TSTP Solution File: LAT275-1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : LAT275-1 : 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 : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 07:26:42 EDT 2024
% Result : Unsatisfiable 2.13s 0.69s
% Output : Refutation 2.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 2655
% Syntax : Number of formulae : 4284 (1771 unt; 0 def)
% Number of atoms : 8039 (1255 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 6188 (2433 ~;2394 |; 0 &)
% (1361 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 1431 (1429 usr;1362 prp; 0-3 aty)
% Number of functors : 183 ( 183 usr; 50 con; 0-5 aty)
% Number of variables : 3780 (3780 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11340,plain,
$false,
inference(avatar_sat_refutation,[],[f3172,f3177,f3182,f3187,f3192,f3197,f3202,f3207,f3212,f3217,f3222,f3227,f3232,f3237,f3242,f3247,f3252,f3257,f3262,f3267,f3272,f3277,f3282,f3287,f3292,f3297,f3302,f3307,f3312,f3317,f3322,f3327,f3332,f3337,f3342,f3347,f3352,f3357,f3362,f3367,f3372,f3377,f3382,f3387,f3392,f3397,f3402,f3407,f3412,f3417,f3422,f3427,f3432,f3437,f3442,f3447,f3452,f3457,f3462,f3467,f3472,f3477,f3482,f3487,f3492,f3497,f3502,f3507,f3512,f3517,f3522,f3527,f3532,f3537,f3542,f3547,f3552,f3557,f3562,f3567,f3572,f3577,f3582,f3587,f3592,f3597,f3602,f3607,f3612,f3617,f3622,f3627,f3632,f3637,f3642,f3648,f3653,f3658,f3662,f3666,f3671,f3676,f3681,f3686,f3691,f3695,f3700,f3705,f3709,f3713,f3717,f3721,f3726,f3731,f3736,f3740,f3744,f3748,f3753,f3757,f3762,f3766,f3770,f3774,f3778,f3782,f3786,f3790,f3794,f3798,f3802,f3806,f3810,f3814,f3818,f3822,f3826,f3830,f3834,f3838,f3842,f3846,f3850,f3854,f3858,f3862,f3866,f3870,f3874,f3878,f3882,f3886,f3890,f3894,f3898,f3902,f3906,f3910,f3914,f3918,f3922,f3926,f3930,f3934,f3938,f3942,f3946,f3950,f3954,f3958,f3962,f3966,f3970,f3974,f3978,f3982,f3986,f3990,f3994,f3998,f4002,f4006,f4010,f4014,f4018,f4022,f4026,f4030,f4034,f4038,f4042,f4046,f4050,f4054,f4058,f4062,f4066,f4070,f4074,f4078,f4082,f4086,f4090,f4094,f4098,f4102,f4106,f4110,f4114,f4118,f4122,f4126,f4130,f4134,f4138,f4142,f4146,f4150,f4154,f4158,f4162,f4166,f4170,f4174,f4178,f4182,f4186,f4190,f4194,f4198,f4202,f4206,f4210,f4214,f4218,f4222,f4226,f4230,f4234,f4238,f4242,f4246,f4250,f4254,f4258,f4262,f4266,f4270,f4274,f4278,f4282,f4286,f4290,f4294,f4298,f4302,f4306,f4310,f4314,f4318,f4322,f4326,f4330,f4334,f4338,f4342,f4346,f4350,f4354,f4358,f4362,f4366,f4370,f4374,f4378,f4382,f4386,f4390,f4394,f4398,f4402,f4406,f4410,f4414,f4418,f4422,f4426,f4430,f4434,f4438,f4442,f4446,f4450,f4454,f4458,f4462,f4466,f4470,f4474,f4478,f4482,f4486,f4490,f4494,f4498,f4502,f4506,f4510,f4514,f4518,f4522,f4526,f4530,f4534,f4538,f4542,f4546,f4550,f4554,f4558,f4562,f4566,f4570,f4574,f4578,f4582,f4586,f4590,f4594,f4598,f4602,f4606,f4610,f4614,f4618,f4622,f4626,f4630,f4634,f4638,f4642,f4646,f4650,f4654,f4658,f4662,f4666,f4670,f4674,f4678,f4682,f4686,f4690,f4694,f4698,f4702,f4706,f4710,f4714,f4718,f4722,f4726,f4730,f4734,f4738,f4742,f4746,f4750,f4754,f4758,f4762,f4766,f4770,f4774,f4778,f4782,f4786,f4790,f4794,f4798,f4802,f4806,f4810,f4814,f4818,f4822,f4826,f4830,f4834,f4838,f4842,f4846,f4850,f4854,f4858,f4862,f4866,f4870,f4874,f4878,f4882,f4886,f4890,f4894,f4898,f4902,f4906,f4910,f4914,f4918,f4922,f4926,f4930,f4934,f4938,f4942,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4978,f4982,f4986,f4990,f4994,f4998,f5002,f5006,f5010,f5014,f5018,f5022,f5026,f5030,f5034,f5038,f5042,f5046,f5050,f5054,f5058,f5062,f5066,f5070,f5074,f5078,f5082,f5086,f5090,f5094,f5098,f5102,f5106,f5110,f5114,f5118,f5122,f5126,f5130,f5134,f5138,f5142,f5146,f5150,f5154,f5158,f5162,f5166,f5170,f5174,f5178,f5182,f5186,f5190,f5194,f5198,f5202,f5206,f5210,f5214,f5218,f5222,f5226,f5230,f5234,f5238,f5242,f5246,f5250,f5254,f5258,f5262,f5266,f5270,f5274,f5278,f5282,f5286,f5290,f5294,f5298,f5302,f5306,f5310,f5314,f5318,f5322,f5326,f5330,f5334,f5338,f5342,f5346,f5350,f5354,f5358,f5362,f5366,f5370,f5374,f5378,f5382,f5386,f5390,f5394,f5398,f5402,f5406,f5410,f5414,f5418,f5422,f5426,f5430,f5434,f5438,f5442,f5446,f5450,f5454,f5458,f5462,f5466,f5470,f5474,f5478,f5482,f5486,f5490,f5494,f5498,f5502,f5506,f5510,f5514,f5518,f5522,f5526,f5530,f5534,f5538,f5542,f5546,f5550,f5554,f5558,f5562,f5566,f5570,f5574,f5578,f5582,f5586,f5590,f5594,f5598,f5602,f5606,f5610,f5614,f5618,f5622,f5626,f5630,f5634,f5638,f5642,f5646,f5650,f5654,f5658,f5662,f5666,f5670,f5674,f5678,f5682,f5686,f5690,f5694,f5698,f5702,f5706,f5710,f5714,f5718,f5722,f5726,f5730,f5734,f5738,f5742,f5746,f5750,f5754,f5758,f5762,f5766,f5770,f5774,f5778,f5782,f5786,f5790,f5794,f5798,f5802,f5806,f5810,f5814,f5818,f5822,f5826,f5830,f5834,f5838,f5842,f5846,f5850,f5854,f5858,f5862,f5866,f5870,f5874,f5878,f5882,f5886,f5891,f5895,f5900,f5905,f5912,f5917,f6681,f6685,f6689,f6693,f6697,f6702,f6707,f6712,f6716,f6720,f6724,f6729,f6733,f6737,f6741,f6745,f6749,f6753,f6757,f6761,f6766,f6771,f6776,f6781,f6786,f6791,f6796,f6801,f6806,f6811,f6816,f6821,f6826,f6831,f6836,f6841,f6845,f6849,f6853,f6857,f6861,f6866,f6871,f6876,f6880,f6884,f6888,f6892,f6896,f6900,f6905,f6910,f6914,f6919,f6924,f6928,f6932,f6936,f6940,f6944,f6948,f6952,f6956,f6960,f6964,f6968,f6972,f6976,f6980,f6985,f6989,f6994,f7005,f7010,f7016,f7021,f7025,f7029,f7033,f7037,f7041,f7045,f7049,f7053,f7058,f7062,f7066,f7070,f7074,f7078,f7082,f7086,f7090,f7094,f7098,f7102,f7106,f7110,f7114,f7118,f7122,f7126,f7130,f7134,f7138,f7142,f7146,f7150,f7154,f7158,f7162,f7166,f7170,f7174,f7178,f7182,f7186,f7190,f7194,f7198,f7202,f7207,f7211,f7215,f7219,f7223,f7227,f7231,f7235,f7239,f7243,f7247,f7251,f7255,f7259,f7263,f7267,f7271,f7275,f7279,f7283,f7287,f7292,f7297,f7302,f7307,f7311,f7316,f7320,f7325,f7329,f7333,f7338,f7342,f7346,f7350,f7354,f7358,f7362,f7366,f7370,f7374,f7383,f7387,f7391,f7395,f7399,f7403,f7407,f7411,f7415,f7419,f7423,f7427,f7431,f7435,f7439,f7443,f7447,f7451,f7455,f7459,f7463,f7469,f7473,f7477,f7481,f7485,f7489,f7493,f7497,f7501,f7505,f7510,f7514,f7518,f7522,f7526,f7530,f7534,f7538,f7542,f7546,f7550,f7554,f7558,f7562,f7566,f7570,f7574,f7578,f7582,f7586,f7591,f7592,f7597,f7601,f7605,f7609,f7629,f7660,f7670,f7688,f7698,f7703,f7708,f7712,f7716,f7720,f7724,f7728,f7732,f7736,f7740,f7744,f7748,f7753,f7757,f7761,f7765,f7769,f7773,f7777,f7781,f7785,f7789,f7793,f7798,f7802,f7806,f7810,f7814,f7818,f7822,f7826,f7830,f7834,f7838,f7847,f7851,f7855,f7859,f7863,f7867,f7871,f7875,f7879,f7883,f7887,f7891,f7895,f7899,f7903,f7907,f7911,f7915,f7919,f7923,f7927,f7931,f7935,f7939,f7943,f7947,f7951,f7955,f7959,f7964,f7968,f7973,f7977,f7981,f7985,f7989,f7993,f7997,f8001,f8005,f8009,f8013,f8017,f8021,f8025,f8029,f8033,f8037,f8041,f8045,f8051,f8073,f8173,f8177,f8181,f8186,f8190,f8194,f8198,f8202,f8206,f8210,f8214,f8218,f8222,f8227,f8231,f8235,f8239,f8243,f8247,f8251,f8255,f8259,f8263,f8268,f8272,f8276,f8280,f8284,f8288,f8292,f8296,f8300,f8304,f8308,f8312,f8316,f8320,f8324,f8328,f8332,f8336,f8340,f8344,f8348,f8353,f8357,f8361,f8365,f8369,f8373,f8377,f8381,f8385,f8389,f8393,f8397,f8401,f8405,f8409,f8413,f8417,f8421,f8425,f8429,f8433,f8438,f8442,f8446,f8450,f8454,f8458,f8462,f8466,f8470,f8474,f8478,f8482,f8486,f8490,f8494,f8498,f8520,f8574,f8612,f8656,f8693,f8720,f8724,f8728,f8732,f8736,f8740,f8744,f8748,f8752,f8757,f8761,f8765,f8769,f8773,f8777,f8781,f8785,f8789,f8793,f8797,f8801,f8805,f8809,f8813,f8817,f8821,f8825,f8829,f8833,f8838,f8842,f8846,f8850,f8854,f8858,f8862,f8866,f8870,f8874,f8878,f8882,f8886,f8890,f8894,f8898,f8902,f8906,f8910,f8914,f8918,f8922,f8926,f8930,f8934,f8938,f8942,f8946,f8950,f8954,f8958,f8962,f8966,f8970,f8975,f8979,f8983,f8987,f8991,f8995,f8999,f9004,f9008,f9013,f9017,f9024,f9028,f9032,f9036,f9040,f9059,f9127,f9147,f9205,f9230,f9245,f9263,f9267,f9271,f9275,f9279,f9283,f9287,f9291,f9295,f9299,f9303,f9308,f9312,f9316,f9320,f9324,f9328,f9332,f9336,f9340,f9344,f9348,f9352,f9356,f9360,f9364,f9368,f9372,f9376,f9380,f9384,f9388,f9392,f9396,f9400,f9404,f9408,f9412,f9416,f9420,f9424,f9428,f9432,f9436,f9440,f9444,f9448,f9452,f9456,f9460,f9464,f9468,f9472,f9476,f9480,f9484,f9488,f9492,f9496,f9500,f9504,f9508,f9512,f9516,f9520,f9524,f9528,f9532,f9536,f9540,f9544,f9548,f9552,f9557,f9565,f9569,f9573,f9577,f9581,f9585,f9589,f9623,f9627,f9671,f9715,f9761,f9855,f9966,f9974,f9978,f9982,f9986,f9990,f9994,f9998,f10002,f10007,f10011,f10015,f10019,f10023,f10027,f10031,f10035,f10039,f10043,f10047,f10056,f10060,f10064,f10068,f10072,f10076,f10081,f10086,f10090,f10100,f10104,f10108,f10112,f10116,f10120,f10124,f10128,f10132,f10136,f10146,f10150,f10154,f10158,f10162,f10166,f10170,f10174,f10178,f10182,f10186,f10190,f10194,f10198,f10202,f10206,f10210,f10214,f10218,f10222,f10226,f10234,f10238,f10242,f10246,f10250,f10254,f10258,f10262,f10266,f10270,f10274,f10278,f10282,f10286,f10290,f10294,f10298,f10302,f10306,f10310,f10314,f10319,f10323,f10327,f10331,f10335,f10339,f10343,f10347,f10351,f10355,f10359,f10363,f10367,f10371,f10375,f10379,f10383,f10387,f10391,f10395,f10399,f10403,f10407,f10411,f10415,f10419,f10423,f10427,f10431,f10435,f10439,f10443,f10447,f10451,f10455,f10459,f10463,f10467,f10471,f10475,f10479,f10483,f10487,f10491,f10495,f10672,f10717,f10910,f10999,f11046,f11187,f11339]) ).
fof(f11339,plain,
( ~ spl0_2
| spl0_96
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f11214,f10453,f3645,f3174]) ).
fof(f3174,plain,
( spl0_2
<=> c_lessequals(v_S,v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f3645,plain,
( spl0_96
<=> c_in(c_Tarski_Olub(v_S,v_cl,t_a),v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f10453,plain,
( spl0_1345
<=> ! [X82] :
( ~ c_lessequals(X82,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(X82,v_cl,t_a),v_A,t_a) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f11214,plain,
( ~ c_lessequals(v_S,v_A,tc_set(t_a))
| spl0_96
| ~ spl0_1345 ),
inference(resolution,[],[f10454,f3647]) ).
fof(f3647,plain,
( ~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),v_A,t_a)
| spl0_96 ),
inference(avatar_component_clause,[],[f3645]) ).
fof(f10454,plain,
( ! [X82] :
( c_in(c_Tarski_Olub(X82,v_cl,t_a),v_A,t_a)
| ~ c_lessequals(X82,v_A,tc_set(t_a)) )
| ~ spl0_1345 ),
inference(avatar_component_clause,[],[f10453]) ).
fof(f11187,plain,
( spl0_1361
| ~ spl0_2
| ~ spl0_1326 ),
inference(avatar_split_clause,[],[f11079,f10377,f3174,f11184]) ).
fof(f11184,plain,
( spl0_1361
<=> c_emptyset = c_minus(v_S,v_A,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f10377,plain,
( spl0_1326
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_emptyset = c_minus(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f11079,plain,
( c_emptyset = c_minus(v_S,v_A,tc_set(t_a))
| ~ spl0_2
| ~ spl0_1326 ),
inference(resolution,[],[f10378,f3176]) ).
fof(f3176,plain,
( c_lessequals(v_S,v_A,tc_set(t_a))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f3174]) ).
fof(f10378,plain,
( ! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_emptyset = c_minus(X27,X31,tc_set(X3)) )
| ~ spl0_1326 ),
inference(avatar_component_clause,[],[f10377]) ).
fof(f11046,plain,
( ~ spl0_110
| spl0_1360 ),
inference(avatar_contradiction_clause,[],[f11045]) ).
fof(f11045,plain,
( $false
| ~ spl0_110
| spl0_1360 ),
inference(resolution,[],[f10998,f3712]) ).
fof(f3712,plain,
( ! [X90] : class_Orderings_Oorder(tc_set(X90))
| ~ spl0_110 ),
inference(avatar_component_clause,[],[f3711]) ).
fof(f3711,plain,
( spl0_110
<=> ! [X90] : class_Orderings_Oorder(tc_set(X90)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f10998,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| spl0_1360 ),
inference(avatar_component_clause,[],[f10996]) ).
fof(f10996,plain,
( spl0_1360
<=> class_Orderings_Oorder(tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f10999,plain,
( spl0_1359
| ~ spl0_1360
| ~ spl0_2
| ~ spl0_1307 ),
inference(avatar_split_clause,[],[f10980,f10300,f3174,f10996,f10992]) ).
fof(f10992,plain,
( spl0_1359
<=> c_emptyset = c_SetInterval_OatLeastLessThan(v_A,v_S,tc_set(t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f10300,plain,
( spl0_1307
<=> ! [X25,X3,X10] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastLessThan(X25,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f10980,plain,
( ~ class_Orderings_Oorder(tc_set(t_a))
| c_emptyset = c_SetInterval_OatLeastLessThan(v_A,v_S,tc_set(t_a))
| ~ spl0_2
| ~ spl0_1307 ),
inference(resolution,[],[f10301,f3176]) ).
fof(f10301,plain,
( ! [X3,X10,X25] :
( ~ c_lessequals(X10,X25,X3)
| ~ class_Orderings_Oorder(X3)
| c_emptyset = c_SetInterval_OatLeastLessThan(X25,X10,X3) )
| ~ spl0_1307 ),
inference(avatar_component_clause,[],[f10300]) ).
fof(f10910,plain,
( spl0_1358
| ~ spl0_711
| ~ spl0_1115 ),
inference(avatar_split_clause,[],[f9231,f8956,f6912,f10908]) ).
fof(f10908,plain,
( spl0_1358
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f6912,plain,
( spl0_711
<=> ! [X3] : c_emptyset = c_Relation_Odiag(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f8956,plain,
( spl0_1115
<=> ! [X27,X3] : c_Relation_Odiag(X27,X3) = c_Relation_Oconverse(c_Relation_Odiag(X27,X3),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f9231,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_711
| ~ spl0_1115 ),
inference(superposition,[],[f8957,f6913]) ).
fof(f6913,plain,
( ! [X3] : c_emptyset = c_Relation_Odiag(c_emptyset,X3)
| ~ spl0_711 ),
inference(avatar_component_clause,[],[f6912]) ).
fof(f8957,plain,
( ! [X3,X27] : c_Relation_Odiag(X27,X3) = c_Relation_Oconverse(c_Relation_Odiag(X27,X3),X3,X3)
| ~ spl0_1115 ),
inference(avatar_component_clause,[],[f8956]) ).
fof(f10717,plain,
( spl0_1357
| ~ spl0_117
| ~ spl0_1085 ),
inference(avatar_split_clause,[],[f9148,f8836,f3742,f10715]) ).
fof(f10715,plain,
( spl0_1357
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f3742,plain,
( spl0_117
<=> ! [X25] : c_Divides_Oop_Advd(X25,X25,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f8836,plain,
( spl0_1085
<=> ! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f9148,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_117
| ~ spl0_1085 ),
inference(resolution,[],[f8837,f3743]) ).
fof(f3743,plain,
( ! [X25] : c_Divides_Oop_Advd(X25,X25,tc_IntDef_Oint)
| ~ spl0_117 ),
inference(avatar_component_clause,[],[f3742]) ).
fof(f8837,plain,
( ! [X37,X35] :
( ~ c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint) )
| ~ spl0_1085 ),
inference(avatar_component_clause,[],[f8836]) ).
fof(f10672,plain,
( spl0_1356
| ~ spl0_117
| ~ spl0_1082 ),
inference(avatar_split_clause,[],[f9138,f8823,f3742,f10670]) ).
fof(f10670,plain,
( spl0_1356
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f8823,plain,
( spl0_1082
<=> ! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f9138,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_117
| ~ spl0_1082 ),
inference(resolution,[],[f8824,f3743]) ).
fof(f8824,plain,
( ! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint) )
| ~ spl0_1082 ),
inference(avatar_component_clause,[],[f8823]) ).
fof(f10495,plain,
spl0_1355,
inference(avatar_split_clause,[],[f3120,f10493]) ).
fof(f10493,plain,
( spl0_1355
<=> ! [X11,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f3120,plain,
! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f3119,f965]) ).
fof(f965,axiom,
! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3119,plain,
! [X3,X11] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f2926,f2756]) ).
fof(f2756,plain,
c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls),
inference(definition_unfolding,[],[f976,f979]) ).
fof(f979,axiom,
! [X35] : c_Numeral_Obin__minus(X35) = c_Numeral_Obin__mult(c_Numeral_OMin,X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Min_0) ).
fof(f976,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Pls_0) ).
fof(f2926,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f188,f979]) ).
fof(f188,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(X11,X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_1) ).
fof(f10491,plain,
spl0_1354,
inference(avatar_split_clause,[],[f3050,f10489]) ).
fof(f10489,plain,
( spl0_1354
<=> ! [X3] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X3)
| ~ class_Power_Orecpower(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f3050,plain,
! [X3] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X3)
| ~ class_Power_Orecpower(X3) ),
inference(forward_demodulation,[],[f3049,f1006]) ).
fof(f1006,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__Pls_0) ).
fof(f3049,plain,
! [X3] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X3)
| ~ class_Power_Orecpower(X3) ),
inference(forward_demodulation,[],[f3048,f1004]) ).
fof(f1004,axiom,
! [X35] : c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X35),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__1_0) ).
fof(f3048,plain,
! [X3] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X3)
| ~ class_Power_Orecpower(X3) ),
inference(forward_demodulation,[],[f728,f1006]) ).
fof(f728,axiom,
! [X3] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Ozero__power2_0) ).
fof(f10487,plain,
spl0_1353,
inference(avatar_split_clause,[],[f3043,f10485]) ).
fof(f10485,plain,
( spl0_1353
<=> ! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f3043,plain,
! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f3042,f1006]) ).
fof(f3042,plain,
! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f3041,f1004]) ).
fof(f3041,plain,
! [X3] :
( c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f178,f1006]) ).
fof(f178,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_plus(c_1,c_1,X3) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__1_0) ).
fof(f10483,plain,
spl0_1352,
inference(avatar_split_clause,[],[f2867,f10481]) ).
fof(f10481,plain,
( spl0_1352
<=> ! [X27,X3,X31] :
( c_UNIV = X31
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f2867,plain,
! [X31,X3,X27] :
( c_UNIV = X31
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1449,f1223]) ).
fof(f1223,axiom,
! [X31,X3,X27] : c_inter(X27,X31,X3) = c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__diag_0) ).
fof(f1449,axiom,
! [X31,X3,X27] :
( c_UNIV = X31
| c_UNIV != c_inter(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_1) ).
fof(f10479,plain,
spl0_1351,
inference(avatar_split_clause,[],[f2866,f10477]) ).
fof(f10477,plain,
( spl0_1351
<=> ! [X27,X3,X31] :
( c_UNIV = X27
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f2866,plain,
! [X31,X3,X27] :
( c_UNIV = X27
| c_UNIV != c_Relation_OImage(c_Relation_Odiag(X27,X3),X31,X3,X3) ),
inference(definition_unfolding,[],[f1448,f1223]) ).
fof(f1448,axiom,
! [X31,X3,X27] :
( c_UNIV = X27
| c_UNIV != c_inter(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV_0) ).
fof(f10475,plain,
spl0_1350,
inference(avatar_split_clause,[],[f2861,f10473]) ).
fof(f10473,plain,
( spl0_1350
<=> ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f2861,plain,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),X3) ),
inference(definition_unfolding,[],[f1196,f1394]) ).
fof(f1394,axiom,
! [X38] : c_Suc(X38) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X38,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
fof(f1196,axiom,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_0 = c_Nat_Opower(c_0,c_Suc(X10),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__0__Suc_0) ).
fof(f10471,plain,
spl0_1349,
inference(avatar_split_clause,[],[f2793,f10469]) ).
fof(f10469,plain,
( spl0_1349
<=> ! [X25] : c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f2793,plain,
! [X25] : c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint) = c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f222,f1394]) ).
fof(f222,axiom,
! [X25] : c_IntDef_Oint(c_Suc(X25)) = c_plus(c_1,c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__Suc_0) ).
fof(f10467,plain,
spl0_1348,
inference(avatar_split_clause,[],[f2790,f10465]) ).
fof(f10465,plain,
( spl0_1348
<=> ! [X27,X3] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X27,tc_set(X3)),X3),X27,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f2790,plain,
! [X3,X27] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_uminus(X27,tc_set(X3)),X3),X27,X3,X3),
inference(definition_unfolding,[],[f1428,f1223]) ).
fof(f1428,axiom,
! [X3,X27] : c_emptyset = c_inter(c_uminus(X27,tc_set(X3)),X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint2_0) ).
fof(f10463,plain,
spl0_1347,
inference(avatar_split_clause,[],[f2789,f10461]) ).
fof(f10461,plain,
( spl0_1347
<=> ! [X27,X3] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),c_uminus(X27,tc_set(X3)),X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f2789,plain,
! [X3,X27] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(X27,X3),c_uminus(X27,tc_set(X3)),X3,X3),
inference(definition_unfolding,[],[f1429,f1223]) ).
fof(f1429,axiom,
! [X3,X27] : c_emptyset = c_inter(X27,c_uminus(X27,tc_set(X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__disjoint_0) ).
fof(f10459,plain,
spl0_1346,
inference(avatar_split_clause,[],[f2744,f10457]) ).
fof(f10457,plain,
( spl0_1346
<=> ! [X94,X3] :
( ~ c_in(X94,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X94,X3,tc_Product__Type_Ounit),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f2744,axiom,
! [X3,X94] :
( ~ c_in(X94,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(X3,tc_Product__Type_Ounit))
| c_Relation_Otrans(c_Tarski_Opotype_Oorder(X94,X3,tc_Product__Type_Ounit),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl1_A_58_ACompleteLattice_A_61_61_62_Atrans_A_Iorder_Acl1_J_A_61_61_ATrue_0) ).
fof(f10455,plain,
spl0_1345,
inference(avatar_split_clause,[],[f2738,f10453]) ).
fof(f2738,axiom,
! [X82] :
( ~ c_lessequals(X82,v_A,tc_set(t_a))
| c_in(c_Tarski_Olub(X82,v_cl,t_a),v_A,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OS_A_60_61_AA_A_61_61_62_Alub_AS_Acl_A_58_AA_0) ).
fof(f10451,plain,
spl0_1344,
inference(avatar_split_clause,[],[f1687,f10449]) ).
fof(f10449,plain,
( spl0_1344
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X27,X31,X3),X31,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f1687,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X27,X31,X3),X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f10447,plain,
spl0_1343,
inference(avatar_split_clause,[],[f1686,f10445]) ).
fof(f10445,plain,
( spl0_1343
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X27,X31,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f1686,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| c_in(c_Main_OsubsetI__1(X27,X31,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f10443,plain,
spl0_1342,
inference(avatar_split_clause,[],[f1626,f10441]) ).
fof(f10441,plain,
( spl0_1342
<=> ! [X41,X3] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X41,X3),tc_List_Olist(X3)),c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f1626,axiom,
! [X41,X3] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X41,X3),tc_List_Olist(X3)),c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__remdups__leq_0) ).
fof(f10439,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1579,f10437]) ).
fof(f10437,plain,
( spl0_1341
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Datatype__Universe_ONumb(X11,X3,X17) != c_Datatype__Universe_ONumb(X8,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f1579,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Datatype__Universe_ONumb(X11,X3,X17) != c_Datatype__Universe_ONumb(X8,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f10435,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1578,f10433]) ).
fof(f10433,plain,
( spl0_1340
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Datatype__Universe_OLeaf(X11,X3,X17) != c_Datatype__Universe_OLeaf(X8,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f1578,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Datatype__Universe_OLeaf(X11,X3,X17) != c_Datatype__Universe_OLeaf(X8,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f10431,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1553,f10429]) ).
fof(f10429,plain,
( spl0_1339
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Sum__Type_OInr(X11,X17,X3) != c_Sum__Type_OInr(X8,X17,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f1553,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Sum__Type_OInr(X11,X17,X3) != c_Sum__Type_OInr(X8,X17,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__eq_0) ).
fof(f10427,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1551,f10425]) ).
fof(f10425,plain,
( spl0_1338
<=> ! [X17,X11,X3,X8] :
( X8 = X11
| c_Sum__Type_OInl(X11,X3,X17) != c_Sum__Type_OInl(X8,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f1551,axiom,
! [X3,X11,X8,X17] :
( X8 = X11
| c_Sum__Type_OInl(X11,X3,X17) != c_Sum__Type_OInl(X8,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInl__eq_0) ).
fof(f10423,plain,
spl0_1337,
inference(avatar_split_clause,[],[f1545,f10421]) ).
fof(f10421,plain,
( spl0_1337
<=> ! [X15,X16,X27,X3] :
( X15 = X16
| c_insert(X15,X27,X3) != c_insert(X16,c_emptyset,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f1545,axiom,
! [X3,X16,X27,X15] :
( X15 = X16
| c_insert(X15,X27,X3) != c_insert(X16,c_emptyset,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osingleton__insert__inj__eq_H_0) ).
fof(f10419,plain,
spl0_1336,
inference(avatar_split_clause,[],[f1538,f10417]) ).
fof(f10417,plain,
( spl0_1336
<=> ! [X31,X11,X27,X3] :
( c_in(X11,X31,X3)
| ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f1538,axiom,
! [X31,X3,X11,X27] :
( c_in(X11,X31,X3)
| ~ c_lessequals(c_insert(X11,X27,X3),X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__subset_0) ).
fof(f10415,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1526,f10413]) ).
fof(f10413,plain,
( spl0_1335
<=> ! [X11,X27,X3] : c_insert(X11,X27,X3) = c_insert(X11,c_insert(X11,X27,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f1526,axiom,
! [X3,X11,X27] : c_insert(X11,X27,X3) = c_insert(X11,c_insert(X11,X27,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__absorb2_0) ).
fof(f10411,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1520,f10409]) ).
fof(f10409,plain,
( spl0_1334
<=> ! [X27,X3] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_Oempty__Union__conv__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f1520,axiom,
! [X3,X27] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_Oempty__Union__conv__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_1) ).
fof(f10407,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1503,f10405]) ).
fof(f10405,plain,
( spl0_1333
<=> ! [X27,X3] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_OUnion__empty__conv__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f1503,axiom,
! [X3,X27] :
( c_emptyset = c_Union(X27,X3)
| c_in(c_Main_OUnion__empty__conv__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_1) ).
fof(f10403,plain,
spl0_1332,
inference(avatar_split_clause,[],[f1478,f10401]) ).
fof(f10401,plain,
( spl0_1332
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_in(X27,c_Pow(X31,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f1478,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_in(X27,c_Pow(X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_1) ).
fof(f10399,plain,
spl0_1331,
inference(avatar_split_clause,[],[f1477,f10397]) ).
fof(f10397,plain,
( spl0_1331
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(X27,c_Pow(X31,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f1477,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| ~ c_in(X27,c_Pow(X31,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__iff_0) ).
fof(f10395,plain,
spl0_1330,
inference(avatar_split_clause,[],[f1467,f10393]) ).
fof(f10393,plain,
( spl0_1330
<=> ! [X27,X3] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__2__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f1467,axiom,
! [X3,X27] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__2__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f10391,plain,
spl0_1329,
inference(avatar_split_clause,[],[f1464,f10389]) ).
fof(f10389,plain,
( spl0_1329
<=> ! [X27,X3] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__1__1(X27,X3),X27,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f1464,axiom,
! [X3,X27] :
( c_UNIV = c_Inter(X27,X3)
| c_in(c_Main_OInter__UNIV__conv__1__1(X27,X3),X27,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f10387,plain,
spl0_1328,
inference(avatar_split_clause,[],[f1445,f10385]) ).
fof(f10385,plain,
( spl0_1328
<=> ! [X3,X31,X27,X26] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f1445,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X31,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_1) ).
fof(f10383,plain,
spl0_1327,
inference(avatar_split_clause,[],[f1444,f10381]) ).
fof(f10381,plain,
( spl0_1327
<=> ! [X31,X27,X3,X26] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f1444,axiom,
! [X31,X3,X26,X27] :
( c_in(X26,X27,X3)
| ~ c_in(X26,c_minus(X27,X31,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__iff_0) ).
fof(f10379,plain,
spl0_1326,
inference(avatar_split_clause,[],[f1442,f10377]) ).
fof(f1442,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X27,X31,tc_set(X3))
| c_emptyset = c_minus(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f10375,plain,
spl0_1325,
inference(avatar_split_clause,[],[f1441,f10373]) ).
fof(f10373,plain,
( spl0_1325
<=> ! [X27,X3,X31] :
( c_lessequals(X27,X31,tc_set(X3))
| c_emptyset != c_minus(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f1441,axiom,
! [X31,X3,X27] :
( c_lessequals(X27,X31,tc_set(X3))
| c_emptyset != c_minus(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f10371,plain,
spl0_1324,
inference(avatar_split_clause,[],[f1431,f10369]) ).
fof(f10369,plain,
( spl0_1324
<=> ! [X27,X3,X31] :
( X27 = X31
| c_uminus(X27,tc_set(X3)) != c_uminus(X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f1431,axiom,
! [X31,X3,X27] :
( X27 = X31
| c_uminus(X27,tc_set(X3)) != c_uminus(X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f10367,plain,
spl0_1323,
inference(avatar_split_clause,[],[f1420,f10365]) ).
fof(f10365,plain,
( spl0_1323
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X24,X9,X3)
| c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f1420,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X24,X9,X3)
| c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_1) ).
fof(f10363,plain,
spl0_1322,
inference(avatar_split_clause,[],[f1419,f10361]) ).
fof(f10361,plain,
( spl0_1322
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f1419,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OlessThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__iff_0) ).
fof(f10359,plain,
spl0_1321,
inference(avatar_split_clause,[],[f1418,f10357]) ).
fof(f10357,plain,
( spl0_1321
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OlessThan(X11,X3) != c_SetInterval_OlessThan(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f1418,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OlessThan(X11,X3) != c_SetInterval_OlessThan(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f10355,plain,
spl0_1320,
inference(avatar_split_clause,[],[f1409,f10353]) ).
fof(f10353,plain,
( spl0_1320
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X9,X24,X3)
| c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f1409,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_less(X9,X24,X3)
| c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f10351,plain,
spl0_1319,
inference(avatar_split_clause,[],[f1408,f10349]) ).
fof(f10349,plain,
( spl0_1319
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_less(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f1408,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_less(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OgreaterThan(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f10347,plain,
spl0_1318,
inference(avatar_split_clause,[],[f1407,f10345]) ).
fof(f10345,plain,
( spl0_1318
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OgreaterThan(X11,X3) != c_SetInterval_OgreaterThan(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f1407,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OgreaterThan(X11,X3) != c_SetInterval_OgreaterThan(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f10343,plain,
spl0_1317,
inference(avatar_split_clause,[],[f1400,f10341]) ).
fof(f10341,plain,
( spl0_1317
<=> ! [X9,X3,X74] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X74,X9,X3)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X74,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f1400,axiom,
! [X3,X9,X74] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X74,X9,X3)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X9,X74,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f10339,plain,
spl0_1316,
inference(avatar_split_clause,[],[f1396,f10337]) ).
fof(f10337,plain,
( spl0_1316
<=> ! [X38,X74] : c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f1396,axiom,
! [X38,X74] : c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f10335,plain,
spl0_1315,
inference(avatar_split_clause,[],[f1393,f10333]) ).
fof(f10333,plain,
( spl0_1315
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f1393,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X38,X74,tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f10331,plain,
spl0_1314,
inference(avatar_split_clause,[],[f1387,f10329]) ).
fof(f10329,plain,
( spl0_1314
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X24,X9,X3)
| c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f1387,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X24,X9,X3)
| c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_1) ).
fof(f10327,plain,
spl0_1313,
inference(avatar_split_clause,[],[f1386,f10325]) ).
fof(f10325,plain,
( spl0_1313
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f1386,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X24,X9,X3)
| ~ c_in(X24,c_SetInterval_OatMost(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__iff_0) ).
fof(f10323,plain,
spl0_1312,
inference(avatar_split_clause,[],[f1385,f10321]) ).
fof(f10321,plain,
( spl0_1312
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatMost(X11,X3) != c_SetInterval_OatMost(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f1385,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatMost(X11,X3) != c_SetInterval_OatMost(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f10319,plain,
( spl0_1311
| ~ spl0_702
| ~ spl0_780
| ~ spl0_1045 ),
inference(avatar_split_clause,[],[f8701,f8476,f7204,f6873,f10316]) ).
fof(f10316,plain,
( spl0_1311
<=> c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f6873,plain,
( spl0_702
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f7204,plain,
( spl0_780
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f8476,plain,
( spl0_1045
<=> ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f8701,plain,
( c_Numeral_OPls = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_702
| ~ spl0_780
| ~ spl0_1045 ),
inference(forward_demodulation,[],[f8698,f6875]) ).
fof(f6875,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_702 ),
inference(avatar_component_clause,[],[f6873]) ).
fof(f8698,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_OMin)
| ~ spl0_780
| ~ spl0_1045 ),
inference(superposition,[],[f8477,f7206]) ).
fof(f7206,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_780 ),
inference(avatar_component_clause,[],[f7204]) ).
fof(f8477,plain,
( ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),c_Numeral_OMin)
| ~ spl0_1045 ),
inference(avatar_component_clause,[],[f8476]) ).
fof(f10314,plain,
spl0_1310,
inference(avatar_split_clause,[],[f1381,f10312]) ).
fof(f10312,plain,
( spl0_1310
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X9,X24,X3)
| c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f1381,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| ~ c_lessequals(X9,X24,X3)
| c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_1) ).
fof(f10310,plain,
spl0_1309,
inference(avatar_split_clause,[],[f1380,f10308]) ).
fof(f10308,plain,
( spl0_1309
<=> ! [X9,X24,X3] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f1380,axiom,
! [X3,X9,X24] :
( ~ class_Orderings_Oord(X3)
| c_lessequals(X9,X24,X3)
| ~ c_in(X24,c_SetInterval_OatLeast(X9,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__iff_0) ).
fof(f10306,plain,
spl0_1308,
inference(avatar_split_clause,[],[f1379,f10304]) ).
fof(f10304,plain,
( spl0_1308
<=> ! [X11,X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatLeast(X11,X3) != c_SetInterval_OatLeast(X8,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f1379,axiom,
! [X3,X11,X8] :
( ~ class_Orderings_Olinorder(X3)
| X8 = X11
| c_SetInterval_OatLeast(X11,X3) != c_SetInterval_OatLeast(X8,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f10302,plain,
spl0_1307,
inference(avatar_split_clause,[],[f1373,f10300]) ).
fof(f1373,axiom,
! [X3,X10,X25] :
( ~ class_Orderings_Oorder(X3)
| ~ c_lessequals(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastLessThan(X25,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f10298,plain,
spl0_1306,
inference(avatar_split_clause,[],[f1368,f10296]) ).
fof(f10296,plain,
( spl0_1306
<=> ! [X25,X3,X10] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastAtMost(X25,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f1368,axiom,
! [X3,X10,X25] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X10,X25,X3)
| c_emptyset = c_SetInterval_OatLeastAtMost(X25,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f10294,plain,
spl0_1305,
inference(avatar_split_clause,[],[f1367,f10292]) ).
fof(f10292,plain,
( spl0_1305
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatLeast(X9,X3) = c_uminus(c_SetInterval_OlessThan(X9,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f1367,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatLeast(X9,X3) = c_uminus(c_SetInterval_OlessThan(X9,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__lessThan_0) ).
fof(f10290,plain,
spl0_1304,
inference(avatar_split_clause,[],[f1366,f10288]) ).
fof(f10288,plain,
( spl0_1304
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatMost(X9,X3) = c_uminus(c_SetInterval_OgreaterThan(X9,X3),tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f1366,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_SetInterval_OatMost(X9,X3) = c_uminus(c_SetInterval_OgreaterThan(X9,X3),tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f10286,plain,
spl0_1303,
inference(avatar_split_clause,[],[f1365,f10284]) ).
fof(f10284,plain,
( spl0_1303
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatMost(X9,X3),tc_set(X3)) = c_SetInterval_OgreaterThan(X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f1365,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatMost(X9,X3),tc_set(X3)) = c_SetInterval_OgreaterThan(X9,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atMost_0) ).
fof(f10282,plain,
spl0_1302,
inference(avatar_split_clause,[],[f1364,f10280]) ).
fof(f10280,plain,
( spl0_1302
<=> ! [X9,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatLeast(X9,X3),tc_set(X3)) = c_SetInterval_OlessThan(X9,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f1364,axiom,
! [X3,X9] :
( ~ class_Orderings_Olinorder(X3)
| c_uminus(c_SetInterval_OatLeast(X9,X3),tc_set(X3)) = c_SetInterval_OlessThan(X9,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OCompl__atLeast_0) ).
fof(f10278,plain,
spl0_1301,
inference(avatar_split_clause,[],[f1152,f10276]) ).
fof(f10276,plain,
( spl0_1301
<=> ! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f1152,axiom,
! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_3) ).
fof(f10274,plain,
spl0_1300,
inference(avatar_split_clause,[],[f1151,f10272]) ).
fof(f10272,plain,
( spl0_1300
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f1151,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_2) ).
fof(f10270,plain,
spl0_1299,
inference(avatar_split_clause,[],[f1150,f10268]) ).
fof(f10268,plain,
( spl0_1299
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f1150,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_1) ).
fof(f10266,plain,
spl0_1298,
inference(avatar_split_clause,[],[f1149,f10264]) ).
fof(f10264,plain,
( spl0_1298
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f1149,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__sum_0) ).
fof(f10262,plain,
spl0_1297,
inference(avatar_split_clause,[],[f1146,f10260]) ).
fof(f10260,plain,
( spl0_1297
<=> ! [X11,X8] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f1146,axiom,
! [X11,X8] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_0) ).
fof(f10258,plain,
spl0_1296,
inference(avatar_split_clause,[],[f1139,f10256]) ).
fof(f10256,plain,
( spl0_1296
<=> ! [X11,X8] :
( c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f1139,axiom,
! [X11,X8] :
( c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_3) ).
fof(f10254,plain,
spl0_1295,
inference(avatar_split_clause,[],[f1138,f10252]) ).
fof(f10252,plain,
( spl0_1295
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f1138,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_2) ).
fof(f10250,plain,
spl0_1294,
inference(avatar_split_clause,[],[f1137,f10248]) ).
fof(f10248,plain,
( spl0_1294
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f1137,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_1) ).
fof(f10246,plain,
spl0_1293,
inference(avatar_split_clause,[],[f1136,f10244]) ).
fof(f10244,plain,
( spl0_1293
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f1136,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_plus(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__sum_0) ).
fof(f10242,plain,
spl0_1292,
inference(avatar_split_clause,[],[f1133,f10240]) ).
fof(f10240,plain,
( spl0_1292
<=> ! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f1133,axiom,
! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(X8,tc_nat)
| ~ c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_0) ).
fof(f10238,plain,
spl0_1291,
inference(avatar_split_clause,[],[f1127,f10236]) ).
fof(f10236,plain,
( spl0_1291
<=> ! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f1127,axiom,
! [X11,X8] :
( c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_3) ).
fof(f10234,plain,
( spl0_1289
| ~ spl0_1290
| ~ spl0_782
| ~ spl0_1019 ),
inference(avatar_split_clause,[],[f8646,f8371,f7213,f10231,f10228]) ).
fof(f10228,plain,
( spl0_1289
<=> ! [X0] : c_Parity_Oeven(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f10231,plain,
( spl0_1290
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f7213,plain,
( spl0_782
<=> ! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f8371,plain,
( spl0_1019
<=> ! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f8646,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_1,tc_nat)
| c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_782
| ~ spl0_1019 ),
inference(superposition,[],[f8372,f7214]) ).
fof(f7214,plain,
( ! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_nat)
| ~ spl0_782 ),
inference(avatar_component_clause,[],[f7213]) ).
fof(f8372,plain,
( ! [X11,X8] :
( ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat)
| c_Parity_Oeven(X11,tc_nat) )
| ~ spl0_1019 ),
inference(avatar_component_clause,[],[f8371]) ).
fof(f10226,plain,
spl0_1288,
inference(avatar_split_clause,[],[f1126,f10224]) ).
fof(f10224,plain,
( spl0_1288
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f1126,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_2) ).
fof(f10222,plain,
spl0_1287,
inference(avatar_split_clause,[],[f1125,f10220]) ).
fof(f10220,plain,
( spl0_1287
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f1125,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(X8,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_1) ).
fof(f10218,plain,
spl0_1286,
inference(avatar_split_clause,[],[f1124,f10216]) ).
fof(f10216,plain,
( spl0_1286
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f1124,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__difference_0) ).
fof(f10214,plain,
spl0_1285,
inference(avatar_split_clause,[],[f1084,f10212]) ).
fof(f10212,plain,
( spl0_1285
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(c_0,X15,X3)
| c_less(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f1084,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(c_0,X15,X3)
| c_less(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f10210,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1083,f10208]) ).
fof(f10208,plain,
( spl0_1284
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(c_0,X15,X3)
| ~ c_less(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f1083,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(c_0,X15,X3)
| ~ c_less(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f10206,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1080,f10204]) ).
fof(f10204,plain,
( spl0_1283
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_0,X15,X3)
| c_lessequals(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f1080,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(c_0,X15,X3)
| c_lessequals(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f10202,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1079,f10200]) ).
fof(f10200,plain,
( spl0_1282
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_0,X15,X3)
| ~ c_lessequals(c_uminus(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f1079,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(c_0,X15,X3)
| ~ c_lessequals(c_uminus(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f10198,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1077,f10196]) ).
fof(f10196,plain,
( spl0_1281
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_uminus(X15,X3) != c_uminus(X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1077,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_uminus(X15,X3) != c_uminus(X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f10194,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1074,f10192]) ).
fof(f10192,plain,
( spl0_1280
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,c_0,X3)
| c_less(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1074,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_less(X15,c_0,X3)
| c_less(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f10190,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1073,f10188]) ).
fof(f10188,plain,
( spl0_1279
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,c_0,X3)
| ~ c_less(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1073,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_less(X15,c_0,X3)
| ~ c_less(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f10186,plain,
( spl0_1278
| ~ spl0_748
| ~ spl0_983 ),
inference(avatar_split_clause,[],[f8557,f8225,f7076,f10184]) ).
fof(f10184,plain,
( spl0_1278
<=> ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f7076,plain,
( spl0_748
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f8225,plain,
( spl0_983
<=> ! [X16,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f8557,plain,
( ! [X0] : c_0 = c_div(X0,c_0,tc_IntDef_Oint)
| ~ spl0_748
| ~ spl0_983 ),
inference(superposition,[],[f8226,f7077]) ).
