
spl0_124,
inference(avatar_split_clause,[],[f1747,f3814]) ).
fof(f3814,plain,
( spl0_124
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1747,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3812,plain,
spl0_123,
inference(avatar_split_clause,[],[f1745,f3809]) ).
fof(f3809,plain,
( spl0_123
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1745,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3807,plain,
spl0_122,
inference(avatar_split_clause,[],[f1744,f3805]) ).
fof(f3805,plain,
( spl0_122
<=> ! [X0] : c_Wellfounded__Recursion_Owf(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1744,axiom,
! [X0] : c_Wellfounded__Recursion_Owf(c_emptyset,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3803,plain,
~ spl0_121,
inference(avatar_split_clause,[],[f1523,f3800]) ).
fof(f3800,plain,
( spl0_121
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1523,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3798,plain,
~ spl0_120,
inference(avatar_split_clause,[],[f1204,f3795]) ).
fof(f3795,plain,
( spl0_120
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f1204,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3793,plain,
spl0_119,
inference(avatar_split_clause,[],[f1197,f3790]) ).
fof(f3790,plain,
( spl0_119
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f1197,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3788,plain,
spl0_118,
inference(avatar_split_clause,[],[f1184,f3785]) ).
fof(f3785,plain,
( spl0_118
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f1184,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3783,plain,
~ spl0_117,
inference(avatar_split_clause,[],[f1053,f3780]) ).
fof(f3780,plain,
( spl0_117
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f1053,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3778,plain,
spl0_116,
inference(avatar_split_clause,[],[f600,f3776]) ).
fof(f3776,plain,
( spl0_116
<=> ! [X14] : c_List_Onull(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f600,axiom,
! [X14] : c_List_Onull(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3774,plain,
spl0_115,
inference(avatar_split_clause,[],[f445,f3772]) ).
fof(f3772,plain,
( spl0_115
<=> ! [X14] : c_List_Odistinct(c_List_Olist_ONil,X14) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f445,axiom,
! [X14] : c_List_Odistinct(c_List_Olist_ONil,X14),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3770,plain,
~ spl0_114,
inference(avatar_split_clause,[],[f264,f3767]) ).
fof(f3767,plain,
( spl0_114
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f264,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3765,plain,
~ spl0_113,
inference(avatar_split_clause,[],[f144,f3762]) ).
fof(f3762,plain,
( spl0_113
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f144,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3760,plain,
spl0_112,
inference(avatar_split_clause,[],[f1866,f3757]) ).
fof(f3757,plain,
( spl0_112
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f1866,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_9) ).
fof(f3755,plain,
spl0_111,
inference(avatar_split_clause,[],[f1865,f3752]) ).
fof(f3752,plain,
( spl0_111
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f1865,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3750,plain,
spl0_110,
inference(avatar_split_clause,[],[f1864,f3747]) ).
fof(f3747,plain,
( spl0_110
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f1864,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3745,plain,
spl0_109,
inference(avatar_split_clause,[],[f1863,f3742]) ).
fof(f3742,plain,
( spl0_109
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1863,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3740,plain,
spl0_108,
inference(avatar_split_clause,[],[f1862,f3737]) ).
fof(f3737,plain,
( spl0_108
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1862,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3735,plain,
spl0_107,
inference(avatar_split_clause,[],[f1860,f3732]) ).
fof(f3732,plain,
( spl0_107
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1860,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3730,plain,
spl0_106,
inference(avatar_split_clause,[],[f1859,f3727]) ).
fof(f3727,plain,
( spl0_106
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1859,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3725,plain,
spl0_105,
inference(avatar_split_clause,[],[f1857,f3722]) ).
fof(f3722,plain,
( spl0_105
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1857,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3720,plain,
spl0_104,
inference(avatar_split_clause,[],[f1856,f3717]) ).
fof(f3717,plain,
( spl0_104
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1856,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3715,plain,
spl0_103,
inference(avatar_split_clause,[],[f1855,f3712]) ).
fof(f3712,plain,
( spl0_103
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1855,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3710,plain,
spl0_102,
inference(avatar_split_clause,[],[f1854,f3707]) ).
fof(f3707,plain,
( spl0_102
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1854,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3705,plain,
spl0_101,
inference(avatar_split_clause,[],[f1853,f3702]) ).
fof(f3702,plain,
( spl0_101
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1853,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3700,plain,
spl0_100,
inference(avatar_split_clause,[],[f1852,f3697]) ).
fof(f3697,plain,
( spl0_100
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f1852,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3695,plain,
spl0_99,
inference(avatar_split_clause,[],[f1851,f3692]) ).