fof(f7077,plain,
( ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8
| ~ spl0_748 ),
inference(avatar_component_clause,[],[f7076]) ).
fof(f8226,plain,
( ! [X16,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint)
| ~ spl0_983 ),
inference(avatar_component_clause,[],[f8225]) ).
fof(f10182,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1072,f10180]) ).
fof(f10180,plain,
( spl0_1277
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_lessequals(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1072,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| ~ c_lessequals(X15,c_0,X3)
| c_lessequals(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f10178,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1071,f10176]) ).
fof(f10176,plain,
( spl0_1276
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,c_0,X3)
| ~ c_lessequals(c_0,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f1071,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X3)
| c_lessequals(X15,c_0,X3)
| ~ c_lessequals(c_0,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f10174,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1017,f10172]) ).
fof(f10172,plain,
( spl0_1275
<=> ! [X37,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(X37,X3) = c_times(X37,c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f1017,axiom,
! [X3,X37] :
( ~ class_Numeral_Onumber__ring(X3)
| c_uminus(X37,X3) = c_times(X37,c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1__right_0) ).
fof(f10170,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1016,f10168]) ).
fof(f10168,plain,
( spl0_1274
<=> ! [X37,X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X37,X3) = c_uminus(X37,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f1016,axiom,
! [X3,X37] :
( ~ class_Numeral_Onumber__ring(X3)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X37,X3) = c_uminus(X37,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Omult__minus1_0) ).
fof(f10166,plain,
spl0_1273,
inference(avatar_split_clause,[],[f936,f10164]) ).
fof(f10164,plain,
( spl0_1273
<=> ! [X25,X9,X10] :
( X10 = X25
| c_plus(X25,X9,tc_nat) != c_plus(X10,X9,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f936,axiom,
! [X10,X9,X25] :
( X10 = X25
| c_plus(X25,X9,tc_nat) != c_plus(X10,X9,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
fof(f10162,plain,
spl0_1272,
inference(avatar_split_clause,[],[f931,f10160]) ).
fof(f10160,plain,
( spl0_1272
<=> ! [X25,X9,X10] :
( X10 = X25
| c_plus(X9,X25,tc_nat) != c_plus(X9,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f931,axiom,
! [X10,X9,X25] :
( X10 = X25
| c_plus(X9,X25,tc_nat) != c_plus(X9,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel_0) ).
fof(f10158,plain,
spl0_1271,
inference(avatar_split_clause,[],[f915,f10156]) ).
fof(f10156,plain,
( spl0_1271
<=> ! [X25,X10] :
( c_0 = X25
| c_0 = X10
| c_0 != c_times(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f915,axiom,
! [X10,X25] :
( c_0 = X25
| c_0 = X10
| c_0 != c_times(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__is__0_0) ).
fof(f10154,plain,
spl0_1270,
inference(avatar_split_clause,[],[f700,f10152]) ).
fof(f10152,plain,
( spl0_1270
<=> ! [X25,X10] : c_IntDef_Oint(c_plus(X25,X10,tc_nat)) = c_plus(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f700,axiom,
! [X10,X25] : c_IntDef_Oint(c_plus(X25,X10,tc_nat)) = c_plus(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f10150,plain,
spl0_1269,
inference(avatar_split_clause,[],[f663,f10148]) ).
fof(f10148,plain,
( spl0_1269
<=> ! [X25,X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X10 = X25
| c_NatArith_Oof__nat(X10,X3) != c_NatArith_Oof__nat(X25,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f663,axiom,
! [X3,X10,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| X10 = X25
| c_NatArith_Oof__nat(X10,X3) != c_NatArith_Oof__nat(X25,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f10146,plain,
spl0_1268,
inference(avatar_split_clause,[],[f657,f10144]) ).
fof(f10144,plain,
( spl0_1268
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f657,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f10136,plain,
spl0_1267,
inference(avatar_split_clause,[],[f656,f10134]) ).
fof(f10134,plain,
( spl0_1267
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f656,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f10132,plain,
spl0_1266,
inference(avatar_split_clause,[],[f634,f10130]) ).
fof(f10130,plain,
( spl0_1266
<=> ! [X52,X24] :
( c_0 = X52
| c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X24,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f634,axiom,
! [X52,X24] :
( c_0 = X52
| c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X24,X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f10128,plain,
spl0_1265,
inference(avatar_split_clause,[],[f593,f10126]) ).
fof(f10126,plain,
( spl0_1265
<=> ! [X41,X42,X44,X3] :
( X42 = X44
| c_append(X41,X42,X3) != c_append(X41,X44,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f593,axiom,
! [X41,X3,X44,X42] :
( X42 = X44
| c_append(X41,X42,X3) != c_append(X41,X44,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osame__append__eq_0) ).
fof(f10124,plain,
spl0_1264,
inference(avatar_split_clause,[],[f587,f10122]) ).
fof(f10122,plain,
( spl0_1264
<=> ! [X8,X3] :
( c_List_Orotate1(X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f587,axiom,
! [X3,X8] :
( c_List_Orotate1(X8,X3) = X8
| ~ c_lessequals(c_Nat_Osize(X8,tc_List_Olist(X3)),c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__length01_0) ).
fof(f10120,plain,
spl0_1263,
inference(avatar_split_clause,[],[f476,f10118]) ).
fof(f10118,plain,
( spl0_1263
<=> ! [X57,X14,X56,X3,X15] :
( X56 = X57
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f476,axiom,
! [X3,X56,X57,X14,X15] :
( X56 = X57
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_1) ).
fof(f10116,plain,
spl0_1262,
inference(avatar_split_clause,[],[f475,f10114]) ).
fof(f10114,plain,
( spl0_1262
<=> ! [X57,X14,X56,X3,X15] :
( X14 = X15
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f475,axiom,
! [X3,X56,X57,X14,X15] :
( X14 = X15
| c_List_Olist_OCons(X14,X56,X3) != c_List_Olist_OCons(X15,X57,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Oinject_0) ).
fof(f10112,plain,
spl0_1261,
inference(avatar_split_clause,[],[f460,f10110]) ).
fof(f10110,plain,
( spl0_1261
<=> ! [X41,X3,X10] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate(X10,X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f460,axiom,
! [X41,X3,X10] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate(X10,X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate_0) ).
fof(f10108,plain,
spl0_1260,
inference(avatar_split_clause,[],[f402,f10106]) ).
fof(f10106,plain,
( spl0_1260
<=> ! [X13,X41,X11] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13)
| ~ c_in(X11,c_List_Oset(X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f402,axiom,
! [X41,X11,X13] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13)
| ~ c_in(X11,c_List_Oset(X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_0) ).
fof(f10104,plain,
spl0_1259,
inference(avatar_split_clause,[],[f380,f10102]) ).
fof(f10102,plain,
( spl0_1259
<=> ! [X41,X42,X44,X3] :
( X42 = X44
| c_append(X42,X41,X3) != c_append(X44,X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f380,axiom,
! [X41,X3,X44,X42] :
( X42 = X44
| c_append(X42,X41,X3) != c_append(X44,X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__same__eq_0) ).
fof(f10100,plain,
spl0_1258,
inference(avatar_split_clause,[],[f343,f10098]) ).
fof(f10098,plain,
( spl0_1258
<=> ! [X16,X15] : c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X16,X15,tc_IntDef_Oint),X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f343,axiom,
! [X16,X15] : c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X16,X15,tc_IntDef_Oint),X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f10090,plain,
spl0_1257,
inference(avatar_split_clause,[],[f342,f10088]) ).
fof(f10088,plain,
( spl0_1257
<=> ! [X16,X15] : c_Divides_Oop_Amod(c_plus(X15,X16,tc_IntDef_Oint),X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f342,axiom,
! [X16,X15] : c_Divides_Oop_Amod(c_plus(X15,X16,tc_IntDef_Oint),X15,tc_IntDef_Oint) = c_Divides_Oop_Amod(X16,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f10086,plain,
spl0_1256,
inference(avatar_split_clause,[],[f335,f10084]) ).
fof(f10084,plain,
( spl0_1256
<=> ! [X11,X10] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f335,axiom,
! [X10,X11] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f10081,plain,
( spl0_1255
| ~ spl0_880
| ~ spl0_1254 ),
inference(avatar_split_clause,[],[f10077,f10074,f7667,f10079]) ).
fof(f10079,plain,
( spl0_1255
<=> ! [X10] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f7667,plain,
( spl0_880
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f10074,plain,
( spl0_1254
<=> ! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f10077,plain,
( ! [X10] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X10 )
| ~ spl0_880
| ~ spl0_1254 ),
inference(forward_demodulation,[],[f10075,f7669]) ).
fof(f7669,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_880 ),
inference(avatar_component_clause,[],[f7667]) ).
fof(f10075,plain,
( ! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1254 ),
inference(avatar_component_clause,[],[f10074]) ).
fof(f10076,plain,
spl0_1254,
inference(avatar_split_clause,[],[f334,f10074]) ).
fof(f334,axiom,
! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f10072,plain,
spl0_1253,
inference(avatar_split_clause,[],[f327,f10070]) ).
fof(f10070,plain,
( spl0_1253
<=> ! [X16,X8] :
( c_0 = X16
| c_div(c_times(X16,X8,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f327,axiom,
! [X8,X16] :
( c_0 = X16
| c_div(c_times(X16,X8,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f10068,plain,
spl0_1252,
inference(avatar_split_clause,[],[f326,f10066]) ).
fof(f10066,plain,
( spl0_1252
<=> ! [X16,X8] :
( c_0 = X16
| c_div(c_times(X8,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f326,axiom,
! [X8,X16] :
( c_0 = X16
| c_div(c_times(X8,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f10064,plain,
spl0_1251,
inference(avatar_split_clause,[],[f307,f10062]) ).
fof(f10062,plain,
( spl0_1251
<=> ! [X16] : c_IntDiv_OposDivAlg(c_Pair(c_0,X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f307,axiom,
! [X16] : c_IntDiv_OposDivAlg(c_Pair(c_0,X16,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_OposDivAlg__0_0) ).
fof(f10060,plain,
spl0_1250,
inference(avatar_split_clause,[],[f292,f10058]) ).
fof(f10058,plain,
( spl0_1250
<=> ! [X16,X15] : c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f292,axiom,
! [X16,X15] : c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f10056,plain,
spl0_1249,
inference(avatar_split_clause,[],[f263,f10054]) ).
fof(f10054,plain,
( spl0_1249
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X35,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f263,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(X35,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f10047,plain,
spl0_1248,
inference(avatar_split_clause,[],[f262,f10045]) ).
fof(f10045,plain,
( spl0_1248
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X35,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f262,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(X35,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f10043,plain,
spl0_1247,
inference(avatar_split_clause,[],[f259,f10041]) ).
fof(f10041,plain,
( spl0_1247
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f259,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(X35,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f10039,plain,
spl0_1246,
inference(avatar_split_clause,[],[f258,f10037]) ).
fof(f10037,plain,
( spl0_1246
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X35,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f258,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(X35,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X35,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f10035,plain,
spl0_1245,
inference(avatar_split_clause,[],[f256,f10033]) ).
fof(f10033,plain,
( spl0_1245
<=> ! [X37,X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X35 = X37
| c_IntDef_Oof__int(X37,X3) != c_IntDef_Oof__int(X35,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f256,axiom,
! [X3,X37,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| X35 = X37
| c_IntDef_Oof__int(X37,X3) != c_IntDef_Oof__int(X35,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f10031,plain,
spl0_1244,
inference(avatar_split_clause,[],[f250,f10029]) ).
fof(f10029,plain,
( spl0_1244
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f250,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f10027,plain,
spl0_1243,
inference(avatar_split_clause,[],[f249,f10025]) ).
fof(f10025,plain,
( spl0_1243
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f249,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f10023,plain,
spl0_1242,
inference(avatar_split_clause,[],[f248,f10021]) ).
fof(f10021,plain,
( spl0_1242
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f248,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f10019,plain,
spl0_1241,
inference(avatar_split_clause,[],[f247,f10017]) ).
fof(f10017,plain,
( spl0_1241
<=> ! [X37,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,X37,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f247,axiom,
! [X3,X37] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_lessequals(c_0,X37,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X37,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f10015,plain,
spl0_1240,
inference(avatar_split_clause,[],[f211,f10013]) ).
fof(f10013,plain,
( spl0_1240
<=> ! [X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| c_in(c_uminus(X15,X3),c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f211,axiom,
! [X3,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| ~ c_in(X15,c_IntDef_OInts,X3)
| c_in(c_uminus(X15,X3),c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__minus_0) ).
fof(f10011,plain,
spl0_1239,
inference(avatar_split_clause,[],[f206,f10009]) ).
fof(f10009,plain,
( spl0_1239
<=> ! [X8] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X8)) = X8
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f206,axiom,
! [X8] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X8)) = X8
| ~ c_in(X8,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f10007,plain,
( spl0_1238
| ~ spl0_54
| ~ spl0_967 ),
inference(avatar_split_clause,[],[f8169,f8043,f3434,f10004]) ).
fof(f10004,plain,
( spl0_1238
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f3434,plain,
( spl0_54
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f8043,plain,
( spl0_967
<=> ! [X3] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f8169,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_967 ),
inference(resolution,[],[f8044,f3436]) ).
fof(f3436,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3434]) ).
fof(f8044,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X3) )
| ~ spl0_967 ),
inference(avatar_component_clause,[],[f8043]) ).
fof(f10002,plain,
spl0_1237,
inference(avatar_split_clause,[],[f192,f10000]) ).
fof(f10000,plain,
( spl0_1237
<=> ! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f192,axiom,
! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f9998,plain,
spl0_1236,
inference(avatar_split_clause,[],[f191,f9996]) ).
fof(f9996,plain,
( spl0_1236
<=> ! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X36,tc_IntDef_Oint)) = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f191,axiom,
! [X36,X25] :
( c_IntDef_Oint(X25) != c_Numeral_Onumber__of(X36,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X36,tc_IntDef_Oint)) = X25 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f9994,plain,
spl0_1235,
inference(avatar_split_clause,[],[f93,f9992]) ).
fof(f9992,plain,
( spl0_1235
<=> ! [X25,X10] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f93,axiom,
! [X10,X25] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f9990,plain,
spl0_1234,
inference(avatar_split_clause,[],[f83,f9988]) ).
fof(f9988,plain,
( spl0_1234
<=> ! [X25,X10] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f83,axiom,
! [X10,X25] : c_Divides_Oop_Amod(X25,X10,tc_nat) = c_Divides_Oop_Amod(c_plus(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self2_0) ).
fof(f9986,plain,
spl0_1233,
inference(avatar_split_clause,[],[f82,f9984]) ).
fof(f9984,plain,
( spl0_1233
<=> ! [X25,X10] : c_Divides_Oop_Amod(c_plus(X10,X25,tc_nat),X10,tc_nat) = c_Divides_Oop_Amod(X25,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f82,axiom,
! [X10,X25] : c_Divides_Oop_Amod(c_plus(X10,X25,tc_nat),X10,tc_nat) = c_Divides_Oop_Amod(X25,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__add__self1_0) ).
fof(f9982,plain,
spl0_1232,
inference(avatar_split_clause,[],[f41,f9980]) ).
fof(f9980,plain,
( spl0_1232
<=> ! [X18,X17,X3,X19] :
( X18 = X19
| c_Datatype__Universe_OIn1(X19,X3,X17) != c_Datatype__Universe_OIn1(X18,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f41,axiom,
! [X3,X18,X19,X17] :
( X18 = X19
| c_Datatype__Universe_OIn1(X19,X3,X17) != c_Datatype__Universe_OIn1(X18,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f9978,plain,
spl0_1231,
inference(avatar_split_clause,[],[f39,f9976]) ).
fof(f9976,plain,
( spl0_1231
<=> ! [X18,X17,X3,X19] :
( X18 = X19
| c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn0(X19,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f39,axiom,
! [X3,X18,X19,X17] :
( X18 = X19
| c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn0(X19,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f9974,plain,
spl0_1230,
inference(avatar_split_clause,[],[f35,f9972]) ).
fof(f9972,plain,
( spl0_1230
<=> ! [X15,X17,X16,X3] :
( X15 = X16
| c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OAtom(X16,X3,X17) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f35,axiom,
! [X3,X16,X17,X15] :
( X15 = X16
| c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OAtom(X16,X3,X17) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f9966,plain,
( spl0_1229
| ~ spl0_862
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8149,f7961,f7544,f9963]) ).
fof(f9963,plain,
( spl0_1229
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f7544,plain,
( spl0_862
<=> ! [X11,X27,X3] : c_in(X11,c_insert(X11,X27,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f7961,plain,
( spl0_947
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f8149,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_862
| ~ spl0_947 ),
inference(superposition,[],[f7545,f7963]) ).
fof(f7963,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_947 ),
inference(avatar_component_clause,[],[f7961]) ).
fof(f7545,plain,
( ! [X3,X11,X27] : c_in(X11,c_insert(X11,X27,X3),X3)
| ~ spl0_862 ),
inference(avatar_component_clause,[],[f7544]) ).
fof(f9855,plain,
( ~ spl0_1227
| spl0_1228
| ~ spl0_770
| ~ spl0_1193 ),
inference(avatar_split_clause,[],[f9813,f9470,f7164,f9853,f9849]) ).
fof(f9849,plain,
( spl0_1227
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f9853,plain,
( spl0_1228
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f7164,plain,
( spl0_770
<=> ! [X10] : c_0 = c_minus(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f9470,plain,
( spl0_1193
<=> ! [X16,X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_0 != c_minus(X15,X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f9813,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_770
| ~ spl0_1193 ),
inference(trivial_inequality_removal,[],[f9806]) ).
fof(f9806,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_770
| ~ spl0_1193 ),
inference(superposition,[],[f9471,f7165]) ).
fof(f7165,plain,
( ! [X10] : c_0 = c_minus(c_0,X10,tc_nat)
| ~ spl0_770 ),
inference(avatar_component_clause,[],[f7164]) ).
fof(f9471,plain,
( ! [X3,X16,X15] :
( c_0 != c_minus(X15,X16,X3)
| X15 = X16
| ~ class_OrderedGroup_Oab__group__add(X3) )
| ~ spl0_1193 ),
inference(avatar_component_clause,[],[f9470]) ).
fof(f9761,plain,
( spl0_1226
| ~ spl0_89
| ~ spl0_935 ),
inference(avatar_split_clause,[],[f8133,f7913,f3609,f9759]) ).
fof(f9759,plain,
( spl0_1226
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f3609,plain,
( spl0_89
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f7913,plain,
( spl0_935
<=> ! [X8,X3] :
( ~ class_Power_Orecpower(X3)
| c_Nat_Opower(X8,c_1,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f8133,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_nat) = X0
| ~ spl0_89
| ~ spl0_935 ),
inference(resolution,[],[f7914,f3611]) ).
fof(f3611,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_89 ),
inference(avatar_component_clause,[],[f3609]) ).
fof(f7914,plain,
( ! [X3,X8] :
( ~ class_Power_Orecpower(X3)
| c_Nat_Opower(X8,c_1,X3) = X8 )
| ~ spl0_935 ),
inference(avatar_component_clause,[],[f7913]) ).
fof(f9715,plain,
( spl0_1225
| ~ spl0_55
| ~ spl0_935 ),
inference(avatar_split_clause,[],[f8132,f7913,f3439,f9713]) ).
fof(f9713,plain,
( spl0_1225
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f3439,plain,
( spl0_55
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f8132,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_55
| ~ spl0_935 ),
inference(resolution,[],[f7914,f3441]) ).
fof(f3441,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_55 ),
inference(avatar_component_clause,[],[f3439]) ).
fof(f9671,plain,
( spl0_1224
| ~ spl0_89
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f8131,f7909,f3609,f9669]) ).
fof(f9669,plain,
( spl0_1224
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f7909,plain,
( spl0_934
<=> ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(c_1,X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f8131,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_nat)
| ~ spl0_89
| ~ spl0_934 ),
inference(resolution,[],[f7910,f3611]) ).
fof(f7910,plain,
( ! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(c_1,X10,X3) )
| ~ spl0_934 ),
inference(avatar_component_clause,[],[f7909]) ).
fof(f9627,plain,
( spl0_1223
| ~ spl0_55
| ~ spl0_934 ),
inference(avatar_split_clause,[],[f8130,f7909,f3439,f9625]) ).
fof(f9625,plain,
( spl0_1223
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f8130,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_55
| ~ spl0_934 ),
inference(resolution,[],[f7910,f3441]) ).
fof(f9623,plain,
( spl0_1222
| ~ spl0_54
| ~ spl0_1013
| ~ spl0_1151 ),
inference(avatar_split_clause,[],[f9304,f9301,f8346,f3434,f9621]) ).
fof(f9621,plain,
( spl0_1222
<=> ! [X3] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X3)
| ~ class_Numeral_Onumber__ring(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f8346,plain,
( spl0_1013
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_uminus(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f9301,plain,
( spl0_1151
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f9304,plain,
( ! [X3] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_54
| ~ spl0_1013
| ~ spl0_1151 ),
inference(forward_demodulation,[],[f9302,f8637]) ).
fof(f8637,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_1013 ),
inference(resolution,[],[f8347,f3436]) ).
fof(f8347,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_uminus(c_1,X3) )
| ~ spl0_1013 ),
inference(avatar_component_clause,[],[f8346]) ).
fof(f9302,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X3) )
| ~ spl0_1151 ),
inference(avatar_component_clause,[],[f9301]) ).
fof(f9589,plain,
( spl0_1221
| ~ spl0_93
| ~ spl0_931 ),
inference(avatar_split_clause,[],[f8126,f7897,f3629,f9587]) ).
fof(f9587,plain,
( spl0_1221
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f3629,plain,
( spl0_93
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f7897,plain,
( spl0_931
<=> ! [X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X8,X8,X17) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f8126,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_nat) = X0
| ~ spl0_93
| ~ spl0_931 ),
inference(resolution,[],[f7898,f3631]) ).
fof(f3631,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_93 ),
inference(avatar_component_clause,[],[f3629]) ).
fof(f7898,plain,
( ! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X8,X8,X17) = X8 )
| ~ spl0_931 ),
inference(avatar_component_clause,[],[f7897]) ).
fof(f9585,plain,
spl0_1220,
inference(avatar_split_clause,[],[f3067,f9583]) ).
fof(f9583,plain,
( spl0_1220
<=> ! [X25,X10] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f3067,plain,
! [X10,X25] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X25,tc_nat) ),
inference(forward_demodulation,[],[f2890,f2757]) ).
fof(f2757,plain,
c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f866,f1394]) ).
fof(f866,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
fof(f2890,plain,
! [X10,X25] :
( c_lessequals(c_1,X25,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X25,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f945,f1394]) ).
fof(f945,axiom,
! [X10,X25] :
( c_lessequals(c_1,X25,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_0) ).
fof(f9581,plain,
spl0_1219,
inference(avatar_split_clause,[],[f3066,f9579]) ).
fof(f9579,plain,
( spl0_1219
<=> ! [X25,X10] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f3066,plain,
! [X10,X25] :
( ~ c_lessequals(c_1,c_times(X25,X10,tc_nat),tc_nat)
| c_lessequals(c_1,X10,tc_nat) ),
inference(forward_demodulation,[],[f2889,f2757]) ).
fof(f2889,plain,
! [X10,X25] :
( c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_times(X25,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f946,f1394]) ).
fof(f946,axiom,
! [X10,X25] :
( c_lessequals(c_1,X10,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__le__mult__iff_1) ).
fof(f9577,plain,
spl0_1218,
inference(avatar_split_clause,[],[f3063,f9575]) ).
fof(f9575,plain,
( spl0_1218
<=> ! [X24,X10] :
( c_lessequals(c_1,c_Nat_Opower(X24,X10,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f3063,plain,
! [X10,X24] :
( c_lessequals(c_1,c_Nat_Opower(X24,X10,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X24,tc_nat) ),
inference(forward_demodulation,[],[f2881,f2757]) ).
fof(f2881,plain,
! [X10,X24] :
( ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Nat_Opower(X24,X10,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1190,f1394]) ).
fof(f1190,axiom,
! [X10,X24] :
( ~ c_lessequals(c_1,X24,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X24,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__one__le__power_0) ).
fof(f9573,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2997,f9571]) ).
fof(f9571,plain,
( spl0_1217
<=> ! [X25,X10] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f2997,plain,
! [X10,X25] : c_less(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
inference(forward_demodulation,[],[f2797,f2793]) ).
fof(f2797,plain,
! [X10,X25] : c_less(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
inference(definition_unfolding,[],[f1615,f1394]) ).
fof(f1615,axiom,
! [X10,X25] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X10)),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zless_0) ).
fof(f9569,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2993,f9567]) ).
fof(f9567,plain,
( spl0_1216
<=> ! [X35] : c_Numeral_OBit(c_Numeral_Obin__add(X35,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f2993,plain,
! [X35] : c_Numeral_OBit(c_Numeral_Obin__add(X35,c_Numeral_OMin),c_Numeral_Obit_OB1) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)),
inference(forward_demodulation,[],[f2795,f2772]) ).
fof(f2772,plain,
! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin),
inference(definition_unfolding,[],[f962,f963]) ).
fof(f963,axiom,
! [X35] : c_Numeral_Obin__pred(X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min__right_0) ).
fof(f962,axiom,
! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__pred(X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Min_0) ).
fof(f2795,plain,
! [X35] : c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB0),c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_Obin__add(X35,c_Numeral_OMin),c_Numeral_Obit_OB1),
inference(definition_unfolding,[],[f981,f963,f963]) ).
fof(f981,axiom,
! [X35] : c_Numeral_Obin__pred(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X35),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__0_0) ).
fof(f9565,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2796,f9563]) ).
fof(f9563,plain,
( spl0_1215
<=> ! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X35),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f2796,plain,
! [X35] : c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__mult(c_Numeral_OMin,X35),c_Numeral_Obit_OB0),
inference(definition_unfolding,[],[f973,f979,f979]) ).
fof(f973,axiom,
! [X35] : c_Numeral_Obin__minus(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X35),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__0_0) ).
fof(f9557,plain,
( spl0_1214
| ~ spl0_1213 ),
inference(avatar_split_clause,[],[f9553,f9550,f9555]) ).
fof(f9555,plain,
( spl0_1214
<=> ! [X10] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f9550,plain,
( spl0_1213
<=> ! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f9553,plain,
( ! [X10] : ~ c_lessequals(c_0,c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1213 ),
inference(forward_demodulation,[],[f9551,f2793]) ).
fof(f9551,plain,
( ! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1213 ),
inference(avatar_component_clause,[],[f9550]) ).
fof(f9552,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2785,f9550]) ).
fof(f2785,plain,
! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f244,f1394]) ).
fof(f244,axiom,
! [X10] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X10)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9548,plain,
spl0_1212,
inference(avatar_split_clause,[],[f1565,f9546]) ).
fof(f9546,plain,
( spl0_1212
<=> ! [X20,X3] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ORange(X20,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f1565,axiom,
! [X3,X20] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ORange(X20,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f9544,plain,
( spl0_1211
| ~ spl0_29
| ~ spl0_931 ),
inference(avatar_split_clause,[],[f8125,f7897,f3309,f9542]) ).
fof(f9542,plain,
( spl0_1211
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f3309,plain,
( spl0_29
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f8125,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_29
| ~ spl0_931 ),
inference(resolution,[],[f7898,f3311]) ).
fof(f3311,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f3309]) ).
fof(f9540,plain,
spl0_1210,
inference(avatar_split_clause,[],[f1563,f9538]) ).
fof(f9538,plain,
( spl0_1210
<=> ! [X20,X3] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ODomain(X20,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f1563,axiom,
! [X3,X20] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X20,X3),X3,X3) = c_Relation_ODomain(X20,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f9536,plain,
spl0_1209,
inference(avatar_split_clause,[],[f1535,f9534]) ).
fof(f9534,plain,
( spl0_1209
<=> ! [X15,X16,X27,X3] :
( ~ c_in(X15,X27,X3)
| c_in(X15,c_insert(X16,X27,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f1535,axiom,
! [X3,X16,X27,X15] :
( ~ c_in(X15,X27,X3)
| c_in(X15,c_insert(X16,X27,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_2) ).
fof(f9532,plain,
spl0_1208,
inference(avatar_split_clause,[],[f1492,f9530]) ).
fof(f9530,plain,
( spl0_1208
<=> ! [X3,X31,X27,X26] :
( ~ c_in(X26,X31,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f1492,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X31,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
fof(f9528,plain,
spl0_1207,
inference(avatar_split_clause,[],[f1491,f9526]) ).
fof(f9526,plain,
( spl0_1207
<=> ! [X31,X27,X3,X26] :
( ~ c_in(X26,X27,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f1491,axiom,
! [X31,X3,X26,X27] :
( ~ c_in(X26,X27,X3)
| c_in(X26,c_union(X27,X31,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
fof(f9524,plain,
spl0_1206,
inference(avatar_split_clause,[],[f1433,f9522]) ).
fof(f9522,plain,
( spl0_1206
<=> ! [X27,X3,X26] :
( c_in(X26,X27,X3)
| c_in(X26,c_uminus(X27,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f1433,axiom,
! [X3,X26,X27] :
( c_in(X26,X27,X3)
| c_in(X26,c_uminus(X27,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_1) ).
fof(f9520,plain,
spl0_1205,
inference(avatar_split_clause,[],[f1432,f9518]) ).
fof(f9518,plain,
( spl0_1205
<=> ! [X27,X3,X26] :
( ~ c_in(X26,X27,X3)
| ~ c_in(X26,c_uminus(X27,tc_set(X3)),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f1432,axiom,
! [X3,X26,X27] :
( ~ c_in(X26,X27,X3)
| ~ c_in(X26,c_uminus(X27,tc_set(X3)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__iff_0) ).
fof(f9516,plain,
spl0_1204,
inference(avatar_split_clause,[],[f1395,f9514]) ).
fof(f9514,plain,
( spl0_1204
<=> ! [X38,X74] : c_minus(X38,X74,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f1395,axiom,
! [X38,X74] : c_minus(X38,X74,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f9512,plain,
spl0_1203,
inference(avatar_split_clause,[],[f1392,f9510]) ).
fof(f9510,plain,
( spl0_1203
<=> ! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,X74,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f1392,axiom,
! [X38,X74] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),tc_nat) = c_minus(X38,X74,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f9508,plain,
spl0_1202,
inference(avatar_split_clause,[],[f1372,f9506]) ).
fof(f9506,plain,
( spl0_1202
<=> ! [X3,X15] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_OatLeastAtMost(X15,X15,X3) = c_insert(X15,c_emptyset,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f1372,axiom,
! [X3,X15] :
( ~ class_Orderings_Oorder(X3)
| c_SetInterval_OatLeastAtMost(X15,X15,X3) = c_insert(X15,c_emptyset,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f9504,plain,
spl0_1201,
inference(avatar_split_clause,[],[f1121,f9502]) ).
fof(f9502,plain,
( spl0_1201
<=> ! [X36] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f1121,axiom,
! [X36] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
fof(f9500,plain,
( spl0_1200
| ~ spl0_93
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f8124,f7893,f3629,f9498]) ).
fof(f9498,plain,
( spl0_1200
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f7893,plain,
( spl0_930
<=> ! [X17,X8] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X8,X8,X17) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f8124,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_nat) = X0
| ~ spl0_93
| ~ spl0_930 ),
inference(resolution,[],[f7894,f3631]) ).
fof(f7894,plain,
( ! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X8,X8,X17) = X8 )
| ~ spl0_930 ),
inference(avatar_component_clause,[],[f7893]) ).
fof(f9496,plain,
spl0_1199,
inference(avatar_split_clause,[],[f1120,f9494]) ).
fof(f9494,plain,
( spl0_1199
<=> ! [X36] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f1120,axiom,
! [X36] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X36,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
fof(f9492,plain,
spl0_1198,
inference(avatar_split_clause,[],[f1102,f9490]) ).
fof(f9490,plain,
( spl0_1198
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_less(c_0,c_HOL_Oabs(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f1102,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_less(c_0,c_HOL_Oabs(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f9488,plain,
spl0_1197,
inference(avatar_split_clause,[],[f1095,f9486]) ).
fof(f9486,plain,
( spl0_1197
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_OrderedGroup_Opprt(X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f1095,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_OrderedGroup_Opprt(X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f9484,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1094,f9482]) ).
fof(f9482,plain,
( spl0_1196
<=> ! [X11,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X11,c_0,X3)
| c_0 = c_OrderedGroup_Opprt(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1094,axiom,
! [X3,X11] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X11,c_0,X3)
| c_0 = c_OrderedGroup_Opprt(X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f9480,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1090,f9478]) ).
fof(f9478,plain,
( spl0_1195
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X8,c_0,X3)
| c_OrderedGroup_Onprt(X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1090,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(X8,c_0,X3)
| c_OrderedGroup_Onprt(X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f9476,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1089,f9474]) ).
fof(f9474,plain,
( spl0_1194
<=> ! [X11,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X11,X3)
| c_0 = c_OrderedGroup_Onprt(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1089,axiom,
! [X3,X11] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| ~ c_lessequals(c_0,X11,X3)
| c_0 = c_OrderedGroup_Onprt(X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f9472,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1049,f9470]) ).
fof(f1049,axiom,
! [X3,X16,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| X15 = X16
| c_0 != c_minus(X15,X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f9468,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1033,f9466]) ).
fof(f9466,plain,
( spl0_1192
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_HOL_Oabs(X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1033,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_lessequals(c_0,X8,X3)
| c_HOL_Oabs(X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f9464,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1031,f9462]) ).
fof(f9462,plain,
( spl0_1191
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1031,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f9460,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1029,f9458]) ).
fof(f9458,plain,
( spl0_1190
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| ~ c_lessequals(c_HOL_Oabs(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1029,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| ~ c_lessequals(c_HOL_Oabs(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f9456,plain,
( spl0_1189
| ~ spl0_29
| ~ spl0_930 ),
inference(avatar_split_clause,[],[f8123,f7893,f3309,f9454]) ).
fof(f9454,plain,
( spl0_1189
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f8123,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_29
| ~ spl0_930 ),
inference(resolution,[],[f7894,f3311]) ).
fof(f9452,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1028,f9450]) ).
fof(f9450,plain,
( spl0_1188
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_HOL_Oabs(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1028,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_HOL_Oabs(X15,X3) = c_HOL_Oabs(c_HOL_Oabs(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f9448,plain,
spl0_1187,
inference(avatar_split_clause,[],[f997,f9446]) ).
fof(f9446,plain,
( spl0_1187
<=> ! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f997,axiom,
! [X3,X35] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f9444,plain,
spl0_1186,
inference(avatar_split_clause,[],[f977,f9442]) ).
fof(f9442,plain,
( spl0_1186
<=> ! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35) = c_Numeral_OBit(c_Numeral_Obin__mult(X36,X35),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f977,axiom,
! [X36,X35] : c_Numeral_Obin__mult(c_Numeral_OBit(X36,c_Numeral_Obit_OB0),X35) = c_Numeral_OBit(c_Numeral_Obin__mult(X36,X35),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__0_0) ).
fof(f9440,plain,
spl0_1185,
inference(avatar_split_clause,[],[f954,f9438]) ).
fof(f9438,plain,
( spl0_1185
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f954,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_1) ).
fof(f9436,plain,
spl0_1184,
inference(avatar_split_clause,[],[f953,f9434]) ).
fof(f9434,plain,
( spl0_1184
<=> ! [X25,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f953,axiom,
! [X10,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_0,c_minus(X10,X25,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__diff_0) ).
fof(f9432,plain,
spl0_1183,
inference(avatar_split_clause,[],[f929,f9430]) ).
fof(f9430,plain,
( spl0_1183
<=> ! [X25,X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f929,axiom,
! [X10,X25] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f9428,plain,
spl0_1182,
inference(avatar_split_clause,[],[f928,f9426]) ).
fof(f9426,plain,
( spl0_1182
<=> ! [X25,X10] :
( c_less(c_0,X25,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f928,axiom,
! [X10,X25] :
( c_less(c_0,X25,tc_nat)
| ~ c_less(c_0,c_times(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f9424,plain,
spl0_1181,
inference(avatar_split_clause,[],[f880,f9422]) ).
fof(f9422,plain,
( spl0_1181
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f880,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_2) ).
fof(f9420,plain,
spl0_1180,
inference(avatar_split_clause,[],[f879,f9418]) ).
fof(f9418,plain,
( spl0_1180
<=> ! [X25,X10] :
( ~ c_less(c_0,X25,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f879,axiom,
! [X10,X25] :
( ~ c_less(c_0,X25,tc_nat)
| c_less(c_0,c_plus(X25,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__gr__0_1) ).
fof(f9416,plain,
spl0_1179,
inference(avatar_split_clause,[],[f701,f9414]) ).
fof(f9414,plain,
( spl0_1179
<=> ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f701,axiom,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X36,tc_nat)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oint__nat__number__of_0) ).
fof(f9412,plain,
( spl0_1178
| ~ spl0_66
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8118,f7877,f3494,f9410]) ).
fof(f9410,plain,
( spl0_1178
<=> ! [X0] : c_times(X0,c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f3494,plain,
( spl0_66
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f7877,plain,
( spl0_926
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(X8,c_1,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f8118,plain,
( ! [X0] : c_times(X0,c_1,tc_nat) = X0
| ~ spl0_66
| ~ spl0_926 ),
inference(resolution,[],[f7878,f3496]) ).
fof(f3496,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_66 ),
inference(avatar_component_clause,[],[f3494]) ).
fof(f7878,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(X8,c_1,X3) = X8 )
| ~ spl0_926 ),
inference(avatar_component_clause,[],[f7877]) ).
fof(f9408,plain,
spl0_1177,
inference(avatar_split_clause,[],[f664,f9406]) ).
fof(f9406,plain,
( spl0_1177
<=> ! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X25
| ~ c_lessequals(c_NatArith_Oof__nat(X25,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f664,axiom,
! [X3,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X25
| ~ c_lessequals(c_NatArith_Oof__nat(X25,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f9404,plain,
spl0_1176,
inference(avatar_split_clause,[],[f584,f9402]) ).
fof(f9402,plain,
( spl0_1176
<=> ! [X11,X3] : c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = c_List_Orev(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f584,axiom,
! [X3,X11] : c_List_Olist_OCons(X11,c_List_Olist_ONil,X3) = c_List_Orev(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__singleton__conv_1) ).
fof(f9400,plain,
spl0_1175,
inference(avatar_split_clause,[],[f581,f9398]) ).
fof(f9398,plain,
( spl0_1175
<=> ! [X11,X3,X10] : c_List_Oreplicate(X10,X11,X3) = c_List_Orev(c_List_Oreplicate(X10,X11,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f581,axiom,
! [X3,X10,X11] : c_List_Oreplicate(X10,X11,X3) = c_List_Orev(c_List_Oreplicate(X10,X11,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__replicate_0) ).
fof(f9396,plain,
spl0_1174,
inference(avatar_split_clause,[],[f562,f9394]) ).
fof(f9394,plain,
( spl0_1174
<=> ! [X42,X11,X13,X8] :
( ~ c_List_Oop_Amem(X11,X42,X13)
| c_List_Oop_Amem(X11,c_List_Olist_OCons(X8,X42,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f562,axiom,
! [X11,X8,X42,X13] :
( ~ c_List_Oop_Amem(X11,X42,X13)
| c_List_Oop_Amem(X11,c_List_Olist_OCons(X8,X42,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f9392,plain,
spl0_1173,
inference(avatar_split_clause,[],[f463,f9390]) ).
fof(f9390,plain,
( spl0_1173
<=> ! [X52,X24] : c_Nat_Osize(c_List_Oupt(X24,X52),tc_List_Olist(tc_nat)) = c_minus(X52,X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f463,axiom,
! [X52,X24] : c_Nat_Osize(c_List_Oupt(X24,X52),tc_List_Olist(tc_nat)) = c_minus(X52,X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__upt_0) ).
fof(f9388,plain,
spl0_1172,
inference(avatar_split_clause,[],[f459,f9386]) ).
fof(f9386,plain,
( spl0_1172
<=> ! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate1(X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f459,axiom,
! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orotate1(X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rotate1_0) ).
fof(f9384,plain,
spl0_1171,
inference(avatar_split_clause,[],[f458,f9382]) ).
fof(f9382,plain,
( spl0_1171
<=> ! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orev(X41,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f458,axiom,
! [X41,X3] : c_Nat_Osize(X41,tc_List_Olist(X3)) = c_Nat_Osize(c_List_Orev(X41,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__rev_0) ).
fof(f9380,plain,
spl0_1170,
inference(avatar_split_clause,[],[f445,f9378]) ).
fof(f9378,plain,
( spl0_1170
<=> ! [X41,X8,X3] : c_List_Olast(c_append(X41,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f445,axiom,
! [X41,X3,X8] : c_List_Olast(c_append(X41,c_List_Olist_OCons(X8,c_List_Olist_ONil,X3),X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__snoc_0) ).
fof(f9376,plain,
spl0_1169,
inference(avatar_split_clause,[],[f444,f9374]) ).
fof(f9374,plain,
( spl0_1169
<=> ! [X8,X3,X10] :
( c_0 = X10
| c_List_Olast(c_List_Oreplicate(X10,X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f444,axiom,
! [X3,X10,X8] :
( c_0 = X10
| c_List_Olast(c_List_Oreplicate(X10,X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__replicate_0) ).
fof(f9372,plain,
spl0_1168,
inference(avatar_split_clause,[],[f443,f9370]) ).
fof(f9370,plain,
( spl0_1168
<=> ! [X53,X3] :
( c_List_Olist_ONil = X53
| c_in(c_List_Olast(X53,X3),c_List_Oset(X53,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f443,axiom,
! [X3,X53] :
( c_List_Olist_ONil = X53
| c_in(c_List_Olast(X53,X3),c_List_Oset(X53,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast__in__set_0) ).
fof(f9368,plain,
( spl0_1167
| ~ spl0_17
| ~ spl0_926 ),
inference(avatar_split_clause,[],[f8117,f7877,f3249,f9366]) ).
fof(f9366,plain,
( spl0_1167
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f3249,plain,
( spl0_17
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f8117,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_17
| ~ spl0_926 ),
inference(resolution,[],[f7878,f3251]) ).
fof(f3251,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f3249]) ).
fof(f9364,plain,
spl0_1166,
inference(avatar_split_clause,[],[f434,f9362]) ).
fof(f9362,plain,
( spl0_1166
<=> ! [X52,X8] :
( ~ c_less(X8,X52,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X52),tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f434,axiom,
! [X8,X52] :
( ~ c_less(X8,X52,tc_nat)
| c_List_Ohd(c_List_Oupt(X8,X52),tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__upt_0) ).
fof(f9360,plain,
spl0_1165,
inference(avatar_split_clause,[],[f433,f9358]) ).
fof(f9358,plain,
( spl0_1165
<=> ! [X8,X3,X10] :
( c_0 = X10
| c_List_Ohd(c_List_Oreplicate(X10,X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f433,axiom,
! [X3,X10,X8] :
( c_0 = X10
| c_List_Ohd(c_List_Oreplicate(X10,X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__replicate_0) ).
fof(f9356,plain,
spl0_1164,
inference(avatar_split_clause,[],[f432,f9354]) ).
fof(f9354,plain,
( spl0_1164
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_in(c_List_Ohd(X41,X3),c_List_Oset(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f432,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_in(c_List_Ohd(X41,X3),c_List_Oset(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd__in__set_0) ).
fof(f9352,plain,
spl0_1163,
inference(avatar_split_clause,[],[f389,f9350]) ).
fof(f9350,plain,
( spl0_1163
<=> ! [X11,X8,X3] : c_List_Obutlast(c_append(X8,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f389,axiom,
! [X3,X11,X8] : c_List_Obutlast(c_append(X8,c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast__snoc_0) ).
fof(f9348,plain,
spl0_1162,
inference(avatar_split_clause,[],[f313,f9346]) ).
fof(f9346,plain,
( spl0_1162
<=> ! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f313,axiom,
! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__sign_0) ).
fof(f9344,plain,
spl0_1161,
inference(avatar_split_clause,[],[f312,f9342]) ).
fof(f9342,plain,
( spl0_1161
<=> ! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f312,axiom,
! [X16,X15] :
( ~ c_less(c_0,X16,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opos__mod__bound_0) ).
fof(f9340,plain,
spl0_1160,
inference(avatar_split_clause,[],[f305,f9338]) ).
fof(f9338,plain,
( spl0_1160
<=> ! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f305,axiom,
! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f9336,plain,
spl0_1159,
inference(avatar_split_clause,[],[f304,f9334]) ).
fof(f9334,plain,
( spl0_1159
<=> ! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_less(X16,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f304,axiom,
! [X16,X15] :
( ~ c_less(X16,c_0,tc_IntDef_Oint)
| c_less(X16,c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f9332,plain,
spl0_1158,
inference(avatar_split_clause,[],[f268,f9330]) ).
fof(f9330,plain,
( spl0_1158
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_NatArith_Oof__nat(X10,X3) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X10,tc_IntDef_Oint),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f268,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_NatArith_Oof__nat(X10,X3) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X10,tc_IntDef_Oint),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f9328,plain,
spl0_1157,
inference(avatar_split_clause,[],[f204,f9326]) ).
fof(f9326,plain,
( spl0_1157
<=> ! [X37,X35] :
( ~ c_less(X35,X37,tc_IntDef_Oint)
| c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f204,axiom,
! [X37,X35] :
( ~ c_less(X35,X37,tc_IntDef_Oint)
| c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f9324,plain,
( spl0_1156
| ~ spl0_66
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f8116,f7873,f3494,f9322]) ).
fof(f9322,plain,
( spl0_1156
<=> ! [X0] : c_times(c_1,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f7873,plain,
( spl0_925
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(c_1,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f8116,plain,
( ! [X0] : c_times(c_1,X0,tc_nat) = X0
| ~ spl0_66
| ~ spl0_925 ),
inference(resolution,[],[f7874,f3496]) ).
fof(f7874,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(c_1,X8,X3) = X8 )
| ~ spl0_925 ),
inference(avatar_component_clause,[],[f7873]) ).
fof(f9320,plain,
spl0_1155,
inference(avatar_split_clause,[],[f203,f9318]) ).
fof(f9318,plain,
( spl0_1155
<=> ! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f203,axiom,
! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_lessequals(X35,c_minus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f9316,plain,
spl0_1154,
inference(avatar_split_clause,[],[f202,f9314]) ).
fof(f9314,plain,
( spl0_1154
<=> ! [X37,X35] :
( ~ c_lessequals(X35,X37,tc_IntDef_Oint)
| c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f202,axiom,
! [X37,X35] :
( ~ c_lessequals(X35,X37,tc_IntDef_Oint)
| c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f9312,plain,
spl0_1153,
inference(avatar_split_clause,[],[f201,f9310]) ).
fof(f9310,plain,
( spl0_1153
<=> ! [X37,X35] :
( c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f201,axiom,
! [X37,X35] :
( c_lessequals(X35,X37,tc_IntDef_Oint)
| ~ c_less(X35,c_plus(X37,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f9308,plain,
spl0_1152,
inference(avatar_split_clause,[],[f198,f9306]) ).
fof(f9306,plain,
( spl0_1152
<=> ! [X37,X35] : c_plus(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X37,X35,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f198,axiom,
! [X37,X35] : c_plus(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X37,X35,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f9303,plain,
spl0_1151,
inference(avatar_split_clause,[],[f195,f9301]) ).
fof(f195,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oof__int__m1_0) ).
fof(f9299,plain,
spl0_1150,
inference(avatar_split_clause,[],[f160,f9297]) ).
fof(f9297,plain,
( spl0_1150
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f160,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oabs__minus__one_0) ).
fof(f9295,plain,
spl0_1149,
inference(avatar_split_clause,[],[f157,f9293]) ).
fof(f9293,plain,
( spl0_1149
<=> ! [X8,X10] : c_GCD_Ogcd(c_Pair(X8,c_times(X8,X10,tc_nat),tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f157,axiom,
! [X10,X8] : c_GCD_Ogcd(c_Pair(X8,c_times(X8,X10,tc_nat),tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__mult_0) ).
fof(f9291,plain,
spl0_1148,
inference(avatar_split_clause,[],[f86,f9289]) ).
fof(f9289,plain,
( spl0_1148
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f86,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less__divisor_0) ).
fof(f9287,plain,
spl0_1147,
inference(avatar_split_clause,[],[f84,f9285]) ).
fof(f9285,plain,
( spl0_1147
<=> ! [X25,X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f84,axiom,
! [X10,X25] :
( ~ c_less(c_0,X10,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__le__divisor_0) ).
fof(f9283,plain,
spl0_1146,
inference(avatar_split_clause,[],[f28,f9281]) ).
fof(f9281,plain,
( spl0_1146
<=> ! [X16,X17,X3,X15] : c_0 = c_Nat_Osize(c_Pair(X15,X16,X3,X17),tc_prod(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f28,axiom,
! [X3,X16,X17,X15] : c_0 = c_Nat_Osize(c_Pair(X15,X16,X3,X17),tc_prod(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oprod_Osize_0) ).
fof(f9279,plain,
( spl0_1145
| ~ spl0_17
| ~ spl0_925 ),
inference(avatar_split_clause,[],[f8115,f7873,f3249,f9277]) ).
fof(f9277,plain,
( spl0_1145
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f8115,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_17
| ~ spl0_925 ),
inference(resolution,[],[f7874,f3251]) ).
fof(f9275,plain,
spl0_1144,
inference(avatar_split_clause,[],[f16,f9273]) ).
fof(f9273,plain,
( spl0_1144
<=> ! [X11,X12,X3] :
( c_Datatype_Ooption_OSome(X11,X3) = X12
| ~ c_in(X11,c_Datatype_Oo2s(X12,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f16,axiom,
! [X3,X11,X12] :
( c_Datatype_Ooption_OSome(X11,X3) = X12
| ~ c_in(X11,c_Datatype_Oo2s(X12,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_0) ).
fof(f9271,plain,
spl0_1143,
inference(avatar_split_clause,[],[f6,f9269]) ).
fof(f9269,plain,
( spl0_1143
<=> ! [X0,X1,X8,X3] : c_Tarski_Opotype_Omore(c_Tarski_Opotype_Opotype__ext(X0,X1,X8,X3,X3),X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f6,axiom,
! [X3,X0,X1,X8] : c_Tarski_Opotype_Omore(c_Tarski_Opotype_Opotype__ext(X0,X1,X8,X3,X3),X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__3_0) ).
fof(f9267,plain,
spl0_1142,
inference(avatar_split_clause,[],[f5,f9265]) ).
fof(f9265,plain,
( spl0_1142
<=> ! [X4,X0,X8,X3,X2] : c_Tarski_Opotype_Oorder(c_Tarski_Opotype_Opotype__ext(X0,X8,X2,X3,X4),X3,X4) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f5,axiom,
! [X2,X3,X0,X8,X4] : c_Tarski_Opotype_Oorder(c_Tarski_Opotype_Opotype__ext(X0,X8,X2,X3,X4),X3,X4) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__2_0) ).
fof(f9263,plain,
spl0_1141,
inference(avatar_split_clause,[],[f4,f9261]) ).
fof(f9261,plain,
( spl0_1141
<=> ! [X4,X8,X3,X2,X1] : c_Tarski_Opotype_Opset(c_Tarski_Opotype_Opotype__ext(X8,X1,X2,X3,X4),X3,X4) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f4,axiom,
! [X2,X3,X1,X8,X4] : c_Tarski_Opotype_Opset(c_Tarski_Opotype_Opotype__ext(X8,X1,X2,X3,X4),X3,X4) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Opotype_Oselect__convs__1_0) ).
fof(f9245,plain,
( spl0_1140
| ~ spl0_11
| ~ spl0_924 ),
inference(avatar_split_clause,[],[f8114,f7869,f3219,f9243]) ).
fof(f9243,plain,
( spl0_1140
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f3219,plain,
( spl0_11
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f7869,plain,
( spl0_924
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_minus(X15,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f8114,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_11
| ~ spl0_924 ),
inference(resolution,[],[f7870,f3221]) ).
fof(f3221,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f3219]) ).
fof(f7870,plain,
( ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_minus(X15,X15,X3) )
| ~ spl0_924 ),
inference(avatar_component_clause,[],[f7869]) ).
fof(f9230,plain,
( spl0_1139
| ~ spl0_11
| ~ spl0_923 ),
inference(avatar_split_clause,[],[f8113,f7865,f3219,f9228]) ).
fof(f9228,plain,
( spl0_1139
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f7865,plain,
( spl0_923
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_minus(X8,c_0,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f8113,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_11
| ~ spl0_923 ),
inference(resolution,[],[f7866,f3221]) ).
fof(f7866,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_minus(X8,c_0,X3) = X8 )
| ~ spl0_923 ),
inference(avatar_component_clause,[],[f7865]) ).
fof(f9205,plain,
( spl0_1138
| ~ spl0_6
| ~ spl0_922 ),
inference(avatar_split_clause,[],[f8111,f7861,f3194,f9203]) ).
fof(f9203,plain,
( spl0_1138
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f3194,plain,
( spl0_6
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f7861,plain,
( spl0_922
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(c_0,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f8111,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_6
| ~ spl0_922 ),
inference(resolution,[],[f7862,f3196]) ).
fof(f3196,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f3194]) ).
fof(f7862,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(c_0,X8,X3) = X8 )
| ~ spl0_922 ),
inference(avatar_component_clause,[],[f7861]) ).
fof(f9147,plain,
( spl0_1137
| ~ spl0_54
| ~ spl0_1013
| ~ spl0_1084 ),
inference(avatar_split_clause,[],[f8834,f8831,f8346,f3434,f9145]) ).
fof(f9145,plain,
( spl0_1137
<=> ! [X15] : c_uminus(X15,tc_IntDef_Oint) = c_div(X15,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f8831,plain,
( spl0_1084
<=> ! [X15] : c_div(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f8834,plain,
( ! [X15] : c_uminus(X15,tc_IntDef_Oint) = c_div(X15,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_1013
| ~ spl0_1084 ),
inference(forward_demodulation,[],[f8832,f8637]) ).
fof(f8832,plain,
( ! [X15] : c_div(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X15,tc_IntDef_Oint)
| ~ spl0_1084 ),
inference(avatar_component_clause,[],[f8831]) ).
fof(f9127,plain,
( spl0_1136
| spl0_670
| ~ spl0_1070 ),
inference(avatar_split_clause,[],[f9084,f8775,f6726,f9124]) ).
fof(f9124,plain,
( spl0_1136
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f6726,plain,
( spl0_670
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f8775,plain,
( spl0_1070
<=> ! [X27,X3] :
( c_0 = c_Finite__Set_Ocard(X27,X3)
| c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f9084,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_670
| ~ spl0_1070 ),
inference(resolution,[],[f8776,f6728]) ).
fof(f6728,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_670 ),
inference(avatar_component_clause,[],[f6726]) ).
fof(f8776,plain,
( ! [X3,X27] :
( c_in(X27,c_Finite__Set_OFinites,tc_set(X3))
| c_0 = c_Finite__Set_Ocard(X27,X3) )
| ~ spl0_1070 ),
inference(avatar_component_clause,[],[f8775]) ).
fof(f9059,plain,
( spl0_1135
| ~ spl0_114
| ~ spl0_1128
| ~ spl0_1129 ),
inference(avatar_split_clause,[],[f9020,f9015,f9011,f3728,f9056]) ).
fof(f9056,plain,
( spl0_1135
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f3728,plain,
( spl0_114
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f9011,plain,
( spl0_1128
<=> ! [X10] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f9015,plain,
( spl0_1129
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f9020,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_114
| ~ spl0_1128
| ~ spl0_1129 ),
inference(forward_demodulation,[],[f9019,f9016]) ).
fof(f9016,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f9015]) ).
fof(f9019,plain,
( c_IntDef_Oneg(c_uminus(c_plus(c_1,c_0,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_114
| ~ spl0_1128 ),
inference(superposition,[],[f9012,f3730]) ).
fof(f3730,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f3728]) ).
fof(f9012,plain,
( ! [X10] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1128 ),
inference(avatar_component_clause,[],[f9011]) ).
fof(f9040,plain,
spl0_1134,
inference(avatar_split_clause,[],[f3115,f9038]) ).
fof(f9038,plain,
( spl0_1134
<=> ! [X11,X3] :
( c_IntDef_Oiszero(c_0,X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f3115,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_0,X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ),
inference(inner_rewriting,[],[f3114]) ).
fof(f3114,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f3113,f965]) ).
fof(f3113,plain,
! [X3,X11] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_OPls),X3),X3)
| ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3) ),
inference(forward_demodulation,[],[f2922,f2756]) ).
fof(f2922,plain,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls)),X3),X3) ),
inference(definition_unfolding,[],[f187,f979]) ).
fof(f187,axiom,
! [X3,X11] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 != c_Numeral_Onumber__of(X11,X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,c_Numeral_Obin__minus(c_Numeral_OPls)),X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oarith__special__8_0) ).
fof(f9036,plain,
spl0_1133,
inference(avatar_split_clause,[],[f3000,f9034]) ).
fof(f9034,plain,
( spl0_1133
<=> ! [X18,X17,X3] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f3000,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
inference(forward_demodulation,[],[f2802,f2757]) ).
fof(f2802,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
inference(definition_unfolding,[],[f59,f1394]) ).
fof(f59,axiom,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X18,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f9032,plain,
spl0_1132,
inference(avatar_split_clause,[],[f2999,f9030]) ).
fof(f9030,plain,
( spl0_1132
<=> ! [X18,X17,X3] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f2999,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
inference(forward_demodulation,[],[f2801,f2757]) ).
fof(f2801,plain,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
inference(definition_unfolding,[],[f60,f1394]) ).
fof(f60,axiom,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X18,X3,X17),X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f9028,plain,
spl0_1131,
inference(avatar_split_clause,[],[f2873,f9026]) ).
fof(f9026,plain,
( spl0_1131
<=> ! [X11] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2873,plain,
! [X11] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1129,f1394]) ).
fof(f1129,axiom,
! [X11] :
( c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9024,plain,
spl0_1130,
inference(avatar_split_clause,[],[f2863,f9022]) ).
fof(f9022,plain,
( spl0_1130
<=> ! [X11] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f2863,plain,
! [X11] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Finite__Set_Ocard(c_SetInterval_OatMost(X11,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f1128,f1394]) ).
fof(f1128,axiom,
! [X11] :
( ~ c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X11),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9017,plain,
( spl0_1129
| ~ spl0_6
| ~ spl0_921 ),
inference(avatar_split_clause,[],[f8109,f7857,f3194,f9015]) ).
fof(f7857,plain,
( spl0_921
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(X8,c_0,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f8109,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_6
| ~ spl0_921 ),
inference(resolution,[],[f7858,f3196]) ).
fof(f7858,plain,
( ! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(X8,c_0,X3) = X8 )
| ~ spl0_921 ),
inference(avatar_component_clause,[],[f7857]) ).
fof(f9013,plain,
( spl0_1128
| ~ spl0_1127 ),
inference(avatar_split_clause,[],[f9009,f9006,f9011]) ).
fof(f9006,plain,
( spl0_1127
<=> ! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f9009,plain,
( ! [X10] : c_IntDef_Oneg(c_uminus(c_plus(c_1,c_IntDef_Oint(X10),tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1127 ),
inference(forward_demodulation,[],[f9007,f2793]) ).
fof(f9007,plain,
( ! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f9006]) ).
fof(f9008,plain,
spl0_1127,
inference(avatar_split_clause,[],[f2784,f9006]) ).
fof(f2784,plain,
! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat)),tc_IntDef_Oint),tc_IntDef_Oint),
inference(definition_unfolding,[],[f238,f1394]) ).
fof(f238,axiom,
! [X10] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X10)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oneg__zminus__int_0) ).
fof(f9004,plain,
( spl0_1126
| ~ spl0_797
| ~ spl0_1125 ),
inference(avatar_split_clause,[],[f9000,f8997,f7273,f9002]) ).
fof(f9002,plain,
( spl0_1126
<=> ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f7273,plain,
( spl0_797
<=> ! [X8,X3] : c_union(c_emptyset,X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f8997,plain,
( spl0_1125
<=> ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X3,X3)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f9000,plain,
( ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X3)
| ~ spl0_797
| ~ spl0_1125 ),
inference(forward_demodulation,[],[f8998,f7274]) ).
fof(f7274,plain,
( ! [X3,X8] : c_union(c_emptyset,X8,X3) = X8
| ~ spl0_797 ),
inference(avatar_component_clause,[],[f7273]) ).
fof(f8998,plain,
( ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X3,X3)),X3)
| ~ spl0_1125 ),
inference(avatar_component_clause,[],[f8997]) ).
fof(f8999,plain,
spl0_1125,
inference(avatar_split_clause,[],[f2758,f8997]) ).
fof(f2758,plain,
! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_union(c_emptyset,c_Relation_OId,tc_prod(X3,X3)),X3),
inference(definition_unfolding,[],[f1559,f1566]) ).
fof(f1566,axiom,
! [X3,X20] : c_Transitive__Closure_Ortrancl(X20,X3) = c_Transitive__Closure_Otrancl(c_union(X20,c_Relation_OId,tc_prod(X3,X3)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f1559,axiom,
! [X3] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f8995,plain,
spl0_1124,
inference(avatar_split_clause,[],[f1682,f8993]) ).
fof(f8993,plain,
( spl0_1124
<=> ! [X16,X3,X15] :
( X15 = X16
| ~ c_in(X16,c_insert(X15,c_emptyset,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f1682,axiom,
! [X3,X16,X15] :
( X15 = X16
| ~ c_in(X16,c_insert(X15,c_emptyset,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsingletonD__dest_0) ).
fof(f8991,plain,
spl0_1123,
inference(avatar_split_clause,[],[f1680,f8989]) ).
fof(f8989,plain,
( spl0_1123
<=> ! [X27,X3,X31] :
( ~ c_less(X27,X31,tc_set(X3))
| c_lessequals(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f1680,axiom,
! [X31,X3,X27] :
( ~ c_less(X27,X31,tc_set(X3))
| c_lessequals(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_1) ).
fof(f8987,plain,
spl0_1122,
inference(avatar_split_clause,[],[f1679,f8985]) ).
fof(f8985,plain,
( spl0_1122
<=> ! [X27,X3,X31] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| ~ c_less(X27,X31,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f1679,axiom,
! [X31,X3,X27] :
( ~ c_lessequals(X31,X27,tc_set(X3))
| ~ c_less(X27,X31,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OpsubsetE_0) ).
fof(f8983,plain,
spl0_1121,
inference(avatar_split_clause,[],[f1521,f8981]) ).
fof(f8981,plain,
( spl0_1121
<=> ! [X27,X3] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f1521,axiom,
! [X3,X27] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Union__conv_2) ).
fof(f8979,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1504,f8977]) ).
fof(f8977,plain,
( spl0_1120
<=> ! [X27,X3] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1504,axiom,
! [X3,X27] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X27,X3)
| c_emptyset = c_Union(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty__conv_2) ).
fof(f8975,plain,
( spl0_1119
| ~ spl0_701
| ~ spl0_874
| ~ spl0_915 ),
inference(avatar_split_clause,[],[f8098,f7832,f7594,f6868,f8972]) ).
fof(f8972,plain,
( spl0_1119
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f6868,plain,
( spl0_701
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f7594,plain,
( spl0_874
<=> c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f7832,plain,
( spl0_915
<=> ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f8098,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_701
| ~ spl0_874
| ~ spl0_915 ),
inference(forward_demodulation,[],[f8096,f6870]) ).
fof(f6870,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_701 ),
inference(avatar_component_clause,[],[f6868]) ).
fof(f8096,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin))
| ~ spl0_874
| ~ spl0_915 ),
inference(superposition,[],[f7833,f7596]) ).
fof(f7596,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin)
| ~ spl0_874 ),
inference(avatar_component_clause,[],[f7594]) ).
fof(f7833,plain,
( ! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB0))
| ~ spl0_915 ),
inference(avatar_component_clause,[],[f7832]) ).
fof(f8970,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1468,f8968]) ).
fof(f8968,plain,
( spl0_1118
<=> ! [X27,X3] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1468,axiom,
! [X3,X27] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f8966,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1465,f8964]) ).
fof(f8964,plain,
( spl0_1117
<=> ! [X27,X3] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1465,axiom,
! [X3,X27] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X27,X3)
| c_UNIV = c_Inter(X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f8962,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1238,f8960]) ).
fof(f8960,plain,
( spl0_1116
<=> ! [X11,X3] : c_in(c_Pair(X11,X11,X3,X3),c_Relation_OId,tc_prod(X3,X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1238,axiom,
! [X3,X11] : c_in(c_Pair(X11,X11,X3,X3),c_Relation_OId,tc_prod(X3,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Opair__in__Id__conv_1) ).
fof(f8958,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1233,f8956]) ).
fof(f1233,axiom,
! [X3,X27] : c_Relation_Odiag(X27,X3) = c_Relation_Oconverse(c_Relation_Odiag(X27,X3),X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__diag_0) ).
fof(f8954,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1216,f8952]) ).
fof(f8952,plain,
( spl0_1114
<=> ! [X17,X8,X3,X15] : c_snd(c_Pair(X15,X8,X17,X3),X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1216,axiom,
! [X3,X8,X17,X15] : c_snd(c_Pair(X15,X8,X17,X3),X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osnd__conv_0) ).
fof(f8950,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1214,f8948]) ).
fof(f8948,plain,
( spl0_1113
<=> ! [X17,X3,X16,X8] : c_fst(c_Pair(X8,X16,X3,X17),X3,X17) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1214,axiom,
! [X3,X8,X16,X17] : c_fst(c_Pair(X8,X16,X3,X17),X3,X17) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Ofst__conv_0) ).
fof(f8946,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1192,f8944]) ).
fof(f8944,plain,
( spl0_1112
<=> ! [X11,X10] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(X11,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1192,axiom,
! [X10,X11] :
( c_0 = X11
| c_less(c_0,c_Nat_Opower(X11,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f8942,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1191,f8940]) ).
fof(f8940,plain,
( spl0_1111
<=> ! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f1191,axiom,
! [X10] :
( c_0 = X10
| ~ c_less(c_0,c_Nat_Opower(c_0,X10,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f8938,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1144,f8936]) ).
fof(f8936,plain,
( spl0_1110
<=> ! [X11,X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1144,axiom,
! [X10,X11] :
( c_less(c_0,X10,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_1) ).
fof(f8934,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1131,f8932]) ).
fof(f8932,plain,
( spl0_1109
<=> ! [X11,X8] :
( c_less(c_0,X8,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1131,axiom,
! [X11,X8] :
( c_less(c_0,X8,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_1) ).
fof(f8930,plain,
( spl0_1108
| ~ spl0_84
| ~ spl0_897 ),
inference(avatar_split_clause,[],[f8075,f7759,f3584,f8928]) ).
fof(f8928,plain,
( spl0_1108
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f3584,plain,
( spl0_84
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f7759,plain,
( spl0_897
<=> ! [X8,X3] :
( ~ class_LOrder_Omeet__semilorder(X3)
| c_LOrder_Omeet(X8,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f8075,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_nat) = X0
| ~ spl0_84
| ~ spl0_897 ),
inference(resolution,[],[f7760,f3586]) ).
fof(f3586,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_84 ),
inference(avatar_component_clause,[],[f3584]) ).
fof(f7760,plain,
( ! [X3,X8] :
( ~ class_LOrder_Omeet__semilorder(X3)
| c_LOrder_Omeet(X8,X8,X3) = X8 )
| ~ spl0_897 ),
inference(avatar_component_clause,[],[f7759]) ).
fof(f8926,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1097,f8924]) ).
fof(f8924,plain,
( spl0_1107
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(X15,c_uminus(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1097,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(X15,c_uminus(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oright__minus_0) ).
fof(f8922,plain,
spl0_1106,
inference(avatar_split_clause,[],[f1075,f8920]) ).
fof(f8920,plain,
( spl0_1106
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = X15
| c_0 != c_uminus(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f1075,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = X15
| c_0 != c_uminus(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f8918,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1063,f8916]) ).
fof(f8916,plain,
( spl0_1105
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1063,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f8914,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1061,f8912]) ).
fof(f8912,plain,
( spl0_1104
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1061,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f8910,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1047,f8908]) ).
fof(f8908,plain,
( spl0_1103
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(X15,X3) = c_minus(c_0,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1047,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(X15,X3) = c_minus(c_0,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0_0) ).
fof(f8906,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1025,f8904]) ).
fof(f8904,plain,
( spl0_1102
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_0 != c_HOL_Oabs(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1025,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = X15
| c_0 != c_HOL_Oabs(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f8902,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1021,f8900]) ).
fof(f8900,plain,
( spl0_1101
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(c_uminus(X15,X3),X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1021,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_plus(c_uminus(X15,X3),X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f8898,plain,
spl0_1100,
inference(avatar_split_clause,[],[f889,f8896]) ).
fof(f8896,plain,
( spl0_1100
<=> ! [X25,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_0 = c_minus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f889,axiom,
! [X10,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_0 = c_minus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f8894,plain,
spl0_1099,
inference(avatar_split_clause,[],[f888,f8892]) ).
fof(f8892,plain,
( spl0_1099
<=> ! [X25,X10] :
( c_lessequals(X25,X10,tc_nat)
| c_0 != c_minus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f888,axiom,
! [X10,X25] :
( c_lessequals(X25,X10,tc_nat)
| c_0 != c_minus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
fof(f8890,plain,
spl0_1098,
inference(avatar_split_clause,[],[f698,f8888]) ).
fof(f8888,plain,
( spl0_1098
<=> ! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f698,axiom,
! [X36] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__number__of__0_1) ).
fof(f8886,plain,
( spl0_1097
| ~ spl0_26
| ~ spl0_897 ),
inference(avatar_split_clause,[],[f8074,f7759,f3294,f8884]) ).
fof(f8884,plain,
( spl0_1097
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f3294,plain,
( spl0_26
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f8074,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_26
| ~ spl0_897 ),
inference(resolution,[],[f7760,f3296]) ).
fof(f3296,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3294]) ).
fof(f8882,plain,
spl0_1096,
inference(avatar_split_clause,[],[f683,f8880]) ).
fof(f8880,plain,
( spl0_1096
<=> ! [X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f683,axiom,
! [X36] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X36,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X36,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Oeq__0__number__of_2) ).
fof(f8878,plain,
spl0_1095,
inference(avatar_split_clause,[],[f661,f8876]) ).
fof(f8876,plain,
( spl0_1095
<=> ! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X25
| c_0 != c_NatArith_Oof__nat(X25,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f661,axiom,
! [X3,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = X25
| c_0 != c_NatArith_Oof__nat(X25,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_0) ).
fof(f8874,plain,
spl0_1094,
inference(avatar_split_clause,[],[f609,f8872]) ).
fof(f8872,plain,
( spl0_1094
<=> ! [X41,X3,X10] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate(X10,X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f609,axiom,
! [X41,X3,X10] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate(X10,X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate_0) ).
fof(f8870,plain,
spl0_1093,
inference(avatar_split_clause,[],[f580,f8868]) ).
fof(f8868,plain,
( spl0_1093
<=> ! [X41,X3,X42] :
( X41 = X42
| c_List_Orev(X41,X3) != c_List_Orev(X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f580,axiom,
! [X41,X3,X42] :
( X41 = X42
| c_List_Orev(X41,X3) != c_List_Orev(X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__is__rev__conv_0) ).
fof(f8866,plain,
spl0_1092,
inference(avatar_split_clause,[],[f453,f8864]) ).
fof(f8864,plain,
( spl0_1092
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_less(c_0,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f453,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_less(c_0,c_Nat_Osize(X41,tc_List_Olist(X3)),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__greater__0__conv_1) ).
fof(f8862,plain,
spl0_1091,
inference(avatar_split_clause,[],[f398,f8860]) ).
fof(f8860,plain,
( spl0_1091
<=> ! [X43,X3] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f398,axiom,
! [X3,X43] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f8858,plain,
spl0_1090,
inference(avatar_split_clause,[],[f391,f8856]) ).
fof(f8856,plain,
( spl0_1090
<=> ! [X50,X48,X47,X49] :
( X48 = X50
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f391,axiom,
! [X50,X48,X49,X47] :
( X48 = X50
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_1) ).
fof(f8854,plain,
spl0_1089,
inference(avatar_split_clause,[],[f390,f8852]) ).
fof(f8852,plain,
( spl0_1089
<=> ! [X48,X47,X50,X49] :
( X47 = X49
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f390,axiom,
! [X50,X48,X49,X47] :
( X47 = X49
| c_List_Ochar_OChar(X47,X48) != c_List_Ochar_OChar(X49,X50) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Oinject_0) ).
fof(f8850,plain,
spl0_1088,
inference(avatar_split_clause,[],[f359,f8848]) ).
fof(f8848,plain,
( spl0_1088
<=> ! [X43,X3] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f359,axiom,
! [X3,X43] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X43,X3)
| c_List_Olist_ONil = c_List_Oconcat(X43,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__eq__concat__conv_2) ).
fof(f8846,plain,
spl0_1087,
inference(avatar_split_clause,[],[f338,f8844]) ).
fof(f8844,plain,
( spl0_1087
<=> ! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f338,axiom,
! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f8842,plain,
( spl0_1086
| ~ spl0_91
| ~ spl0_896 ),
inference(avatar_split_clause,[],[f8068,f7755,f3619,f8840]) ).
fof(f8840,plain,
( spl0_1086
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f3619,plain,
( spl0_91
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f7755,plain,
( spl0_896
<=> ! [X8,X3] :
( ~ class_LOrder_Ojoin__semilorder(X3)
| c_LOrder_Ojoin(X8,X8,X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f8068,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_nat) = X0
| ~ spl0_91
| ~ spl0_896 ),
inference(resolution,[],[f7756,f3621]) ).
fof(f3621,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_91 ),
inference(avatar_component_clause,[],[f3619]) ).
fof(f7756,plain,
( ! [X3,X8] :
( ~ class_LOrder_Ojoin__semilorder(X3)
| c_LOrder_Ojoin(X8,X8,X3) = X8 )
| ~ spl0_896 ),
inference(avatar_component_clause,[],[f7755]) ).
fof(f8838,plain,
spl0_1085,
inference(avatar_split_clause,[],[f337,f8836]) ).
fof(f337,axiom,
! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X37,tc_IntDef_Oint),X35,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f8833,plain,
spl0_1084,
inference(avatar_split_clause,[],[f317,f8831]) ).
fof(f317,axiom,
! [X15] : c_div(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f8829,plain,
spl0_1083,
inference(avatar_split_clause,[],[f290,f8827]) ).
fof(f8827,plain,
( spl0_1083
<=> ! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f290,axiom,
! [X37,X35] :
( ~ c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f8825,plain,
spl0_1082,
inference(avatar_split_clause,[],[f289,f8823]) ).
fof(f289,axiom,
! [X37,X35] :
( c_Divides_Oop_Advd(X37,X35,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X37,c_uminus(X35,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f8821,plain,
spl0_1081,
inference(avatar_split_clause,[],[f280,f8819]) ).
fof(f8819,plain,
( spl0_1081
<=> ! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f280,axiom,
! [X37,X35] :
( c_less(X35,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_1) ).
fof(f8817,plain,
spl0_1080,
inference(avatar_split_clause,[],[f279,f8815]) ).
fof(f8815,plain,
( spl0_1080
<=> ! [X37,X35] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f279,axiom,
! [X37,X35] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X35),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__nat__conj_0) ).
fof(f8813,plain,
spl0_1079,
inference(avatar_split_clause,[],[f278,f8811]) ).
fof(f8811,plain,
( spl0_1079
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f278,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_1) ).
fof(f8809,plain,
spl0_1078,
inference(avatar_split_clause,[],[f277,f8807]) ).
fof(f8807,plain,
( spl0_1078
<=> ! [X25,X10] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f277,axiom,
! [X10,X25] :
( c_less(X25,X10,tc_nat)
| ~ c_less(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozless__int_0) ).
fof(f8805,plain,
spl0_1077,
inference(avatar_split_clause,[],[f276,f8803]) ).
fof(f8803,plain,
( spl0_1077
<=> ! [X25,X10] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f276,axiom,
! [X10,X25] :
( ~ c_lessequals(X25,X10,tc_nat)
| c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_1) ).
fof(f8801,plain,
spl0_1076,
inference(avatar_split_clause,[],[f275,f8799]) ).
fof(f8799,plain,
( spl0_1076
<=> ! [X25,X10] :
( c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f275,axiom,
! [X10,X25] :
( c_lessequals(X25,X10,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X25),c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozle__int_0) ).
fof(f8797,plain,
( spl0_1075
| ~ spl0_27
| ~ spl0_896 ),
inference(avatar_split_clause,[],[f8067,f7755,f3299,f8795]) ).
fof(f8795,plain,
( spl0_1075
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f3299,plain,
( spl0_27
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f8067,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_27
| ~ spl0_896 ),
inference(resolution,[],[f7756,f3301]) ).
fof(f3301,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f3299]) ).
fof(f8793,plain,
spl0_1074,
inference(avatar_split_clause,[],[f257,f8791]) ).
fof(f8791,plain,
( spl0_1074
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_IntDef_Oint(X10),X3) = c_NatArith_Oof__nat(X10,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f257,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_IntDef_Oof__int(c_IntDef_Oint(X10),X3) = c_NatArith_Oof__nat(X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__int__eq_0) ).
fof(f8789,plain,
spl0_1073,
inference(avatar_split_clause,[],[f254,f8787]) ).
fof(f8787,plain,
( spl0_1073
<=> ! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X35
| c_0 != c_IntDef_Oof__int(X35,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f254,axiom,
! [X3,X35] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = X35
| c_0 != c_IntDef_Oof__int(X35,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__eq__0__iff_0) ).
fof(f8785,plain,
spl0_1072,
inference(avatar_split_clause,[],[f240,f8783]) ).
fof(f8783,plain,
( spl0_1072
<=> ! [X25,X10] :
( c_0 = X25
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f240,axiom,
! [X10,X25] :
( c_0 = X25
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_1) ).
fof(f8781,plain,
spl0_1071,
inference(avatar_split_clause,[],[f239,f8779]) ).
fof(f8779,plain,
( spl0_1071
<=> ! [X25,X10] :
( c_0 = X10
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f239,axiom,
! [X10,X25] :
( c_0 = X10
| c_IntDef_Oint(X25) != c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_0) ).
fof(f8777,plain,
spl0_1070,
inference(avatar_split_clause,[],[f129,f8775]) ).
fof(f129,axiom,
! [X3,X27] :
( c_0 = c_Finite__Set_Ocard(X27,X3)
| c_in(X27,c_Finite__Set_OFinites,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__infinite_0) ).
fof(f8773,plain,
spl0_1069,
inference(avatar_split_clause,[],[f125,f8771]) ).
fof(f8771,plain,
( spl0_1069
<=> ! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f125,axiom,
! [X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMin(c_insert(X8,c_emptyset,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMin__singleton_0) ).
fof(f8769,plain,
spl0_1068,
inference(avatar_split_clause,[],[f115,f8767]) ).
fof(f8767,plain,
( spl0_1068
<=> ! [X8,X3] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f115,axiom,
! [X3,X8] :
( ~ class_Orderings_Olinorder(X3)
| c_Finite__Set_OMax(c_insert(X8,c_emptyset,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OMax__singleton_0) ).
fof(f8765,plain,
spl0_1067,
inference(avatar_split_clause,[],[f85,f8763]) ).
fof(f8763,plain,
( spl0_1067
<=> ! [X8,X10] :
( ~ c_less(X8,X10,tc_nat)
| c_Divides_Oop_Amod(X8,X10,tc_nat) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f85,axiom,
! [X10,X8] :
( ~ c_less(X8,X10,tc_nat)
| c_Divides_Oop_Amod(X8,X10,tc_nat) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__less_0) ).
fof(f8761,plain,
spl0_1066,
inference(avatar_split_clause,[],[f74,f8759]) ).
fof(f8759,plain,
( spl0_1066
<=> ! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_1 = c_div(X10,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f74,axiom,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_1 = c_div(X10,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__self_0) ).
fof(f8757,plain,
spl0_1065,
inference(avatar_split_clause,[],[f66,f8755]) ).
fof(f8755,plain,
( spl0_1065
<=> ! [X25,X10] :
( ~ c_less(X25,X10,tc_nat)
| c_0 = c_div(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f66,axiom,
! [X10,X25] :
( ~ c_less(X25,X10,tc_nat)
| c_0 = c_div(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__less_0) ).
fof(f8752,plain,
spl0_1064,
inference(avatar_split_clause,[],[f46,f8750]) ).
fof(f8750,plain,
( spl0_1064
<=> ! [X17,X19,X18,X9,X3] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f46,axiom,
! [X3,X18,X19,X9,X17] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Scons_0) ).
fof(f8748,plain,
spl0_1063,
inference(avatar_split_clause,[],[f44,f8746]) ).
fof(f8746,plain,
( spl0_1063
<=> ! [X15,X17,X18,X3,X19] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OLeaf(X15,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f44,axiom,
! [X3,X18,X19,X17,X15] : c_Datatype__Universe_OScons(X18,X19,X3,X17) != c_Datatype__Universe_OLeaf(X15,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OLeaf__not__Scons_0) ).
fof(f8744,plain,
spl0_1062,
inference(avatar_split_clause,[],[f36,f8742]) ).
fof(f8742,plain,
( spl0_1062
<=> ! [X15,X18,X17,X3,X19] : c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OScons(X18,X19,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f36,axiom,
! [X3,X18,X19,X17,X15] : c_Datatype__Universe_OAtom(X15,X3,X17) != c_Datatype__Universe_OScons(X18,X19,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f8740,plain,
spl0_1061,
inference(avatar_split_clause,[],[f30,f8738]) ).
fof(f8738,plain,
( spl0_1061
<=> ! [X16,X17,X3] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X16,X17,X3),tc_sum(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f30,axiom,
! [X3,X16,X17] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X16,X17,X3),tc_sum(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__2_0) ).
fof(f8736,plain,
spl0_1060,
inference(avatar_split_clause,[],[f29,f8734]) ).
fof(f8734,plain,
( spl0_1060
<=> ! [X17,X3,X15] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X15,X3,X17),tc_sum(X3,X17)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f29,axiom,
! [X3,X17,X15] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X15,X3,X17),tc_sum(X3,X17)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Osum_Osize__1_0) ).
fof(f8732,plain,
spl0_1059,
inference(avatar_split_clause,[],[f25,f8730]) ).
fof(f8730,plain,
( spl0_1059
<=> ! [X3,X14,X15] :
( X14 = X15
| c_Datatype_Ooption_OSome(X14,X3) != c_Datatype_Ooption_OSome(X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f25,axiom,
! [X3,X14,X15] :
( X14 = X15
| c_Datatype_Ooption_OSome(X14,X3) != c_Datatype_Ooption_OSome(X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Oinject_0) ).
fof(f8728,plain,
spl0_1058,
inference(avatar_split_clause,[],[f20,f8726]) ).
fof(f8726,plain,
( spl0_1058
<=> ! [X13,X11] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X13),X13) = c_insert(X11,c_emptyset,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f20,axiom,
! [X11,X13] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X13),X13) = c_insert(X11,c_emptyset,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f8724,plain,
spl0_1057,
inference(avatar_split_clause,[],[f19,f8722]) ).
fof(f8722,plain,
( spl0_1057
<=> ! [X11,X3] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X11,X3),X3) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f19,axiom,
! [X3,X11] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X11,X3),X3) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__Some__eq_0) ).
fof(f8720,plain,
spl0_1056,
inference(avatar_split_clause,[],[f18,f8718]) ).
fof(f8718,plain,
( spl0_1056
<=> ! [X11,X3] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X11,X3),X3) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f18,axiom,
! [X3,X11] :
( c_Datatype_Ooption_ONone = X11
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X11,X3),X3) = X11 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Onot__None__eq_0) ).
fof(f8693,plain,
( spl0_1055
| ~ spl0_799
| ~ spl0_1028 ),
inference(avatar_split_clause,[],[f8659,f8407,f7281,f8691]) ).
fof(f8691,plain,
( spl0_1055
<=> ! [X0] : c_emptyset != c_Pow(c_emptyset,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f7281,plain,
( spl0_799
<=> ! [X27,X3,X15] : c_emptyset != c_insert(X15,X27,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f8407,plain,
( spl0_1028
<=> ! [X3] : c_Pow(c_emptyset,X3) = c_insert(c_emptyset,c_emptyset,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f8659,plain,
( ! [X0] : c_emptyset != c_Pow(c_emptyset,X0)
| ~ spl0_799
| ~ spl0_1028 ),
inference(superposition,[],[f7282,f8408]) ).
fof(f8408,plain,
( ! [X3] : c_Pow(c_emptyset,X3) = c_insert(c_emptyset,c_emptyset,tc_set(X3))
| ~ spl0_1028 ),
inference(avatar_component_clause,[],[f8407]) ).
fof(f7282,plain,
( ! [X3,X27,X15] : c_emptyset != c_insert(X15,X27,X3)
| ~ spl0_799 ),
inference(avatar_component_clause,[],[f7281]) ).
fof(f8656,plain,
( spl0_1054
| ~ spl0_878
| ~ spl0_1010 ),
inference(avatar_split_clause,[],[f8620,f8334,f7627,f8654]) ).
fof(f8654,plain,
( spl0_1054
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f7627,plain,
( spl0_878
<=> ! [X0] : c_lessequals(X0,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f8334,plain,
( spl0_1010
<=> ! [X52,X24] :
( ~ c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,X52) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f8620,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_878
| ~ spl0_1010 ),
inference(resolution,[],[f8335,f7628]) ).
fof(f7628,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_878 ),
inference(avatar_component_clause,[],[f7627]) ).
fof(f8335,plain,
( ! [X52,X24] :
( ~ c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,X52) )
| ~ spl0_1010 ),
inference(avatar_component_clause,[],[f8334]) ).
fof(f8612,plain,
( spl0_1053
| ~ spl0_799
| ~ spl0_1002 ),
inference(avatar_split_clause,[],[f8604,f8302,f7281,f8610]) ).
fof(f8610,plain,
( spl0_1053
<=> ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f8302,plain,
( spl0_1002
<=> ! [X13] : c_List_Olistset(c_List_Olist_ONil,X13) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X13)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f8604,plain,
( ! [X0] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X0)
| ~ spl0_799
| ~ spl0_1002 ),
inference(superposition,[],[f7282,f8303]) ).
fof(f8303,plain,
( ! [X13] : c_List_Olistset(c_List_Olist_ONil,X13) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X13))
| ~ spl0_1002 ),
inference(avatar_component_clause,[],[f8302]) ).
fof(f8574,plain,
( ~ spl0_76
| spl0_1052
| ~ spl0_668
| ~ spl0_893 ),
inference(avatar_split_clause,[],[f8066,f7742,f6718,f8572,f3544]) ).
fof(f3544,plain,
( spl0_76
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f8572,plain,
( spl0_1052
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f6718,plain,
( spl0_668
<=> ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f7742,plain,
( spl0_893
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_NatArith_Oof__nat(X10,X3),c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f8066,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_668
| ~ spl0_893 ),
inference(superposition,[],[f7743,f6719]) ).
fof(f6719,plain,
( ! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8
| ~ spl0_668 ),
inference(avatar_component_clause,[],[f6718]) ).
fof(f7743,plain,
( ! [X3,X10] :
( c_in(c_NatArith_Oof__nat(X10,X3),c_IntDef_ONats,X3)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3) )
| ~ spl0_893 ),
inference(avatar_component_clause,[],[f7742]) ).
fof(f8520,plain,
( spl0_1051
| ~ spl0_826
| ~ spl0_867 ),
inference(avatar_split_clause,[],[f7681,f7564,f7397,f8518]) ).
fof(f8518,plain,
( spl0_1051
<=> ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f7397,plain,
( spl0_826
<=> ! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f7564,plain,
( spl0_867
<=> ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f7681,plain,
( ! [X0] : c_0 = c_times(X0,c_0,tc_IntDef_Oint)
| ~ spl0_826
| ~ spl0_867 ),
inference(resolution,[],[f7565,f7398]) ).
fof(f7398,plain,
( ! [X25] :
( ~ c_Divides_Oop_Advd(c_0,X25,tc_IntDef_Oint)
| c_0 = X25 )
| ~ spl0_826 ),
inference(avatar_component_clause,[],[f7397]) ).
fof(f7565,plain,
( ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_867 ),
inference(avatar_component_clause,[],[f7564]) ).
fof(f8498,plain,
spl0_1050,
inference(avatar_split_clause,[],[f3068,f8496]) ).
fof(f8496,plain,
( spl0_1050
<=> ! [X37] :
( ~ c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| c_less(c_1,X37,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f3068,plain,
! [X37] :
( ~ c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| c_less(c_1,X37,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2894,f2757]) ).
fof(f2894,plain,
! [X37] :
( c_less(c_1,X37,tc_IntDef_Oint)
| ~ c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X37),tc_nat) ),
inference(definition_unfolding,[],[f196,f1394]) ).
fof(f196,axiom,
! [X37] :
( c_less(c_1,X37,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f8494,plain,
spl0_1049,
inference(avatar_split_clause,[],[f3056,f8492]) ).
fof(f8492,plain,
( spl0_1049
<=> ! [X37] :
( c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| ~ c_less(c_1,X37,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f3056,plain,
! [X37] :
( c_less(c_1,c_IntDef_Onat(X37),tc_nat)
| ~ c_less(c_1,X37,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2874,f2757]) ).
fof(f2874,plain,
! [X37] :
( ~ c_less(c_1,X37,tc_IntDef_Oint)
| c_less(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),c_IntDef_Onat(X37),tc_nat) ),
inference(definition_unfolding,[],[f197,f1394]) ).
fof(f197,axiom,
! [X37] :
( ~ c_less(c_1,X37,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f8490,plain,
spl0_1048,
inference(avatar_split_clause,[],[f3052,f8488]) ).
fof(f8488,plain,
( spl0_1048
<=> ! [X25,X10] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f3052,plain,
! [X10,X25] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X25 ),
inference(forward_demodulation,[],[f2869,f2757]) ).
fof(f2869,plain,
! [X10,X25] :
( c_1 = X25
| c_times(X25,X10,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f912,f1394]) ).
fof(f912,axiom,
! [X10,X25] :
( c_1 = X25
| c_Suc(c_0) != c_times(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_0) ).
fof(f8486,plain,
spl0_1047,
inference(avatar_split_clause,[],[f3051,f8484]) ).
fof(f8484,plain,
( spl0_1047
<=> ! [X25,X10] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X10 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f3051,plain,
! [X10,X25] :
( c_1 != c_times(X25,X10,tc_nat)
| c_1 = X10 ),
inference(forward_demodulation,[],[f2868,f2757]) ).
fof(f2868,plain,
! [X10,X25] :
( c_1 = X10
| c_times(X25,X10,tc_nat) != c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f943,f1394]) ).
fof(f943,axiom,
! [X10,X25] :
( c_1 = X10
| c_Suc(c_0) != c_times(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oone__eq__mult__iff_1) ).
fof(f8482,plain,
( spl0_1046
| ~ spl0_826
| ~ spl0_866 ),
inference(avatar_split_clause,[],[f7680,f7560,f7397,f8480]) ).
fof(f8480,plain,
( spl0_1046
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f7560,plain,
( spl0_866
<=> ! [X25,X9] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f7680,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_826
| ~ spl0_866 ),
inference(resolution,[],[f7561,f7398]) ).
fof(f7561,plain,
( ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_866 ),
inference(avatar_component_clause,[],[f7560]) ).
fof(f8478,plain,
spl0_1045,
inference(avatar_split_clause,[],[f2788,f8476]) ).
fof(f2788,plain,
! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OBit(X35,c_Numeral_Obit_OB1),c_Numeral_OMin),
inference(definition_unfolding,[],[f982,f963]) ).
fof(f982,axiom,
! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__1_0) ).
fof(f8474,plain,
spl0_1044,
inference(avatar_split_clause,[],[f2777,f8472]) ).
fof(f8472,plain,
( spl0_1044
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_Odiag(X8,X3),X8,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f2777,plain,
! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X3),X8,X3,X3) = X8,
inference(definition_unfolding,[],[f1453,f1223]) ).
fof(f1453,axiom,
! [X3,X8] : c_inter(X8,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__absorb_0) ).
fof(f8470,plain,
spl0_1043,
inference(avatar_split_clause,[],[f2776,f8468]) ).
fof(f8468,plain,
( spl0_1043
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X3),X8,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f2776,plain,
! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(c_UNIV,X3),X8,X3,X3) = X8,
inference(definition_unfolding,[],[f1451,f1223]) ).
fof(f1451,axiom,
! [X3,X8] : c_inter(c_UNIV,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__left_0) ).
fof(f8466,plain,
spl0_1042,
inference(avatar_split_clause,[],[f2775,f8464]) ).
fof(f8464,plain,
( spl0_1042
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_Odiag(X8,X3),c_UNIV,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f2775,plain,
! [X3,X8] : c_Relation_OImage(c_Relation_Odiag(X8,X3),c_UNIV,X3,X3) = X8,
inference(definition_unfolding,[],[f1452,f1223]) ).
fof(f1452,axiom,
! [X3,X8] : c_inter(X8,c_UNIV,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__UNIV__right_0) ).