fof(f3692,plain,
( spl0_99
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f1851,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3690,plain,
spl0_98,
inference(avatar_split_clause,[],[f1850,f3687]) ).
fof(f3687,plain,
( spl0_98
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f1850,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3685,plain,
spl0_97,
inference(avatar_split_clause,[],[f1849,f3682]) ).
fof(f3682,plain,
( spl0_97
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f1849,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3680,plain,
spl0_96,
inference(avatar_split_clause,[],[f1848,f3677]) ).
fof(f3677,plain,
( spl0_96
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f1848,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3675,plain,
spl0_95,
inference(avatar_split_clause,[],[f1847,f3672]) ).
fof(f3672,plain,
( spl0_95
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f1847,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3670,plain,
spl0_94,
inference(avatar_split_clause,[],[f1846,f3667]) ).
fof(f3667,plain,
( spl0_94
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1846,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3665,plain,
spl0_93,
inference(avatar_split_clause,[],[f1845,f3662]) ).
fof(f3662,plain,
( spl0_93
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f1845,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3660,plain,
spl0_92,
inference(avatar_split_clause,[],[f1844,f3657]) ).
fof(f3657,plain,
( spl0_92
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1844,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3655,plain,
spl0_91,
inference(avatar_split_clause,[],[f1843,f3652]) ).
fof(f3652,plain,
( spl0_91
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f1843,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3650,plain,
spl0_90,
inference(avatar_split_clause,[],[f1842,f3647]) ).
fof(f3647,plain,
( spl0_90
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1842,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3645,plain,
spl0_89,
inference(avatar_split_clause,[],[f1841,f3642]) ).
fof(f3642,plain,
( spl0_89
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f1841,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3640,plain,
spl0_88,
inference(avatar_split_clause,[],[f1840,f3637]) ).
fof(f3637,plain,
( spl0_88
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1840,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3635,plain,
spl0_87,
inference(avatar_split_clause,[],[f1839,f3632]) ).
fof(f3632,plain,
( spl0_87
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1839,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3630,plain,
spl0_86,
inference(avatar_split_clause,[],[f1838,f3627]) ).
fof(f3627,plain,
( spl0_86
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1838,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3625,plain,
spl0_85,
inference(avatar_split_clause,[],[f1837,f3622]) ).
fof(f3622,plain,
( spl0_85
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1837,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3620,plain,
spl0_84,
inference(avatar_split_clause,[],[f1836,f3617]) ).
fof(f3617,plain,
( spl0_84
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f1836,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3615,plain,
spl0_83,
inference(avatar_split_clause,[],[f1835,f3612]) ).
fof(f3612,plain,
( spl0_83
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1835,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3610,plain,
spl0_82,
inference(avatar_split_clause,[],[f1834,f3607]) ).
fof(f3607,plain,
( spl0_82
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1834,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3605,plain,
spl0_81,
inference(avatar_split_clause,[],[f1833,f3602]) ).
fof(f3602,plain,
( spl0_81
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1833,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3600,plain,
spl0_80,
inference(avatar_split_clause,[],[f1832,f3597]) ).
fof(f3597,plain,
( spl0_80
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1832,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3595,plain,
spl0_79,
inference(avatar_split_clause,[],[f1831,f3592]) ).
fof(f3592,plain,
( spl0_79
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1831,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3590,plain,
spl0_78,
inference(avatar_split_clause,[],[f1830,f3587]) ).
fof(f3587,plain,
( spl0_78
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1830,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3585,plain,
spl0_77,
inference(avatar_split_clause,[],[f1829,f3582]) ).
fof(f3582,plain,
( spl0_77
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1829,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3580,plain,
spl0_76,
inference(avatar_split_clause,[],[f1828,f3577]) ).
fof(f3577,plain,
( spl0_76
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f1828,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_17) ).
fof(f3575,plain,
spl0_75,
inference(avatar_split_clause,[],[f1827,f3572]) ).
fof(f3572,plain,
( spl0_75
<=> class_OrderedGroup_Osemigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1827,axiom,
class_OrderedGroup_Osemigroup__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_16) ).
fof(f3570,plain,
spl0_74,
inference(avatar_split_clause,[],[f1826,f3567]) ).
fof(f3567,plain,
( spl0_74
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1826,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_15) ).
fof(f3565,plain,
spl0_73,
inference(avatar_split_clause,[],[f1825,f3562]) ).
fof(f3562,plain,
( spl0_73
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1825,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_14) ).
fof(f3560,plain,
spl0_72,
inference(avatar_split_clause,[],[f1824,f3557]) ).
fof(f3557,plain,
( spl0_72
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1824,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3555,plain,
spl0_71,
inference(avatar_split_clause,[],[f1822,f3552]) ).