fof(f8462,plain,
spl0_1041,
inference(avatar_split_clause,[],[f2769,f8460]) ).
fof(f8460,plain,
( spl0_1041
<=> ! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f2769,plain,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X9,tc_nat),tc_nat)),
inference(definition_unfolding,[],[f10,f1394]) ).
fof(f10,axiom,
! [X9] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X9)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8458,plain,
spl0_1040,
inference(avatar_split_clause,[],[f1640,f8456]) ).
fof(f8456,plain,
( spl0_1040
<=> ! [X20,X3] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X20,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f1640,axiom,
! [X3,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X20,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lex_0) ).
fof(f8454,plain,
spl0_1039,
inference(avatar_split_clause,[],[f1639,f8452]) ).
fof(f8452,plain,
( spl0_1039
<=> ! [X20,X3] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X20,X3),tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f1639,axiom,
! [X3,X20] :
( ~ c_Wellfounded__Recursion_Owf(X20,X3)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X20,X3),tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Owf__lenlex_0) ).
fof(f8450,plain,
spl0_1038,
inference(avatar_split_clause,[],[f1612,f8448]) ).
fof(f8448,plain,
( spl0_1038
<=> ! [X25,X10] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f1612,axiom,
! [X10,X25] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd2_0) ).
fof(f8446,plain,
spl0_1037,
inference(avatar_split_clause,[],[f1611,f8444]) ).
fof(f8444,plain,
( spl0_1037
<=> ! [X25,X10] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f1611,axiom,
! [X10,X25] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X25,X10,tc_nat,tc_nat)),X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__dvd1_0) ).
fof(f8442,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1568,f8440]) ).
fof(f8440,plain,
( spl0_1036
<=> ! [X20,X3] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1568,axiom,
! [X3,X20] :
( ~ c_Wellfounded__Recursion_Oacyclic(X20,X3)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f8438,plain,
( spl0_1035
| ~ spl0_113
| ~ spl0_823 ),
inference(avatar_split_clause,[],[f7619,f7385,f3723,f8435]) ).
fof(f8435,plain,
( spl0_1035
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f3723,plain,
( spl0_113
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f7385,plain,
( spl0_823
<=> ! [X10] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f7619,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_113
| ~ spl0_823 ),
inference(superposition,[],[f7386,f3725]) ).
fof(f3725,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_113 ),
inference(avatar_component_clause,[],[f3723]) ).
fof(f7386,plain,
( ! [X10] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint))
| ~ spl0_823 ),
inference(avatar_component_clause,[],[f7385]) ).
fof(f8433,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1567,f8431]) ).
fof(f8431,plain,
( spl0_1034
<=> ! [X20,X3] :
( c_Wellfounded__Recursion_Oacyclic(X20,X3)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1567,axiom,
! [X3,X20] :
( c_Wellfounded__Recursion_Oacyclic(X20,X3)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X20,X3,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f8429,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1554,f8427]) ).
fof(f8427,plain,
( spl0_1033
<=> ! [X16,X17,X3,X15] : c_Sum__Type_OInl(X15,X3,X17) != c_Sum__Type_OInr(X16,X17,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f1554,axiom,
! [X3,X16,X17,X15] : c_Sum__Type_OInl(X15,X3,X17) != c_Sum__Type_OInr(X16,X17,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OInr__not__Inl_0) ).
fof(f8425,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1517,f8423]) ).
fof(f8423,plain,
( spl0_1032
<=> ! [X8,X3] : c_uminus(c_uminus(X8,tc_set(X3)),tc_set(X3)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1517,axiom,
! [X3,X8] : c_uminus(c_uminus(X8,tc_set(X3)),tc_set(X3)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Odouble__complement_0) ).
fof(f8421,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1509,f8419]) ).
fof(f8419,plain,
( spl0_1031
<=> ! [X27,X3] :
( c_emptyset = X27
| c_in(c_Main_Oall__not__in__conv__1(X27,X3),X27,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1509,axiom,
! [X3,X27] :
( c_emptyset = X27
| c_in(c_Main_Oall__not__in__conv__1(X27,X3),X27,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oall__not__in__conv_0) ).
fof(f8417,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1486,f8415]) ).
fof(f8415,plain,
( spl0_1030
<=> ! [X27,X3,X31] :
( c_emptyset = X31
| c_emptyset != c_union(X27,X31,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1486,axiom,
! [X31,X3,X27] :
( c_emptyset = X31
| c_emptyset != c_union(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_1) ).
fof(f8413,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1485,f8411]) ).
fof(f8411,plain,
( spl0_1029
<=> ! [X27,X3,X31] :
( c_emptyset = X27
| c_emptyset != c_union(X27,X31,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1485,axiom,
! [X31,X3,X27] :
( c_emptyset = X27
| c_emptyset != c_union(X27,X31,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty_0) ).
fof(f8409,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1476,f8407]) ).
fof(f1476,axiom,
! [X3] : c_Pow(c_emptyset,X3) = c_insert(c_emptyset,c_emptyset,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__empty_0) ).
fof(f8405,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1240,f8403]) ).
fof(f8403,plain,
( spl0_1027
<=> ! [X13,X79] : c_Relation_OId = c_Nat_Opower(X79,c_0,tc_set(tc_prod(X13,X13))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1240,axiom,
! [X79,X13] : c_Relation_OId = c_Nat_Opower(X79,c_0,tc_set(tc_prod(X13,X13))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f8401,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1239,f8399]) ).
fof(f8399,plain,
( spl0_1026
<=> ! [X8,X3] : c_Nat_Opower(X8,c_1,tc_set(tc_prod(X3,X3))) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1239,axiom,
! [X3,X8] : c_Nat_Opower(X8,c_1,tc_set(tc_prod(X3,X3))) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation__Power_Orel__pow__1_0) ).
fof(f8397,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1232,f8395]) ).
fof(f8395,plain,
( spl0_1025
<=> ! [X17,X8,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X3,X17),X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1232,axiom,
! [X3,X8,X17] : c_Relation_Oconverse(c_Relation_Oconverse(X8,X3,X17),X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__converse_0) ).
fof(f8393,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1148,f8391]) ).
fof(f8391,plain,
( spl0_1024
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1148,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_2) ).
fof(f8389,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1147,f8387]) ).
fof(f8387,plain,
( spl0_1023
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1147,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X11,X8,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__product_1) ).
fof(f8385,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1143,f8383]) ).
fof(f8383,plain,
( spl0_1022
<=> ! [X11,X10] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1143,axiom,
! [X10,X11] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__power_0) ).
fof(f8381,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1135,f8379]) ).
fof(f8379,plain,
( spl0_1021
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1135,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X8,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_2) ).
fof(f8377,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1134,f8375]) ).
fof(f8375,plain,
( spl0_1020
<=> ! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1134,axiom,
! [X11,X8] :
( ~ c_Parity_Oeven(X11,tc_nat)
| c_Parity_Oeven(c_times(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__product_1) ).
fof(f8373,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1130,f8371]) ).
fof(f1130,axiom,
! [X11,X8] :
( c_Parity_Oeven(X11,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X11,X8,tc_nat),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__power_0) ).
fof(f8369,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1066,f8367]) ).
fof(f8367,plain,
( spl0_1018
<=> ! [X8,X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_uminus(X8,X3),X3) = X8 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1066,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_uminus(c_uminus(X8,X3),X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ominus__minus_0) ).
fof(f8365,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1004,f8363]) ).
fof(f8363,plain,
( spl0_1017
<=> ! [X35] : c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X35),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f8361,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1000,f8359]) ).
fof(f8359,plain,
( spl0_1016
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1000,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f8357,plain,
spl0_1015,
inference(avatar_split_clause,[],[f986,f8355]) ).
fof(f8355,plain,
( spl0_1015
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f986,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ class_Ring__and__Field_Oordered__idom(X3)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f8353,plain,
( ~ spl0_54
| spl0_1014
| ~ spl0_841
| ~ spl0_949 ),
inference(avatar_split_clause,[],[f8165,f7970,f7457,f8350,f3434]) ).
fof(f8350,plain,
( spl0_1014
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f7457,plain,
( spl0_841
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f7970,plain,
( spl0_949
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f8165,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_841
| ~ spl0_949 ),
inference(superposition,[],[f7458,f7972]) ).
fof(f7972,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_949 ),
inference(avatar_component_clause,[],[f7970]) ).
fof(f7458,plain,
( ! [X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3)
| ~ class_Numeral_Onumber__ring(X3) )
| ~ spl0_841 ),
inference(avatar_component_clause,[],[f7457]) ).
fof(f8348,plain,
spl0_1013,
inference(avatar_split_clause,[],[f968,f8346]) ).
fof(f968,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_Numeral_Onumber__of(c_Numeral_OMin,X3) = c_uminus(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f8344,plain,
spl0_1012,
inference(avatar_split_clause,[],[f882,f8342]) ).
fof(f8342,plain,
( spl0_1012
<=> ! [X25,X10] :
( c_0 = X10
| c_0 != c_plus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f882,axiom,
! [X10,X25] :
( c_0 = X10
| c_0 != c_plus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_1) ).
fof(f8340,plain,
spl0_1011,
inference(avatar_split_clause,[],[f881,f8338]) ).
fof(f8338,plain,
( spl0_1011
<=> ! [X25,X10] :
( c_0 = X25
| c_0 != c_plus(X25,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f881,axiom,
! [X10,X25] :
( c_0 = X25
| c_0 != c_plus(X25,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__is__0_0) ).
fof(f8336,plain,
spl0_1010,
inference(avatar_split_clause,[],[f636,f8334]) ).
fof(f636,axiom,
! [X52,X24] :
( ~ c_lessequals(X52,X24,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X24,X52) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f8332,plain,
spl0_1009,
inference(avatar_split_clause,[],[f608,f8330]) ).
fof(f8330,plain,
( spl0_1009
<=> ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate1(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f608,axiom,
! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orotate1(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rotate1_0) ).
fof(f8328,plain,
spl0_1008,
inference(avatar_split_clause,[],[f607,f8326]) ).
fof(f8326,plain,
( spl0_1008
<=> ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orev(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f607,axiom,
! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Orev(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__rev_0) ).
fof(f8324,plain,
spl0_1007,
inference(avatar_split_clause,[],[f604,f8322]) ).
fof(f8322,plain,
( spl0_1007
<=> ! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Oremdups(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f604,axiom,
! [X41,X3] : c_List_Oset(X41,X3) = c_List_Oset(c_List_Oremdups(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__remdups_0) ).
fof(f8320,plain,
spl0_1006,
inference(avatar_split_clause,[],[f594,f8318]) ).
fof(f8318,plain,
( spl0_1006
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_append(X41,X42,X3) != X42 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f594,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_append(X41,X42,X3) != X42 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oself__append__conv2_0) ).
fof(f8316,plain,
spl0_1005,
inference(avatar_split_clause,[],[f590,f8314]) ).
fof(f8314,plain,
( spl0_1005
<=> ! [X41,X3,X10] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate(X10,X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f590,axiom,
! [X41,X10,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate(X10,X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_0) ).
fof(f8312,plain,
spl0_1004,
inference(avatar_split_clause,[],[f570,f8310]) ).
fof(f8310,plain,
( spl0_1004
<=> ! [X41,X11,X3] : c_List_Oremove1(X11,c_List_Olist_OCons(X11,X41,X3),X3) = X41 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f570,axiom,
! [X41,X3,X11] : c_List_Oremove1(X11,c_List_Olist_OCons(X11,X41,X3),X3) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__2_0) ).
fof(f8308,plain,
spl0_1003,
inference(avatar_split_clause,[],[f542,f8306]) ).
fof(f8306,plain,
( spl0_1003
<=> ! [X41,X8,X3] : c_List_Onth(c_List_Olist_OCons(X8,X41,X3),c_0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f542,axiom,
! [X41,X3,X8] : c_List_Onth(c_List_Olist_OCons(X8,X41,X3),c_0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onth__Cons__0_0) ).
fof(f8304,plain,
spl0_1002,
inference(avatar_split_clause,[],[f489,f8302]) ).
fof(f489,axiom,
! [X13] : c_List_Olistset(c_List_Olist_ONil,X13) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X13)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olistset_Osimps__1_0) ).
fof(f8300,plain,
spl0_1001,
inference(avatar_split_clause,[],[f457,f8298]) ).
fof(f8298,plain,
( spl0_1001
<=> ! [X11,X8,X3] : c_Nat_Osize(c_List_Oreplicate(X8,X11,X3),tc_List_Olist(X3)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f457,axiom,
! [X3,X11,X8] : c_Nat_Osize(c_List_Oreplicate(X8,X11,X3),tc_List_Olist(X3)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__replicate_0) ).
fof(f8296,plain,
spl0_1000,
inference(avatar_split_clause,[],[f447,f8294]) ).
fof(f8294,plain,
( spl0_1000
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_0 != c_Nat_Osize(X41,tc_List_Olist(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f447,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_0 != c_Nat_Osize(X41,tc_List_Olist(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_0) ).
fof(f8292,plain,
spl0_999,
inference(avatar_split_clause,[],[f415,f8290]) ).
fof(f8290,plain,
( spl0_999
<=> ! [X51,X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Osublist(X41,X51,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f415,axiom,
! [X51,X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Osublist(X41,X51,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__sublistI_0) ).
fof(f8288,plain,
spl0_998,
inference(avatar_split_clause,[],[f414,f8286]) ).
fof(f8286,plain,
( spl0_998
<=> ! [X41,X3,X10] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f414,axiom,
! [X41,X3,X10] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_1) ).
fof(f8284,plain,
spl0_997,
inference(avatar_split_clause,[],[f413,f8282]) ).
fof(f8282,plain,
( spl0_997
<=> ! [X41,X3,X10] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f413,axiom,
! [X41,X3,X10] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate(X10,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rotate_0) ).
fof(f8280,plain,
spl0_996,
inference(avatar_split_clause,[],[f410,f8278]) ).
fof(f8278,plain,
( spl0_996
<=> ! [X41,X11,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Oremove1(X11,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f410,axiom,
! [X41,X3,X11] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Oremove1(X11,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remove1_0) ).
fof(f8276,plain,
spl0_995,
inference(avatar_split_clause,[],[f409,f8274]) ).
fof(f8274,plain,
( spl0_995
<=> ! [X41,X24,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Odrop(X24,X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f409,axiom,
! [X41,X3,X24] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Odrop(X24,X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__drop_0) ).
fof(f8272,plain,
spl0_994,
inference(avatar_split_clause,[],[f406,f8270]) ).
fof(f8270,plain,
( spl0_994
<=> ! [X41,X3,X42] :
( c_List_Odistinct(X42,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f406,axiom,
! [X3,X41,X42] :
( c_List_Odistinct(X42,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_1) ).
fof(f8268,plain,
( ~ spl0_993
| ~ spl0_799
| ~ spl0_947 ),
inference(avatar_split_clause,[],[f8150,f7961,f7281,f8265]) ).
fof(f8265,plain,
( spl0_993
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f8150,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_799
| ~ spl0_947 ),
inference(superposition,[],[f7282,f7963]) ).
fof(f8263,plain,
spl0_992,
inference(avatar_split_clause,[],[f405,f8261]) ).
fof(f8261,plain,
( spl0_992
<=> ! [X41,X3,X42] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f405,axiom,
! [X41,X3,X42] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_append(X41,X42,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__append_0) ).
fof(f8259,plain,
spl0_991,
inference(avatar_split_clause,[],[f403,f8257]) ).
fof(f8257,plain,
( spl0_991
<=> ! [X13,X41,X11] :
( c_List_Odistinct(X41,X13)
| ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f403,axiom,
! [X41,X11,X13] :
( c_List_Odistinct(X41,X13)
| ~ c_List_Odistinct(c_List_Olist_OCons(X11,X41,X13),X13) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__2_1) ).
fof(f8255,plain,
spl0_990,
inference(avatar_split_clause,[],[f383,f8253]) ).
fof(f8253,plain,
( spl0_990
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_append(X41,X42,X3) != X41 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f383,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_append(X41,X42,X3) != X41 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_0) ).
fof(f8251,plain,
spl0_989,
inference(avatar_split_clause,[],[f361,f8249]) ).
fof(f8249,plain,
( spl0_989
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_List_Olist_ONil != c_append(X41,X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f361,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X42
| c_List_Olist_ONil != c_append(X41,X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_1) ).
fof(f8247,plain,
spl0_988,
inference(avatar_split_clause,[],[f360,f8245]) ).
fof(f8245,plain,
( spl0_988
<=> ! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_append(X41,X42,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f360,axiom,
! [X41,X3,X42] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_append(X41,X42,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__append__conv_0) ).
fof(f8243,plain,
spl0_987,
inference(avatar_split_clause,[],[f347,f8241]) ).
fof(f8241,plain,
( spl0_987
<=> ! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X16,X15,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f347,axiom,
! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X16,X15,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f8239,plain,
spl0_986,
inference(avatar_split_clause,[],[f346,f8237]) ).
fof(f8237,plain,
( spl0_986
<=> ! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f346,axiom,
! [X16,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f8235,plain,
spl0_985,
inference(avatar_split_clause,[],[f333,f8233]) ).
fof(f8233,plain,
( spl0_985
<=> ! [X11,X10] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f333,axiom,
! [X10,X11] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X11,tc_IntDef_Oint),X10,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f8231,plain,
spl0_984,
inference(avatar_split_clause,[],[f321,f8229]) ).
fof(f8229,plain,
( spl0_984
<=> ! [X15] :
( c_0 = X15
| c_1 = c_div(X15,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f321,axiom,
! [X15] :
( c_0 = X15
| c_1 = c_div(X15,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__self_0) ).
fof(f8227,plain,
spl0_983,
inference(avatar_split_clause,[],[f291,f8225]) ).
fof(f291,axiom,
! [X16,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X16,tc_IntDef_Oint),X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Omod__div__trivial_0) ).
fof(f8222,plain,
spl0_982,
inference(avatar_split_clause,[],[f273,f8220]) ).
fof(f8220,plain,
( spl0_982
<=> ! [X37] :
( ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f273,axiom,
! [X37] :
( ~ c_less(c_0,X37,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f8218,plain,
spl0_981,
inference(avatar_split_clause,[],[f272,f8216]) ).
fof(f8216,plain,
( spl0_981
<=> ! [X37] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X37),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f272,axiom,
! [X37] :
( c_less(c_0,X37,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X37),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f8214,plain,
spl0_980,
inference(avatar_split_clause,[],[f271,f8212]) ).
fof(f8212,plain,
( spl0_980
<=> ! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f271,axiom,
! [X10] :
( ~ c_less(c_0,X10,tc_nat)
| c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f8210,plain,
spl0_979,
inference(avatar_split_clause,[],[f270,f8208]) ).
fof(f8208,plain,
( spl0_979
<=> ! [X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f270,axiom,
! [X10] :
( c_less(c_0,X10,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f8206,plain,
spl0_978,
inference(avatar_split_clause,[],[f230,f8204]) ).
fof(f8204,plain,
( spl0_978
<=> ! [X37] :
( c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f230,axiom,
! [X37] :
( c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X37)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_1) ).
fof(f8202,plain,
spl0_977,
inference(avatar_split_clause,[],[f229,f8200]) ).
fof(f8200,plain,
( spl0_977
<=> ! [X37] :
( ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X37)) = X37 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f229,axiom,
! [X37] :
( ~ c_lessequals(c_0,X37,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X37)) = X37 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__nat__eq_0) ).
fof(f8198,plain,
spl0_976,
inference(avatar_split_clause,[],[f199,f8196]) ).
fof(f8196,plain,
( spl0_976
<=> ! [X37] :
( c_0 = X37
| ~ c_less(c_HOL_Oabs(X37,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f199,axiom,
! [X37] :
( c_0 = X37
| ~ c_less(c_HOL_Oabs(X37,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f8194,plain,
spl0_975,
inference(avatar_split_clause,[],[f96,f8192]) ).
fof(f8192,plain,
( spl0_975
<=> ! [X20,X27,X3] :
( c_emptyset = X27
| c_emptyset != c_Equiv__Relations_Oquotient(X27,X20,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f96,axiom,
! [X3,X27,X20] :
( c_emptyset = X27
| c_emptyset != c_Equiv__Relations_Oquotient(X27,X20,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_0) ).
fof(f8190,plain,
spl0_974,
inference(avatar_split_clause,[],[f92,f8188]) ).
fof(f8188,plain,
( spl0_974
<=> ! [X25,X10] : c_0 = c_div(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f92,axiom,
! [X10,X25] : c_0 = c_div(c_Divides_Oop_Amod(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f8186,plain,
spl0_973,
inference(avatar_split_clause,[],[f90,f8184]) ).
fof(f8184,plain,
( spl0_973
<=> ! [X25,X10] : c_0 = c_Divides_Oop_Amod(c_times(X25,X10,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f90,axiom,
! [X10,X25] : c_0 = c_Divides_Oop_Amod(c_times(X25,X10,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f8181,plain,
spl0_972,
inference(avatar_split_clause,[],[f88,f8179]) ).
fof(f8179,plain,
( spl0_972
<=> ! [X25,X10] : c_0 = c_Divides_Oop_Amod(c_times(X10,X25,tc_nat),X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f88,axiom,
! [X10,X25] : c_0 = c_Divides_Oop_Amod(c_times(X10,X25,tc_nat),X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f8177,plain,
spl0_971,
inference(avatar_split_clause,[],[f45,f8175]) ).
fof(f8175,plain,
( spl0_971
<=> ! [X9,X17,X3,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f45,axiom,
! [X3,X9,X17,X15] : c_Datatype__Universe_OLeaf(X15,X3,X17) != c_Datatype__Universe_ONumb(X9,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f8173,plain,
spl0_970,
inference(avatar_split_clause,[],[f42,f8171]) ).
fof(f8171,plain,
( spl0_970
<=> ! [X19,X18,X17,X3] : c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn1(X19,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f42,axiom,
! [X3,X18,X19,X17] : c_Datatype__Universe_OIn0(X18,X3,X17) != c_Datatype__Universe_OIn1(X19,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_OIn1__not__In0_0) ).
fof(f8073,plain,
( spl0_969
| ~ spl0_42
| ~ spl0_851 ),
inference(avatar_split_clause,[],[f7663,f7499,f3374,f8070]) ).
fof(f8070,plain,
( spl0_969
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f3374,plain,
( spl0_42
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f7499,plain,
( spl0_851
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f7663,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_42
| ~ spl0_851 ),
inference(resolution,[],[f7500,f3376]) ).
fof(f3376,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_42 ),
inference(avatar_component_clause,[],[f3374]) ).
fof(f7500,plain,
( ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(c_0,X3) )
| ~ spl0_851 ),
inference(avatar_component_clause,[],[f7499]) ).
fof(f8051,plain,
( spl0_968
| ~ spl0_42
| ~ spl0_850 ),
inference(avatar_split_clause,[],[f7662,f7495,f3374,f8048]) ).
fof(f8048,plain,
( spl0_968
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f7495,plain,
( spl0_850
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f7662,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_42
| ~ spl0_850 ),
inference(resolution,[],[f7496,f3376]) ).
fof(f7496,plain,
( ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(c_0,X3) )
| ~ spl0_850 ),
inference(avatar_component_clause,[],[f7495]) ).
fof(f8045,plain,
spl0_967,
inference(avatar_split_clause,[],[f3040,f8043]) ).
fof(f3040,plain,
! [X3] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X3)
| ~ class_Numeral_Onumber__ring(X3) ),
inference(forward_demodulation,[],[f1020,f1006]) ).
fof(f1020,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f8041,plain,
spl0_966,
inference(avatar_split_clause,[],[f2992,f8039]) ).
fof(f8039,plain,
( spl0_966
<=> ! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X25,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f2992,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X25,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2792,f2757]) ).
fof(f2792,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),X25,tc_nat,tc_nat)),
inference(definition_unfolding,[],[f150,f1394]) ).
fof(f150,axiom,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X25,tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1__left_0) ).
fof(f8037,plain,
spl0_965,
inference(avatar_split_clause,[],[f2991,f8035]) ).
fof(f8035,plain,
( spl0_965
<=> ! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f2991,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f2791,f2757]) ).
fof(f2791,plain,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat,tc_nat)),
inference(definition_unfolding,[],[f149,f1394]) ).
fof(f149,axiom,
! [X25] : c_1 = c_GCD_Ogcd(c_Pair(X25,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__1_0) ).
fof(f8033,plain,
spl0_964,
inference(avatar_split_clause,[],[f2763,f8031]) ).
fof(f8031,plain,
( spl0_964
<=> ! [X10] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f2763,plain,
! [X10] : c_less(c_0,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1644,f1394]) ).
fof(f1644,axiom,
! [X10] : c_less(c_0,c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ozero__less__Suc_0) ).
fof(f8029,plain,
spl0_963,
inference(avatar_split_clause,[],[f2762,f8027]) ).
fof(f8027,plain,
( spl0_963
<=> ! [X10] : c_less(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f2762,plain,
! [X10] : c_less(X10,c_Finite__Set_Ocard(c_SetInterval_OatMost(X10,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f1642,f1394]) ).
fof(f1642,axiom,
! [X10] : c_less(X10,c_Suc(X10),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
fof(f8025,plain,
spl0_962,
inference(avatar_split_clause,[],[f1829,f8023]) ).
fof(f8023,plain,
( spl0_962
<=> ! [X91,X90] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_sum(X91,X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f1829,axiom,
! [X90,X91] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_sum(X91,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_sum_0) ).
fof(f8021,plain,
spl0_961,
inference(avatar_split_clause,[],[f1823,f8019]) ).
fof(f8019,plain,
( spl0_961
<=> ! [X91,X90] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_prod(X91,X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1823,axiom,
! [X90,X91] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_prod(X91,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_prod_0) ).
fof(f8017,plain,
spl0_960,
inference(avatar_split_clause,[],[f1773,f8015]) ).
fof(f8015,plain,
( spl0_960
<=> ! [X91,X90] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_fun(X91,X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1773,axiom,
! [X90,X91] :
( ~ class_Finite__Set_Ofinite(X91)
| ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_fun(X91,X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun_0) ).
fof(f8013,plain,
spl0_959,
inference(avatar_split_clause,[],[f1671,f8011]) ).
fof(f8011,plain,
( spl0_959
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1671,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f8009,plain,
spl0_958,
inference(avatar_split_clause,[],[f1670,f8007]) ).
fof(f8007,plain,
( spl0_958
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f1670,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f8005,plain,
spl0_957,
inference(avatar_split_clause,[],[f1669,f8003]) ).
fof(f8003,plain,
( spl0_957
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f1669,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f8001,plain,
spl0_956,
inference(avatar_split_clause,[],[f1668,f7999]) ).
fof(f7999,plain,
( spl0_956
<=> ! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1668,axiom,
! [X38,X74] : c_in(c_SetInterval_OgreaterThanAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f7997,plain,
spl0_955,
inference(avatar_split_clause,[],[f1666,f7995]) ).
fof(f7995,plain,
( spl0_955
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1666,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f7993,plain,
spl0_954,
inference(avatar_split_clause,[],[f1665,f7991]) ).
fof(f7991,plain,
( spl0_954
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1665,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastLessThan(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f7989,plain,
spl0_953,
inference(avatar_split_clause,[],[f1664,f7987]) ).
fof(f7987,plain,
( spl0_953
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1664,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f7985,plain,
spl0_952,
inference(avatar_split_clause,[],[f1663,f7983]) ).
fof(f7983,plain,
( spl0_952
<=> ! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1663,axiom,
! [X38,X74] : c_in(c_SetInterval_OatLeastAtMost(X74,X38,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f7981,plain,
spl0_951,
inference(avatar_split_clause,[],[f1614,f7979]) ).
fof(f7979,plain,
( spl0_951
<=> ! [X25,X10] : c_lessequals(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1614,axiom,
! [X10,X25] : c_lessequals(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint),c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__zle_0) ).
fof(f7977,plain,
spl0_950,
inference(avatar_split_clause,[],[f1549,f7975]) ).
fof(f7975,plain,
( spl0_950
<=> ! [X27,X3] :
( c_emptyset = X27
| ~ c_lessequals(X27,c_emptyset,tc_set(X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f1549,axiom,
! [X3,X27] :
( c_emptyset = X27
| ~ c_lessequals(X27,c_emptyset,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__empty_0) ).
fof(f7973,plain,
( spl0_949
| ~ spl0_54
| ~ spl0_847 ),
inference(avatar_split_clause,[],[f7654,f7483,f3434,f7970]) ).
fof(f7483,plain,
( spl0_847
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f7654,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_847 ),
inference(resolution,[],[f7484,f3436]) ).
fof(f7484,plain,
( ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X3) )
| ~ spl0_847 ),
inference(avatar_component_clause,[],[f7483]) ).
fof(f7968,plain,
spl0_948,
inference(avatar_split_clause,[],[f1510,f7966]) ).
fof(f7966,plain,
( spl0_948
<=> ! [X8,X3] : c_Set_Ocontents(c_insert(X8,c_emptyset,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1510,axiom,
! [X3,X8] : c_Set_Ocontents(c_insert(X8,c_emptyset,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Ocontents__eq_0) ).
fof(f7964,plain,
spl0_947,
inference(avatar_split_clause,[],[f1384,f7961]) ).
fof(f1384,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatMost__0_0) ).
fof(f7959,plain,
spl0_946,
inference(avatar_split_clause,[],[f1342,f7957]) ).
fof(f7957,plain,
( spl0_946
<=> ! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(X15,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1342,axiom,
! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(X15,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f7955,plain,
spl0_945,
inference(avatar_split_clause,[],[f1341,f7953]) ).
fof(f7953,plain,
( spl0_945
<=> ! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(c_0,X15,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1341,axiom,
! [X3,X15] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X3)
| c_0 = c_times(c_0,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f7951,plain,
spl0_944,
inference(avatar_split_clause,[],[f1324,f7949]) ).
fof(f7949,plain,
( spl0_944
<=> ! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(c_1,X26,X3) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1324,axiom,
! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(c_1,X26,X3) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f7947,plain,
spl0_943,
inference(avatar_split_clause,[],[f1323,f7945]) ).
fof(f7945,plain,
( spl0_943
<=> ! [X16,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(X16,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1323,axiom,
! [X3,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(X16,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f7943,plain,
spl0_942,
inference(avatar_split_clause,[],[f1320,f7941]) ).
fof(f7941,plain,
( spl0_942
<=> ! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(X26,c_1,X3) = X26 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1320,axiom,
! [X3,X26] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_times(X26,c_1,X3) = X26 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f7939,plain,
spl0_941,
inference(avatar_split_clause,[],[f1319,f7937]) ).
fof(f7937,plain,
( spl0_941
<=> ! [X16,X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(c_0,X16,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1319,axiom,
! [X3,X16] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_times(c_0,X16,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f7935,plain,
spl0_940,
inference(avatar_split_clause,[],[f1229,f7933]) ).
fof(f7933,plain,
( spl0_940
<=> ! [X8,X3] : c_Relation_ORange(c_Relation_Odiag(X8,X3),X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1229,axiom,
! [X3,X8] : c_Relation_ORange(c_Relation_Odiag(X8,X3),X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__diag_0) ).
fof(f7931,plain,
spl0_939,
inference(avatar_split_clause,[],[f1227,f7929]) ).
fof(f7929,plain,
( spl0_939
<=> ! [X17,X8,X3] : c_Relation_Orel__comp(X8,c_Relation_OId,X3,X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1227,axiom,
! [X3,X8,X17] : c_Relation_Orel__comp(X8,c_Relation_OId,X3,X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OR__O__Id_0) ).
fof(f7927,plain,
spl0_938,
inference(avatar_split_clause,[],[f1221,f7925]) ).
fof(f7925,plain,
( spl0_938
<=> ! [X17,X8,X3] : c_Relation_Orel__comp(c_Relation_OId,X8,X17,X17,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1221,axiom,
! [X3,X8,X17] : c_Relation_Orel__comp(c_Relation_OId,X8,X17,X17,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OId__O__R_0) ).
fof(f7923,plain,
spl0_937,
inference(avatar_split_clause,[],[f1219,f7921]) ).
fof(f7921,plain,
( spl0_937
<=> ! [X8,X3] : c_Relation_ODomain(c_Relation_Odiag(X8,X3),X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1219,axiom,
! [X3,X8] : c_Relation_ODomain(c_Relation_Odiag(X8,X3),X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__diag_0) ).
fof(f7919,plain,
spl0_936,
inference(avatar_split_clause,[],[f1207,f7917]) ).
fof(f7917,plain,
( spl0_936
<=> ! [X3,X15] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(X15,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1207,axiom,
! [X3,X15] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(X15,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f7915,plain,
spl0_935,
inference(avatar_split_clause,[],[f1204,f7913]) ).
fof(f1204,axiom,
! [X3,X8] :
( ~ class_Power_Orecpower(X3)
| c_Nat_Opower(X8,c_1,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one__right_0) ).
fof(f7911,plain,
spl0_934,
inference(avatar_split_clause,[],[f1203,f7909]) ).
fof(f1203,axiom,
! [X3,X10] :
( ~ class_Power_Orecpower(X3)
| c_1 = c_Nat_Opower(c_1,X10,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower__one_0) ).
fof(f7907,plain,
spl0_933,
inference(avatar_split_clause,[],[f1142,f7905]) ).
fof(f7905,plain,
( spl0_933
<=> ! [X11] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1142,axiom,
! [X11] :
( ~ c_Parity_Oeven(X11,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_1) ).
fof(f7903,plain,
spl0_932,
inference(avatar_split_clause,[],[f1141,f7901]) ).
fof(f7901,plain,
( spl0_932
<=> ! [X11] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1141,axiom,
! [X11] :
( c_Parity_Oeven(X11,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__neg_0) ).
fof(f7899,plain,
spl0_931,
inference(avatar_split_clause,[],[f1117,f7897]) ).
fof(f1117,axiom,
! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omax(X8,X8,X17) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f7895,plain,
spl0_930,
inference(avatar_split_clause,[],[f1112,f7893]) ).
fof(f1112,axiom,
! [X8,X17] :
( ~ class_Orderings_Olinorder(X17)
| c_Orderings_Omin(X8,X8,X17) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f7891,plain,
spl0_929,
inference(avatar_split_clause,[],[f1101,f7889]) ).
fof(f7889,plain,
( spl0_929
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1101,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f7887,plain,
spl0_928,
inference(avatar_split_clause,[],[f1100,f7885]) ).
fof(f7885,plain,
( spl0_928
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1100,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f7883,plain,
spl0_927,
inference(avatar_split_clause,[],[f1091,f7881]) ).
fof(f7881,plain,
( spl0_927
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1091,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_lessequals(c_OrderedGroup_Onprt(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f7879,plain,
spl0_926,
inference(avatar_split_clause,[],[f1068,f7877]) ).
fof(f1068,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(X8,c_1,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f7875,plain,
spl0_925,
inference(avatar_split_clause,[],[f1067,f7873]) ).
fof(f1067,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Omonoid__mult(X3)
| c_times(c_1,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f7871,plain,
spl0_924,
inference(avatar_split_clause,[],[f1055,f7869]) ).
fof(f1055,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_minus(X15,X15,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__self_0) ).
fof(f7867,plain,
spl0_923,
inference(avatar_split_clause,[],[f1048,f7865]) ).
fof(f1048,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_minus(X8,c_0,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f7863,plain,
spl0_922,
inference(avatar_split_clause,[],[f1046,f7861]) ).
fof(f1046,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(c_0,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f7859,plain,
spl0_921,
inference(avatar_split_clause,[],[f1035,f7857]) ).
fof(f1035,axiom,
! [X3,X8] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X3)
| c_plus(X8,c_0,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f7855,plain,
spl0_920,
inference(avatar_split_clause,[],[f1032,f7853]) ).
fof(f7853,plain,
( spl0_920
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_HOL_Oabs(X15,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1032,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| ~ c_less(c_HOL_Oabs(X15,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f7851,plain,
spl0_919,
inference(avatar_split_clause,[],[f1030,f7849]) ).
fof(f7849,plain,
( spl0_919
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_HOL_Oabs(c_0,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f1030,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_HOL_Oabs(c_0,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f7847,plain,
( ~ spl0_917
| spl0_918
| ~ spl0_700
| ~ spl0_841 ),
inference(avatar_split_clause,[],[f7653,f7457,f6863,f7844,f7840]) ).
fof(f7840,plain,
( spl0_917
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f7844,plain,
( spl0_918
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f6863,plain,
( spl0_700
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f7653,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_700
| ~ spl0_841 ),
inference(superposition,[],[f7458,f6865]) ).
fof(f6865,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_700 ),
inference(avatar_component_clause,[],[f6863]) ).
fof(f7838,plain,
spl0_916,
inference(avatar_split_clause,[],[f1027,f7836]) ).
fof(f7836,plain,
( spl0_916
<=> ! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_0,c_HOL_Oabs(X15,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1027,axiom,
! [X3,X15] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_lessequals(c_0,c_HOL_Oabs(X15,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f7834,plain,
spl0_915,
inference(avatar_split_clause,[],[f1003,f7832]) ).
fof(f1003,axiom,
! [X35] : c_Numeral_OBit(X35,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X35,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__succ__0_0) ).
fof(f7830,plain,
spl0_914,
inference(avatar_split_clause,[],[f715,f7828]) ).
fof(f7828,plain,
( spl0_914
<=> ! [X35] : c_IntDef_Onat(c_Numeral_Onumber__of(X35,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X35,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f715,axiom,
! [X35] : c_IntDef_Onat(c_Numeral_Onumber__of(X35,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X35,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__number__of_0) ).
fof(f7826,plain,
spl0_913,
inference(avatar_split_clause,[],[f668,f7824]) ).
fof(f7824,plain,
( spl0_913
<=> ! [X25,X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_NatArith_Oof__nat(X25,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f668,axiom,
! [X3,X25] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_NatArith_Oof__nat(X25,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f7822,plain,
spl0_912,
inference(avatar_split_clause,[],[f665,f7820]) ).
fof(f7820,plain,
( spl0_912
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_NatArith_Oof__nat(c_0,X3),c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f665,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_NatArith_Oof__nat(c_0,X3),c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f7818,plain,
spl0_911,
inference(avatar_split_clause,[],[f655,f7816]) ).
fof(f7816,plain,
( spl0_911
<=> ! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_NatArith_Oof__nat(X10,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f655,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_NatArith_Oof__nat(X10,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f7814,plain,
spl0_910,
inference(avatar_split_clause,[],[f629,f7812]) ).
fof(f7812,plain,
( spl0_910
<=> ! [X13,X11,X8] : c_List_Otl(c_List_Olist_OCons(X11,X8,X13),X13) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f629,axiom,
! [X11,X8,X13] : c_List_Otl(c_List_Olist_OCons(X11,X8,X13),X13) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__2_0) ).
fof(f7810,plain,
spl0_909,
inference(avatar_split_clause,[],[f600,f7808]) ).
fof(f7808,plain,
( spl0_909
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_emptyset != c_List_Oset(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f600,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_emptyset != c_List_Oset(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty2_0) ).
fof(f7806,plain,
spl0_908,
inference(avatar_split_clause,[],[f585,f7804]) ).
fof(f7804,plain,
( spl0_908
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate1(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f585,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orotate1(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f7802,plain,
spl0_907,
inference(avatar_split_clause,[],[f567,f7800]) ).
fof(f7800,plain,
( spl0_907
<=> ! [X11,X3] :
( c_List_Olist_ONil = X11
| c_List_Olist_ONil != c_List_Oremdups(X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f567,axiom,
! [X3,X11] :
( c_List_Olist_ONil = X11
| c_List_Olist_ONil != c_List_Oremdups(X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__right__iff_0) ).
fof(f7798,plain,
( spl0_906
| ~ spl0_50
| ~ spl0_834 ),
inference(avatar_split_clause,[],[f7633,f7429,f3414,f7795]) ).
fof(f7795,plain,
( spl0_906
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f3414,plain,
( spl0_50
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f7429,plain,
( spl0_834
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = c_NatArith_Oof__nat(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f7633,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_50
| ~ spl0_834 ),
inference(resolution,[],[f7430,f3416]) ).
fof(f3416,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_50 ),
inference(avatar_component_clause,[],[f3414]) ).
fof(f7430,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = c_NatArith_Oof__nat(c_0,X3) )
| ~ spl0_834 ),
inference(avatar_component_clause,[],[f7429]) ).
fof(f7793,plain,
spl0_905,
inference(avatar_split_clause,[],[f438,f7791]) ).
fof(f7791,plain,
( spl0_905
<=> ! [X11,X3] : c_List_Olast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) = X11 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f438,axiom,
! [X3,X11] : c_List_Olast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X3),X3) = X11,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olast_Osimps_0) ).
fof(f7789,plain,
spl0_904,
inference(avatar_split_clause,[],[f429,f7787]) ).
fof(f7787,plain,
( spl0_904
<=> ! [X41,X8,X3] : c_List_Ohd(c_List_Olist_OCons(X8,X41,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f429,axiom,
! [X41,X3,X8] : c_List_Ohd(c_List_Olist_OCons(X8,X41,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ohd_Osimps_0) ).
fof(f7785,plain,
spl0_903,
inference(avatar_split_clause,[],[f412,f7783]) ).
fof(f7783,plain,
( spl0_903
<=> ! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orev(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f412,axiom,
! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orev(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_1) ).
fof(f7781,plain,
spl0_902,
inference(avatar_split_clause,[],[f411,f7779]) ).
fof(f7779,plain,
( spl0_902
<=> ! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orev(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f411,axiom,
! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orev(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__rev_0) ).
fof(f7777,plain,
spl0_901,
inference(avatar_split_clause,[],[f400,f7775]) ).
fof(f7775,plain,
( spl0_901
<=> ! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f400,axiom,
! [X41,X3] :
( ~ c_List_Odistinct(X41,X3)
| c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_1) ).
fof(f7773,plain,
spl0_900,
inference(avatar_split_clause,[],[f399,f7771]) ).
fof(f7771,plain,
( spl0_900
<=> ! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f399,axiom,
! [X41,X3] :
( c_List_Odistinct(X41,X3)
| ~ c_List_Odistinct(c_List_Orotate1(X41,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct1__rotate_0) ).
fof(f7769,plain,
spl0_899,
inference(avatar_split_clause,[],[f387,f7767]) ).
fof(f7767,plain,
( spl0_899
<=> ! [X13,X11] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f387,axiom,
! [X11,X13] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X11,c_List_Olist_ONil,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__2_0) ).
fof(f7765,plain,
spl0_898,
inference(avatar_split_clause,[],[f363,f7763]) ).
fof(f7763,plain,
( spl0_898
<=> ! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orev(X41,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f363,axiom,
! [X41,X3] :
( c_List_Olist_ONil = X41
| c_List_Olist_ONil != c_List_Orev(X41,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_0) ).
fof(f7761,plain,
spl0_897,
inference(avatar_split_clause,[],[f349,f7759]) ).
fof(f349,axiom,
! [X3,X8] :
( ~ class_LOrder_Omeet__semilorder(X3)
| c_LOrder_Omeet(X8,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Omeet__idempotent_0) ).
fof(f7757,plain,
spl0_896,
inference(avatar_split_clause,[],[f348,f7755]) ).
fof(f348,axiom,
! [X3,X8] :
( ~ class_LOrder_Ojoin__semilorder(X3)
| c_LOrder_Ojoin(X8,X8,X3) = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_LOrder_Ojoin__idempotent_0) ).
fof(f7753,plain,
( spl0_895
| ~ spl0_23
| ~ spl0_833 ),
inference(avatar_split_clause,[],[f7631,f7425,f3279,f7750]) ).
fof(f7750,plain,
( spl0_895
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f3279,plain,
( spl0_23
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f7425,plain,
( spl0_833
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_1 = c_NatArith_Oof__nat(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f7631,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_23
| ~ spl0_833 ),
inference(resolution,[],[f7426,f3281]) ).
fof(f3281,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f3279]) ).
fof(f7426,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_1 = c_NatArith_Oof__nat(c_1,X3) )
| ~ spl0_833 ),
inference(avatar_component_clause,[],[f7425]) ).
fof(f7748,plain,
spl0_894,
inference(avatar_split_clause,[],[f340,f7746]) ).
fof(f7746,plain,
( spl0_894
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f340,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f7744,plain,
spl0_893,
inference(avatar_split_clause,[],[f269,f7742]) ).
fof(f269,axiom,
! [X3,X10] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_NatArith_Oof__nat(X10,X3),c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f7740,plain,
spl0_892,
inference(avatar_split_clause,[],[f242,f7738]) ).
fof(f7738,plain,
( spl0_892
<=> ! [X25,X10] : ~ c_less(c_IntDef_Oint(X10),c_uminus(c_IntDef_Oint(X25),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f242,axiom,
! [X10,X25] : ~ c_less(c_IntDef_Oint(X10),c_uminus(c_IntDef_Oint(X25),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f7736,plain,
spl0_891,
inference(avatar_split_clause,[],[f235,f7734]) ).
fof(f7734,plain,
( spl0_891
<=> ! [X37] :
( ~ c_lessequals(X37,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X37) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f235,axiom,
! [X37] :
( ~ c_lessequals(X37,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X37) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__le__0_0) ).
fof(f7732,plain,
spl0_890,
inference(avatar_split_clause,[],[f226,f7730]) ).
fof(f7730,plain,
( spl0_890
<=> ! [X10] :
( c_0 = X10
| ~ c_lessequals(c_IntDef_Oint(X10),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f226,axiom,
! [X10] :
( c_0 = X10
| ~ c_lessequals(c_IntDef_Oint(X10),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__le__0__conv_0) ).
fof(f7728,plain,
spl0_889,
inference(avatar_split_clause,[],[f225,f7726]) ).
fof(f7726,plain,
( spl0_889
<=> ! [X25,X10] :
( X10 = X25
| c_IntDef_Oint(X25) != c_IntDef_Oint(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f225,axiom,
! [X10,X25] :
( X10 = X25
| c_IntDef_Oint(X25) != c_IntDef_Oint(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__int__eq_0) ).
fof(f7724,plain,
spl0_888,
inference(avatar_split_clause,[],[f158,f7722]) ).
fof(f7722,plain,
( spl0_888
<=> ! [X8] : c_GCD_Ogcd(c_Pair(X8,X8,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f158,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(X8,X8,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__self_0) ).
fof(f7720,plain,
spl0_887,
inference(avatar_split_clause,[],[f148,f7718]) ).
fof(f7718,plain,
( spl0_887
<=> ! [X8] : c_GCD_Ogcd(c_Pair(c_0,X8,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f148,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(c_0,X8,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0__left_0) ).
fof(f7716,plain,
spl0_886,
inference(avatar_split_clause,[],[f147,f7714]) ).
fof(f7714,plain,
( spl0_886
<=> ! [X8] : c_GCD_Ogcd(c_Pair(X8,c_0,tc_nat,tc_nat)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f147,axiom,
! [X8] : c_GCD_Ogcd(c_Pair(X8,c_0,tc_nat,tc_nat)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_GCD_Ogcd__0_0) ).
fof(f7712,plain,
spl0_885,
inference(avatar_split_clause,[],[f27,f7710]) ).
fof(f7710,plain,
( spl0_885
<=> ! [X3,X15] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X15,X3),tc_Datatype_Ooption(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f27,axiom,
! [X3,X15] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X15,X3),tc_Datatype_Ooption(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__2_0) ).
fof(f7708,plain,
( spl0_884
| ~ spl0_24
| ~ spl0_825 ),
inference(avatar_split_clause,[],[f7623,f7393,f3284,f7705]) ).
fof(f7705,plain,
( spl0_884
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f3284,plain,
( spl0_24
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f7393,plain,
( spl0_825
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_1 = c_IntDef_Oof__int(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f7623,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_24
| ~ spl0_825 ),
inference(resolution,[],[f7394,f3286]) ).
fof(f3286,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f3284]) ).
fof(f7394,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_1 = c_IntDef_Oof__int(c_1,X3) )
| ~ spl0_825 ),
inference(avatar_component_clause,[],[f7393]) ).
fof(f7703,plain,
spl0_883,
inference(avatar_split_clause,[],[f21,f7701]) ).
fof(f7701,plain,
( spl0_883
<=> ! [X12,X3] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Oo2s(X12,X3) != c_emptyset ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f21,axiom,
! [X3,X12] :
( c_Datatype_Ooption_ONone = X12
| c_Datatype_Oo2s(X12,X3) != c_emptyset ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f7698,plain,
spl0_882,
inference(avatar_split_clause,[],[f17,f7696]) ).
fof(f7696,plain,
( spl0_882
<=> ! [X11,X3] : c_in(X11,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X3),X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f17,axiom,
! [X3,X11] : c_in(X11,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X11,X3),X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oelem__o2s_1) ).
fof(f7688,plain,
( spl0_881
| ~ spl0_52
| ~ spl0_824 ),
inference(avatar_split_clause,[],[f7622,f7389,f3424,f7685]) ).
fof(f7685,plain,
( spl0_881
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f3424,plain,
( spl0_52
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f7389,plain,
( spl0_824
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_IntDef_Oof__int(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f7622,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_52
| ~ spl0_824 ),
inference(resolution,[],[f7390,f3426]) ).
fof(f3426,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_52 ),
inference(avatar_component_clause,[],[f3424]) ).
fof(f7390,plain,
( ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_IntDef_Oof__int(c_0,X3) )
| ~ spl0_824 ),
inference(avatar_component_clause,[],[f7389]) ).
fof(f7670,plain,
( spl0_880
| ~ spl0_114
| ~ spl0_819 ),
inference(avatar_split_clause,[],[f7616,f7368,f3728,f7667]) ).
fof(f7368,plain,
( spl0_819
<=> ! [X25] : c_IntDef_Oint(X25) = c_HOL_Oabs(c_IntDef_Oint(X25),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f7616,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_114
| ~ spl0_819 ),
inference(superposition,[],[f7369,f3730]) ).
fof(f7369,plain,
( ! [X25] : c_IntDef_Oint(X25) = c_HOL_Oabs(c_IntDef_Oint(X25),tc_IntDef_Oint)
| ~ spl0_819 ),
inference(avatar_component_clause,[],[f7368]) ).
fof(f7660,plain,
( spl0_879
| ~ spl0_113
| ~ spl0_819 ),
inference(avatar_split_clause,[],[f7615,f7368,f3723,f7657]) ).
fof(f7657,plain,
( spl0_879
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f7615,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_819 ),
inference(superposition,[],[f7369,f3725]) ).
fof(f7629,plain,
( spl0_878
| ~ spl0_809
| ~ spl0_813 ),
inference(avatar_split_clause,[],[f7611,f7344,f7327,f7627]) ).
fof(f7327,plain,
( spl0_809
<=> ! [X8] : c_div(X8,c_1,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f7344,plain,
( spl0_813
<=> ! [X25,X10] : c_lessequals(c_div(X25,X10,tc_nat),X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f7611,plain,
( ! [X0] : c_lessequals(X0,X0,tc_nat)
| ~ spl0_809
| ~ spl0_813 ),
inference(superposition,[],[f7345,f7328]) ).
fof(f7328,plain,
( ! [X8] : c_div(X8,c_1,tc_nat) = X8
| ~ spl0_809 ),
inference(avatar_component_clause,[],[f7327]) ).
fof(f7345,plain,
( ! [X10,X25] : c_lessequals(c_div(X25,X10,tc_nat),X25,tc_nat)
| ~ spl0_813 ),
inference(avatar_component_clause,[],[f7344]) ).
fof(f7609,plain,
spl0_877,
inference(avatar_split_clause,[],[f3065,f7607]) ).
fof(f7607,plain,
( spl0_877
<=> ! [X25] :
( ~ c_Divides_Oop_Advd(X25,c_1,tc_nat)
| c_1 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f3065,plain,
! [X25] :
( ~ c_Divides_Oop_Advd(X25,c_1,tc_nat)
| c_1 = X25 ),
inference(forward_demodulation,[],[f3064,f2757]) ).
fof(f3064,plain,
! [X25] :
( c_1 = X25
| ~ c_Divides_Oop_Advd(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2888,f2757]) ).
fof(f2888,plain,
! [X25] :
( c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) = X25
| ~ c_Divides_Oop_Advd(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) ),
inference(definition_unfolding,[],[f77,f1394,f1394]) ).
fof(f77,axiom,
! [X25] :
( c_Suc(c_0) = X25
| ~ c_Divides_Oop_Advd(X25,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__1__iff__1_0) ).
fof(f7605,plain,
spl0_876,
inference(avatar_split_clause,[],[f2979,f7603]) ).
fof(f7603,plain,
( spl0_876
<=> ! [X3,X31] : c_emptyset = c_Relation_OImage(c_emptyset,X31,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f2979,plain,
! [X31,X3] : c_emptyset = c_Relation_OImage(c_emptyset,X31,X3,X3),
inference(forward_demodulation,[],[f2768,f1236]) ).
fof(f1236,axiom,
! [X3] : c_emptyset = c_Relation_Odiag(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Odiag__empty_0) ).
fof(f2768,plain,
! [X31,X3] : c_emptyset = c_Relation_OImage(c_Relation_Odiag(c_emptyset,X3),X31,X3,X3),
inference(definition_unfolding,[],[f1454,f1223]) ).
fof(f1454,axiom,
! [X31,X3] : c_emptyset = c_inter(c_emptyset,X31,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__empty__left_0) ).
fof(f7601,plain,
spl0_875,
inference(avatar_split_clause,[],[f2772,f7599]) ).
fof(f7599,plain,
( spl0_875
<=> ! [X35] : c_Numeral_Obin__add(c_Numeral_OMin,X35) = c_Numeral_Obin__add(X35,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f7597,plain,
spl0_874,
inference(avatar_split_clause,[],[f2770,f7594]) ).
fof(f2770,plain,
c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) = c_Numeral_Obin__add(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f983,f963]) ).
fof(f983,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__pred__Min_0) ).
fof(f7592,plain,
( ~ spl0_1
| spl0_821
| ~ spl0_659
| spl0_822 ),
inference(avatar_split_clause,[],[f7464,f7380,f6679,f7376,f3169]) ).
fof(f3169,plain,
( spl0_1
<=> c_in(v_L,v_A,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f7376,plain,
( spl0_821
<=> c_in(v_x(v_L),v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f6679,plain,
( spl0_659
<=> ! [X30] :
( ~ c_in(X30,v_A,t_a)
| c_in(v_x(X30),v_S,t_a)
| c_in(c_Pair(v_L,X30,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f7380,plain,
( spl0_822
<=> c_in(c_Pair(v_L,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f7464,plain,
( c_in(v_x(v_L),v_S,t_a)
| ~ c_in(v_L,v_A,t_a)
| ~ spl0_659
| spl0_822 ),
inference(resolution,[],[f7381,f6680]) ).
fof(f6680,plain,
( ! [X30] :
( c_in(c_Pair(v_L,X30,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(v_x(X30),v_S,t_a)
| ~ c_in(X30,v_A,t_a) )
| ~ spl0_659 ),
inference(avatar_component_clause,[],[f6679]) ).
fof(f7381,plain,
( ~ c_in(c_Pair(v_L,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| spl0_822 ),
inference(avatar_component_clause,[],[f7380]) ).
fof(f7591,plain,
spl0_873,
inference(avatar_split_clause,[],[f2757,f7588]) ).
fof(f7588,plain,
( spl0_873
<=> c_1 = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f7586,plain,
spl0_872,
inference(avatar_split_clause,[],[f2753,f7584]) ).
fof(f7584,plain,
( spl0_872
<=> ! [X25] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f2753,plain,
! [X25] : c_0 != c_Finite__Set_Ocard(c_SetInterval_OatMost(X25,tc_nat),tc_nat),
inference(definition_unfolding,[],[f873,f1394]) ).
fof(f873,axiom,
! [X25] : c_0 != c_Suc(X25),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_OSuc__not__Zero_0) ).
fof(f7582,plain,
spl0_871,
inference(avatar_split_clause,[],[f1672,f7580]) ).
fof(f7580,plain,
( spl0_871
<=> ! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f1672,axiom,
! [X9] : c_in(c_SetInterval_OlessThan(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f7578,plain,
spl0_870,
inference(avatar_split_clause,[],[f1667,f7576]) ).
fof(f7576,plain,
( spl0_870
<=> ! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f1667,axiom,
! [X9] : c_in(c_SetInterval_OatMost(X9,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ofinite__atMost_0) ).
fof(f7574,plain,
spl0_869,
inference(avatar_split_clause,[],[f1638,f7572]) ).
fof(f7572,plain,
( spl0_869
<=> ! [X27,X3] : c_in(c_List_Olist_ONil,c_List_Olists(X27,X3),tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f1638,axiom,
! [X3,X27] : c_in(c_List_Olist_ONil,c_List_Olists(X27,X3),tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists_ONil_0) ).
fof(f7570,plain,
spl0_868,
inference(avatar_split_clause,[],[f1622,f7568]) ).
fof(f7568,plain,
( spl0_868
<=> ! [X41,X3] : c_in(c_List_Oset(X41,X3),c_Finite__Set_OFinites,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f1622,axiom,
! [X41,X3] : c_in(c_List_Oset(X41,X3),c_Finite__Set_OFinites,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ofinite__set_0) ).
fof(f7566,plain,
spl0_867,
inference(avatar_split_clause,[],[f1619,f7564]) ).
fof(f1619,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f7562,plain,
spl0_866,
inference(avatar_split_clause,[],[f1618,f7560]) ).
fof(f1618,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f7558,plain,
spl0_865,
inference(avatar_split_clause,[],[f1603,f7556]) ).
fof(f7556,plain,
( spl0_865
<=> ! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f1603,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X25,X9,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__right_0) ).
fof(f7554,plain,
spl0_864,
inference(avatar_split_clause,[],[f1602,f7552]) ).
fof(f7552,plain,
( spl0_864
<=> ! [X25,X9] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f1602,axiom,
! [X9,X25] : c_Divides_Oop_Advd(X9,c_times(X9,X25,tc_nat),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__triv__left_0) ).
fof(f7550,plain,
spl0_863,
inference(avatar_split_clause,[],[f1555,f7548]) ).
fof(f7548,plain,
( spl0_863
<=> ! [X17,X3] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f1555,axiom,
! [X3,X17] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f7546,plain,
spl0_862,
inference(avatar_split_clause,[],[f1534,f7544]) ).
fof(f1534,axiom,
! [X3,X11,X27] : c_in(X11,c_insert(X11,X27,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).
fof(f7542,plain,
spl0_861,
inference(avatar_split_clause,[],[f1518,f7540]) ).
fof(f7540,plain,
( spl0_861
<=> ! [X27,X3] : c_emptyset = c_minus(c_emptyset,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f1518,axiom,
! [X3,X27] : c_emptyset = c_minus(c_emptyset,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__Diff_0) ).
fof(f7538,plain,
spl0_860,
inference(avatar_split_clause,[],[f1498,f7536]) ).
fof(f7536,plain,
( spl0_860
<=> ! [X8,X3] : c_Union(c_Pow(X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f1498,axiom,
! [X3,X8] : c_Union(c_Pow(X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__Pow__eq_0) ).
fof(f7534,plain,
spl0_859,
inference(avatar_split_clause,[],[f1440,f7532]) ).
fof(f7532,plain,
( spl0_859
<=> ! [X8,X3] : c_minus(X8,c_emptyset,tc_set(X3)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f1440,axiom,
! [X3,X8] : c_minus(X8,c_emptyset,tc_set(X3)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__empty_0) ).
fof(f7530,plain,
spl0_858,
inference(avatar_split_clause,[],[f1438,f7528]) ).
fof(f7528,plain,
( spl0_858
<=> ! [X27,X3] : c_emptyset = c_minus(X27,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f1438,axiom,
! [X3,X27] : c_emptyset = c_minus(X27,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__cancel_0) ).
fof(f7526,plain,
spl0_857,
inference(avatar_split_clause,[],[f1437,f7524]) ).
fof(f7524,plain,
( spl0_857
<=> ! [X27,X3] : c_emptyset = c_minus(X27,c_UNIV,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f1437,axiom,
! [X3,X27] : c_emptyset = c_minus(X27,c_UNIV,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiff__UNIV_0) ).
fof(f7522,plain,
spl0_856,
inference(avatar_split_clause,[],[f1399,f7520]) ).
fof(f7520,plain,
( spl0_856
<=> ! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f1399,axiom,
! [X8] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X8,tc_nat),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_Ocard__lessThan_0) ).
fof(f7518,plain,
spl0_855,
inference(avatar_split_clause,[],[f1244,f7516]) ).
fof(f7516,plain,
( spl0_855
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f1244,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_1 = c_HOL_Oabs(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oabs__one_0) ).
fof(f7514,plain,
spl0_854,
inference(avatar_split_clause,[],[f1224,f7512]) ).
fof(f7512,plain,
( spl0_854
<=> ! [X17,X3,X79] : c_emptyset = c_Relation_OImage(X79,c_emptyset,X17,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f1224,axiom,
! [X3,X79,X17] : c_emptyset = c_Relation_OImage(X79,c_emptyset,X17,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__empty_0) ).
fof(f7510,plain,
( ~ spl0_853
| ~ spl0_111
| spl0_822 ),
inference(avatar_split_clause,[],[f7465,f7380,f3715,f7507]) ).
fof(f7507,plain,
( spl0_853
<=> c_in(v_L,v_S,t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f3715,plain,
( spl0_111
<=> ! [X30] :
( ~ c_in(X30,v_S,t_a)
| c_in(c_Pair(X30,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f7465,plain,
( ~ c_in(v_L,v_S,t_a)
| ~ spl0_111
| spl0_822 ),
inference(resolution,[],[f7381,f3716]) ).
fof(f3716,plain,
( ! [X30] :
( c_in(c_Pair(X30,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X30,v_S,t_a) )
| ~ spl0_111 ),
inference(avatar_component_clause,[],[f3715]) ).
fof(f7505,plain,
spl0_852,
inference(avatar_split_clause,[],[f1222,f7503]) ).
fof(f7503,plain,
( spl0_852
<=> ! [X8,X3] : c_Relation_OImage(c_Relation_OId,X8,X3,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f1222,axiom,
! [X3,X8] : c_Relation_OImage(c_Relation_OId,X8,X3,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_OImage__Id_0) ).
fof(f7501,plain,
spl0_851,
inference(avatar_split_clause,[],[f1093,f7499]) ).
fof(f1093,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Opprt(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Opprt__0_0) ).
fof(f7497,plain,
spl0_850,
inference(avatar_split_clause,[],[f1088,f7495]) ).
fof(f1088,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X3)
| c_0 = c_OrderedGroup_Onprt(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Onprt__0_0) ).
fof(f7493,plain,
spl0_849,
inference(avatar_split_clause,[],[f1076,f7491]) ).
fof(f7491,plain,
( spl0_849
<=> ! [X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_uminus(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f1076,axiom,
! [X3] :
( ~ class_OrderedGroup_Oab__group__add(X3)
| c_0 = c_uminus(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oneg__equal__0__iff__equal_1) ).
fof(f7489,plain,
spl0_848,
inference(avatar_split_clause,[],[f1026,f7487]) ).
fof(f7487,plain,
( spl0_848
<=> ! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = c_HOL_Oabs(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f1026,axiom,
! [X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X3)
| c_0 = c_HOL_Oabs(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OrderedGroup_Oabs__eq__0_1) ).
fof(f7485,plain,
spl0_847,
inference(avatar_split_clause,[],[f1019,f7483]) ).
fof(f1019,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f7481,plain,
spl0_846,
inference(avatar_split_clause,[],[f1012,f7479]) ).
fof(f7479,plain,
( spl0_846
<=> ! [X29,X8,X3] : c_Numeral_Obit_Obit__rec(X29,X8,c_Numeral_Obit_OB1,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f1012,axiom,
! [X3,X29,X8] : c_Numeral_Obit_Obit__rec(X29,X8,c_Numeral_Obit_OB1,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__2_0) ).
fof(f7477,plain,
spl0_845,
inference(avatar_split_clause,[],[f1011,f7475]) ).
fof(f7475,plain,
( spl0_845
<=> ! [X28,X8,X3] : c_Numeral_Obit_Obit__rec(X8,X28,c_Numeral_Obit_OB0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f1011,axiom,
! [X28,X3,X8] : c_Numeral_Obit_Obit__rec(X8,X28,c_Numeral_Obit_OB0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Orecs__1_0) ).
fof(f7473,plain,
spl0_844,
inference(avatar_split_clause,[],[f1008,f7471]) ).
fof(f7471,plain,
( spl0_844
<=> ! [X29,X8,X3] : c_Numeral_Obit_Obit__case(X29,X8,c_Numeral_Obit_OB1,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f1008,axiom,
! [X3,X29,X8] : c_Numeral_Obit_Obit__case(X29,X8,c_Numeral_Obit_OB1,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__2_0) ).
fof(f7469,plain,
spl0_843,
inference(avatar_split_clause,[],[f1007,f7467]) ).
fof(f7467,plain,
( spl0_843
<=> ! [X28,X8,X3] : c_Numeral_Obit_Obit__case(X8,X28,c_Numeral_Obit_OB0,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f1007,axiom,
! [X28,X3,X8] : c_Numeral_Obit_Obit__case(X8,X28,c_Numeral_Obit_OB0,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Ocases__1_0) ).
fof(f7463,plain,
spl0_842,
inference(avatar_split_clause,[],[f994,f7461]) ).
fof(f7461,plain,
( spl0_842
<=> ! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f994,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f7459,plain,
spl0_841,
inference(avatar_split_clause,[],[f993,f7457]) ).
fof(f993,axiom,
! [X3] :
( ~ class_Numeral_Onumber__ring(X3)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X3),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f7455,plain,
spl0_840,
inference(avatar_split_clause,[],[f939,f7453]) ).
fof(f7453,plain,
( spl0_840
<=> ! [X10] :
( c_0 = X10
| c_less(c_0,X10,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f939,axiom,
! [X10] :
( c_0 = X10
| c_less(c_0,X10,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__gr0_0) ).
fof(f7451,plain,
spl0_839,
inference(avatar_split_clause,[],[f938,f7449]) ).
fof(f7449,plain,
( spl0_839
<=> ! [X52,X24] : ~ c_less(c_plus(X52,X24,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f938,axiom,
! [X52,X24] : ~ c_less(c_plus(X52,X24,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
fof(f7447,plain,
spl0_838,
inference(avatar_split_clause,[],[f937,f7445]) ).
fof(f7445,plain,
( spl0_838
<=> ! [X52,X24] : ~ c_less(c_plus(X24,X52,tc_nat),X24,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f937,axiom,
! [X52,X24] : ~ c_less(c_plus(X24,X52,tc_nat),X24,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__add__less1_0) ).
fof(f7443,plain,
spl0_837,
inference(avatar_split_clause,[],[f898,f7441]) ).
fof(f7441,plain,
( spl0_837
<=> ! [X10] :
( c_0 = X10
| ~ c_less(X10,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f898,axiom,
! [X10] :
( c_0 = X10
| ~ c_less(X10,c_1,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_0) ).
fof(f7439,plain,
spl0_836,
inference(avatar_split_clause,[],[f892,f7437]) ).
fof(f7437,plain,
( spl0_836
<=> ! [X24] :
( c_0 = X24
| ~ c_lessequals(X24,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f892,axiom,
! [X24] :
( c_0 = X24
| ~ c_lessequals(X24,c_0,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__0__eq_0) ).
fof(f7435,plain,
spl0_835,
inference(avatar_split_clause,[],[f890,f7433]) ).
fof(f7433,plain,
( spl0_835
<=> ! [X25,X10] : c_lessequals(c_minus(X25,X10,tc_nat),X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f890,axiom,
! [X10,X25] : c_lessequals(c_minus(X25,X10,tc_nat),X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__le__self_0) ).
fof(f7431,plain,
spl0_834,
inference(avatar_split_clause,[],[f662,f7429]) ).
fof(f662,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_0 = c_NatArith_Oof__nat(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__eq__0__iff_1) ).
fof(f7427,plain,
spl0_833,
inference(avatar_split_clause,[],[f658,f7425]) ).
fof(f658,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_1 = c_NatArith_Oof__nat(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatArith_Oof__nat__1_0) ).
fof(f7423,plain,
spl0_832,
inference(avatar_split_clause,[],[f640,f7421]) ).
fof(f7421,plain,
( spl0_832
<=> ! [X17,X3,X42] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X42,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f640,axiom,
! [X3,X17,X42] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X42,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip__Nil_0) ).
fof(f7419,plain,
spl0_831,
inference(avatar_split_clause,[],[f638,f7417]) ).
fof(f7417,plain,
( spl0_831
<=> ! [X13,X41,X76] : c_List_Olist_ONil = c_List_Ozip(X41,c_List_Olist_ONil,X13,X76) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f638,axiom,
! [X41,X76,X13] : c_List_Olist_ONil = c_List_Ozip(X41,c_List_Olist_ONil,X13,X76),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ozip_Osimps__1_0) ).
fof(f7415,plain,
spl0_830,
inference(avatar_split_clause,[],[f582,f7413]) ).
fof(f7413,plain,
( spl0_830
<=> ! [X8,X3] : c_List_Orev(c_List_Orev(X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f582,axiom,
! [X3,X8] : c_List_Orev(c_List_Orev(X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orev__rev__ident_0) ).
fof(f7411,plain,
spl0_829,
inference(avatar_split_clause,[],[f561,f7409]) ).
fof(f7409,plain,
( spl0_829
<=> ! [X11,X3,X42] : c_List_Oop_Amem(X11,c_List_Olist_OCons(X11,X42,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f561,axiom,
! [X3,X11,X42] : c_List_Oop_Amem(X11,c_List_Olist_OCons(X11,X42,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f7407,plain,
spl0_828,
inference(avatar_split_clause,[],[f481,f7405]) ).
fof(f7405,plain,
( spl0_828
<=> ! [X13,X36,X24] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X24,X36,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f481,axiom,
! [X36,X24,X13] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X24,X36,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__update_Osimps__1_0) ).
fof(f7403,plain,
spl0_827,
inference(avatar_split_clause,[],[f392,f7401]) ).
fof(f7401,plain,
( spl0_827
<=> ! [X48,X47] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X47,X48),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f392,axiom,
! [X48,X47] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X47,X48),tc_List_Ochar),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ochar_Osize_0) ).
fof(f7399,plain,
spl0_826,
inference(avatar_split_clause,[],[f328,f7397]) ).
fof(f328,axiom,
! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_IntDef_Oint) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f7395,plain,
spl0_825,
inference(avatar_split_clause,[],[f251,f7393]) ).
fof(f251,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_1 = c_IntDef_Oof__int(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__1_0) ).
fof(f7391,plain,
spl0_824,
inference(avatar_split_clause,[],[f246,f7389]) ).
fof(f246,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| c_0 = c_IntDef_Oof__int(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oof__int__0__eq__iff_1) ).
fof(f7387,plain,
spl0_823,
inference(avatar_split_clause,[],[f237,f7385]) ).
fof(f237,axiom,
! [X10] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X10),tc_IntDef_Oint)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zminus__int_0) ).
fof(f7383,plain,
( ~ spl0_821
| ~ spl0_1
| spl0_822
| ~ spl0_111
| ~ spl0_810 ),
inference(avatar_split_clause,[],[f7334,f7331,f3715,f7380,f3169,f7376]) ).
fof(f7331,plain,
( spl0_810
<=> ! [X30] :
( ~ c_in(X30,v_A,t_a)
| c_in(c_Pair(v_L,X30,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(X30),X30,t_a,t_a),v_r,tc_prod(t_a,t_a)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f7334,plain,
( c_in(c_Pair(v_L,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(v_L,v_A,t_a)
| ~ c_in(v_x(v_L),v_S,t_a)
| ~ spl0_111
| ~ spl0_810 ),
inference(resolution,[],[f7332,f3716]) ).
fof(f7332,plain,
( ! [X30] :
( ~ c_in(c_Pair(v_x(X30),X30,t_a,t_a),v_r,tc_prod(t_a,t_a))
| c_in(c_Pair(v_L,X30,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(X30,v_A,t_a) )
| ~ spl0_810 ),
inference(avatar_component_clause,[],[f7331]) ).
fof(f7374,plain,
spl0_820,
inference(avatar_split_clause,[],[f223,f7372]) ).
fof(f7372,plain,
( spl0_820
<=> ! [X10] :
( c_0 = X10
| c_0 != c_IntDef_Oint(X10) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f223,axiom,
! [X10] :
( c_0 = X10
| c_0 != c_IntDef_Oint(X10) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f7370,plain,
spl0_819,
inference(avatar_split_clause,[],[f217,f7368]) ).
fof(f217,axiom,
! [X25] : c_IntDef_Oint(X25) = c_HOL_Oabs(c_IntDef_Oint(X25),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oabs__int__eq_0) ).
fof(f7366,plain,
spl0_818,
inference(avatar_split_clause,[],[f103,f7364]) ).
fof(f7364,plain,
( spl0_818
<=> ! [X29,X8,X3] : c_Extraction_Osumbool_Osumbool__rec(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f103,axiom,
! [X3,X29,X8] : c_Extraction_Osumbool_Osumbool__rec(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f7362,plain,
spl0_817,
inference(avatar_split_clause,[],[f102,f7360]) ).
fof(f7360,plain,
( spl0_817
<=> ! [X28,X8,X3] : c_Extraction_Osumbool_Osumbool__rec(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f102,axiom,
! [X28,X3,X8] : c_Extraction_Osumbool_Osumbool__rec(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f7358,plain,
spl0_816,
inference(avatar_split_clause,[],[f99,f7356]) ).
fof(f7356,plain,
( spl0_816
<=> ! [X29,X8,X3] : c_Extraction_Osumbool_Osumbool__case(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f99,axiom,
! [X3,X29,X8] : c_Extraction_Osumbool_Osumbool__case(X29,X8,c_Extraction_Osumbool_ORight,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f7354,plain,
spl0_815,
inference(avatar_split_clause,[],[f98,f7352]) ).
fof(f7352,plain,
( spl0_815
<=> ! [X28,X8,X3] : c_Extraction_Osumbool_Osumbool__case(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f98,axiom,
! [X28,X3,X8] : c_Extraction_Osumbool_Osumbool__case(X8,X28,c_Extraction_Osumbool_OLeft,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f7350,plain,
spl0_814,
inference(avatar_split_clause,[],[f75,f7348]) ).
fof(f7348,plain,
( spl0_814
<=> ! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f75,axiom,
! [X25] :
( c_0 = X25
| ~ c_Divides_Oop_Advd(c_0,X25,tc_nat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__left__iff_0) ).
fof(f7346,plain,
spl0_813,
inference(avatar_split_clause,[],[f65,f7344]) ).
fof(f65,axiom,
! [X10,X25] : c_lessequals(c_div(X25,X10,tc_nat),X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__le__dividend_0) ).
fof(f7342,plain,
spl0_812,
inference(avatar_split_clause,[],[f52,f7340]) ).
fof(f7340,plain,
( spl0_812
<=> ! [X18,X17,X3] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X18,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f52,axiom,
! [X3,X18,X17] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X18,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f7338,plain,
spl0_811,
inference(avatar_split_clause,[],[f31,f7336]) ).
fof(f7336,plain,
( spl0_811
<=> ! [X8,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X3),X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f31,axiom,
! [X3,X8] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X8,X3),X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Othe_Osimps_0) ).
fof(f7333,plain,
spl0_810,
inference(avatar_split_clause,[],[f2752,f7331]) ).
fof(f2752,axiom,
! [X30] :
( ~ c_in(X30,v_A,t_a)
| c_in(c_Pair(v_L,X30,t_a,t_a),v_r,tc_prod(t_a,t_a))
| ~ c_in(c_Pair(v_x(X30),X30,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f7329,plain,
spl0_809,
inference(avatar_split_clause,[],[f2989,f7327]) ).
fof(f2989,plain,
! [X8] : c_div(X8,c_1,tc_nat) = X8,
inference(forward_demodulation,[],[f2783,f2757]) ).
fof(f2783,plain,
! [X8] : c_div(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat) = X8,
inference(definition_unfolding,[],[f64,f1394]) ).
fof(f64,axiom,
! [X8] : c_div(X8,c_Suc(c_0),tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__1_0) ).
fof(f7325,plain,
spl0_808,
inference(avatar_split_clause,[],[f2987,f7322]) ).
fof(f7322,plain,
( spl0_808
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f2987,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2780,f2757]) ).
fof(f2780,plain,
c_times(c_1,c_1,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f914,f1394]) ).
fof(f914,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__eq__1__iff_2) ).
fof(f7320,plain,
spl0_807,
inference(avatar_split_clause,[],[f2985,f7318]) ).
fof(f7318,plain,
( spl0_807
<=> ! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f2985,plain,
! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_1,tc_nat),
inference(forward_demodulation,[],[f2779,f2757]) ).
fof(f2779,plain,
! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),tc_nat),
inference(definition_unfolding,[],[f81,f1394]) ).
fof(f81,axiom,
! [X25] : c_0 = c_Divides_Oop_Amod(X25,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__1_0) ).
fof(f7316,plain,
spl0_806,
inference(avatar_split_clause,[],[f2984,f7313]) ).
fof(f7313,plain,
( spl0_806
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f2984,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f717,f1006]) ).
fof(f717,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f7311,plain,
spl0_805,
inference(avatar_split_clause,[],[f2982,f7309]) ).
fof(f7309,plain,
( spl0_805
<=> ! [X13,X8] : c_append(c_List_Olist_ONil,X8,X13) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f2982,plain,
! [X8,X13] : c_append(c_List_Olist_ONil,X8,X13) = X8,
inference(forward_demodulation,[],[f2774,f364]) ).
fof(f364,axiom,
! [X3] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_ONil__is__rev__conv_1) ).
fof(f2774,plain,
! [X8,X13] : c_append(c_List_Orev(c_List_Olist_ONil,X13),X8,X13) = X8,
inference(definition_unfolding,[],[f436,f435]) ).
fof(f435,axiom,
! [X41,X3,X11] : c_List_Oitrev(X41,X11,X3) = c_append(c_List_Orev(X41,X3),X11,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_0) ).
fof(f436,axiom,
! [X8,X13] : c_List_Oitrev(c_List_Olist_ONil,X8,X13) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oitrev_Osimps__1_0) ).
fof(f7307,plain,
spl0_804,
inference(avatar_split_clause,[],[f2980,f7304]) ).
fof(f7304,plain,
( spl0_804
<=> c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f2980,plain,
c_Numeral_Obin__succ(c_Numeral_OPls) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(forward_demodulation,[],[f2771,f1006]) ).
fof(f2771,plain,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OMin),
inference(definition_unfolding,[],[f975,f979]) ).
fof(f975,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__minus__Min_0) ).
fof(f7302,plain,
spl0_803,
inference(avatar_split_clause,[],[f2746,f7299]) ).
fof(f7299,plain,
( spl0_803
<=> v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f2746,axiom,
v_r = c_Tarski_Opotype_Oorder(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Or_A_61_61_Aorder_Acl_0) ).
fof(f7297,plain,
spl0_802,
inference(avatar_split_clause,[],[f2745,f7294]) ).
fof(f7294,plain,
( spl0_802
<=> c_in(v_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f2745,axiom,
c_in(v_cl,c_Tarski_OCompleteLattice,tc_Tarski_Opotype_Opotype__ext__type(t_a,tc_Product__Type_Ounit)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_Ocl_A_58_ACompleteLattice_A_61_61_ATrue_0) ).
fof(f7292,plain,
spl0_801,
inference(avatar_split_clause,[],[f2737,f7289]) ).
fof(f7289,plain,
( spl0_801
<=> v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f2737,axiom,
v_A = c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Tarski_OA_A_61_61_Apset_Acl_0) ).
fof(f7287,plain,
spl0_800,
inference(avatar_split_clause,[],[f1645,f7285]) ).
fof(f7285,plain,
( spl0_800
<=> ! [X11,X3] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X11,X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f1645,axiom,
! [X3,X11] :
( ~ class_Orderings_Oorder(X3)
| c_lessequals(X11,X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f7283,plain,
spl0_799,
inference(avatar_split_clause,[],[f1537,f7281]) ).
fof(f1537,axiom,
! [X3,X27,X15] : c_emptyset != c_insert(X15,X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__not__empty_0) ).
fof(f7279,plain,
spl0_798,
inference(avatar_split_clause,[],[f1489,f7277]) ).
fof(f7277,plain,
( spl0_798
<=> ! [X8,X3] : c_union(X8,c_emptyset,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f1489,axiom,
! [X3,X8] : c_union(X8,c_emptyset,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__right_0) ).
fof(f7275,plain,
spl0_797,
inference(avatar_split_clause,[],[f1488,f7273]) ).
fof(f1488,axiom,
! [X3,X8] : c_union(c_emptyset,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__empty__left_0) ).
fof(f7271,plain,
spl0_796,
inference(avatar_split_clause,[],[f1484,f7269]) ).
fof(f7269,plain,
( spl0_796
<=> ! [X8,X3] : c_union(X8,X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f1484,axiom,
! [X3,X8] : c_union(X8,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__absorb_0) ).
fof(f7267,plain,
spl0_795,
inference(avatar_split_clause,[],[f1483,f7265]) ).
fof(f7265,plain,
( spl0_795
<=> ! [X27,X3] : c_UNIV = c_union(X27,c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f1483,axiom,
! [X3,X27] : c_UNIV = c_union(X27,c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__right_0) ).
fof(f7263,plain,
spl0_794,
inference(avatar_split_clause,[],[f1482,f7261]) ).
fof(f7261,plain,
( spl0_794
<=> ! [X3,X31] : c_UNIV = c_union(c_UNIV,X31,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f1482,axiom,
! [X31,X3] : c_UNIV = c_union(c_UNIV,X31,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__UNIV__left_0) ).
fof(f7259,plain,
spl0_793,
inference(avatar_split_clause,[],[f1430,f7257]) ).
fof(f7257,plain,
( spl0_793
<=> ! [X3] : c_UNIV = c_uminus(c_emptyset,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f1430,axiom,
! [X3] : c_UNIV = c_uminus(c_emptyset,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__empty__eq_0) ).
fof(f7255,plain,
spl0_792,
inference(avatar_split_clause,[],[f1426,f7253]) ).
fof(f7253,plain,
( spl0_792
<=> ! [X3] : c_emptyset = c_uminus(c_UNIV,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f1426,axiom,
! [X3] : c_emptyset = c_uminus(c_UNIV,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OCompl__UNIV__eq_0) ).
fof(f7251,plain,
spl0_791,
inference(avatar_split_clause,[],[f1361,f7249]) ).
fof(f7249,plain,
( spl0_791
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f1361,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_lessequals(c_0,c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f7247,plain,
spl0_790,
inference(avatar_split_clause,[],[f1349,f7245]) ).
fof(f7245,plain,
( spl0_790
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f1349,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| c_less(c_0,c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f7243,plain,
spl0_789,
inference(avatar_split_clause,[],[f1344,f7241]) ).
fof(f7241,plain,
( spl0_789
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f1344,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_less(c_1,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f7239,plain,
spl0_788,
inference(avatar_split_clause,[],[f1343,f7237]) ).
fof(f7237,plain,
( spl0_788
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_1,c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f1343,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__semidom(X3)
| ~ c_lessequals(c_1,c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f7235,plain,
spl0_787,
inference(avatar_split_clause,[],[f1231,f7233]) ).
fof(f7233,plain,
( spl0_787
<=> ! [X3] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f1231,axiom,
! [X3] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_Oconverse__Id_0) ).
fof(f7231,plain,
spl0_786,
inference(avatar_split_clause,[],[f1230,f7229]) ).
fof(f7229,plain,
( spl0_786
<=> ! [X17,X3] : c_emptyset = c_Relation_ORange(c_emptyset,X17,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f1230,axiom,
! [X3,X17] : c_emptyset = c_Relation_ORange(c_emptyset,X17,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__empty_0) ).
fof(f7227,plain,
spl0_785,
inference(avatar_split_clause,[],[f1228,f7225]) ).
fof(f7225,plain,
( spl0_785
<=> ! [X3] : c_UNIV = c_Relation_ORange(c_Relation_OId,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f1228,axiom,
! [X3] : c_UNIV = c_Relation_ORange(c_Relation_OId,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ORange__Id_0) ).
fof(f7223,plain,
spl0_784,
inference(avatar_split_clause,[],[f1220,f7221]) ).
fof(f7221,plain,
( spl0_784
<=> ! [X17,X3] : c_emptyset = c_Relation_ODomain(c_emptyset,X3,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f1220,axiom,
! [X3,X17] : c_emptyset = c_Relation_ODomain(c_emptyset,X3,X17),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__empty_0) ).
fof(f7219,plain,
spl0_783,
inference(avatar_split_clause,[],[f1218,f7217]) ).
fof(f7217,plain,
( spl0_783
<=> ! [X3] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X3,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f1218,axiom,
! [X3] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X3,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Relation_ODomain__Id_0) ).
fof(f7215,plain,
spl0_782,
inference(avatar_split_clause,[],[f1194,f7213]) ).
fof(f1194,axiom,
! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Power_Opower_Osimps__1_0) ).
fof(f7211,plain,
spl0_781,
inference(avatar_split_clause,[],[f1119,f7209]) ).
fof(f7209,plain,
( spl0_781
<=> ! [X11,X3] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X11,X11,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f1119,axiom,
! [X3,X11] :
( ~ class_Orderings_Oorder(X3)
| ~ c_less(X11,X11,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f7207,plain,
spl0_780,
inference(avatar_split_clause,[],[f1006,f7204]) ).
fof(f7202,plain,
spl0_779,
inference(avatar_split_clause,[],[f952,f7200]) ).
fof(f7200,plain,
( spl0_779
<=> ! [X8] : c_minus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f952,axiom,
! [X8] : c_minus(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f7198,plain,
spl0_778,
inference(avatar_split_clause,[],[f950,f7196]) ).
fof(f7196,plain,
( spl0_778
<=> ! [X8] : c_plus(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f950,axiom,
! [X8] : c_plus(c_0,X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f7194,plain,
spl0_777,
inference(avatar_split_clause,[],[f948,f7192]) ).
fof(f7192,plain,
( spl0_777
<=> ! [X10] : c_0 = c_times(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f948,axiom,
! [X10] : c_0 = c_times(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f7190,plain,
spl0_776,
inference(avatar_split_clause,[],[f906,f7188]) ).
fof(f7188,plain,
( spl0_776
<=> ! [X25] : c_0 = c_times(X25,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f906,axiom,
! [X25] : c_0 = c_times(X25,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omult__0__right_0) ).
fof(f7186,plain,
spl0_775,
inference(avatar_split_clause,[],[f904,f7184]) ).
fof(f7184,plain,
( spl0_775
<=> ! [X10] : c_0 = c_Orderings_Omin(X10,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f904,axiom,
! [X10] : c_0 = c_Orderings_Omin(X10,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0R_0) ).
fof(f7182,plain,
spl0_774,
inference(avatar_split_clause,[],[f903,f7180]) ).
fof(f7180,plain,
( spl0_774
<=> ! [X10] : c_0 = c_Orderings_Omin(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f903,axiom,
! [X10] : c_0 = c_Orderings_Omin(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omin__0L_0) ).
fof(f7178,plain,
spl0_773,
inference(avatar_split_clause,[],[f901,f7176]) ).
fof(f7176,plain,
( spl0_773
<=> ! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f901,axiom,
! [X8] : c_Orderings_Omax(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0R_0) ).
fof(f7174,plain,
spl0_772,
inference(avatar_split_clause,[],[f900,f7172]) ).
fof(f7172,plain,
( spl0_772
<=> ! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f900,axiom,
! [X8] : c_Orderings_Omax(c_0,X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Omax__0L_0) ).
fof(f7170,plain,
spl0_771,
inference(avatar_split_clause,[],[f891,f7168]) ).
fof(f7168,plain,
( spl0_771
<=> ! [X25] : c_0 = c_minus(X25,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f891,axiom,
! [X25] : c_0 = c_minus(X25,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
fof(f7166,plain,
spl0_770,
inference(avatar_split_clause,[],[f884,f7164]) ).
fof(f884,axiom,
! [X10] : c_0 = c_minus(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Odiff__0__eq__0_0) ).
fof(f7162,plain,
spl0_769,
inference(avatar_split_clause,[],[f876,f7160]) ).
fof(f7160,plain,
( spl0_769
<=> ! [X8] : c_plus(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f876,axiom,
! [X8] : c_plus(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).
fof(f7158,plain,
spl0_768,
inference(avatar_split_clause,[],[f637,f7156]) ).
fof(f7156,plain,
( spl0_768
<=> ! [X11,X75,X3] : c_List_Olist_OCons(X11,X75,X3) != X75 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f637,axiom,
! [X3,X11,X75] : c_List_Olist_OCons(X11,X75,X3) != X75,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Ox2_A_D_At1_A_61_At1_A_61_61_AFalse_0) ).
fof(f7154,plain,
spl0_767,
inference(avatar_split_clause,[],[f613,f7152]) ).
fof(f7152,plain,
( spl0_767
<=> ! [X27,X3] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X27,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f613,axiom,
! [X3,X27] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X27,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__nil_0) ).
fof(f7150,plain,
spl0_766,
inference(avatar_split_clause,[],[f612,f7148]) ).
fof(f7148,plain,
( spl0_766
<=> ! [X41,X3] : c_List_Olist_ONil = c_List_Osublist(X41,c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f612,axiom,
! [X41,X3] : c_List_Olist_ONil = c_List_Osublist(X41,c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Osublist__empty_0) ).
fof(f7146,plain,
spl0_765,
inference(avatar_split_clause,[],[f591,f7144]) ).
fof(f7144,plain,
( spl0_765
<=> ! [X3,X10] : c_List_Olist_ONil = c_List_Orotate(X10,c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f591,axiom,
! [X3,X10] : c_List_Olist_ONil = c_List_Orotate(X10,c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate__is__Nil__conv_1) ).
fof(f7142,plain,
spl0_764,
inference(avatar_split_clause,[],[f572,f7140]) ).
fof(f7140,plain,
( spl0_764
<=> ! [X13,X11] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X11,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f572,axiom,
! [X11,X13] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X11,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f7138,plain,
spl0_763,
inference(avatar_split_clause,[],[f569,f7136]) ).
fof(f7136,plain,
( spl0_763
<=> ! [X13,X11] : c_List_Olist_ONil = c_List_Oremove1(X11,c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f569,axiom,
! [X11,X13] : c_List_Olist_ONil = c_List_Oremove1(X11,c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremove1_Osimps__1_0) ).
fof(f7134,plain,
spl0_762,
inference(avatar_split_clause,[],[f557,f7132]) ).
fof(f7132,plain,
( spl0_762
<=> ! [X13,X41,X11] : ~ c_List_Onull(c_List_Olist_OCons(X11,X41,X13),X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f557,axiom,
! [X41,X11,X13] : ~ c_List_Onull(c_List_Olist_OCons(X11,X41,X13),X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__2_0) ).
fof(f7130,plain,
spl0_761,
inference(avatar_split_clause,[],[f478,f7128]) ).
fof(f7128,plain,
( spl0_761
<=> ! [X13,X58] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X58,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f478,axiom,
! [X58,X13] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X58,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist__inter_Osimps__1_0) ).
fof(f7126,plain,
spl0_760,
inference(avatar_split_clause,[],[f474,f7124]) ).
fof(f7124,plain,
( spl0_760
<=> ! [X56,X3,X14] : c_List_Olist_ONil != c_List_Olist_OCons(X14,X56,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f474,axiom,
! [X3,X56,X14] : c_List_Olist_ONil != c_List_Olist_OCons(X14,X56,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__2_0) ).
fof(f7122,plain,
spl0_759,
inference(avatar_split_clause,[],[f465,f7120]) ).
fof(f7120,plain,
( spl0_759
<=> ! [X13,X20] : c_emptyset = c_List_Olexn(X20,c_0,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f465,axiom,
! [X13,X20] : c_emptyset = c_List_Olexn(X20,c_0,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olexn_Osimps__1_0) ).
fof(f7118,plain,
spl0_758,
inference(avatar_split_clause,[],[f448,f7116]) ).
fof(f7116,plain,
( spl0_758
<=> ! [X3] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f448,axiom,
! [X3] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olength__0__conv_1) ).
fof(f7114,plain,
spl0_757,
inference(avatar_split_clause,[],[f419,f7112]) ).
fof(f7112,plain,
( spl0_757
<=> ! [X8,X3] : c_List_Odrop(c_0,X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f419,axiom,
! [X3,X8] : c_List_Odrop(c_0,X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop__0_0) ).
fof(f7110,plain,
spl0_756,
inference(avatar_split_clause,[],[f418,f7108]) ).
fof(f7108,plain,
( spl0_756
<=> ! [X13,X10] : c_List_Olist_ONil = c_List_Odrop(X10,c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f418,axiom,
! [X10,X13] : c_List_Olist_ONil = c_List_Odrop(X10,c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odrop_Odrop__Nil_0) ).
fof(f7106,plain,
spl0_755,
inference(avatar_split_clause,[],[f384,f7104]) ).
fof(f7104,plain,
( spl0_755
<=> ! [X41,X3] : c_append(X41,c_List_Olist_ONil,X3) = X41 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f384,axiom,
! [X41,X3] : c_append(X41,c_List_Olist_ONil,X3) = X41,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oappend__self__conv_1) ).
fof(f7102,plain,
spl0_754,
inference(avatar_split_clause,[],[f344,f7100]) ).