fof(f3552,plain,
( spl0_71
<=> class_HOL_Otimes(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1822,axiom,
class_HOL_Otimes(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_11) ).
fof(f3550,plain,
spl0_70,
inference(avatar_split_clause,[],[f1821,f3547]) ).
fof(f3547,plain,
( spl0_70
<=> class_HOL_Oplus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1821,axiom,
class_HOL_Oplus(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_10) ).
fof(f3545,plain,
spl0_69,
inference(avatar_split_clause,[],[f1820,f3542]) ).
fof(f3542,plain,
( spl0_69
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1820,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_1) ).
fof(f3540,plain,
spl0_68,
inference(avatar_split_clause,[],[f1819,f3537]) ).
fof(f3537,plain,
( spl0_68
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1819,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3535,plain,
spl0_67,
inference(avatar_split_clause,[],[f1816,f3532]) ).
fof(f3532,plain,
( spl0_67
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1816,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3530,plain,
spl0_66,
inference(avatar_split_clause,[],[f1815,f3527]) ).
fof(f3527,plain,
( spl0_66
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f1815,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3525,plain,
spl0_65,
inference(avatar_split_clause,[],[f1814,f3522]) ).
fof(f3522,plain,
( spl0_65
<=> class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1814,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_9) ).
fof(f3520,plain,
spl0_64,
inference(avatar_split_clause,[],[f1813,f3517]) ).
fof(f3517,plain,
( spl0_64
<=> class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1813,axiom,
class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_8) ).
fof(f3515,plain,
spl0_63,
inference(avatar_split_clause,[],[f1812,f3512]) ).
fof(f3512,plain,
( spl0_63
<=> class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1812,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_7) ).
fof(f3510,plain,
spl0_62,
inference(avatar_split_clause,[],[f1810,f3507]) ).
fof(f3507,plain,
( spl0_62
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1810,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3505,plain,
spl0_61,
inference(avatar_split_clause,[],[f1807,f3502]) ).
fof(f3502,plain,
( spl0_61
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1807,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3500,plain,
spl0_60,
inference(avatar_split_clause,[],[f1806,f3497]) ).
fof(f3497,plain,
( spl0_60
<=> class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1806,axiom,
class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_6) ).
fof(f3495,plain,
spl0_59,
inference(avatar_split_clause,[],[f1805,f3492]) ).
fof(f3492,plain,
( spl0_59
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1805,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3490,plain,
spl0_58,
inference(avatar_split_clause,[],[f1804,f3487]) ).
fof(f3487,plain,
( spl0_58
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1804,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3485,plain,
spl0_57,
inference(avatar_split_clause,[],[f1803,f3482]) ).
fof(f3482,plain,
( spl0_57
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1803,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3480,plain,
spl0_56,
inference(avatar_split_clause,[],[f1802,f3477]) ).
fof(f3477,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1802,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3475,plain,
spl0_55,
inference(avatar_split_clause,[],[f1801,f3472]) ).
fof(f3472,plain,
( spl0_55
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f1801,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3470,plain,
spl0_54,
inference(avatar_split_clause,[],[f1800,f3467]) ).
fof(f3467,plain,
( spl0_54
<=> class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f1800,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_54) ).
fof(f3465,plain,
spl0_53,
inference(avatar_split_clause,[],[f1799,f3462]) ).
fof(f3462,plain,
( spl0_53
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1799,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3460,plain,
spl0_52,
inference(avatar_split_clause,[],[f1798,f3457]) ).
fof(f3457,plain,
( spl0_52
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f1798,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3455,plain,
spl0_51,
inference(avatar_split_clause,[],[f1797,f3452]) ).
fof(f3452,plain,
( spl0_51
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1797,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3450,plain,
spl0_50,
inference(avatar_split_clause,[],[f1796,f3447]) ).
fof(f3447,plain,
( spl0_50
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f1796,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3445,plain,
spl0_49,
inference(avatar_split_clause,[],[f1795,f3442]) ).
fof(f3442,plain,
( spl0_49
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1795,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3440,plain,
spl0_48,
inference(avatar_split_clause,[],[f1794,f3437]) ).
fof(f3437,plain,
( spl0_48
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1794,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3435,plain,
spl0_47,
inference(avatar_split_clause,[],[f1793,f3432]) ).
fof(f3432,plain,
( spl0_47
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1793,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3430,plain,
spl0_46,
inference(avatar_split_clause,[],[f1792,f3427]) ).
fof(f3427,plain,
( spl0_46
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1792,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3425,plain,
spl0_45,
inference(avatar_split_clause,[],[f1791,f3422]) ).