fof(f7100,plain,
( spl0_754
<=> ! [X16] : c_0 = c_Divides_Oop_Amod(c_0,X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f344,axiom,
! [X16] : c_0 = c_Divides_Oop_Amod(c_0,X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__zero_0) ).
fof(f7098,plain,
spl0_753,
inference(avatar_split_clause,[],[f341,f7096]) ).
fof(f7096,plain,
( spl0_753
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f341,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__self_0) ).
fof(f7094,plain,
spl0_752,
inference(avatar_split_clause,[],[f339,f7092]) ).
fof(f7092,plain,
( spl0_752
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f339,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozmod__1_0) ).
fof(f7090,plain,
spl0_751,
inference(avatar_split_clause,[],[f324,f7088]) ).
fof(f7088,plain,
( spl0_751
<=> ! [X16] : c_0 = c_div(c_0,X16,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f324,axiom,
! [X16] : c_0 = c_div(c_0,X16,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__zero_0) ).
fof(f7086,plain,
spl0_750,
inference(avatar_split_clause,[],[f316,f7084]) ).
fof(f7084,plain,
( spl0_750
<=> ! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f316,axiom,
! [X8] : c_div(X8,c_1,tc_IntDef_Oint) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdiv__1_0) ).
fof(f7082,plain,
spl0_749,
inference(avatar_split_clause,[],[f314,f7080]) ).
fof(f7080,plain,
( spl0_749
<=> ! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f314,axiom,
! [X40] : c_1 = c_Nat_Opower(X40,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f7078,plain,
spl0_748,
inference(avatar_split_clause,[],[f282,f7076]) ).
fof(f282,axiom,
! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_IntDef_Oint) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f7074,plain,
spl0_747,
inference(avatar_split_clause,[],[f214,f7072]) ).
fof(f7072,plain,
( spl0_747
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_1,c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f214,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_1,c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__1_0) ).
fof(f7070,plain,
spl0_746,
inference(avatar_split_clause,[],[f213,f7068]) ).
fof(f7068,plain,
( spl0_746
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_0,c_IntDef_ONats,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f213,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| c_in(c_0,c_IntDef_ONats,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_ONats__0_0) ).
fof(f7066,plain,
spl0_745,
inference(avatar_split_clause,[],[f208,f7064]) ).
fof(f7064,plain,
( spl0_745
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_1,c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f208,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_1,c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__1_0) ).
fof(f7062,plain,
spl0_744,
inference(avatar_split_clause,[],[f207,f7060]) ).
fof(f7060,plain,
( spl0_744
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_0,c_IntDef_OInts,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f207,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X3)
| c_in(c_0,c_IntDef_OInts,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_OInts__0_0) ).
fof(f7058,plain,
spl0_743,
inference(avatar_split_clause,[],[f200,f7055]) ).
fof(f7055,plain,
( spl0_743
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f200,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f7053,plain,
spl0_742,
inference(avatar_split_clause,[],[f97,f7051]) ).
fof(f7051,plain,
( spl0_742
<=> ! [X20,X3] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X20,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f97,axiom,
! [X3,X20] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X20,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Equiv__Relations_Oquotient__is__empty_1) ).
fof(f7049,plain,
spl0_741,
inference(avatar_split_clause,[],[f91,f7047]) ).
fof(f7047,plain,
( spl0_741
<=> ! [X10] : c_0 = c_Divides_Oop_Amod(X10,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f91,axiom,
! [X10] : c_0 = c_Divides_Oop_Amod(X10,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__self_0) ).
fof(f7045,plain,
spl0_740,
inference(avatar_split_clause,[],[f80,f7043]) ).
fof(f7043,plain,
( spl0_740
<=> ! [X25] : c_0 = c_Divides_Oop_Amod(c_0,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f80,axiom,
! [X25] : c_0 = c_Divides_Oop_Amod(c_0,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Omod__0_0) ).
fof(f7041,plain,
spl0_739,
inference(avatar_split_clause,[],[f63,f7039]) ).
fof(f7039,plain,
( spl0_739
<=> ! [X25] : c_0 = c_div(c_0,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f63,axiom,
! [X25] : c_0 = c_div(c_0,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odiv__0_0) ).
fof(f7037,plain,
spl0_738,
inference(avatar_split_clause,[],[f62,f7035]) ).
fof(f7035,plain,
( spl0_738
<=> ! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f62,axiom,
! [X8] : c_Divides_Oop_Amod(X8,c_0,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f7033,plain,
spl0_737,
inference(avatar_split_clause,[],[f61,f7031]) ).
fof(f7031,plain,
( spl0_737
<=> ! [X15] : c_0 = c_div(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f61,axiom,
! [X15] : c_0 = c_div(X15,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f7029,plain,
spl0_736,
inference(avatar_split_clause,[],[f33,f7027]) ).
fof(f7027,plain,
( spl0_736
<=> ! [X8,X3] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f33,axiom,
! [X3,X8] : c_Datatype_Ounit_Ounit__rec(X8,c_Product__Type_OUnity,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Orecs_0) ).
fof(f7025,plain,
spl0_735,
inference(avatar_split_clause,[],[f32,f7023]) ).
fof(f7023,plain,
( spl0_735
<=> ! [X8,X3] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f32,axiom,
! [X3,X8] : c_Datatype_Ounit_Ounit__case(X8,c_Product__Type_OUnity,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Ocases_0) ).
fof(f7021,plain,
spl0_734,
inference(avatar_split_clause,[],[f26,f7019]) ).
fof(f7019,plain,
( spl0_734
<=> ! [X3] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f26,axiom,
! [X3] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Osize__1_0) ).
fof(f7016,plain,
( spl0_733
| ~ spl0_113
| ~ spl0_673 ),
inference(avatar_split_clause,[],[f6999,f6739,f3723,f7013]) ).
fof(f7013,plain,
( spl0_733
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f6739,plain,
( spl0_673
<=> ! [X10] : c_lessequals(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f6999,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_673 ),
inference(superposition,[],[f6740,f3725]) ).
fof(f6740,plain,
( ! [X10] : c_lessequals(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ spl0_673 ),
inference(avatar_component_clause,[],[f6739]) ).
fof(f7010,plain,
( ~ spl0_732
| ~ spl0_114
| ~ spl0_671 ),
inference(avatar_split_clause,[],[f6996,f6731,f3728,f7007]) ).
fof(f7007,plain,
( spl0_732
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f6731,plain,
( spl0_671
<=> ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f6996,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_114
| ~ spl0_671 ),
inference(superposition,[],[f6732,f3730]) ).
fof(f6732,plain,
( ! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint)
| ~ spl0_671 ),
inference(avatar_component_clause,[],[f6731]) ).
fof(f7005,plain,
( ~ spl0_731
| ~ spl0_113
| ~ spl0_671 ),
inference(avatar_split_clause,[],[f6995,f6731,f3723,f7002]) ).
fof(f7002,plain,
( spl0_731
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f6995,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_671 ),
inference(superposition,[],[f6732,f3725]) ).
fof(f6994,plain,
spl0_730,
inference(avatar_split_clause,[],[f2986,f6991]) ).
fof(f6991,plain,
( spl0_730
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f2986,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f241,f224]) ).
fof(f224,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f241,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onegative__eq__positive_2) ).
fof(f6989,plain,
spl0_729,
inference(avatar_split_clause,[],[f2981,f6987]) ).
fof(f6987,plain,
( spl0_729
<=> ! [X8] : c_Binomial_Obinomial(X8,c_1) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f2981,plain,
! [X8] : c_Binomial_Obinomial(X8,c_1) = X8,
inference(forward_demodulation,[],[f2773,f2757]) ).
fof(f2773,plain,
! [X8] : c_Binomial_Obinomial(X8,c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)) = X8,
inference(definition_unfolding,[],[f11,f1394]) ).
fof(f11,axiom,
! [X8] : c_Binomial_Obinomial(X8,c_Suc(c_0)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
fof(f6985,plain,
spl0_728,
inference(avatar_split_clause,[],[f2756,f6982]) ).
fof(f6982,plain,
( spl0_728
<=> c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OMin,c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f6980,plain,
spl0_727,
inference(avatar_split_clause,[],[f1827,f6978]) ).
fof(f6978,plain,
( spl0_727
<=> ! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_set(X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f1827,axiom,
! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_set(X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_3) ).
fof(f6976,plain,
spl0_726,
inference(avatar_split_clause,[],[f1705,f6974]) ).
fof(f6974,plain,
( spl0_726
<=> ! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X90)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f1705,axiom,
! [X90] :
( ~ class_Finite__Set_Ofinite(X90)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X90)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Datatype__Ooption_0) ).
fof(f6972,plain,
spl0_725,
inference(avatar_split_clause,[],[f1689,f6970]) ).
fof(f6970,plain,
( spl0_725
<=> ! [X27,X3] : c_lessequals(X27,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f1689,axiom,
! [X3,X27] : c_lessequals(X27,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f6968,plain,
spl0_724,
inference(avatar_split_clause,[],[f1678,f6966]) ).
fof(f6966,plain,
( spl0_724
<=> ! [X27,X3] : c_lessequals(c_emptyset,X27,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f1678,axiom,
! [X3,X27] : c_lessequals(c_emptyset,X27,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__subsetI_0) ).
fof(f6964,plain,
spl0_723,
inference(avatar_split_clause,[],[f1621,f6962]) ).
fof(f6962,plain,
( spl0_723
<=> ! [X41,X3] : c_List_Odistinct(c_List_Oremdups(X41,X3),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f1621,axiom,
! [X41,X3] : c_List_Odistinct(c_List_Oremdups(X41,X3),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__remdups_0) ).
fof(f6960,plain,
spl0_722,
inference(avatar_split_clause,[],[f1605,f6958]) ).
fof(f6958,plain,
( spl0_722
<=> ! [X3] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f1605,axiom,
! [X3] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f6956,plain,
spl0_721,
inference(avatar_split_clause,[],[f1564,f6954]) ).
fof(f6954,plain,
( spl0_721
<=> ! [X3] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f1564,axiom,
! [X3] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f6952,plain,
spl0_720,
inference(avatar_split_clause,[],[f1548,f6950]) ).
fof(f6950,plain,
( spl0_720
<=> ! [X27,X3] : c_lessequals(X27,c_UNIV,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f1548,axiom,
! [X3,X27] : c_lessequals(X27,c_UNIV,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__UNIV_0) ).
fof(f6948,plain,
spl0_719,
inference(avatar_split_clause,[],[f1541,f6946]) ).
fof(f6946,plain,
( spl0_719
<=> ! [X27,X3] : ~ c_less(X27,c_emptyset,tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f1541,axiom,
! [X3,X27] : ~ c_less(X27,c_emptyset,tc_set(X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Onot__psubset__empty_0) ).
fof(f6944,plain,
spl0_718,
inference(avatar_split_clause,[],[f1501,f6942]) ).
fof(f6942,plain,
( spl0_718
<=> ! [X3] : c_emptyset = c_Union(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f1501,axiom,
! [X3] : c_emptyset = c_Union(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__empty_0) ).
fof(f6940,plain,
spl0_717,
inference(avatar_split_clause,[],[f1499,f6938]) ).
fof(f6938,plain,
( spl0_717
<=> ! [X3] : c_UNIV = c_Union(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f1499,axiom,
! [X3] : c_UNIV = c_Union(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__UNIV_0) ).
fof(f6936,plain,
spl0_716,
inference(avatar_split_clause,[],[f1475,f6934]) ).
fof(f6934,plain,
( spl0_716
<=> ! [X3] : c_UNIV = c_Pow(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f1475,axiom,
! [X3] : c_UNIV = c_Pow(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OPow__UNIV_0) ).
fof(f6932,plain,
spl0_715,
inference(avatar_split_clause,[],[f1469,f6930]) ).
fof(f6930,plain,
( spl0_715
<=> ! [X3] : c_UNIV = c_Inter(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f1469,axiom,
! [X3] : c_UNIV = c_Inter(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__empty_0) ).
fof(f6928,plain,
spl0_714,
inference(avatar_split_clause,[],[f1462,f6926]) ).
fof(f6926,plain,
( spl0_714
<=> ! [X3] : c_emptyset = c_Inter(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f1462,axiom,
! [X3] : c_emptyset = c_Inter(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInter__UNIV_0) ).
fof(f6924,plain,
spl0_713,
inference(avatar_split_clause,[],[f1417,f6921]) ).
fof(f6921,plain,
( spl0_713
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f1417,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OlessThan__0_0) ).
fof(f6919,plain,
spl0_712,
inference(avatar_split_clause,[],[f1378,f6916]) ).
fof(f6916,plain,
( spl0_712
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f1378,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeast__0_0) ).
fof(f6914,plain,
spl0_711,
inference(avatar_split_clause,[],[f1236,f6912]) ).
fof(f6910,plain,
spl0_710,
inference(avatar_split_clause,[],[f1014,f6907]) ).
fof(f6907,plain,
( spl0_710
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f1014,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__2_0) ).
fof(f6905,plain,
spl0_709,
inference(avatar_split_clause,[],[f1013,f6902]) ).
fof(f6902,plain,
( spl0_709
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f1013,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Osize__1_0) ).
fof(f6900,plain,
spl0_708,
inference(avatar_split_clause,[],[f1002,f6898]) ).
fof(f6898,plain,
( spl0_708
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f1002,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f6896,plain,
spl0_707,
inference(avatar_split_clause,[],[f1001,f6894]) ).
fof(f6894,plain,
( spl0_707
<=> ! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_0,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f1001,axiom,
! [X3] :
( ~ class_Ring__and__Field_Oordered__idom(X3)
| ~ c_IntDef_Oneg(c_0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f6892,plain,
spl0_706,
inference(avatar_split_clause,[],[f985,f6890]) ).
fof(f6890,plain,
( spl0_706
<=> ! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_IntDef_Oiszero(c_1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f985,axiom,
! [X3] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X3)
| ~ c_IntDef_Oiszero(c_1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f6888,plain,
spl0_705,
inference(avatar_split_clause,[],[f980,f6886]) ).
fof(f6886,plain,
( spl0_705
<=> ! [X35] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X35) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f980,axiom,
! [X35] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X35),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__mult__Pls_0) ).
fof(f6884,plain,
spl0_704,
inference(avatar_split_clause,[],[f965,f6882]) ).
fof(f6882,plain,
( spl0_704
<=> ! [X8] : c_Numeral_Obin__add(X8,c_Numeral_OPls) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f6880,plain,
spl0_703,
inference(avatar_split_clause,[],[f964,f6878]) ).
fof(f6878,plain,
( spl0_703
<=> ! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f964,axiom,
! [X8] : c_Numeral_Obin__add(c_Numeral_OPls,X8) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obin__add__Pls_0) ).
fof(f6876,plain,
spl0_702,
inference(avatar_split_clause,[],[f956,f6873]) ).
fof(f956,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OPls__0__eq_0) ).
fof(f6871,plain,
spl0_701,
inference(avatar_split_clause,[],[f955,f6868]) ).
fof(f955,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_OMin__1__eq_0) ).
fof(f6866,plain,
spl0_700,
inference(avatar_split_clause,[],[f716,f6863]) ).
fof(f716,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f6861,plain,
spl0_699,
inference(avatar_split_clause,[],[f635,f6859]) ).
fof(f6859,plain,
( spl0_699
<=> ! [X24] : c_List_Olist_ONil = c_List_Oupt(X24,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f635,axiom,
! [X24] : c_List_Olist_ONil = c_List_Oupt(X24,c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f6857,plain,
spl0_698,
inference(avatar_split_clause,[],[f628,f6855]) ).
fof(f6855,plain,
( spl0_698
<=> ! [X13] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f628,axiom,
! [X13] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Otl_Osimps__1_0) ).
fof(f6853,plain,
spl0_697,
inference(avatar_split_clause,[],[f603,f6851]) ).
fof(f6851,plain,
( spl0_697
<=> ! [X3] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f603,axiom,
! [X3] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oset__empty_1) ).
fof(f6849,plain,
spl0_696,
inference(avatar_split_clause,[],[f586,f6847]) ).
fof(f6847,plain,
( spl0_696
<=> ! [X3] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f586,axiom,
! [X3] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f6845,plain,
spl0_695,
inference(avatar_split_clause,[],[f566,f6843]) ).
fof(f6843,plain,
( spl0_695
<=> ! [X3] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f566,axiom,
! [X3] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oremdups__eq__nil__iff_1) ).
fof(f6841,plain,
spl0_694,
inference(avatar_split_clause,[],[f538,f6838]) ).
fof(f6838,plain,
( spl0_694
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f538,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__9_0) ).
fof(f6836,plain,
spl0_693,
inference(avatar_split_clause,[],[f537,f6833]) ).
fof(f6833,plain,
( spl0_693
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f537,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__8_0) ).
fof(f6831,plain,
spl0_692,
inference(avatar_split_clause,[],[f536,f6828]) ).
fof(f6828,plain,
( spl0_692
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f536,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__7_0) ).
fof(f6826,plain,
spl0_691,
inference(avatar_split_clause,[],[f535,f6823]) ).
fof(f6823,plain,
( spl0_691
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f535,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__6_0) ).
fof(f6821,plain,
spl0_690,
inference(avatar_split_clause,[],[f534,f6818]) ).
fof(f6818,plain,
( spl0_690
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f534,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__5_0) ).
fof(f6816,plain,
spl0_689,
inference(avatar_split_clause,[],[f533,f6813]) ).
fof(f6813,plain,
( spl0_689
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f533,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__4_0) ).
fof(f6811,plain,
spl0_688,
inference(avatar_split_clause,[],[f532,f6808]) ).
fof(f6808,plain,
( spl0_688
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f532,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__3_0) ).
fof(f6806,plain,
spl0_687,
inference(avatar_split_clause,[],[f531,f6803]) ).
fof(f6803,plain,
( spl0_687
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f531,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__2_0) ).
fof(f6801,plain,
spl0_686,
inference(avatar_split_clause,[],[f530,f6798]) ).
fof(f6798,plain,
( spl0_686
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f530,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__1_0) ).
fof(f6796,plain,
spl0_685,
inference(avatar_split_clause,[],[f529,f6793]) ).
fof(f6793,plain,
( spl0_685
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f529,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__16_0) ).
fof(f6791,plain,
spl0_684,
inference(avatar_split_clause,[],[f528,f6788]) ).
fof(f6788,plain,
( spl0_684
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f528,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__15_0) ).
fof(f6786,plain,
spl0_683,
inference(avatar_split_clause,[],[f527,f6783]) ).
fof(f6783,plain,
( spl0_683
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f527,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__14_0) ).
fof(f6781,plain,
spl0_682,
inference(avatar_split_clause,[],[f526,f6778]) ).
fof(f6778,plain,
( spl0_682
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f526,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__13_0) ).
fof(f6776,plain,
spl0_681,
inference(avatar_split_clause,[],[f525,f6773]) ).
fof(f6773,plain,
( spl0_681
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f525,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__12_0) ).
fof(f6771,plain,
spl0_680,
inference(avatar_split_clause,[],[f524,f6768]) ).
fof(f6768,plain,
( spl0_680
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f524,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__11_0) ).
fof(f6766,plain,
spl0_679,
inference(avatar_split_clause,[],[f523,f6763]) ).
fof(f6763,plain,
( spl0_679
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f523,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onibble_Osize__10_0) ).
fof(f6761,plain,
spl0_678,
inference(avatar_split_clause,[],[f488,f6759]) ).
fof(f6759,plain,
( spl0_678
<=> ! [X3] : c_UNIV = c_List_Olists(c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f488,axiom,
! [X3] : c_UNIV = c_List_Olists(c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olists__UNIV_0) ).
fof(f6757,plain,
spl0_677,
inference(avatar_split_clause,[],[f417,f6755]) ).
fof(f6755,plain,
( spl0_677
<=> ! [X52,X24] : c_List_Odistinct(c_List_Oupt(X24,X52),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f417,axiom,
! [X52,X24] : c_List_Odistinct(c_List_Oupt(X24,X52),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct__upt_0) ).
fof(f6753,plain,
spl0_676,
inference(avatar_split_clause,[],[f393,f6751]) ).
fof(f6751,plain,
( spl0_676
<=> ! [X13] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f393,axiom,
! [X13] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oconcat_Osimps__1_0) ).
fof(f6749,plain,
spl0_675,
inference(avatar_split_clause,[],[f386,f6747]) ).
fof(f6747,plain,
( spl0_675
<=> ! [X13] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f386,axiom,
! [X13] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Obutlast_Osimps__1_0) ).
fof(f6745,plain,
spl0_674,
inference(avatar_split_clause,[],[f364,f6743]) ).
fof(f6743,plain,
( spl0_674
<=> ! [X3] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f6741,plain,
spl0_673,
inference(avatar_split_clause,[],[f274,f6739]) ).
fof(f274,axiom,
! [X10] : c_lessequals(c_0,c_IntDef_Oint(X10),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Ozero__zle__int_0) ).
fof(f6737,plain,
spl0_672,
inference(avatar_split_clause,[],[f234,f6735]) ).
fof(f6735,plain,
( spl0_672
<=> ! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f234,axiom,
! [X8] : c_IntDef_Onat(c_IntDef_Oint(X8)) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__int_0) ).
fof(f6733,plain,
spl0_671,
inference(avatar_split_clause,[],[f228,f6731]) ).
fof(f228,axiom,
! [X9] : ~ c_less(c_IntDef_Oint(X9),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__less__0__conv_0) ).
fof(f6729,plain,
~ spl0_670,
inference(avatar_split_clause,[],[f159,f6726]) ).
fof(f159,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Infinite__Set_Onat__infinite_0) ).
fof(f6724,plain,
spl0_669,
inference(avatar_split_clause,[],[f146,f6722]) ).
fof(f6722,plain,
( spl0_669
<=> ! [X8,X3] : c_Fun_Oid(X8,X3) = X8 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f146,axiom,
! [X3,X8] : c_Fun_Oid(X8,X3) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Fun_Oid__apply_0) ).
fof(f6720,plain,
spl0_668,
inference(avatar_split_clause,[],[f145,f6718]) ).
fof(f145,axiom,
! [X8] : c_NatArith_Oof__nat(X8,tc_nat) = X8,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Oof__nat__id_0) ).
fof(f6716,plain,
spl0_667,
inference(avatar_split_clause,[],[f128,f6714]) ).
fof(f6714,plain,
( spl0_667
<=> ! [X3] : c_0 = c_Finite__Set_Ocard(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f128,axiom,
! [X3] : c_0 = c_Finite__Set_Ocard(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__empty_0) ).
fof(f6712,plain,
spl0_666,
inference(avatar_split_clause,[],[f105,f6709]) ).
fof(f6709,plain,
( spl0_666
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f105,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f6707,plain,
spl0_665,
inference(avatar_split_clause,[],[f104,f6704]) ).
fof(f6704,plain,
( spl0_665
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f104,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f6702,plain,
spl0_664,
inference(avatar_split_clause,[],[f34,f6699]) ).
fof(f6699,plain,
( spl0_664
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f34,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ounit_Osize_0) ).
fof(f6697,plain,
spl0_663,
inference(avatar_split_clause,[],[f23,f6695]) ).
fof(f6695,plain,
( spl0_663
<=> ! [X3,X14] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X14,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f23,axiom,
! [X3,X14] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X14,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Ooption_Odistinct__1_0) ).
fof(f6693,plain,
spl0_662,
inference(avatar_split_clause,[],[f22,f6691]) ).
fof(f6691,plain,
( spl0_662
<=> ! [X3] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f22,axiom,
! [X3] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f6689,plain,
spl0_661,
inference(avatar_split_clause,[],[f15,f6687]) ).
fof(f6687,plain,
( spl0_661
<=> ! [X10] : c_1 = c_Binomial_Obinomial(X10,X10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f15,axiom,
! [X10] : c_1 = c_Binomial_Obinomial(X10,X10),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__n_0) ).
fof(f6685,plain,
spl0_660,
inference(avatar_split_clause,[],[f14,f6683]) ).
fof(f6683,plain,
( spl0_660
<=> ! [X10] : c_Binomial_Obinomial(X10,c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f14,axiom,
! [X10] : c_Binomial_Obinomial(X10,c_0) = c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
fof(f6681,plain,
spl0_659,
inference(avatar_split_clause,[],[f2751,f6679]) ).
fof(f2751,axiom,
! [X30] :
( ~ c_in(X30,v_A,t_a)
| c_in(v_x(X30),v_S,t_a)
| c_in(c_Pair(v_L,X30,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f5917,plain,
( ~ spl0_658
| ~ spl0_114
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f5907,f3738,f3728,f5914]) ).
fof(f5914,plain,
( spl0_658
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f3738,plain,
( spl0_116
<=> ! [X10] : ~ c_IntDef_Oneg(c_IntDef_Oint(X10),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f5907,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_114
| ~ spl0_116 ),
inference(superposition,[],[f3739,f3730]) ).
fof(f3739,plain,
( ! [X10] : ~ c_IntDef_Oneg(c_IntDef_Oint(X10),tc_IntDef_Oint)
| ~ spl0_116 ),
inference(avatar_component_clause,[],[f3738]) ).
fof(f5912,plain,
( ~ spl0_657
| ~ spl0_113
| ~ spl0_116 ),
inference(avatar_split_clause,[],[f5906,f3738,f3723,f5909]) ).
fof(f5909,plain,
( spl0_657
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f5906,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_113
| ~ spl0_116 ),
inference(superposition,[],[f3739,f3725]) ).
fof(f5905,plain,
spl0_656,
inference(avatar_split_clause,[],[f2996,f5902]) ).
fof(f5902,plain,
( spl0_656
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f2996,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f336,f314]) ).
fof(f336,axiom,
! [X11] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X11,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(f5900,plain,
spl0_655,
inference(avatar_split_clause,[],[f2977,f5897]) ).
fof(f5897,plain,
( spl0_655
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f2977,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f227,f224]) ).
fof(f227,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(f5895,plain,
spl0_654,
inference(avatar_split_clause,[],[f2976,f5893]) ).
fof(f5893,plain,
( spl0_654
<=> ! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f2976,plain,
! [X9] : c_Divides_Oop_Advd(c_1,X9,tc_nat),
inference(forward_demodulation,[],[f2761,f2757]) ).
fof(f2761,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,[],[f1601,f1394]) ).
fof(f1601,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(f5891,plain,
spl0_653,
inference(avatar_split_clause,[],[f2974,f5888]) ).
fof(f5888,plain,
( spl0_653
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f2974,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f2759,f2757]) ).
fof(f2759,plain,
c_IntDef_Onat(c_1) = c_Finite__Set_Ocard(c_SetInterval_OatMost(c_0,tc_nat),tc_nat),
inference(definition_unfolding,[],[f194,f1394]) ).
fof(f194,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntArith_Onat__1_0) ).
fof(f5886,plain,
spl0_652,
inference(avatar_split_clause,[],[f2736,f5884]) ).
fof(f5884,plain,
( spl0_652
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f2736,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f5882,plain,
spl0_651,
inference(avatar_split_clause,[],[f2735,f5880]) ).
fof(f5880,plain,
( spl0_651
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f2735,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f5878,plain,
spl0_650,
inference(avatar_split_clause,[],[f2734,f5876]) ).
fof(f5876,plain,
( spl0_650
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f2734,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f5874,plain,
spl0_649,
inference(avatar_split_clause,[],[f2733,f5872]) ).
fof(f5872,plain,
( spl0_649
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f2733,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f5870,plain,
spl0_648,
inference(avatar_split_clause,[],[f2732,f5868]) ).
fof(f5868,plain,
( spl0_648
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f2732,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f5866,plain,
spl0_647,
inference(avatar_split_clause,[],[f2731,f5864]) ).
fof(f5864,plain,
( spl0_647
<=> ! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f2731,axiom,
! [X92] :
( ~ class_Wellfounded__Recursion_Owellorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f5862,plain,
spl0_646,
inference(avatar_split_clause,[],[f2730,f5860]) ).
fof(f5860,plain,
( spl0_646
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f2730,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f5858,plain,
spl0_645,
inference(avatar_split_clause,[],[f2725,f5856]) ).
fof(f5856,plain,
( spl0_645
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f2725,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f5854,plain,
spl0_644,
inference(avatar_split_clause,[],[f2724,f5852]) ).
fof(f5852,plain,
( spl0_644
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f2724,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f5850,plain,
spl0_643,
inference(avatar_split_clause,[],[f2723,f5848]) ).
fof(f5848,plain,
( spl0_643
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f2723,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f5846,plain,
spl0_642,
inference(avatar_split_clause,[],[f2722,f5844]) ).
fof(f5844,plain,
( spl0_642
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f2722,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f5842,plain,
spl0_641,
inference(avatar_split_clause,[],[f2721,f5840]) ).
fof(f5840,plain,
( spl0_641
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f2721,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f5838,plain,
spl0_640,
inference(avatar_split_clause,[],[f2720,f5836]) ).
fof(f5836,plain,
( spl0_640
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f2720,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f5834,plain,
spl0_639,
inference(avatar_split_clause,[],[f2717,f5832]) ).
fof(f5832,plain,
( spl0_639
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f2717,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f5830,plain,
spl0_638,
inference(avatar_split_clause,[],[f2716,f5828]) ).
fof(f5828,plain,
( spl0_638
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f2716,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f5826,plain,
spl0_637,
inference(avatar_split_clause,[],[f2715,f5824]) ).
fof(f5824,plain,
( spl0_637
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f2715,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f5822,plain,
spl0_636,
inference(avatar_split_clause,[],[f2712,f5820]) ).
fof(f5820,plain,
( spl0_636
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f2712,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f5818,plain,
spl0_635,
inference(avatar_split_clause,[],[f2709,f5816]) ).
fof(f5816,plain,
( spl0_635
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f2709,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f5814,plain,
spl0_634,
inference(avatar_split_clause,[],[f2708,f5812]) ).
fof(f5812,plain,
( spl0_634
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f2708,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f5810,plain,
spl0_633,
inference(avatar_split_clause,[],[f2707,f5808]) ).
fof(f5808,plain,
( spl0_633
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f2707,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f5806,plain,
spl0_632,
inference(avatar_split_clause,[],[f2706,f5804]) ).
fof(f5804,plain,
( spl0_632
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f2706,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f5802,plain,
spl0_631,
inference(avatar_split_clause,[],[f2703,f5800]) ).
fof(f5800,plain,
( spl0_631
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f2703,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f5798,plain,
spl0_630,
inference(avatar_split_clause,[],[f2702,f5796]) ).
fof(f5796,plain,
( spl0_630
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f2702,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f5794,plain,
spl0_629,
inference(avatar_split_clause,[],[f2697,f5792]) ).
fof(f5792,plain,
( spl0_629
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f2697,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f5790,plain,
spl0_628,
inference(avatar_split_clause,[],[f2694,f5788]) ).
fof(f5788,plain,
( spl0_628
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f2694,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f5786,plain,
spl0_627,
inference(avatar_split_clause,[],[f2693,f5784]) ).
fof(f5784,plain,
( spl0_627
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f2693,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f5782,plain,
spl0_626,
inference(avatar_split_clause,[],[f2692,f5780]) ).
fof(f5780,plain,
( spl0_626
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f2692,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f5778,plain,
spl0_625,
inference(avatar_split_clause,[],[f2690,f5776]) ).
fof(f5776,plain,
( spl0_625
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f2690,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f5774,plain,
spl0_624,
inference(avatar_split_clause,[],[f2684,f5772]) ).
fof(f5772,plain,
( spl0_624
<=> ! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f2684,axiom,
! [X92] :
( ~ class_Ring__and__Field_Osemiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f5770,plain,
spl0_623,
inference(avatar_split_clause,[],[f2676,f5768]) ).
fof(f5768,plain,
( spl0_623
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f2676,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f5766,plain,
spl0_622,
inference(avatar_split_clause,[],[f2675,f5764]) ).
fof(f5764,plain,
( spl0_622
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f2675,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f5762,plain,
spl0_621,
inference(avatar_split_clause,[],[f2674,f5760]) ).
fof(f5760,plain,
( spl0_621
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f2674,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f5758,plain,
spl0_620,
inference(avatar_split_clause,[],[f2673,f5756]) ).
fof(f5756,plain,
( spl0_620
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f2673,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f5754,plain,
spl0_619,
inference(avatar_split_clause,[],[f2672,f5752]) ).
fof(f5752,plain,
( spl0_619
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f2672,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f5750,plain,
spl0_618,
inference(avatar_split_clause,[],[f2670,f5748]) ).
fof(f5748,plain,
( spl0_618
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f2670,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f5746,plain,
spl0_617,
inference(avatar_split_clause,[],[f2669,f5744]) ).
fof(f5744,plain,
( spl0_617
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f2669,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f5742,plain,
spl0_616,
inference(avatar_split_clause,[],[f2668,f5740]) ).
fof(f5740,plain,
( spl0_616
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f2668,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f5738,plain,
spl0_615,
inference(avatar_split_clause,[],[f2667,f5736]) ).
fof(f5736,plain,
( spl0_615
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f2667,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f5734,plain,
spl0_614,
inference(avatar_split_clause,[],[f2666,f5732]) ).
fof(f5732,plain,
( spl0_614
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f2666,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f5730,plain,
spl0_613,
inference(avatar_split_clause,[],[f2661,f5728]) ).
fof(f5728,plain,
( spl0_613
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f2661,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f5726,plain,
spl0_612,
inference(avatar_split_clause,[],[f2660,f5724]) ).
fof(f5724,plain,
( spl0_612
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f2660,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f5722,plain,
spl0_611,
inference(avatar_split_clause,[],[f2659,f5720]) ).
fof(f5720,plain,
( spl0_611
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f2659,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring__1(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f5718,plain,
spl0_610,
inference(avatar_split_clause,[],[f2657,f5716]) ).
fof(f5716,plain,
( spl0_610
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f2657,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_8) ).
fof(f5714,plain,
spl0_609,
inference(avatar_split_clause,[],[f2655,f5712]) ).
fof(f5712,plain,
( spl0_609
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f2655,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_6) ).
fof(f5710,plain,
spl0_608,
inference(avatar_split_clause,[],[f2650,f5708]) ).
fof(f5708,plain,
( spl0_608
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f2650,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_13) ).
fof(f5706,plain,
spl0_607,
inference(avatar_split_clause,[],[f2649,f5704]) ).
fof(f5704,plain,
( spl0_607
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f2649,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_12) ).
fof(f5702,plain,
spl0_606,
inference(avatar_split_clause,[],[f2648,f5700]) ).
fof(f5700,plain,
( spl0_606
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f2648,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_11) ).
fof(f5698,plain,
spl0_605,
inference(avatar_split_clause,[],[f2647,f5696]) ).
fof(f5696,plain,
( spl0_605
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f2647,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_10) ).
fof(f5694,plain,
spl0_604,
inference(avatar_split_clause,[],[f2645,f5692]) ).
fof(f5692,plain,
( spl0_604
<=> ! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f2645,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oring_0) ).
fof(f5690,plain,
spl0_603,
inference(avatar_split_clause,[],[f2644,f5688]) ).
fof(f5688,plain,
( spl0_603
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f2644,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f5686,plain,
spl0_602,
inference(avatar_split_clause,[],[f2639,f5684]) ).
fof(f5684,plain,
( spl0_602
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f2639,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f5682,plain,
spl0_601,
inference(avatar_split_clause,[],[f2636,f5680]) ).
fof(f5680,plain,
( spl0_601
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f2636,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f5678,plain,
spl0_600,
inference(avatar_split_clause,[],[f2635,f5676]) ).
fof(f5676,plain,
( spl0_600
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f2635,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f5674,plain,
spl0_599,
inference(avatar_split_clause,[],[f2634,f5672]) ).
fof(f5672,plain,
( spl0_599
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f2634,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f5670,plain,
spl0_598,
inference(avatar_split_clause,[],[f2633,f5668]) ).
fof(f5668,plain,
( spl0_598
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f2633,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f5666,plain,
spl0_597,
inference(avatar_split_clause,[],[f2630,f5664]) ).
fof(f5664,plain,
( spl0_597
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f2630,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f5662,plain,
spl0_596,
inference(avatar_split_clause,[],[f2629,f5660]) ).
fof(f5660,plain,
( spl0_596
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f2629,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f5658,plain,
spl0_595,
inference(avatar_split_clause,[],[f2628,f5656]) ).
fof(f5656,plain,
( spl0_595
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f2628,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f5654,plain,
spl0_594,
inference(avatar_split_clause,[],[f2627,f5652]) ).
fof(f5652,plain,
( spl0_594
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f2627,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f5650,plain,
spl0_593,
inference(avatar_split_clause,[],[f2626,f5648]) ).
fof(f5648,plain,
( spl0_593
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f2626,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f5646,plain,
spl0_592,
inference(avatar_split_clause,[],[f2625,f5644]) ).
fof(f5644,plain,
( spl0_592
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f2625,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f5642,plain,
spl0_591,
inference(avatar_split_clause,[],[f2624,f5640]) ).
fof(f5640,plain,
( spl0_591
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f2624,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f5638,plain,
spl0_590,
inference(avatar_split_clause,[],[f2623,f5636]) ).
fof(f5636,plain,
( spl0_590
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f2623,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f5634,plain,
spl0_589,
inference(avatar_split_clause,[],[f2621,f5632]) ).
fof(f5632,plain,
( spl0_589
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f2621,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f5630,plain,
spl0_588,
inference(avatar_split_clause,[],[f2620,f5628]) ).
fof(f5628,plain,
( spl0_588
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f2620,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f5626,plain,
spl0_587,
inference(avatar_split_clause,[],[f2619,f5624]) ).
fof(f5624,plain,
( spl0_587
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f2619,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f5622,plain,
spl0_586,
inference(avatar_split_clause,[],[f2618,f5620]) ).
fof(f5620,plain,
( spl0_586
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f2618,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f5618,plain,
spl0_585,
inference(avatar_split_clause,[],[f2617,f5616]) ).
fof(f5616,plain,
( spl0_585
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f2617,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f5614,plain,
spl0_584,
inference(avatar_split_clause,[],[f2612,f5612]) ).
fof(f5612,plain,
( spl0_584
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f2612,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f5610,plain,
spl0_583,
inference(avatar_split_clause,[],[f2611,f5608]) ).
fof(f5608,plain,
( spl0_583
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f2611,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f5606,plain,
spl0_582,
inference(avatar_split_clause,[],[f2610,f5604]) ).
fof(f5604,plain,
( spl0_582
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f2610,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f5602,plain,
spl0_581,
inference(avatar_split_clause,[],[f2607,f5600]) ).
fof(f5600,plain,
( spl0_581
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f2607,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f5598,plain,
spl0_580,
inference(avatar_split_clause,[],[f2604,f5596]) ).
fof(f5596,plain,
( spl0_580
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f2604,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f5594,plain,
spl0_579,
inference(avatar_split_clause,[],[f2603,f5592]) ).
fof(f5592,plain,
( spl0_579
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f2603,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f5590,plain,
spl0_578,
inference(avatar_split_clause,[],[f2601,f5588]) ).
fof(f5588,plain,
( spl0_578
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f2601,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f5586,plain,
spl0_577,
inference(avatar_split_clause,[],[f2600,f5584]) ).
fof(f5584,plain,
( spl0_577
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f2600,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f5582,plain,
spl0_576,
inference(avatar_split_clause,[],[f2599,f5580]) ).
fof(f5580,plain,
( spl0_576
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f2599,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f5578,plain,
spl0_575,
inference(avatar_split_clause,[],[f2598,f5576]) ).
fof(f5576,plain,
( spl0_575
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f2598,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f5574,plain,
spl0_574,
inference(avatar_split_clause,[],[f2595,f5572]) ).
fof(f5572,plain,
( spl0_574
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f2595,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f5570,plain,
spl0_573,
inference(avatar_split_clause,[],[f2594,f5568]) ).
fof(f5568,plain,
( spl0_573
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f2594,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f5566,plain,
spl0_572,
inference(avatar_split_clause,[],[f2566,f5564]) ).
fof(f5564,plain,
( spl0_572
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f2566,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f5562,plain,
spl0_571,
inference(avatar_split_clause,[],[f2564,f5560]) ).
fof(f5560,plain,
( spl0_571
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f2564,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f5558,plain,
spl0_570,
inference(avatar_split_clause,[],[f2561,f5556]) ).
fof(f5556,plain,
( spl0_570
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f2561,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f5554,plain,
spl0_569,
inference(avatar_split_clause,[],[f2560,f5552]) ).
fof(f5552,plain,
( spl0_569
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f2560,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f5550,plain,
spl0_568,
inference(avatar_split_clause,[],[f2559,f5548]) ).
fof(f5548,plain,
( spl0_568
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f2559,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f5546,plain,
spl0_567,
inference(avatar_split_clause,[],[f2558,f5544]) ).
fof(f5544,plain,
( spl0_567
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f2558,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f5542,plain,
spl0_566,
inference(avatar_split_clause,[],[f2557,f5540]) ).
fof(f5540,plain,
( spl0_566
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f2557,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f5538,plain,
spl0_565,
inference(avatar_split_clause,[],[f2556,f5536]) ).
fof(f5536,plain,
( spl0_565
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f2556,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f5534,plain,
spl0_564,
inference(avatar_split_clause,[],[f2554,f5532]) ).
fof(f5532,plain,
( spl0_564
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f2554,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f5530,plain,
spl0_563,
inference(avatar_split_clause,[],[f2553,f5528]) ).
fof(f5528,plain,
( spl0_563
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f2553,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f5526,plain,
spl0_562,
inference(avatar_split_clause,[],[f2551,f5524]) ).
fof(f5524,plain,
( spl0_562
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f2551,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f5522,plain,
spl0_561,
inference(avatar_split_clause,[],[f2548,f5520]) ).
fof(f5520,plain,
( spl0_561
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f2548,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f5518,plain,
spl0_560,
inference(avatar_split_clause,[],[f2547,f5516]) ).
fof(f5516,plain,
( spl0_560
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f2547,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f5514,plain,
spl0_559,
inference(avatar_split_clause,[],[f2545,f5512]) ).
fof(f5512,plain,
( spl0_559
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f2545,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f5510,plain,
spl0_558,
inference(avatar_split_clause,[],[f2544,f5508]) ).
fof(f5508,plain,
( spl0_558
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f2544,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f5506,plain,
spl0_557,
inference(avatar_split_clause,[],[f2543,f5504]) ).
fof(f5504,plain,
( spl0_557
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f2543,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f5502,plain,
spl0_556,
inference(avatar_split_clause,[],[f2542,f5500]) ).
fof(f5500,plain,
( spl0_556
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f2542,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f5498,plain,
spl0_555,
inference(avatar_split_clause,[],[f2541,f5496]) ).
fof(f5496,plain,
( spl0_555
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f2541,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f5494,plain,
spl0_554,
inference(avatar_split_clause,[],[f2540,f5492]) ).
fof(f5492,plain,
( spl0_554
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f2540,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f5490,plain,
spl0_553,
inference(avatar_split_clause,[],[f2539,f5488]) ).
fof(f5488,plain,
( spl0_553
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f2539,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f5486,plain,
spl0_552,
inference(avatar_split_clause,[],[f2538,f5484]) ).
fof(f5484,plain,
( spl0_552
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f2538,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f5482,plain,
spl0_551,
inference(avatar_split_clause,[],[f2534,f5480]) ).
fof(f5480,plain,
( spl0_551
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f2534,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f5478,plain,
spl0_550,
inference(avatar_split_clause,[],[f2533,f5476]) ).
fof(f5476,plain,
( spl0_550
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f2533,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f5474,plain,
spl0_549,
inference(avatar_split_clause,[],[f2532,f5472]) ).
fof(f5472,plain,
( spl0_549
<=> ! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f2532,axiom,
! [X92] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f5470,plain,
spl0_548,
inference(avatar_split_clause,[],[f2531,f5468]) ).
fof(f5468,plain,
( spl0_548
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f2531,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f5466,plain,
spl0_547,
inference(avatar_split_clause,[],[f2526,f5464]) ).
fof(f5464,plain,
( spl0_547
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f2526,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f5462,plain,
spl0_546,
inference(avatar_split_clause,[],[f2524,f5460]) ).
fof(f5460,plain,
( spl0_546
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f2524,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f5458,plain,
spl0_545,
inference(avatar_split_clause,[],[f2523,f5456]) ).
fof(f5456,plain,
( spl0_545
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f2523,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f5454,plain,
spl0_544,
inference(avatar_split_clause,[],[f2522,f5452]) ).
fof(f5452,plain,
( spl0_544
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f2522,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f5450,plain,
spl0_543,
inference(avatar_split_clause,[],[f2521,f5448]) ).
fof(f5448,plain,
( spl0_543
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f2521,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f5446,plain,
spl0_542,
inference(avatar_split_clause,[],[f2519,f5444]) ).
fof(f5444,plain,
( spl0_542
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f2519,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f5442,plain,
spl0_541,
inference(avatar_split_clause,[],[f2518,f5440]) ).
fof(f5440,plain,
( spl0_541
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f2518,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f5438,plain,
spl0_540,
inference(avatar_split_clause,[],[f2517,f5436]) ).
fof(f5436,plain,
( spl0_540
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f2517,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f5434,plain,
spl0_539,
inference(avatar_split_clause,[],[f2516,f5432]) ).
fof(f5432,plain,
( spl0_539
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f2516,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f5430,plain,
spl0_538,
inference(avatar_split_clause,[],[f2515,f5428]) ).
fof(f5428,plain,
( spl0_538
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f2515,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f5426,plain,
spl0_537,
inference(avatar_split_clause,[],[f2514,f5424]) ).
fof(f5424,plain,
( spl0_537
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f2514,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f5422,plain,
spl0_536,
inference(avatar_split_clause,[],[f2513,f5420]) ).
fof(f5420,plain,
( spl0_536
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f2513,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f5418,plain,
spl0_535,
inference(avatar_split_clause,[],[f2512,f5416]) ).
fof(f5416,plain,
( spl0_535
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f2512,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f5414,plain,
spl0_534,
inference(avatar_split_clause,[],[f2511,f5412]) ).
fof(f5412,plain,
( spl0_534
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f2511,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f5410,plain,
spl0_533,
inference(avatar_split_clause,[],[f2510,f5408]) ).
fof(f5408,plain,
( spl0_533
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f2510,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f5406,plain,
spl0_532,
inference(avatar_split_clause,[],[f2509,f5404]) ).
fof(f5404,plain,
( spl0_532
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f2509,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f5402,plain,
spl0_531,
inference(avatar_split_clause,[],[f2508,f5400]) ).
fof(f5400,plain,
( spl0_531
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f2508,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f5398,plain,
spl0_530,
inference(avatar_split_clause,[],[f2507,f5396]) ).
fof(f5396,plain,
( spl0_530
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f2507,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f5394,plain,
spl0_529,
inference(avatar_split_clause,[],[f2506,f5392]) ).
fof(f5392,plain,
( spl0_529
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f2506,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f5390,plain,
spl0_528,
inference(avatar_split_clause,[],[f2505,f5388]) ).
fof(f5388,plain,
( spl0_528
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f2505,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f5386,plain,
spl0_527,
inference(avatar_split_clause,[],[f2504,f5384]) ).
fof(f5384,plain,
( spl0_527
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f2504,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f5382,plain,
spl0_526,
inference(avatar_split_clause,[],[f2503,f5380]) ).
fof(f5380,plain,
( spl0_526
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f2503,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f5378,plain,
spl0_525,
inference(avatar_split_clause,[],[f2502,f5376]) ).
fof(f5376,plain,
( spl0_525
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f2502,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f5374,plain,
spl0_524,
inference(avatar_split_clause,[],[f2501,f5372]) ).
fof(f5372,plain,
( spl0_524
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f2501,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f5370,plain,
spl0_523,
inference(avatar_split_clause,[],[f2500,f5368]) ).
fof(f5368,plain,
( spl0_523
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f2500,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f5366,plain,
spl0_522,
inference(avatar_split_clause,[],[f2499,f5364]) ).
fof(f5364,plain,
( spl0_522
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f2499,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f5362,plain,
spl0_521,
inference(avatar_split_clause,[],[f2498,f5360]) ).
fof(f5360,plain,
( spl0_521
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f2498,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f5358,plain,
spl0_520,
inference(avatar_split_clause,[],[f2497,f5356]) ).
fof(f5356,plain,
( spl0_520
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f2497,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f5354,plain,
spl0_519,
inference(avatar_split_clause,[],[f2496,f5352]) ).
fof(f5352,plain,
( spl0_519
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f2496,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f5350,plain,
spl0_518,
inference(avatar_split_clause,[],[f2495,f5348]) ).
fof(f5348,plain,
( spl0_518
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f2495,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f5346,plain,
spl0_517,
inference(avatar_split_clause,[],[f2494,f5344]) ).
fof(f5344,plain,
( spl0_517
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f2494,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f5342,plain,
spl0_516,
inference(avatar_split_clause,[],[f2493,f5340]) ).
fof(f5340,plain,
( spl0_516
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f2493,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f5338,plain,
spl0_515,
inference(avatar_split_clause,[],[f2492,f5336]) ).
fof(f5336,plain,
( spl0_515
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f2492,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f5334,plain,
spl0_514,
inference(avatar_split_clause,[],[f2491,f5332]) ).
fof(f5332,plain,
( spl0_514
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f2491,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f5330,plain,
spl0_513,
inference(avatar_split_clause,[],[f2490,f5328]) ).
fof(f5328,plain,
( spl0_513
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f2490,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f5326,plain,
spl0_512,
inference(avatar_split_clause,[],[f2489,f5324]) ).
fof(f5324,plain,
( spl0_512
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f2489,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f5322,plain,
spl0_511,
inference(avatar_split_clause,[],[f2488,f5320]) ).
fof(f5320,plain,
( spl0_511
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f2488,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f5318,plain,
spl0_510,
inference(avatar_split_clause,[],[f2487,f5316]) ).
fof(f5316,plain,
( spl0_510
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f2487,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f5314,plain,
spl0_509,
inference(avatar_split_clause,[],[f2486,f5312]) ).
fof(f5312,plain,
( spl0_509
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f2486,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f5310,plain,
spl0_508,
inference(avatar_split_clause,[],[f2485,f5308]) ).
fof(f5308,plain,
( spl0_508
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f2485,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f5306,plain,
spl0_507,
inference(avatar_split_clause,[],[f2482,f5304]) ).
fof(f5304,plain,
( spl0_507
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f2482,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f5302,plain,
spl0_506,
inference(avatar_split_clause,[],[f2480,f5300]) ).
fof(f5300,plain,
( spl0_506
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f2480,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f5298,plain,
spl0_505,
inference(avatar_split_clause,[],[f2479,f5296]) ).
fof(f5296,plain,
( spl0_505
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f2479,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f5294,plain,
spl0_504,
inference(avatar_split_clause,[],[f2477,f5292]) ).
fof(f5292,plain,
( spl0_504
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f2477,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f5290,plain,
spl0_503,
inference(avatar_split_clause,[],[f2474,f5288]) ).
fof(f5288,plain,
( spl0_503
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f2474,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f5286,plain,
spl0_502,
inference(avatar_split_clause,[],[f2473,f5284]) ).
fof(f5284,plain,
( spl0_502
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f2473,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f5282,plain,
spl0_501,
inference(avatar_split_clause,[],[f2472,f5280]) ).
fof(f5280,plain,
( spl0_501
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f2472,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f5278,plain,
spl0_500,
inference(avatar_split_clause,[],[f2470,f5276]) ).
fof(f5276,plain,
( spl0_500
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f2470,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f5274,plain,
spl0_499,
inference(avatar_split_clause,[],[f2469,f5272]) ).
fof(f5272,plain,
( spl0_499
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f2469,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f5270,plain,
spl0_498,
inference(avatar_split_clause,[],[f2468,f5268]) ).
fof(f5268,plain,
( spl0_498
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f2468,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__semidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f5266,plain,
spl0_497,
inference(avatar_split_clause,[],[f2465,f5264]) ).
fof(f5264,plain,
( spl0_497
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f2465,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f5262,plain,
spl0_496,
inference(avatar_split_clause,[],[f2464,f5260]) ).
fof(f5260,plain,
( spl0_496
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f2464,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f5258,plain,
spl0_495,
inference(avatar_split_clause,[],[f2463,f5256]) ).
fof(f5256,plain,
( spl0_495
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f2463,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f5254,plain,
spl0_494,
inference(avatar_split_clause,[],[f2462,f5252]) ).
fof(f5252,plain,
( spl0_494
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f2462,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f5250,plain,
spl0_493,
inference(avatar_split_clause,[],[f2460,f5248]) ).
fof(f5248,plain,
( spl0_493
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f2460,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f5246,plain,
spl0_492,
inference(avatar_split_clause,[],[f2459,f5244]) ).
fof(f5244,plain,
( spl0_492
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f2459,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f5242,plain,
spl0_491,
inference(avatar_split_clause,[],[f2458,f5240]) ).
fof(f5240,plain,
( spl0_491
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f2458,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f5238,plain,
spl0_490,
inference(avatar_split_clause,[],[f2457,f5236]) ).
fof(f5236,plain,
( spl0_490
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f2457,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f5234,plain,
spl0_489,
inference(avatar_split_clause,[],[f2456,f5232]) ).
fof(f5232,plain,
( spl0_489
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Olordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f2456,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Olordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f5230,plain,
spl0_488,
inference(avatar_split_clause,[],[f2455,f5228]) ).
fof(f5228,plain,
( spl0_488
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f2455,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f5226,plain,
spl0_487,
inference(avatar_split_clause,[],[f2454,f5224]) ).
fof(f5224,plain,
( spl0_487
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f2454,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f5222,plain,
spl0_486,
inference(avatar_split_clause,[],[f2453,f5220]) ).
fof(f5220,plain,
( spl0_486
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f2453,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f5218,plain,
spl0_485,
inference(avatar_split_clause,[],[f2452,f5216]) ).
fof(f5216,plain,
( spl0_485
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f2452,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f5214,plain,
spl0_484,
inference(avatar_split_clause,[],[f2451,f5212]) ).
fof(f5212,plain,
( spl0_484
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f2451,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f5210,plain,
spl0_483,
inference(avatar_split_clause,[],[f2450,f5208]) ).
fof(f5208,plain,
( spl0_483
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f2450,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f5206,plain,
spl0_482,
inference(avatar_split_clause,[],[f2449,f5204]) ).
fof(f5204,plain,
( spl0_482
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f2449,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f5202,plain,
spl0_481,
inference(avatar_split_clause,[],[f2448,f5200]) ).
fof(f5200,plain,
( spl0_481
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f2448,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f5198,plain,
spl0_480,
inference(avatar_split_clause,[],[f2447,f5196]) ).
fof(f5196,plain,
( spl0_480
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f2447,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f5194,plain,
spl0_479,
inference(avatar_split_clause,[],[f2446,f5192]) ).
fof(f5192,plain,
( spl0_479
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f2446,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f5190,plain,
spl0_478,
inference(avatar_split_clause,[],[f2445,f5188]) ).
fof(f5188,plain,
( spl0_478
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f2445,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f5186,plain,
spl0_477,
inference(avatar_split_clause,[],[f2444,f5184]) ).
fof(f5184,plain,
( spl0_477
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f2444,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f5182,plain,
spl0_476,
inference(avatar_split_clause,[],[f2442,f5180]) ).
fof(f5180,plain,
( spl0_476
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f2442,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f5178,plain,
spl0_475,
inference(avatar_split_clause,[],[f2441,f5176]) ).
fof(f5176,plain,
( spl0_475
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f2441,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f5174,plain,
spl0_474,
inference(avatar_split_clause,[],[f2440,f5172]) ).
fof(f5172,plain,
( spl0_474
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f2440,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f5170,plain,
spl0_473,
inference(avatar_split_clause,[],[f2439,f5168]) ).
fof(f5168,plain,
( spl0_473
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f2439,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f5166,plain,
spl0_472,
inference(avatar_split_clause,[],[f2438,f5164]) ).
fof(f5164,plain,
( spl0_472
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f2438,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f5162,plain,
spl0_471,
inference(avatar_split_clause,[],[f2433,f5160]) ).
fof(f5160,plain,
( spl0_471
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f2433,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f5158,plain,
spl0_470,
inference(avatar_split_clause,[],[f2432,f5156]) ).
fof(f5156,plain,
( spl0_470
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f2432,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f5154,plain,
spl0_469,
inference(avatar_split_clause,[],[f2431,f5152]) ).
fof(f5152,plain,
( spl0_469
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f2431,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f5150,plain,
spl0_468,
inference(avatar_split_clause,[],[f2430,f5148]) ).
fof(f5148,plain,
( spl0_468
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f2430,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f5146,plain,
spl0_467,
inference(avatar_split_clause,[],[f2429,f5144]) ).
fof(f5144,plain,
( spl0_467
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f2429,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f5142,plain,
spl0_466,
inference(avatar_split_clause,[],[f2428,f5140]) ).
fof(f5140,plain,
( spl0_466
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f2428,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f5138,plain,
spl0_465,
inference(avatar_split_clause,[],[f2427,f5136]) ).
fof(f5136,plain,
( spl0_465
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f2427,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f5134,plain,
spl0_464,
inference(avatar_split_clause,[],[f2426,f5132]) ).
fof(f5132,plain,
( spl0_464
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oidom(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f2426,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oidom(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f5130,plain,
spl0_463,
inference(avatar_split_clause,[],[f2424,f5128]) ).
fof(f5128,plain,
( spl0_463
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semidom(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f2424,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semidom(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f5126,plain,
spl0_462,
inference(avatar_split_clause,[],[f2423,f5124]) ).
fof(f5124,plain,
( spl0_462
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f2423,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f5122,plain,
spl0_461,
inference(avatar_split_clause,[],[f2422,f5120]) ).
fof(f5120,plain,
( spl0_461
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f2422,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f5118,plain,
spl0_460,
inference(avatar_split_clause,[],[f2421,f5116]) ).
fof(f5116,plain,
( spl0_460
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f2421,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f5114,plain,
spl0_459,
inference(avatar_split_clause,[],[f2420,f5112]) ).
fof(f5112,plain,
( spl0_459
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f2420,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f5110,plain,
spl0_458,
inference(avatar_split_clause,[],[f2419,f5108]) ).
fof(f5108,plain,
( spl0_458
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f2419,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f5106,plain,
spl0_457,
inference(avatar_split_clause,[],[f2417,f5104]) ).
fof(f5104,plain,
( spl0_457
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f2417,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f5102,plain,
spl0_456,
inference(avatar_split_clause,[],[f2416,f5100]) ).
fof(f5100,plain,
( spl0_456
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Olordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f2416,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Olordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f5098,plain,
spl0_455,
inference(avatar_split_clause,[],[f2415,f5096]) ).
fof(f5096,plain,
( spl0_455
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__ring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f2415,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__ring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f5094,plain,
spl0_454,
inference(avatar_split_clause,[],[f2414,f5092]) ).
fof(f5092,plain,
( spl0_454
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f2414,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__abs__if(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f5090,plain,
spl0_453,
inference(avatar_split_clause,[],[f2413,f5088]) ).
fof(f5088,plain,
( spl0_453
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f2413,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f5086,plain,
spl0_452,
inference(avatar_split_clause,[],[f2412,f5084]) ).
fof(f5084,plain,
( spl0_452
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f2412,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f5082,plain,
spl0_451,
inference(avatar_split_clause,[],[f2411,f5080]) ).
fof(f5080,plain,
( spl0_451
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f2411,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f5078,plain,
spl0_450,
inference(avatar_split_clause,[],[f2410,f5076]) ).
fof(f5076,plain,
( spl0_450
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f2410,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f5074,plain,
spl0_449,
inference(avatar_split_clause,[],[f2409,f5072]) ).
fof(f5072,plain,
( spl0_449
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f2409,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f5070,plain,
spl0_448,
inference(avatar_split_clause,[],[f2408,f5068]) ).
fof(f5068,plain,
( spl0_448
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f2408,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f5066,plain,
spl0_447,
inference(avatar_split_clause,[],[f2407,f5064]) ).
fof(f5064,plain,
( spl0_447
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f2407,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f5062,plain,
spl0_446,
inference(avatar_split_clause,[],[f2406,f5060]) ).
fof(f5060,plain,
( spl0_446
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f2406,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f5058,plain,
spl0_445,
inference(avatar_split_clause,[],[f2405,f5056]) ).
fof(f5056,plain,
( spl0_445
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f2405,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f5054,plain,
spl0_444,
inference(avatar_split_clause,[],[f2404,f5052]) ).
fof(f5052,plain,
( spl0_444
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f2404,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f5050,plain,
spl0_443,
inference(avatar_split_clause,[],[f2403,f5048]) ).
fof(f5048,plain,
( spl0_443
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f2403,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5046,plain,
spl0_442,
inference(avatar_split_clause,[],[f2402,f5044]) ).
fof(f5044,plain,
( spl0_442
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f2402,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5042,plain,
spl0_441,
inference(avatar_split_clause,[],[f2401,f5040]) ).
fof(f5040,plain,
( spl0_441
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f2401,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5038,plain,
spl0_440,
inference(avatar_split_clause,[],[f2400,f5036]) ).
fof(f5036,plain,
( spl0_440
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f2400,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5034,plain,
spl0_439,
inference(avatar_split_clause,[],[f2399,f5032]) ).
fof(f5032,plain,
( spl0_439
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f2399,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5030,plain,
spl0_438,
inference(avatar_split_clause,[],[f2398,f5028]) ).
fof(f5028,plain,
( spl0_438
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f2398,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5026,plain,
spl0_437,
inference(avatar_split_clause,[],[f2397,f5024]) ).
fof(f5024,plain,
( spl0_437
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f2397,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5022,plain,
spl0_436,
inference(avatar_split_clause,[],[f2396,f5020]) ).
fof(f5020,plain,
( spl0_436
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f2396,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5018,plain,
spl0_435,
inference(avatar_split_clause,[],[f2393,f5016]) ).
fof(f5016,plain,
( spl0_435
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f2393,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5014,plain,
spl0_434,
inference(avatar_split_clause,[],[f2391,f5012]) ).
fof(f5012,plain,
( spl0_434
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f2391,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5010,plain,
spl0_433,
inference(avatar_split_clause,[],[f2389,f5008]) ).
fof(f5008,plain,
( spl0_433
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f2389,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5006,plain,
spl0_432,
inference(avatar_split_clause,[],[f2386,f5004]) ).
fof(f5004,plain,
( spl0_432
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f2386,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5002,plain,
spl0_431,
inference(avatar_split_clause,[],[f2385,f5000]) ).
fof(f5000,plain,
( spl0_431
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f2385,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f4998,plain,
spl0_430,
inference(avatar_split_clause,[],[f2384,f4996]) ).
fof(f4996,plain,
( spl0_430
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f2384,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f4994,plain,
spl0_429,
inference(avatar_split_clause,[],[f2383,f4992]) ).
fof(f4992,plain,
( spl0_429
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f2383,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f4990,plain,
spl0_428,
inference(avatar_split_clause,[],[f2381,f4988]) ).
fof(f4988,plain,
( spl0_428
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f2381,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f4986,plain,
spl0_427,
inference(avatar_split_clause,[],[f2380,f4984]) ).
fof(f4984,plain,
( spl0_427
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f2380,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f4982,plain,
spl0_426,
inference(avatar_split_clause,[],[f2379,f4980]) ).
fof(f4980,plain,
( spl0_426
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f2379,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f4978,plain,
spl0_425,
inference(avatar_split_clause,[],[f2378,f4976]) ).
fof(f4976,plain,
( spl0_425
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f2378,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f4974,plain,
spl0_424,
inference(avatar_split_clause,[],[f2377,f4972]) ).
fof(f4972,plain,
( spl0_424
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f2377,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f4970,plain,
spl0_423,
inference(avatar_split_clause,[],[f2376,f4968]) ).
fof(f4968,plain,
( spl0_423
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f2376,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f4966,plain,
spl0_422,
inference(avatar_split_clause,[],[f2375,f4964]) ).
fof(f4964,plain,
( spl0_422
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f2375,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f4962,plain,
spl0_421,
inference(avatar_split_clause,[],[f2374,f4960]) ).
fof(f4960,plain,
( spl0_421
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f2374,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f4958,plain,
spl0_420,
inference(avatar_split_clause,[],[f2373,f4956]) ).
fof(f4956,plain,
( spl0_420
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f2373,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__idom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f4954,plain,
spl0_419,
inference(avatar_split_clause,[],[f2309,f4952]) ).
fof(f4952,plain,
( spl0_419
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f2309,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f4950,plain,
spl0_418,
inference(avatar_split_clause,[],[f2306,f4948]) ).
fof(f4948,plain,
( spl0_418
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f2306,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f4946,plain,
spl0_417,
inference(avatar_split_clause,[],[f2305,f4944]) ).
fof(f4944,plain,
( spl0_417
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f2305,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f4942,plain,
spl0_416,
inference(avatar_split_clause,[],[f2304,f4940]) ).
fof(f4940,plain,
( spl0_416
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f2304,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f4938,plain,
spl0_415,
inference(avatar_split_clause,[],[f2303,f4936]) ).
fof(f4936,plain,
( spl0_415
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f2303,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f4934,plain,
spl0_414,
inference(avatar_split_clause,[],[f2302,f4932]) ).
fof(f4932,plain,
( spl0_414
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f2302,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f4930,plain,
spl0_413,
inference(avatar_split_clause,[],[f2301,f4928]) ).
fof(f4928,plain,
( spl0_413
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f2301,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f4926,plain,
spl0_412,
inference(avatar_split_clause,[],[f2300,f4924]) ).
fof(f4924,plain,
( spl0_412
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f2300,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f4922,plain,
spl0_411,
inference(avatar_split_clause,[],[f2299,f4920]) ).
fof(f4920,plain,
( spl0_411
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f2299,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Oordered__semiring__strict(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f4918,plain,
spl0_410,
inference(avatar_split_clause,[],[f2298,f4916]) ).
fof(f4916,plain,
( spl0_410
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f2298,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f4914,plain,
spl0_409,
inference(avatar_split_clause,[],[f2297,f4912]) ).
fof(f4912,plain,
( spl0_409
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f2297,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f4910,plain,
spl0_408,
inference(avatar_split_clause,[],[f2296,f4908]) ).
fof(f4908,plain,
( spl0_408
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f2296,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f4906,plain,
spl0_407,
inference(avatar_split_clause,[],[f2295,f4904]) ).
fof(f4904,plain,
( spl0_407
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f2295,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f4902,plain,
spl0_406,
inference(avatar_split_clause,[],[f2293,f4900]) ).
fof(f4900,plain,
( spl0_406
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f2293,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f4898,plain,
spl0_405,
inference(avatar_split_clause,[],[f2292,f4896]) ).
fof(f4896,plain,
( spl0_405
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f2292,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f4894,plain,
spl0_404,
inference(avatar_split_clause,[],[f2291,f4892]) ).
fof(f4892,plain,
( spl0_404
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f2291,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f4890,plain,
spl0_403,
inference(avatar_split_clause,[],[f2290,f4888]) ).
fof(f4888,plain,
( spl0_403
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f2290,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f4886,plain,
spl0_402,
inference(avatar_split_clause,[],[f2289,f4884]) ).
fof(f4884,plain,
( spl0_402
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f2289,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f4882,plain,
spl0_401,
inference(avatar_split_clause,[],[f2288,f4880]) ).
fof(f4880,plain,
( spl0_401
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f2288,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f4878,plain,
spl0_400,
inference(avatar_split_clause,[],[f2287,f4876]) ).
fof(f4876,plain,
( spl0_400
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f2287,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f4874,plain,
spl0_399,
inference(avatar_split_clause,[],[f2286,f4872]) ).
fof(f4872,plain,
( spl0_399
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f2286,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f4870,plain,
spl0_398,
inference(avatar_split_clause,[],[f2283,f4868]) ).
fof(f4868,plain,
( spl0_398
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f2283,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f4866,plain,
spl0_397,
inference(avatar_split_clause,[],[f2282,f4864]) ).
fof(f4864,plain,
( spl0_397
<=> ! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f2282,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f4862,plain,
spl0_396,
inference(avatar_split_clause,[],[f2281,f4860]) ).
fof(f4860,plain,
( spl0_396
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f2281,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f4858,plain,
spl0_395,
inference(avatar_split_clause,[],[f2280,f4856]) ).
fof(f4856,plain,
( spl0_395
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f2280,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f4854,plain,
spl0_394,
inference(avatar_split_clause,[],[f2279,f4852]) ).
fof(f4852,plain,
( spl0_394
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f2279,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__cancel__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f4850,plain,
spl0_393,
inference(avatar_split_clause,[],[f2278,f4848]) ).
fof(f4848,plain,
( spl0_393
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f2278,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f4846,plain,
spl0_392,
inference(avatar_split_clause,[],[f2277,f4844]) ).
fof(f4844,plain,
( spl0_392
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f2277,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f4842,plain,
spl0_391,
inference(avatar_split_clause,[],[f2275,f4840]) ).
fof(f4840,plain,
( spl0_391
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f2275,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__join(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f4838,plain,
spl0_390,
inference(avatar_split_clause,[],[f2274,f4836]) ).
fof(f4836,plain,
( spl0_390
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f2274,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f4834,plain,
spl0_389,
inference(avatar_split_clause,[],[f2273,f4832]) ).
fof(f4832,plain,
( spl0_389
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f2273,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__meet(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f4830,plain,
spl0_388,
inference(avatar_split_clause,[],[f2272,f4828]) ).
fof(f4828,plain,
( spl0_388
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f2272,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f4826,plain,
spl0_387,
inference(avatar_split_clause,[],[f2271,f4824]) ).
fof(f4824,plain,
( spl0_387
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f2271,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f4822,plain,
spl0_386,
inference(avatar_split_clause,[],[f2270,f4820]) ).
fof(f4820,plain,
( spl0_386
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f2270,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f4818,plain,
spl0_385,
inference(avatar_split_clause,[],[f2269,f4816]) ).
fof(f4816,plain,
( spl0_385
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f2269,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f4814,plain,
spl0_384,
inference(avatar_split_clause,[],[f2268,f4812]) ).
fof(f4812,plain,
( spl0_384
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f2268,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Olordered__ab__group__abs(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f4810,plain,
spl0_383,
inference(avatar_split_clause,[],[f2265,f4808]) ).
fof(f4808,plain,
( spl0_383
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f2265,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f4806,plain,
spl0_382,
inference(avatar_split_clause,[],[f2263,f4804]) ).
fof(f4804,plain,
( spl0_382
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f2263,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f4802,plain,
spl0_381,
inference(avatar_split_clause,[],[f2262,f4800]) ).
fof(f4800,plain,
( spl0_381
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f2262,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f4798,plain,
spl0_380,
inference(avatar_split_clause,[],[f2260,f4796]) ).
fof(f4796,plain,
( spl0_380
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f2260,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f4794,plain,
spl0_379,
inference(avatar_split_clause,[],[f2257,f4792]) ).
fof(f4792,plain,
( spl0_379
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f2257,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f4790,plain,
spl0_378,
inference(avatar_split_clause,[],[f2256,f4788]) ).
fof(f4788,plain,
( spl0_378
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f2256,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f4786,plain,
spl0_377,
inference(avatar_split_clause,[],[f2255,f4784]) ).
fof(f4784,plain,
( spl0_377
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f2255,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f4782,plain,
spl0_376,
inference(avatar_split_clause,[],[f2254,f4780]) ).
fof(f4780,plain,
( spl0_376
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f2254,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f4778,plain,
spl0_375,
inference(avatar_split_clause,[],[f2253,f4776]) ).
fof(f4776,plain,
( spl0_375
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f2253,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f4774,plain,
spl0_374,
inference(avatar_split_clause,[],[f2252,f4772]) ).
fof(f4772,plain,
( spl0_374
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f2252,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f4770,plain,
spl0_373,
inference(avatar_split_clause,[],[f2251,f4768]) ).
fof(f4768,plain,
( spl0_373
<=> ! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f2251,axiom,
! [X92] :
( ~ class_Ring__and__Field_Olordered__ring(X92)
| class_Ring__and__Field_Opordered__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f4766,plain,
spl0_372,
inference(avatar_split_clause,[],[f2250,f4764]) ).
fof(f4764,plain,
( spl0_372
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f2250,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_9) ).
fof(f4762,plain,
spl0_371,
inference(avatar_split_clause,[],[f2249,f4760]) ).
fof(f4760,plain,
( spl0_371
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f2249,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_8) ).
fof(f4758,plain,
spl0_370,
inference(avatar_split_clause,[],[f2248,f4756]) ).
fof(f4756,plain,
( spl0_370
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f2248,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_7) ).
fof(f4754,plain,
spl0_369,
inference(avatar_split_clause,[],[f2247,f4752]) ).
fof(f4752,plain,
( spl0_369
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f2247,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_6) ).
fof(f4750,plain,
spl0_368,
inference(avatar_split_clause,[],[f2245,f4748]) ).
fof(f4748,plain,
( spl0_368
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f2245,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_4) ).
fof(f4746,plain,
spl0_367,
inference(avatar_split_clause,[],[f2243,f4744]) ).
fof(f4744,plain,
( spl0_367
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f2243,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_3) ).
fof(f4742,plain,
spl0_366,
inference(avatar_split_clause,[],[f2240,f4740]) ).
fof(f4740,plain,
( spl0_366
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f2240,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_27) ).
fof(f4738,plain,
spl0_365,
inference(avatar_split_clause,[],[f2238,f4736]) ).
fof(f4736,plain,
( spl0_365
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f2238,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_25) ).
fof(f4734,plain,
spl0_364,
inference(avatar_split_clause,[],[f2236,f4732]) ).
fof(f4732,plain,
( spl0_364
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f2236,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_23) ).
fof(f4730,plain,
spl0_363,
inference(avatar_split_clause,[],[f2233,f4728]) ).
fof(f4728,plain,
( spl0_363
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f2233,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_20) ).
fof(f4726,plain,
spl0_362,
inference(avatar_split_clause,[],[f2232,f4724]) ).
fof(f4724,plain,
( spl0_362
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f2232,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_2) ).
fof(f4722,plain,
spl0_361,
inference(avatar_split_clause,[],[f2231,f4720]) ).
fof(f4720,plain,
( spl0_361
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f2231,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_19) ).
fof(f4718,plain,
spl0_360,
inference(avatar_split_clause,[],[f2230,f4716]) ).
fof(f4716,plain,
( spl0_360
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f2230,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_18) ).
fof(f4714,plain,
spl0_359,
inference(avatar_split_clause,[],[f2228,f4712]) ).
fof(f4712,plain,
( spl0_359
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f2228,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_16) ).
fof(f4710,plain,
spl0_358,
inference(avatar_split_clause,[],[f2227,f4708]) ).
fof(f4708,plain,
( spl0_358
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f2227,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_15) ).
fof(f4706,plain,
spl0_357,
inference(avatar_split_clause,[],[f2226,f4704]) ).
fof(f4704,plain,
( spl0_357
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f2226,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_14) ).
fof(f4702,plain,
spl0_356,
inference(avatar_split_clause,[],[f2225,f4700]) ).
fof(f4700,plain,
( spl0_356
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f2225,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_13) ).
fof(f4698,plain,
spl0_355,
inference(avatar_split_clause,[],[f2224,f4696]) ).
fof(f4696,plain,
( spl0_355
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f2224,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_12) ).
fof(f4694,plain,
spl0_354,
inference(avatar_split_clause,[],[f2223,f4692]) ).
fof(f4692,plain,
( spl0_354
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f2223,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_11) ).
fof(f4690,plain,
spl0_353,
inference(avatar_split_clause,[],[f2222,f4688]) ).
fof(f4688,plain,
( spl0_353
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f2222,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_10) ).
fof(f4686,plain,
spl0_352,
inference(avatar_split_clause,[],[f2221,f4684]) ).
fof(f4684,plain,
( spl0_352
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f2221,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_1) ).
fof(f4682,plain,
spl0_351,
inference(avatar_split_clause,[],[f2220,f4680]) ).
fof(f4680,plain,
( spl0_351
<=> ! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f2220,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oidom(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oidom_0) ).
fof(f4678,plain,
spl0_350,
inference(avatar_split_clause,[],[f2184,f4676]) ).
fof(f4676,plain,
( spl0_350
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f2184,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f4674,plain,
spl0_349,
inference(avatar_split_clause,[],[f2183,f4672]) ).
fof(f4672,plain,
( spl0_349
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f2183,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f4670,plain,
spl0_348,
inference(avatar_split_clause,[],[f2182,f4668]) ).
fof(f4668,plain,
( spl0_348
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f2182,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f4666,plain,
spl0_347,
inference(avatar_split_clause,[],[f2181,f4664]) ).
fof(f4664,plain,
( spl0_347
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f2181,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f4662,plain,
spl0_346,
inference(avatar_split_clause,[],[f2180,f4660]) ).
fof(f4660,plain,
( spl0_346
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f2180,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f4658,plain,
spl0_345,
inference(avatar_split_clause,[],[f2178,f4656]) ).
fof(f4656,plain,
( spl0_345
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f2178,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f4654,plain,
spl0_344,
inference(avatar_split_clause,[],[f2177,f4652]) ).
fof(f4652,plain,
( spl0_344
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f2177,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f4650,plain,
spl0_343,
inference(avatar_split_clause,[],[f2176,f4648]) ).
fof(f4648,plain,
( spl0_343
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f2176,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f4646,plain,
spl0_342,
inference(avatar_split_clause,[],[f2175,f4644]) ).
fof(f4644,plain,
( spl0_342
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f2175,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f4642,plain,
spl0_341,
inference(avatar_split_clause,[],[f2174,f4640]) ).
fof(f4640,plain,
( spl0_341
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f2174,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f4638,plain,
spl0_340,
inference(avatar_split_clause,[],[f2173,f4636]) ).
fof(f4636,plain,
( spl0_340
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f2173,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f4634,plain,
spl0_339,
inference(avatar_split_clause,[],[f2172,f4632]) ).
fof(f4632,plain,
( spl0_339
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f2172,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f4630,plain,
spl0_338,
inference(avatar_split_clause,[],[f2169,f4628]) ).
fof(f4628,plain,
( spl0_338
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f2169,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f4626,plain,
spl0_337,
inference(avatar_split_clause,[],[f2168,f4624]) ).
fof(f4624,plain,
( spl0_337
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f2168,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f4622,plain,
spl0_336,
inference(avatar_split_clause,[],[f2163,f4620]) ).
fof(f4620,plain,
( spl0_336
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f2163,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f4618,plain,
spl0_335,
inference(avatar_split_clause,[],[f2162,f4616]) ).
fof(f4616,plain,
( spl0_335
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f2162,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f4614,plain,
spl0_334,
inference(avatar_split_clause,[],[f2159,f4612]) ).
fof(f4612,plain,
( spl0_334
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f2159,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f4610,plain,
spl0_333,
inference(avatar_split_clause,[],[f2158,f4608]) ).
fof(f4608,plain,
( spl0_333
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f2158,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f4606,plain,
spl0_332,
inference(avatar_split_clause,[],[f2156,f4604]) ).
fof(f4604,plain,
( spl0_332
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f2156,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f4602,plain,
spl0_331,
inference(avatar_split_clause,[],[f2155,f4600]) ).
fof(f4600,plain,
( spl0_331
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f2155,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f4598,plain,
spl0_330,
inference(avatar_split_clause,[],[f2154,f4596]) ).
fof(f4596,plain,
( spl0_330
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f2154,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f4594,plain,
spl0_329,
inference(avatar_split_clause,[],[f2153,f4592]) ).
fof(f4592,plain,
( spl0_329
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f2153,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4590,plain,
spl0_328,
inference(avatar_split_clause,[],[f2152,f4588]) ).
fof(f4588,plain,
( spl0_328
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f2152,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4586,plain,
spl0_327,
inference(avatar_split_clause,[],[f2151,f4584]) ).
fof(f4584,plain,
( spl0_327
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f2151,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4582,plain,
spl0_326,
inference(avatar_split_clause,[],[f2147,f4580]) ).
fof(f4580,plain,
( spl0_326
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f2147,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4578,plain,
spl0_325,
inference(avatar_split_clause,[],[f2145,f4576]) ).
fof(f4576,plain,
( spl0_325
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f2145,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4574,plain,
spl0_324,
inference(avatar_split_clause,[],[f2142,f4572]) ).
fof(f4572,plain,
( spl0_324
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f2142,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4570,plain,
spl0_323,
inference(avatar_split_clause,[],[f2139,f4568]) ).
fof(f4568,plain,
( spl0_323
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f2139,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4566,plain,
spl0_322,
inference(avatar_split_clause,[],[f2138,f4564]) ).
fof(f4564,plain,
( spl0_322
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f2138,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4562,plain,
spl0_321,
inference(avatar_split_clause,[],[f2136,f4560]) ).
fof(f4560,plain,
( spl0_321
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f2136,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4558,plain,
spl0_320,
inference(avatar_split_clause,[],[f2135,f4556]) ).
fof(f4556,plain,
( spl0_320
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f2135,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4554,plain,
spl0_319,
inference(avatar_split_clause,[],[f2134,f4552]) ).
fof(f4552,plain,
( spl0_319
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f2134,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4550,plain,
spl0_318,
inference(avatar_split_clause,[],[f2131,f4548]) ).
fof(f4548,plain,
( spl0_318
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f2131,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4546,plain,
spl0_317,
inference(avatar_split_clause,[],[f2130,f4544]) ).
fof(f4544,plain,
( spl0_317
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f2130,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4542,plain,
spl0_316,
inference(avatar_split_clause,[],[f2128,f4540]) ).
fof(f4540,plain,
( spl0_316
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f2128,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4538,plain,
spl0_315,
inference(avatar_split_clause,[],[f2122,f4536]) ).
fof(f4536,plain,
( spl0_315
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f2122,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4534,plain,
spl0_314,
inference(avatar_split_clause,[],[f2121,f4532]) ).
fof(f4532,plain,
( spl0_314
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f2121,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4530,plain,
spl0_313,
inference(avatar_split_clause,[],[f2119,f4528]) ).
fof(f4528,plain,
( spl0_313
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f2119,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4526,plain,
spl0_312,
inference(avatar_split_clause,[],[f2118,f4524]) ).
fof(f4524,plain,
( spl0_312
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f2118,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__semiring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4522,plain,
spl0_311,
inference(avatar_split_clause,[],[f2111,f4520]) ).
fof(f4520,plain,
( spl0_311
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f2111,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4518,plain,
spl0_310,
inference(avatar_split_clause,[],[f2110,f4516]) ).
fof(f4516,plain,
( spl0_310
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f2110,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4514,plain,
spl0_309,
inference(avatar_split_clause,[],[f2108,f4512]) ).
fof(f4512,plain,
( spl0_309
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f2108,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4510,plain,
spl0_308,
inference(avatar_split_clause,[],[f2107,f4508]) ).
fof(f4508,plain,
( spl0_308
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f2107,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4506,plain,
spl0_307,
inference(avatar_split_clause,[],[f2106,f4504]) ).
fof(f4504,plain,
( spl0_307
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f2106,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4502,plain,
spl0_306,
inference(avatar_split_clause,[],[f2104,f4500]) ).
fof(f4500,plain,
( spl0_306
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f2104,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4498,plain,
spl0_305,
inference(avatar_split_clause,[],[f2103,f4496]) ).
fof(f4496,plain,
( spl0_305
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f2103,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4494,plain,
spl0_304,
inference(avatar_split_clause,[],[f2102,f4492]) ).
fof(f4492,plain,
( spl0_304
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f2102,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4490,plain,
spl0_303,
inference(avatar_split_clause,[],[f2101,f4488]) ).
fof(f4488,plain,
( spl0_303
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f2101,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4486,plain,
spl0_302,
inference(avatar_split_clause,[],[f2100,f4484]) ).
fof(f4484,plain,
( spl0_302
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f2100,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4482,plain,
spl0_301,
inference(avatar_split_clause,[],[f2099,f4480]) ).
fof(f4480,plain,
( spl0_301
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f2099,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4478,plain,
spl0_300,
inference(avatar_split_clause,[],[f2098,f4476]) ).
fof(f4476,plain,
( spl0_300
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f2098,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4474,plain,
spl0_299,
inference(avatar_split_clause,[],[f2097,f4472]) ).
fof(f4472,plain,
( spl0_299
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f2097,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4470,plain,
spl0_298,
inference(avatar_split_clause,[],[f2096,f4468]) ).
fof(f4468,plain,
( spl0_298
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f2096,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4466,plain,
spl0_297,
inference(avatar_split_clause,[],[f2095,f4464]) ).
fof(f4464,plain,
( spl0_297
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f2095,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4462,plain,
spl0_296,
inference(avatar_split_clause,[],[f2092,f4460]) ).
fof(f4460,plain,
( spl0_296
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f2092,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4458,plain,
spl0_295,
inference(avatar_split_clause,[],[f2090,f4456]) ).
fof(f4456,plain,
( spl0_295
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f2090,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4454,plain,
spl0_294,
inference(avatar_split_clause,[],[f2088,f4452]) ).
fof(f4452,plain,
( spl0_294
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f2088,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4450,plain,
spl0_293,
inference(avatar_split_clause,[],[f2085,f4448]) ).
fof(f4448,plain,
( spl0_293
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f2085,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4446,plain,
spl0_292,
inference(avatar_split_clause,[],[f2084,f4444]) ).
fof(f4444,plain,
( spl0_292
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f2084,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4442,plain,
spl0_291,
inference(avatar_split_clause,[],[f2083,f4440]) ).
fof(f4440,plain,
( spl0_291
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f2083,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4438,plain,
spl0_290,
inference(avatar_split_clause,[],[f2080,f4436]) ).
fof(f4436,plain,
( spl0_290
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f2080,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4434,plain,
spl0_289,
inference(avatar_split_clause,[],[f2077,f4432]) ).
fof(f4432,plain,
( spl0_289
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f2077,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4430,plain,
spl0_288,
inference(avatar_split_clause,[],[f2076,f4428]) ).
fof(f4428,plain,
( spl0_288
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f2076,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4426,plain,
spl0_287,
inference(avatar_split_clause,[],[f2074,f4424]) ).
fof(f4424,plain,
( spl0_287
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f2074,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4422,plain,
spl0_286,
inference(avatar_split_clause,[],[f2073,f4420]) ).
fof(f4420,plain,
( spl0_286
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f2073,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4418,plain,
spl0_285,
inference(avatar_split_clause,[],[f2072,f4416]) ).
fof(f4416,plain,
( spl0_285
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f2072,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4414,plain,
spl0_284,
inference(avatar_split_clause,[],[f2071,f4412]) ).
fof(f4412,plain,
( spl0_284
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f2071,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4410,plain,
spl0_283,
inference(avatar_split_clause,[],[f2070,f4408]) ).
fof(f4408,plain,
( spl0_283
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f2070,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4406,plain,
spl0_282,
inference(avatar_split_clause,[],[f2068,f4404]) ).
fof(f4404,plain,
( spl0_282
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f2068,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4402,plain,
spl0_281,
inference(avatar_split_clause,[],[f2065,f4400]) ).
fof(f4400,plain,
( spl0_281
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f2065,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4398,plain,
spl0_280,
inference(avatar_split_clause,[],[f2064,f4396]) ).
fof(f4396,plain,
( spl0_280
<=> ! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f2064,axiom,
! [X92] :
( ~ class_Ring__and__Field_Ocomm__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4394,plain,
spl0_279,
inference(avatar_split_clause,[],[f2060,f4392]) ).
fof(f4392,plain,
( spl0_279
<=> ! [X92] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f2060,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4390,plain,
spl0_278,
inference(avatar_split_clause,[],[f2058,f4388]) ).
fof(f4388,plain,
( spl0_278
<=> ! [X92] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f2058,axiom,
! [X92] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4386,plain,
spl0_277,
inference(avatar_split_clause,[],[f2050,f4384]) ).
fof(f4384,plain,
( spl0_277
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f2050,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_3) ).
fof(f4382,plain,
spl0_276,
inference(avatar_split_clause,[],[f2049,f4380]) ).
fof(f4380,plain,
( spl0_276
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f2049,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_24) ).
fof(f4378,plain,
spl0_275,
inference(avatar_split_clause,[],[f2048,f4376]) ).
fof(f4376,plain,
( spl0_275
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f2048,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_23) ).
fof(f4374,plain,
spl0_274,
inference(avatar_split_clause,[],[f2047,f4372]) ).
fof(f4372,plain,
( spl0_274
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f2047,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_22) ).
fof(f4370,plain,
spl0_273,
inference(avatar_split_clause,[],[f2046,f4368]) ).
fof(f4368,plain,
( spl0_273
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f2046,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_21) ).
fof(f4366,plain,
spl0_272,
inference(avatar_split_clause,[],[f2045,f4364]) ).
fof(f4364,plain,
( spl0_272
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f2045,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_20) ).
fof(f4362,plain,
spl0_271,
inference(avatar_split_clause,[],[f2044,f4360]) ).
fof(f4360,plain,
( spl0_271
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f2044,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_2) ).
fof(f4358,plain,
spl0_270,
inference(avatar_split_clause,[],[f2043,f4356]) ).
fof(f4356,plain,
( spl0_270
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f2043,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_19) ).
fof(f4354,plain,
spl0_269,
inference(avatar_split_clause,[],[f2042,f4352]) ).
fof(f4352,plain,
( spl0_269
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f2042,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_18) ).
fof(f4350,plain,
spl0_268,
inference(avatar_split_clause,[],[f2041,f4348]) ).
fof(f4348,plain,
( spl0_268
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f2041,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_17) ).
fof(f4346,plain,
spl0_267,
inference(avatar_split_clause,[],[f2040,f4344]) ).
fof(f4344,plain,
( spl0_267
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f2040,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_16) ).
fof(f4342,plain,
spl0_266,
inference(avatar_split_clause,[],[f2039,f4340]) ).
fof(f4340,plain,
( spl0_266
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f2039,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_15) ).
fof(f4338,plain,
spl0_265,
inference(avatar_split_clause,[],[f2038,f4336]) ).
fof(f4336,plain,
( spl0_265
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f2038,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_14) ).
fof(f4334,plain,
spl0_264,
inference(avatar_split_clause,[],[f2037,f4332]) ).
fof(f4332,plain,
( spl0_264
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f2037,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_13) ).
fof(f4330,plain,
spl0_263,
inference(avatar_split_clause,[],[f2036,f4328]) ).
fof(f4328,plain,
( spl0_263
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f2036,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_12) ).
fof(f4326,plain,
spl0_262,
inference(avatar_split_clause,[],[f2035,f4324]) ).
fof(f4324,plain,
( spl0_262
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f2035,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_11) ).
fof(f4322,plain,
spl0_261,
inference(avatar_split_clause,[],[f2034,f4320]) ).
fof(f4320,plain,
( spl0_261
<=> ! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f2034,axiom,
! [X92] :
( ~ class_Power_Orecpower(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Power_Orecpower_10) ).
fof(f4318,plain,
spl0_260,
inference(avatar_split_clause,[],[f2031,f4316]) ).
fof(f4316,plain,
( spl0_260
<=> ! [X92] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f2031,axiom,
! [X92] :
( ~ class_Orderings_Oorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Oorder_0) ).
fof(f4314,plain,
spl0_259,
inference(avatar_split_clause,[],[f2030,f4312]) ).
fof(f4312,plain,
( spl0_259
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f2030,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_4) ).
fof(f4310,plain,
spl0_258,
inference(avatar_split_clause,[],[f2029,f4308]) ).
fof(f4308,plain,
( spl0_258
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f2029,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_3) ).
fof(f4306,plain,
spl0_257,
inference(avatar_split_clause,[],[f2028,f4304]) ).
fof(f4304,plain,
( spl0_257
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f2028,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_2) ).
fof(f4302,plain,
spl0_256,
inference(avatar_split_clause,[],[f2027,f4300]) ).
fof(f4300,plain,
( spl0_256
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f2027,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_1) ).
fof(f4298,plain,
spl0_255,
inference(avatar_split_clause,[],[f2026,f4296]) ).
fof(f4296,plain,
( spl0_255
<=> ! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f2026,axiom,
! [X92] :
( ~ class_Orderings_Olinorder(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Orderings_Olinorder_0) ).
fof(f4294,plain,
spl0_254,
inference(avatar_split_clause,[],[f2023,f4292]) ).
fof(f4292,plain,
( spl0_254
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f2023,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4290,plain,
spl0_253,
inference(avatar_split_clause,[],[f2022,f4288]) ).
fof(f4288,plain,
( spl0_253
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f2022,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4286,plain,
spl0_252,
inference(avatar_split_clause,[],[f2018,f4284]) ).
fof(f4284,plain,
( spl0_252
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f2018,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4282,plain,
spl0_251,
inference(avatar_split_clause,[],[f2017,f4280]) ).
fof(f4280,plain,
( spl0_251
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f2017,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4278,plain,
spl0_250,
inference(avatar_split_clause,[],[f2016,f4276]) ).
fof(f4276,plain,
( spl0_250
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f2016,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4274,plain,
spl0_249,
inference(avatar_split_clause,[],[f2013,f4272]) ).
fof(f4272,plain,
( spl0_249
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f2013,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4270,plain,
spl0_248,
inference(avatar_split_clause,[],[f2011,f4268]) ).
fof(f4268,plain,
( spl0_248
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f2011,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4266,plain,
spl0_247,
inference(avatar_split_clause,[],[f2010,f4264]) ).
fof(f4264,plain,
( spl0_247
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f2010,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4262,plain,
spl0_246,
inference(avatar_split_clause,[],[f2009,f4260]) ).