fof(f3422,plain,
( spl0_45
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1791,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3420,plain,
spl0_44,
inference(avatar_split_clause,[],[f1790,f3417]) ).
fof(f3417,plain,
( spl0_44
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1790,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3415,plain,
spl0_43,
inference(avatar_split_clause,[],[f1789,f3412]) ).
fof(f3412,plain,
( spl0_43
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1789,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3410,plain,
spl0_42,
inference(avatar_split_clause,[],[f1788,f3407]) ).
fof(f3407,plain,
( spl0_42
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f1788,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3405,plain,
spl0_41,
inference(avatar_split_clause,[],[f1787,f3402]) ).
fof(f3402,plain,
( spl0_41
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1787,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3400,plain,
spl0_40,
inference(avatar_split_clause,[],[f1786,f3397]) ).
fof(f3397,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1786,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3395,plain,
spl0_39,
inference(avatar_split_clause,[],[f1785,f3392]) ).
fof(f3392,plain,
( spl0_39
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1785,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3390,plain,
spl0_38,
inference(avatar_split_clause,[],[f1784,f3387]) ).
fof(f3387,plain,
( spl0_38
<=> class_HOL_Ozero(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1784,axiom,
class_HOL_Ozero(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_4) ).
fof(f3385,plain,
spl0_37,
inference(avatar_split_clause,[],[f1783,f3382]) ).
fof(f3382,plain,
( spl0_37
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1783,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3380,plain,
spl0_36,
inference(avatar_split_clause,[],[f1782,f3377]) ).
fof(f3377,plain,
( spl0_36
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1782,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3375,plain,
spl0_35,
inference(avatar_split_clause,[],[f1781,f3372]) ).
fof(f3372,plain,
( spl0_35
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1781,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3370,plain,
spl0_34,
inference(avatar_split_clause,[],[f1780,f3367]) ).
fof(f3367,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1780,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3365,plain,
spl0_33,
inference(avatar_split_clause,[],[f1779,f3362]) ).
fof(f3362,plain,
( spl0_33
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1779,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3360,plain,
spl0_32,
inference(avatar_split_clause,[],[f1778,f3357]) ).
fof(f3357,plain,
( spl0_32
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1778,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3355,plain,
spl0_31,
inference(avatar_split_clause,[],[f1777,f3352]) ).
fof(f3352,plain,
( spl0_31
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1777,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3350,plain,
spl0_30,
inference(avatar_split_clause,[],[f1776,f3347]) ).
fof(f3347,plain,
( spl0_30
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1776,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3345,plain,
spl0_29,
inference(avatar_split_clause,[],[f1775,f3342]) ).
fof(f3342,plain,
( spl0_29
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f1775,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3340,plain,
spl0_28,
inference(avatar_split_clause,[],[f1774,f3337]) ).
fof(f3337,plain,
( spl0_28
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1774,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3335,plain,
spl0_27,
inference(avatar_split_clause,[],[f1773,f3332]) ).
fof(f3332,plain,
( spl0_27
<=> class_HOL_Otimes(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f1773,axiom,
class_HOL_Otimes(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_3) ).
fof(f3330,plain,
spl0_26,
inference(avatar_split_clause,[],[f1772,f3327]) ).
fof(f3327,plain,
( spl0_26
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f1772,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3325,plain,
spl0_25,
inference(avatar_split_clause,[],[f1771,f3322]) ).
fof(f3322,plain,
( spl0_25
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1771,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3320,plain,
spl0_24,
inference(avatar_split_clause,[],[f1770,f3317]) ).
fof(f3317,plain,
( spl0_24
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f1770,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3315,plain,
spl0_23,
inference(avatar_split_clause,[],[f1769,f3312]) ).
fof(f3312,plain,
( spl0_23
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f1769,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3310,plain,
spl0_22,
inference(avatar_split_clause,[],[f1768,f3307]) ).
fof(f3307,plain,
( spl0_22
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1768,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3305,plain,
spl0_21,
inference(avatar_split_clause,[],[f1767,f3302]) ).
fof(f3302,plain,
( spl0_21
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1767,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3300,plain,
spl0_20,
inference(avatar_split_clause,[],[f1766,f3297]) ).
fof(f3297,plain,
( spl0_20
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1766,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3295,plain,
spl0_19,
inference(avatar_split_clause,[],[f1765,f3292]) ).
fof(f3292,plain,
( spl0_19
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1765,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3290,plain,
spl0_18,
inference(avatar_split_clause,[],[f1764,f3287]) ).
fof(f3287,plain,
( spl0_18
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1764,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3285,plain,
spl0_17,
inference(avatar_split_clause,[],[f1763,f3282]) ).