fof(f4260,plain,
( spl0_246
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f2009,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4258,plain,
spl0_245,
inference(avatar_split_clause,[],[f2008,f4256]) ).
fof(f4256,plain,
( spl0_245
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f2008,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4254,plain,
spl0_244,
inference(avatar_split_clause,[],[f2007,f4252]) ).
fof(f4252,plain,
( spl0_244
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f2007,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4250,plain,
spl0_243,
inference(avatar_split_clause,[],[f2003,f4248]) ).
fof(f4248,plain,
( spl0_243
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f2003,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4246,plain,
spl0_242,
inference(avatar_split_clause,[],[f2002,f4244]) ).
fof(f4244,plain,
( spl0_242
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f2002,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4242,plain,
spl0_241,
inference(avatar_split_clause,[],[f2001,f4240]) ).
fof(f4240,plain,
( spl0_241
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f2001,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4238,plain,
spl0_240,
inference(avatar_split_clause,[],[f1998,f4236]) ).
fof(f4236,plain,
( spl0_240
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f1998,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4234,plain,
spl0_239,
inference(avatar_split_clause,[],[f1996,f4232]) ).
fof(f4232,plain,
( spl0_239
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f1996,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4230,plain,
spl0_238,
inference(avatar_split_clause,[],[f1994,f4228]) ).
fof(f4228,plain,
( spl0_238
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f1994,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4226,plain,
spl0_237,
inference(avatar_split_clause,[],[f1993,f4224]) ).
fof(f4224,plain,
( spl0_237
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f1993,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4222,plain,
spl0_236,
inference(avatar_split_clause,[],[f1992,f4220]) ).
fof(f4220,plain,
( spl0_236
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f1992,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4218,plain,
spl0_235,
inference(avatar_split_clause,[],[f1991,f4216]) ).
fof(f4216,plain,
( spl0_235
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f1991,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4214,plain,
spl0_234,
inference(avatar_split_clause,[],[f1990,f4212]) ).
fof(f4212,plain,
( spl0_234
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f1990,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4210,plain,
spl0_233,
inference(avatar_split_clause,[],[f1988,f4208]) ).
fof(f4208,plain,
( spl0_233
<=> ! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f1988,axiom,
! [X92] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4206,plain,
spl0_232,
inference(avatar_split_clause,[],[f1987,f4204]) ).
fof(f4204,plain,
( spl0_232
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Olinorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f1987,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Olinorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4202,plain,
spl0_231,
inference(avatar_split_clause,[],[f1984,f4200]) ).
fof(f4200,plain,
( spl0_231
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f1984,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4198,plain,
spl0_230,
inference(avatar_split_clause,[],[f1982,f4196]) ).
fof(f4196,plain,
( spl0_230
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f1982,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4194,plain,
spl0_229,
inference(avatar_split_clause,[],[f1981,f4192]) ).
fof(f4192,plain,
( spl0_229
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f1981,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4190,plain,
spl0_228,
inference(avatar_split_clause,[],[f1980,f4188]) ).
fof(f4188,plain,
( spl0_228
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f1980,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4186,plain,
spl0_227,
inference(avatar_split_clause,[],[f1979,f4184]) ).
fof(f4184,plain,
( spl0_227
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f1979,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4182,plain,
spl0_226,
inference(avatar_split_clause,[],[f1978,f4180]) ).
fof(f4180,plain,
( spl0_226
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f1978,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4178,plain,
spl0_225,
inference(avatar_split_clause,[],[f1977,f4176]) ).
fof(f4176,plain,
( spl0_225
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f1977,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4174,plain,
spl0_224,
inference(avatar_split_clause,[],[f1976,f4172]) ).
fof(f4172,plain,
( spl0_224
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f1976,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4170,plain,
spl0_223,
inference(avatar_split_clause,[],[f1975,f4168]) ).
fof(f4168,plain,
( spl0_223
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f1975,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4166,plain,
spl0_222,
inference(avatar_split_clause,[],[f1974,f4164]) ).
fof(f4164,plain,
( spl0_222
<=> ! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f1974,axiom,
! [X92] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4162,plain,
spl0_221,
inference(avatar_split_clause,[],[f1971,f4160]) ).
fof(f4160,plain,
( spl0_221
<=> ! [X92] :
( ~ class_OrderedGroup_Omonoid__mult(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f1971,axiom,
! [X92] :
( ~ class_OrderedGroup_Omonoid__mult(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4158,plain,
spl0_220,
inference(avatar_split_clause,[],[f1970,f4156]) ).
fof(f4156,plain,
( spl0_220
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f1970,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4154,plain,
spl0_219,
inference(avatar_split_clause,[],[f1969,f4152]) ).
fof(f4152,plain,
( spl0_219
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f1969,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4150,plain,
spl0_218,
inference(avatar_split_clause,[],[f1968,f4148]) ).
fof(f4148,plain,
( spl0_218
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f1968,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4146,plain,
spl0_217,
inference(avatar_split_clause,[],[f1967,f4144]) ).
fof(f4144,plain,
( spl0_217
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f1967,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4142,plain,
spl0_216,
inference(avatar_split_clause,[],[f1966,f4140]) ).
fof(f4140,plain,
( spl0_216
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f1966,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4138,plain,
spl0_215,
inference(avatar_split_clause,[],[f1964,f4136]) ).
fof(f4136,plain,
( spl0_215
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f1964,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4134,plain,
spl0_214,
inference(avatar_split_clause,[],[f1962,f4132]) ).
fof(f4132,plain,
( spl0_214
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f1962,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4130,plain,
spl0_213,
inference(avatar_split_clause,[],[f1961,f4128]) ).
fof(f4128,plain,
( spl0_213
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f1961,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4126,plain,
spl0_212,
inference(avatar_split_clause,[],[f1960,f4124]) ).
fof(f4124,plain,
( spl0_212
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f1960,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4122,plain,
spl0_211,
inference(avatar_split_clause,[],[f1959,f4120]) ).
fof(f4120,plain,
( spl0_211
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f1959,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4118,plain,
spl0_210,
inference(avatar_split_clause,[],[f1956,f4116]) ).
fof(f4116,plain,
( spl0_210
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f1956,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4114,plain,
spl0_209,
inference(avatar_split_clause,[],[f1954,f4112]) ).
fof(f4112,plain,
( spl0_209
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f1954,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4110,plain,
spl0_208,
inference(avatar_split_clause,[],[f1953,f4108]) ).
fof(f4108,plain,
( spl0_208
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f1953,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4106,plain,
spl0_207,
inference(avatar_split_clause,[],[f1952,f4104]) ).
fof(f4104,plain,
( spl0_207
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f1952,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4102,plain,
spl0_206,
inference(avatar_split_clause,[],[f1951,f4100]) ).
fof(f4100,plain,
( spl0_206
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f1951,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4098,plain,
spl0_205,
inference(avatar_split_clause,[],[f1950,f4096]) ).
fof(f4096,plain,
( spl0_205
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f1950,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4094,plain,
spl0_204,
inference(avatar_split_clause,[],[f1949,f4092]) ).
fof(f4092,plain,
( spl0_204
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f1949,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4090,plain,
spl0_203,
inference(avatar_split_clause,[],[f1948,f4088]) ).
fof(f4088,plain,
( spl0_203
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f1948,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4086,plain,
spl0_202,
inference(avatar_split_clause,[],[f1947,f4084]) ).
fof(f4084,plain,
( spl0_202
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f1947,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4082,plain,
spl0_201,
inference(avatar_split_clause,[],[f1945,f4080]) ).
fof(f4080,plain,
( spl0_201
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f1945,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4078,plain,
spl0_200,
inference(avatar_split_clause,[],[f1943,f4076]) ).
fof(f4076,plain,
( spl0_200
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f1943,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4074,plain,
spl0_199,
inference(avatar_split_clause,[],[f1942,f4072]) ).
fof(f4072,plain,
( spl0_199
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f1942,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4070,plain,
spl0_198,
inference(avatar_split_clause,[],[f1941,f4068]) ).
fof(f4068,plain,
( spl0_198
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f1941,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4066,plain,
spl0_197,
inference(avatar_split_clause,[],[f1940,f4064]) ).
fof(f4064,plain,
( spl0_197
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f1940,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4062,plain,
spl0_196,
inference(avatar_split_clause,[],[f1937,f4060]) ).
fof(f4060,plain,
( spl0_196
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f1937,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4058,plain,
spl0_195,
inference(avatar_split_clause,[],[f1935,f4056]) ).
fof(f4056,plain,
( spl0_195
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f1935,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4054,plain,
spl0_194,
inference(avatar_split_clause,[],[f1934,f4052]) ).
fof(f4052,plain,
( spl0_194
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f1934,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4050,plain,
spl0_193,
inference(avatar_split_clause,[],[f1933,f4048]) ).
fof(f4048,plain,
( spl0_193
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f1933,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4046,plain,
spl0_192,
inference(avatar_split_clause,[],[f1932,f4044]) ).
fof(f4044,plain,
( spl0_192
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f1932,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4042,plain,
spl0_191,
inference(avatar_split_clause,[],[f1931,f4040]) ).
fof(f4040,plain,
( spl0_191
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f1931,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4038,plain,
spl0_190,
inference(avatar_split_clause,[],[f1930,f4036]) ).
fof(f4036,plain,
( spl0_190
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f1930,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4034,plain,
spl0_189,
inference(avatar_split_clause,[],[f1929,f4032]) ).
fof(f4032,plain,
( spl0_189
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f1929,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4030,plain,
spl0_188,
inference(avatar_split_clause,[],[f1927,f4028]) ).
fof(f4028,plain,
( spl0_188
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f1927,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4026,plain,
spl0_187,
inference(avatar_split_clause,[],[f1925,f4024]) ).
fof(f4024,plain,
( spl0_187
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f1925,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4022,plain,
spl0_186,
inference(avatar_split_clause,[],[f1924,f4020]) ).
fof(f4020,plain,
( spl0_186
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f1924,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4018,plain,
spl0_185,
inference(avatar_split_clause,[],[f1923,f4016]) ).
fof(f4016,plain,
( spl0_185
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f1923,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4014,plain,
spl0_184,
inference(avatar_split_clause,[],[f1922,f4012]) ).
fof(f4012,plain,
( spl0_184
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f1922,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4010,plain,
spl0_183,
inference(avatar_split_clause,[],[f1921,f4008]) ).
fof(f4008,plain,
( spl0_183
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f1921,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4006,plain,
spl0_182,
inference(avatar_split_clause,[],[f1920,f4004]) ).
fof(f4004,plain,
( spl0_182
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f1920,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4002,plain,
spl0_181,
inference(avatar_split_clause,[],[f1917,f4000]) ).
fof(f4000,plain,
( spl0_181
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f1917,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f3998,plain,
spl0_180,
inference(avatar_split_clause,[],[f1915,f3996]) ).
fof(f3996,plain,
( spl0_180
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f1915,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f3994,plain,
spl0_179,
inference(avatar_split_clause,[],[f1914,f3992]) ).
fof(f3992,plain,
( spl0_179
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f1914,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X92)
| class_OrderedGroup_Olordered__ab__group(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f3990,plain,
spl0_178,
inference(avatar_split_clause,[],[f1913,f3988]) ).
fof(f3988,plain,
( spl0_178
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f1913,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f3986,plain,
spl0_177,
inference(avatar_split_clause,[],[f1912,f3984]) ).
fof(f3984,plain,
( spl0_177
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f1912,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f3982,plain,
spl0_176,
inference(avatar_split_clause,[],[f1911,f3980]) ).
fof(f3980,plain,
( spl0_176
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f1911,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f3978,plain,
spl0_175,
inference(avatar_split_clause,[],[f1910,f3976]) ).
fof(f3976,plain,
( spl0_175
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f1910,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f3974,plain,
spl0_174,
inference(avatar_split_clause,[],[f1909,f3972]) ).
fof(f3972,plain,
( spl0_174
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f1909,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f3970,plain,
spl0_173,
inference(avatar_split_clause,[],[f1907,f3968]) ).
fof(f3968,plain,
( spl0_173
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f1907,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f3966,plain,
spl0_172,
inference(avatar_split_clause,[],[f1905,f3964]) ).
fof(f3964,plain,
( spl0_172
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f1905,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f3962,plain,
spl0_171,
inference(avatar_split_clause,[],[f1904,f3960]) ).
fof(f3960,plain,
( spl0_171
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f1904,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f3958,plain,
spl0_170,
inference(avatar_split_clause,[],[f1903,f3956]) ).
fof(f3956,plain,
( spl0_170
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Olorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f1903,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_LOrder_Olorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3954,plain,
spl0_169,
inference(avatar_split_clause,[],[f1900,f3952]) ).
fof(f3952,plain,
( spl0_169
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f1900,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3950,plain,
spl0_168,
inference(avatar_split_clause,[],[f1898,f3948]) ).
fof(f3948,plain,
( spl0_168
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f1898,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3946,plain,
spl0_167,
inference(avatar_split_clause,[],[f1897,f3944]) ).
fof(f3944,plain,
( spl0_167
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f1897,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3942,plain,
spl0_166,
inference(avatar_split_clause,[],[f1896,f3940]) ).
fof(f3940,plain,
( spl0_166
<=> ! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f1896,axiom,
! [X92] :
( ~ class_OrderedGroup_Olordered__ab__group(X92)
| class_OrderedGroup_Opordered__ab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3938,plain,
spl0_165,
inference(avatar_split_clause,[],[f1895,f3936]) ).
fof(f3936,plain,
( spl0_165
<=> ! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f1895,axiom,
! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3934,plain,
spl0_164,
inference(avatar_split_clause,[],[f1891,f3932]) ).
fof(f3932,plain,
( spl0_164
<=> ! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f1891,axiom,
! [X92] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3930,plain,
spl0_163,
inference(avatar_split_clause,[],[f1884,f3928]) ).
fof(f3928,plain,
( spl0_163
<=> ! [X92] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f1884,axiom,
! [X92] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3926,plain,
spl0_162,
inference(avatar_split_clause,[],[f1876,f3924]) ).
fof(f3924,plain,
( spl0_162
<=> ! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f1876,axiom,
! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3922,plain,
spl0_161,
inference(avatar_split_clause,[],[f1875,f3920]) ).
fof(f3920,plain,
( spl0_161
<=> ! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f1875,axiom,
! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3918,plain,
spl0_160,
inference(avatar_split_clause,[],[f1870,f3916]) ).
fof(f3916,plain,
( spl0_160
<=> ! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f1870,axiom,
! [X92] :
( ~ class_OrderedGroup_Oab__group__add(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3914,plain,
spl0_159,
inference(avatar_split_clause,[],[f1868,f3912]) ).
fof(f3912,plain,
( spl0_159
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f1868,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_9) ).
fof(f3910,plain,
spl0_158,
inference(avatar_split_clause,[],[f1866,f3908]) ).
fof(f3908,plain,
( spl0_158
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f1866,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_7) ).
fof(f3906,plain,
spl0_157,
inference(avatar_split_clause,[],[f1865,f3904]) ).
fof(f3904,plain,
( spl0_157
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f1865,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_6) ).
fof(f3902,plain,
spl0_156,
inference(avatar_split_clause,[],[f1862,f3900]) ).
fof(f3900,plain,
( spl0_156
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Numeral_Onumber(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f1862,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Numeral_Onumber(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_30) ).
fof(f3898,plain,
spl0_155,
inference(avatar_split_clause,[],[f1860,f3896]) ).
fof(f3896,plain,
( spl0_155
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f1860,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_29) ).
fof(f3894,plain,
spl0_154,
inference(avatar_split_clause,[],[f1859,f3892]) ).
fof(f3892,plain,
( spl0_154
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f1859,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_28) ).
fof(f3890,plain,
spl0_153,
inference(avatar_split_clause,[],[f1858,f3888]) ).
fof(f3888,plain,
( spl0_153
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f1858,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_27) ).
fof(f3886,plain,
spl0_152,
inference(avatar_split_clause,[],[f1857,f3884]) ).
fof(f3884,plain,
( spl0_152
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f1857,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_26) ).
fof(f3882,plain,
spl0_151,
inference(avatar_split_clause,[],[f1856,f3880]) ).
fof(f3880,plain,
( spl0_151
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f1856,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_25) ).
fof(f3878,plain,
spl0_150,
inference(avatar_split_clause,[],[f1855,f3876]) ).
fof(f3876,plain,
( spl0_150
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f1855,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_24) ).
fof(f3874,plain,
spl0_149,
inference(avatar_split_clause,[],[f1854,f3872]) ).
fof(f3872,plain,
( spl0_149
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f1854,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocomm__monoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_23) ).
fof(f3870,plain,
spl0_148,
inference(avatar_split_clause,[],[f1853,f3868]) ).
fof(f3868,plain,
( spl0_148
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Omonoid__mult(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f1853,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Omonoid__mult(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_22) ).
fof(f3866,plain,
spl0_147,
inference(avatar_split_clause,[],[f1852,f3864]) ).
fof(f3864,plain,
( spl0_147
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f1852,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oaxclass__0__neq__1(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_21) ).
fof(f3862,plain,
spl0_146,
inference(avatar_split_clause,[],[f1851,f3860]) ).
fof(f3860,plain,
( spl0_146
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_HOL_Oone(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f1851,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_HOL_Oone(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_20) ).
fof(f3858,plain,
spl0_145,
inference(avatar_split_clause,[],[f1849,f3856]) ).
fof(f3856,plain,
( spl0_145
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f1849,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__ring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_19) ).
fof(f3854,plain,
spl0_144,
inference(avatar_split_clause,[],[f1848,f3852]) ).
fof(f3852,plain,
( spl0_144
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f1848,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_18) ).
fof(f3850,plain,
spl0_143,
inference(avatar_split_clause,[],[f1847,f3848]) ).
fof(f3848,plain,
( spl0_143
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f1847,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Oring(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_17) ).
fof(f3846,plain,
spl0_142,
inference(avatar_split_clause,[],[f1846,f3844]) ).
fof(f3844,plain,
( spl0_142
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f1846,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0__cancel(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_16) ).
fof(f3842,plain,
spl0_141,
inference(avatar_split_clause,[],[f1845,f3840]) ).
fof(f3840,plain,
( spl0_141
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f1845,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Oab__group__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_15) ).
fof(f3838,plain,
spl0_140,
inference(avatar_split_clause,[],[f1844,f3836]) ).
fof(f3836,plain,
( spl0_140
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f1844,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_14) ).
fof(f3834,plain,
spl0_139,
inference(avatar_split_clause,[],[f1843,f3832]) ).
fof(f3832,plain,
( spl0_139
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f1843,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_OrderedGroup_Ocancel__semigroup__add(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_13) ).
fof(f3830,plain,
spl0_138,
inference(avatar_split_clause,[],[f1841,f3828]) ).
fof(f3828,plain,
( spl0_138
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f1841,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Ocomm__semiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_11) ).
fof(f3826,plain,
spl0_137,
inference(avatar_split_clause,[],[f1840,f3824]) ).
fof(f3824,plain,
( spl0_137
<=> ! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f1840,axiom,
! [X92] :
( ~ class_Numeral_Onumber__ring(X92)
| class_Ring__and__Field_Osemiring__0(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_Numeral_Onumber__ring_10) ).
fof(f3822,plain,
spl0_136,
inference(avatar_split_clause,[],[f1837,f3820]) ).
fof(f3820,plain,
( spl0_136
<=> ! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f1837,axiom,
! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3818,plain,
spl0_135,
inference(avatar_split_clause,[],[f1836,f3816]) ).
fof(f3816,plain,
( spl0_135
<=> ! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f1836,axiom,
! [X92] :
( ~ class_LOrder_Omeet__semilorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3814,plain,
spl0_134,
inference(avatar_split_clause,[],[f1835,f3812]) ).
fof(f3812,plain,
( spl0_134
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f1835,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Ojoin__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_3) ).
fof(f3810,plain,
spl0_133,
inference(avatar_split_clause,[],[f1834,f3808]) ).
fof(f3808,plain,
( spl0_133
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f1834,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_2) ).
fof(f3806,plain,
spl0_132,
inference(avatar_split_clause,[],[f1833,f3804]) ).
fof(f3804,plain,
( spl0_132
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f1833,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_1) ).
fof(f3802,plain,
spl0_131,
inference(avatar_split_clause,[],[f1832,f3800]) ).
fof(f3800,plain,
( spl0_131
<=> ! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Omeet__semilorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f1832,axiom,
! [X92] :
( ~ class_LOrder_Olorder(X92)
| class_LOrder_Omeet__semilorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Olorder_0) ).
fof(f3798,plain,
spl0_130,
inference(avatar_split_clause,[],[f1831,f3796]) ).
fof(f3796,plain,
( spl0_130
<=> ! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oorder(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f1831,axiom,
! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oorder(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3794,plain,
spl0_129,
inference(avatar_split_clause,[],[f1830,f3792]) ).
fof(f3792,plain,
( spl0_129
<=> ! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oord(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1830,axiom,
! [X92] :
( ~ class_LOrder_Ojoin__semilorder(X92)
| class_Orderings_Oord(X92) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3790,plain,
spl0_128,
inference(avatar_split_clause,[],[f1675,f3788]) ).
fof(f3788,plain,
( spl0_128
<=> ! [X11,X3] : c_in(X11,c_UNIV,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1675,axiom,
! [X3,X11] : c_in(X11,c_UNIV,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__I_0) ).
fof(f3786,plain,
spl0_127,
inference(avatar_split_clause,[],[f1643,f3784]) ).
fof(f3784,plain,
( spl0_127
<=> ! [X10] : ~ c_less(X10,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f1643,axiom,
! [X10] : ~ c_less(X10,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__irrefl_0) ).
fof(f3782,plain,
spl0_126,
inference(avatar_split_clause,[],[f1641,f3780]) ).
fof(f3780,plain,
( spl0_126
<=> ! [X10] : c_lessequals(c_0,X10,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1641,axiom,
! [X10] : c_lessequals(c_0,X10,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole0_0) ).
fof(f3778,plain,
spl0_125,
inference(avatar_split_clause,[],[f1617,f3776]) ).
fof(f3776,plain,
( spl0_125
<=> ! [X25] : c_Divides_Oop_Advd(c_1,X25,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f1617,axiom,
! [X25] : c_Divides_Oop_Advd(c_1,X25,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3774,plain,
spl0_124,
inference(avatar_split_clause,[],[f1616,f3772]) ).
fof(f3772,plain,
( spl0_124
<=> ! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f1616,axiom,
! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3770,plain,
spl0_123,
inference(avatar_split_clause,[],[f1600,f3768]) ).
fof(f3768,plain,
( spl0_123
<=> ! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f1600,axiom,
! [X25] : c_Divides_Oop_Advd(X25,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__0__right_0) ).
fof(f3766,plain,
spl0_122,
inference(avatar_split_clause,[],[f1522,f3764]) ).
fof(f3764,plain,
( spl0_122
<=> ! [X3,X26] : ~ c_in(X26,c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f1522,axiom,
! [X3,X26] : ~ c_in(X26,c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).
fof(f3762,plain,
spl0_121,
inference(avatar_split_clause,[],[f1005,f3759]) ).
fof(f3759,plain,
( spl0_121
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f1005,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(f3757,plain,
spl0_120,
inference(avatar_split_clause,[],[f941,f3755]) ).
fof(f3755,plain,
( spl0_120
<=> ! [X10] : ~ c_less(X10,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f941,axiom,
! [X10] : ~ c_less(X10,c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onot__less0_0) ).
fof(f3753,plain,
spl0_119,
inference(avatar_split_clause,[],[f899,f3750]) ).
fof(f3750,plain,
( spl0_119
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f899,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oless__one_1) ).
fof(f3748,plain,
spl0_118,
inference(avatar_split_clause,[],[f559,f3746]) ).
fof(f3746,plain,
( spl0_118
<=> ! [X13,X11] : ~ c_List_Oop_Amem(X11,c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f559,axiom,
! [X11,X13] : ~ c_List_Oop_Amem(X11,c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f3744,plain,
spl0_117,
inference(avatar_split_clause,[],[f332,f3742]) ).
fof(f332,axiom,
! [X25] : c_Divides_Oop_Advd(X25,X25,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDiv_Ozdvd__refl_0) ).
fof(f3740,plain,
spl0_116,
inference(avatar_split_clause,[],[f243,f3738]) ).
fof(f243,axiom,
! [X10] : ~ c_IntDef_Oneg(c_IntDef_Oint(X10),tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onot__neg__int_0) ).
fof(f3736,plain,
spl0_115,
inference(avatar_split_clause,[],[f236,f3733]) ).
fof(f3733,plain,
( spl0_115
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f236,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Onat__zero_0) ).
fof(f3731,plain,
spl0_114,
inference(avatar_split_clause,[],[f224,f3728]) ).
fof(f3726,plain,
spl0_113,
inference(avatar_split_clause,[],[f221,f3723]) ).
fof(f221,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__1_0) ).
fof(f3721,plain,
spl0_112,
inference(avatar_split_clause,[],[f79,f3719]) ).
fof(f3719,plain,
( spl0_112
<=> ! [X25] : c_Divides_Oop_Advd(X25,X25,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f79,axiom,
! [X25] : c_Divides_Oop_Advd(X25,X25,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Divides_Odvd__refl_0) ).
fof(f3717,plain,
spl0_111,
inference(avatar_split_clause,[],[f2750,f3715]) ).
fof(f2750,axiom,
! [X30] :
( ~ c_in(X30,v_S,t_a)
| c_in(c_Pair(X30,v_L,t_a,t_a),v_r,tc_prod(t_a,t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3713,plain,
spl0_110,
inference(avatar_split_clause,[],[f1826,f3711]) ).
fof(f1826,axiom,
! [X90] : class_Orderings_Oorder(tc_set(X90)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_2) ).
fof(f3709,plain,
spl0_109,
inference(avatar_split_clause,[],[f1825,f3707]) ).
fof(f3707,plain,
( spl0_109
<=> ! [X90] : class_Orderings_Oord(tc_set(X90)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f1825,axiom,
! [X90] : class_Orderings_Oord(tc_set(X90)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_set_1) ).
fof(f3705,plain,
spl0_108,
inference(avatar_split_clause,[],[f1703,f3702]) ).
fof(f3702,plain,
( spl0_108
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f1703,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(f3700,plain,
spl0_107,
inference(avatar_split_clause,[],[f1701,f3697]) ).
fof(f3697,plain,
( spl0_107
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f1701,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(f3695,plain,
spl0_106,
inference(avatar_split_clause,[],[f1700,f3693]) ).
fof(f3693,plain,
( spl0_106
<=> ! [X3] : c_Wellfounded__Recursion_Owf(c_emptyset,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f1700,axiom,
! [X3] : c_Wellfounded__Recursion_Owf(c_emptyset,X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3691,plain,
~ spl0_105,
inference(avatar_split_clause,[],[f1479,f3688]) ).
fof(f3688,plain,
( spl0_105
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f1479,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUNIV__not__empty_0) ).
fof(f3686,plain,
~ spl0_104,
inference(avatar_split_clause,[],[f1160,f3683]) ).
fof(f3683,plain,
( spl0_104
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f1160,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oodd__one_0) ).
fof(f3681,plain,
spl0_103,
inference(avatar_split_clause,[],[f1153,f3678]) ).
fof(f3678,plain,
( spl0_103
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f1153,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__zero_0) ).
fof(f3676,plain,
spl0_102,
inference(avatar_split_clause,[],[f1140,f3673]) ).
fof(f3673,plain,
( spl0_102
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f1140,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Parity_Oeven__nat__zero_0) ).
fof(f3671,plain,
~ spl0_101,
inference(avatar_split_clause,[],[f1010,f3668]) ).
fof(f3668,plain,
( spl0_101
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f1010,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Numeral_Obit_Odistinct__2_0) ).
fof(f3666,plain,
spl0_100,
inference(avatar_split_clause,[],[f556,f3664]) ).
fof(f3664,plain,
( spl0_100
<=> ! [X13] : c_List_Onull(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f556,axiom,
! [X13] : c_List_Onull(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Onull_Osimps__1_0) ).
fof(f3662,plain,
spl0_99,
inference(avatar_split_clause,[],[f401,f3660]) ).
fof(f3660,plain,
( spl0_99
<=> ! [X13] : c_List_Odistinct(c_List_Olist_ONil,X13) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f401,axiom,
! [X13] : c_List_Odistinct(c_List_Olist_ONil,X13),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Odistinct_Osimps__1_0) ).
fof(f3658,plain,
~ spl0_98,
inference(avatar_split_clause,[],[f220,f3655]) ).
fof(f3655,plain,
( spl0_98
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f220,axiom,
c_0 != c_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3653,plain,
~ spl0_97,
inference(avatar_split_clause,[],[f101,f3650]) ).
fof(f3650,plain,
( spl0_97
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f101,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Extraction_Osumbool_Odistinct__2_0) ).
fof(f3648,plain,
( ~ spl0_96
| spl0_95 ),
inference(avatar_split_clause,[],[f3643,f3639,f3645]) ).
fof(f3639,plain,
( spl0_95
<=> c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f3643,plain,
( ~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),v_A,t_a)
| spl0_95 ),
inference(forward_demodulation,[],[f3641,f2737]) ).
fof(f3641,plain,
( ~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a)
| spl0_95 ),
inference(avatar_component_clause,[],[f3639]) ).
fof(f3642,plain,
~ spl0_95,
inference(avatar_split_clause,[],[f2749,f3639]) ).
fof(f2749,axiom,
~ c_in(c_Tarski_Olub(v_S,v_cl,t_a),c_Tarski_Opotype_Opset(v_cl,t_a,tc_Product__Type_Ounit),t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f3637,plain,
spl0_94,
inference(avatar_split_clause,[],[f1821,f3634]) ).
fof(f3634,plain,
( spl0_94
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f1821,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_8) ).
fof(f3632,plain,
spl0_93,
inference(avatar_split_clause,[],[f1820,f3629]) ).
fof(f1820,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_7) ).
fof(f3627,plain,
spl0_92,
inference(avatar_split_clause,[],[f1819,f3624]) ).
fof(f3624,plain,
( spl0_92
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f1819,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_6) ).
fof(f3622,plain,
spl0_91,
inference(avatar_split_clause,[],[f1818,f3619]) ).
fof(f1818,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_5) ).
fof(f3617,plain,
spl0_90,
inference(avatar_split_clause,[],[f1816,f3614]) ).
fof(f3614,plain,
( spl0_90
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f1816,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_46) ).
fof(f3612,plain,
spl0_89,
inference(avatar_split_clause,[],[f1815,f3609]) ).
fof(f1815,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_45) ).
fof(f3607,plain,
spl0_88,
inference(avatar_split_clause,[],[f1813,f3604]) ).
fof(f3604,plain,
( spl0_88
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f1813,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_43) ).
fof(f3602,plain,
spl0_87,
inference(avatar_split_clause,[],[f1812,f3599]) ).
fof(f3599,plain,
( spl0_87
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f1812,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_42) ).
fof(f3597,plain,
spl0_86,
inference(avatar_split_clause,[],[f1811,f3594]) ).
fof(f3594,plain,
( spl0_86
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f1811,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_41) ).
fof(f3592,plain,
spl0_85,
inference(avatar_split_clause,[],[f1810,f3589]) ).
fof(f3589,plain,
( spl0_85
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f1810,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_40) ).
fof(f3587,plain,
spl0_84,
inference(avatar_split_clause,[],[f1809,f3584]) ).
fof(f1809,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_4) ).
fof(f3582,plain,
spl0_83,
inference(avatar_split_clause,[],[f1808,f3579]) ).
fof(f3579,plain,
( spl0_83
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f1808,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_39) ).
fof(f3577,plain,
spl0_82,
inference(avatar_split_clause,[],[f1807,f3574]) ).
fof(f3574,plain,
( spl0_82
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f1807,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_38) ).
fof(f3572,plain,
spl0_81,
inference(avatar_split_clause,[],[f1806,f3569]) ).
fof(f3569,plain,
( spl0_81
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f1806,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_37) ).
fof(f3567,plain,
spl0_80,
inference(avatar_split_clause,[],[f1805,f3564]) ).
fof(f3564,plain,
( spl0_80
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f1805,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_36) ).
fof(f3562,plain,
spl0_79,
inference(avatar_split_clause,[],[f1804,f3559]) ).
fof(f3559,plain,
( spl0_79
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f1804,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_35) ).
fof(f3557,plain,
spl0_78,
inference(avatar_split_clause,[],[f1803,f3554]) ).
fof(f3554,plain,
( spl0_78
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f1803,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_34) ).
fof(f3552,plain,
spl0_77,
inference(avatar_split_clause,[],[f1802,f3549]) ).
fof(f3549,plain,
( spl0_77
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f1802,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_33) ).
fof(f3547,plain,
spl0_76,
inference(avatar_split_clause,[],[f1801,f3544]) ).
fof(f1801,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_32) ).
fof(f3542,plain,
spl0_75,
inference(avatar_split_clause,[],[f1800,f3539]) ).
fof(f3539,plain,
( spl0_75
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f1800,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_31) ).
fof(f3537,plain,
spl0_74,
inference(avatar_split_clause,[],[f1799,f3534]) ).
fof(f3534,plain,
( spl0_74
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f1799,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_30) ).
fof(f3532,plain,
spl0_73,
inference(avatar_split_clause,[],[f1798,f3529]) ).
fof(f3529,plain,
( spl0_73
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f1798,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f3527,plain,
spl0_72,
inference(avatar_split_clause,[],[f1797,f3524]) ).
fof(f3524,plain,
( spl0_72
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f1797,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_29) ).
fof(f3522,plain,
spl0_71,
inference(avatar_split_clause,[],[f1796,f3519]) ).
fof(f3519,plain,
( spl0_71
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f1796,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_28) ).
fof(f3517,plain,
spl0_70,
inference(avatar_split_clause,[],[f1795,f3514]) ).
fof(f3514,plain,
( spl0_70
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f1795,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_27) ).
fof(f3512,plain,
spl0_69,
inference(avatar_split_clause,[],[f1794,f3509]) ).
fof(f3509,plain,
( spl0_69
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f1794,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_26) ).
fof(f3507,plain,
spl0_68,
inference(avatar_split_clause,[],[f1793,f3504]) ).
fof(f3504,plain,
( spl0_68
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f1793,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_25) ).
fof(f3502,plain,
spl0_67,
inference(avatar_split_clause,[],[f1792,f3499]) ).
fof(f3499,plain,
( spl0_67
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f1792,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_24) ).
fof(f3497,plain,
spl0_66,
inference(avatar_split_clause,[],[f1791,f3494]) ).
fof(f1791,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_23) ).
fof(f3492,plain,
spl0_65,
inference(avatar_split_clause,[],[f1790,f3489]) ).
fof(f3489,plain,
( spl0_65
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f1790,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_22) ).
fof(f3487,plain,
spl0_64,
inference(avatar_split_clause,[],[f1789,f3484]) ).
fof(f3484,plain,
( spl0_64
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f1789,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_21) ).
fof(f3482,plain,
spl0_63,
inference(avatar_split_clause,[],[f1788,f3479]) ).
fof(f3479,plain,
( spl0_63
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f1788,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_20) ).
fof(f3477,plain,
spl0_62,
inference(avatar_split_clause,[],[f1787,f3474]) ).
fof(f3474,plain,
( spl0_62
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f1787,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_2) ).
fof(f3472,plain,
spl0_61,
inference(avatar_split_clause,[],[f1786,f3469]) ).
fof(f3469,plain,
( spl0_61
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f1786,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_19) ).
fof(f3467,plain,
spl0_60,
inference(avatar_split_clause,[],[f1785,f3464]) ).
fof(f3464,plain,
( spl0_60
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f1785,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_18) ).
fof(f3462,plain,
spl0_59,
inference(avatar_split_clause,[],[f1780,f3459]) ).
fof(f3459,plain,
( spl0_59
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f1780,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_13) ).
fof(f3457,plain,
spl0_58,
inference(avatar_split_clause,[],[f1775,f3454]) ).
fof(f3454,plain,
( spl0_58
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f1775,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_0) ).
fof(f3452,plain,
spl0_57,
inference(avatar_split_clause,[],[f1772,f3449]) ).
fof(f3449,plain,
( spl0_57
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f1772,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool_0) ).
fof(f3447,plain,
spl0_56,
inference(avatar_split_clause,[],[f1771,f3444]) ).
fof(f3444,plain,
( spl0_56
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f1771,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Product____Type__Ounit_0) ).
fof(f3442,plain,
spl0_55,
inference(avatar_split_clause,[],[f1766,f3439]) ).
fof(f1766,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_63) ).
fof(f3437,plain,
spl0_54,
inference(avatar_split_clause,[],[f1763,f3434]) ).
fof(f1763,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_60) ).
fof(f3432,plain,
spl0_53,
inference(avatar_split_clause,[],[f1761,f3429]) ).
fof(f3429,plain,
( spl0_53
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f1761,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_59) ).
fof(f3427,plain,
spl0_52,
inference(avatar_split_clause,[],[f1760,f3424]) ).
fof(f1760,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_58) ).
fof(f3422,plain,
spl0_51,
inference(avatar_split_clause,[],[f1759,f3419]) ).
fof(f3419,plain,
( spl0_51
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f1759,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_57) ).
fof(f3417,plain,
spl0_50,
inference(avatar_split_clause,[],[f1758,f3414]) ).
fof(f1758,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_56) ).
fof(f3412,plain,
spl0_49,
inference(avatar_split_clause,[],[f1757,f3409]) ).
fof(f3409,plain,
( spl0_49
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f1757,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_55) ).
fof(f3407,plain,
spl0_48,
inference(avatar_split_clause,[],[f1755,f3404]) ).
fof(f3404,plain,
( spl0_48
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f1755,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_53) ).
fof(f3402,plain,
spl0_47,
inference(avatar_split_clause,[],[f1754,f3399]) ).
fof(f3399,plain,
( spl0_47
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f1754,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_52) ).
fof(f3397,plain,
spl0_46,
inference(avatar_split_clause,[],[f1753,f3394]) ).
fof(f3394,plain,
( spl0_46
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f1753,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_51) ).
fof(f3392,plain,
spl0_45,
inference(avatar_split_clause,[],[f1752,f3389]) ).
fof(f3389,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f1752,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_50) ).
fof(f3387,plain,
spl0_44,
inference(avatar_split_clause,[],[f1751,f3384]) ).
fof(f3384,plain,
( spl0_44
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f1751,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_5) ).
fof(f3382,plain,
spl0_43,
inference(avatar_split_clause,[],[f1750,f3379]) ).
fof(f3379,plain,
( spl0_43
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f1750,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_49) ).
fof(f3377,plain,
spl0_42,
inference(avatar_split_clause,[],[f1749,f3374]) ).
fof(f1749,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_48) ).
fof(f3372,plain,
spl0_41,
inference(avatar_split_clause,[],[f1748,f3369]) ).
fof(f3369,plain,
( spl0_41
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f1748,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_47) ).
fof(f3367,plain,
spl0_40,
inference(avatar_split_clause,[],[f1747,f3364]) ).
fof(f3364,plain,
( spl0_40
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f1747,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_46) ).
fof(f3362,plain,
spl0_39,
inference(avatar_split_clause,[],[f1746,f3359]) ).
fof(f3359,plain,
( spl0_39
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f1746,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_45) ).
fof(f3357,plain,
spl0_38,
inference(avatar_split_clause,[],[f1745,f3354]) ).
fof(f3354,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f1745,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_44) ).
fof(f3352,plain,
spl0_37,
inference(avatar_split_clause,[],[f1744,f3349]) ).
fof(f3349,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f1744,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_43) ).
fof(f3347,plain,
spl0_36,
inference(avatar_split_clause,[],[f1743,f3344]) ).
fof(f3344,plain,
( spl0_36
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f1743,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_42) ).
fof(f3342,plain,
spl0_35,
inference(avatar_split_clause,[],[f1742,f3339]) ).
fof(f3339,plain,
( spl0_35
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f1742,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_41) ).
fof(f3337,plain,
spl0_34,
inference(avatar_split_clause,[],[f1741,f3334]) ).
fof(f3334,plain,
( spl0_34
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f1741,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_40) ).
fof(f3332,plain,
spl0_33,
inference(avatar_split_clause,[],[f1739,f3329]) ).
fof(f3329,plain,
( spl0_33
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f1739,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_39) ).
fof(f3327,plain,
spl0_32,
inference(avatar_split_clause,[],[f1738,f3324]) ).
fof(f3324,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f1738,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_38) ).
fof(f3322,plain,
spl0_31,
inference(avatar_split_clause,[],[f1737,f3319]) ).
fof(f3319,plain,
( spl0_31
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f1737,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_37) ).
fof(f3317,plain,
spl0_30,
inference(avatar_split_clause,[],[f1736,f3314]) ).
fof(f3314,plain,
( spl0_30
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f1736,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_36) ).
fof(f3312,plain,
spl0_29,
inference(avatar_split_clause,[],[f1735,f3309]) ).
fof(f1735,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_35) ).
fof(f3307,plain,
spl0_28,
inference(avatar_split_clause,[],[f1734,f3304]) ).
fof(f3304,plain,
( spl0_28
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f1734,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_34) ).
fof(f3302,plain,
spl0_27,
inference(avatar_split_clause,[],[f1733,f3299]) ).
fof(f1733,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_33) ).
fof(f3297,plain,
spl0_26,
inference(avatar_split_clause,[],[f1732,f3294]) ).
fof(f1732,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_32) ).
fof(f3292,plain,
spl0_25,
inference(avatar_split_clause,[],[f1731,f3289]) ).
fof(f3289,plain,
( spl0_25
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f1731,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_31) ).
fof(f3287,plain,
spl0_24,
inference(avatar_split_clause,[],[f1730,f3284]) ).
fof(f1730,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_30) ).
fof(f3282,plain,
spl0_23,
inference(avatar_split_clause,[],[f1728,f3279]) ).
fof(f1728,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_29) ).
fof(f3277,plain,
spl0_22,
inference(avatar_split_clause,[],[f1727,f3274]) ).
fof(f3274,plain,
( spl0_22
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f1727,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_28) ).
fof(f3272,plain,
spl0_21,
inference(avatar_split_clause,[],[f1726,f3269]) ).
fof(f3269,plain,
( spl0_21
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f1726,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_27) ).
fof(f3267,plain,
spl0_20,
inference(avatar_split_clause,[],[f1725,f3264]) ).
fof(f3264,plain,
( spl0_20
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f1725,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_26) ).
fof(f3262,plain,
spl0_19,
inference(avatar_split_clause,[],[f1724,f3259]) ).
fof(f3259,plain,
( spl0_19
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f1724,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_25) ).
fof(f3257,plain,
spl0_18,
inference(avatar_split_clause,[],[f1723,f3254]) ).
fof(f3254,plain,
( spl0_18
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f1723,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_24) ).
fof(f3252,plain,
spl0_17,
inference(avatar_split_clause,[],[f1722,f3249]) ).
fof(f1722,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_23) ).
fof(f3247,plain,
spl0_16,
inference(avatar_split_clause,[],[f1721,f3244]) ).
fof(f3244,plain,
( spl0_16
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f1721,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_22) ).
fof(f3242,plain,
spl0_15,
inference(avatar_split_clause,[],[f1720,f3239]) ).
fof(f3239,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f1720,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_21) ).
fof(f3237,plain,
spl0_14,
inference(avatar_split_clause,[],[f1719,f3234]) ).
fof(f3234,plain,
( spl0_14
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f1719,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_20) ).
fof(f3232,plain,
spl0_13,
inference(avatar_split_clause,[],[f1717,f3229]) ).
fof(f3229,plain,
( spl0_13
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f1717,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_19) ).
fof(f3227,plain,
spl0_12,
inference(avatar_split_clause,[],[f1716,f3224]) ).
fof(f3224,plain,
( spl0_12
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f1716,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_18) ).
fof(f3222,plain,
spl0_11,
inference(avatar_split_clause,[],[f1715,f3219]) ).
fof(f1715,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_17) ).
fof(f3217,plain,
spl0_10,
inference(avatar_split_clause,[],[f1714,f3214]) ).
fof(f3214,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f1714,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_16) ).
fof(f3212,plain,
spl0_9,
inference(avatar_split_clause,[],[f1713,f3209]) ).
fof(f3209,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f1713,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_15) ).
fof(f3207,plain,
spl0_8,
inference(avatar_split_clause,[],[f1712,f3204]) ).
fof(f3204,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f1712,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_14) ).
fof(f3202,plain,
spl0_7,
inference(avatar_split_clause,[],[f1711,f3199]) ).
fof(f3199,plain,
( spl0_7
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f1711,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_13) ).
fof(f3197,plain,
spl0_6,
inference(avatar_split_clause,[],[f1710,f3194]) ).
fof(f1710,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_12) ).
fof(f3192,plain,
spl0_5,
inference(avatar_split_clause,[],[f1709,f3189]) ).
fof(f3189,plain,
( spl0_5
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f1709,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_11) ).
fof(f3187,plain,
spl0_4,
inference(avatar_split_clause,[],[f1708,f3184]) ).
fof(f3184,plain,
( spl0_4
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f1708,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_10) ).
fof(f3182,plain,
spl0_3,
inference(avatar_split_clause,[],[f1707,f3179]) ).
fof(f3179,plain,
( spl0_3
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f1707,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_IntDef__Oint_1) ).
fof(f3177,plain,
spl0_2,
inference(avatar_split_clause,[],[f2747,f3174]) ).
fof(f2747,axiom,
c_lessequals(v_S,v_A,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f3172,plain,
spl0_1,
inference(avatar_split_clause,[],[f2748,f3169]) ).
fof(f2748,axiom,
c_in(v_L,v_A,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : LAT275-1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.13 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.33 % Computer : n004.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri May 3 12:15:33 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (10340)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.42 % (10341)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.42 % (10343)WARNING: value z3 for option sas not known
% 0.16/0.42 % (10342)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.42 % (10344)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.42 % (10347)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)
% 0.16/0.42 % (10343)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)
% 0.16/0.42 % (10345)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.16/0.42 % (10346)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 1.71/0.65 % (10345)First to succeed.
% 1.71/0.69 % (10345)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-10340"
% 2.13/0.69 TRYING [1]
% 2.13/0.69 % (10345)Refutation found. Thanks to Tanya!
% 2.13/0.69 % SZS status Unsatisfiable for theBenchmark
% 2.13/0.69 % SZS output start Proof for theBenchmark
% See solution above
% 2.13/0.72 % (10345)------------------------------
% 2.13/0.72 % (10345)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.13/0.72 % (10345)Termination reason: Refutation
% 2.13/0.72
% 2.13/0.72 % (10345)Memory used [KB]: 6589
% 2.13/0.72 % (10345)Time elapsed: 0.267 s
% 2.13/0.72 % (10345)Instructions burned: 519 (million)
% 2.13/0.72 % (10340)Success in time 0.373 s
%------------------------------------------------------------------------------