fof(f3282,plain,
( spl0_17
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f1763,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3280,plain,
spl0_16,
inference(avatar_split_clause,[],[f1762,f3277]) ).
fof(f3277,plain,
( spl0_16
<=> class_HOL_Oplus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1762,axiom,
class_HOL_Oplus(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_2) ).
fof(f3275,plain,
spl0_15,
inference(avatar_split_clause,[],[f1761,f3272]) ).
fof(f3272,plain,
( spl0_15
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1761,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3270,plain,
spl0_14,
inference(avatar_split_clause,[],[f1760,f3267]) ).
fof(f3267,plain,
( spl0_14
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1760,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3265,plain,
spl0_13,
inference(avatar_split_clause,[],[f1759,f3262]) ).
fof(f3262,plain,
( spl0_13
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1759,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3260,plain,
spl0_12,
inference(avatar_split_clause,[],[f1758,f3257]) ).
fof(f3257,plain,
( spl0_12
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1758,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3255,plain,
spl0_11,
inference(avatar_split_clause,[],[f1757,f3252]) ).
fof(f3252,plain,
( spl0_11
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f1757,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3250,plain,
spl0_10,
inference(avatar_split_clause,[],[f1756,f3247]) ).
fof(f3247,plain,
( spl0_10
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1756,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3245,plain,
spl0_9,
inference(avatar_split_clause,[],[f1755,f3242]) ).
fof(f3242,plain,
( spl0_9
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1755,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3240,plain,
spl0_8,
inference(avatar_split_clause,[],[f1754,f3237]) ).
fof(f3237,plain,
( spl0_8
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1754,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3235,plain,
spl0_7,
inference(avatar_split_clause,[],[f1753,f3232]) ).
fof(f3232,plain,
( spl0_7
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1753,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3230,plain,
spl0_6,
inference(avatar_split_clause,[],[f1752,f3227]) ).
fof(f3227,plain,
( spl0_6
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f1752,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3225,plain,
spl0_5,
inference(avatar_split_clause,[],[f1751,f3222]) ).
fof(f3222,plain,
( spl0_5
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1751,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3220,plain,
spl0_4,
inference(avatar_split_clause,[],[f1750,f3217]) ).
fof(f3217,plain,
( spl0_4
<=> class_HOL_Ominus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1750,axiom,
class_HOL_Ominus(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_0) ).
fof(f3215,plain,
spl0_3,
inference(avatar_split_clause,[],[f2785,f3213]) ).
fof(f3213,plain,
( spl0_3
<=> ! [X29] : c_in(v_xb(X29),v_A(v_xa(X29)),t_b) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f2785,axiom,
! [X29] : c_in(v_xb(X29),v_A(v_xa(X29)),t_b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3211,plain,
spl0_2,
inference(avatar_split_clause,[],[f2783,f3209]) ).
fof(f3209,plain,
( spl0_2
<=> ! [X29,X52] : c_lessequals(c_0,v_h(X29,X52),t_c) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f2783,axiom,
! [X29,X52] : c_lessequals(c_0,v_h(X29,X52),t_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3207,plain,
spl0_1,
inference(avatar_split_clause,[],[f2787,f3204]) ).
fof(f2787,axiom,
class_Ring__and__Field_Oordered__idom(t_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tfree_tcs) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : ANA042-1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n020.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 00:13:17 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (26403)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.43 % (26406)WARNING: value z3 for option sas not known
% 0.17/0.43 % (26410)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.17/0.43 % (26409)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)
% 0.17/0.43 % (26404)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.17/0.43 % (26406)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)
% 0.17/0.43 % (26407)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.17/0.43 % (26405)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.17/0.43 % (26408)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 1.15/0.57 % (26408)First to succeed.
% 1.29/0.60 % (26408)Refutation found. Thanks to Tanya!
% 1.29/0.60 % SZS status Unsatisfiable for theBenchmark
% 1.29/0.60 % SZS output start Proof for theBenchmark
% See solution above
% 1.29/0.62 % (26408)------------------------------
% 1.29/0.62 % (26408)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 1.29/0.62 % (26408)Termination reason: Refutation
% 1.29/0.62
% 1.29/0.62 % (26408)Memory used [KB]: 5266
% 1.29/0.62 % (26408)Time elapsed: 0.161 s
% 1.29/0.62 % (26408)Instructions burned: 316 (million)
% 1.29/0.62 % (26408)------------------------------
% 1.29/0.62 % (26408)------------------------------
% 1.29/0.62 % (26403)Success in time 0.274 s
%------------------------------------------------------------------------------