TSTP Solution File: SWV272-1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV272-1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n025.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 : Sat Sep 2 12:58:19 EDT 2023
% Result : Unsatisfiable 10.06s 2.00s
% Output : Refutation 10.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5665
% Syntax : Number of formulae : 9422 (3397 unt; 0 def)
% Number of atoms : 21172 (3140 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 20117 (8367 ~;8783 |; 0 &)
% (2967 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 4 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 3055 (3053 usr;2968 prp; 0-3 aty)
% Number of functors : 252 ( 252 usr; 51 con; 0-18 aty)
% Number of variables : 12435 (;12435 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f36403,plain,
$false,
inference(avatar_sat_refutation,[],[f3016,f3021,f3026,f3031,f3036,f3041,f3046,f3051,f3056,f3061,f3066,f3071,f3076,f3081,f3086,f3091,f3096,f3101,f3106,f3111,f3116,f3121,f3126,f3131,f3136,f3141,f3146,f3151,f3156,f3161,f3166,f3171,f3176,f3181,f3186,f3191,f3196,f3201,f3206,f3211,f3216,f3221,f3226,f3231,f3236,f3241,f3246,f3251,f3256,f3261,f3266,f3271,f3276,f3281,f3286,f3291,f3296,f3301,f3306,f3311,f3316,f3321,f3326,f3331,f3336,f3341,f3346,f3351,f3356,f3361,f3366,f3371,f3376,f3381,f3386,f3391,f3396,f3401,f3406,f3411,f3416,f3421,f3426,f3431,f3436,f3441,f3446,f3451,f3456,f3461,f3466,f3471,f3476,f3481,f3486,f3491,f3496,f3501,f3506,f3511,f3516,f3521,f3526,f3531,f3536,f3541,f3546,f3551,f3556,f3561,f3566,f3571,f3576,f3581,f3586,f3591,f3596,f3601,f3605,f3610,f3615,f3619,f3623,f3627,f3631,f3636,f3641,f3645,f3649,f3654,f3659,f3664,f3669,f3674,f3679,f3683,f3687,f3691,f3695,f3699,f3703,f3707,f3711,f3715,f3719,f3723,f3727,f3731,f3735,f3739,f3743,f3747,f3751,f3755,f3759,f3763,f3767,f3771,f3775,f3779,f3783,f3787,f3791,f3795,f3799,f3803,f3807,f3811,f3815,f3819,f3823,f3827,f3831,f3835,f3839,f3843,f3847,f3851,f3855,f3859,f3863,f3867,f3871,f3875,f3879,f3883,f3887,f3891,f3895,f3899,f3903,f3907,f3911,f3915,f3919,f3923,f3927,f3931,f3935,f3939,f3943,f3947,f3951,f3955,f3959,f3963,f3967,f3971,f3975,f3979,f3983,f3987,f3991,f3995,f3999,f4003,f4007,f4011,f4015,f4019,f4023,f4027,f4031,f4035,f4039,f4043,f4047,f4051,f4055,f4059,f4063,f4067,f4071,f4075,f4079,f4083,f4087,f4091,f4095,f4099,f4103,f4107,f4111,f4115,f4119,f4123,f4127,f4131,f4135,f4139,f4143,f4147,f4151,f4155,f4159,f4163,f4167,f4171,f4175,f4179,f4183,f4187,f4191,f4195,f4199,f4203,f4207,f4211,f4215,f4219,f4223,f4227,f4231,f4235,f4239,f4243,f4247,f4251,f4255,f4259,f4263,f4267,f4271,f4275,f4279,f4283,f4287,f4291,f4295,f4299,f4303,f4307,f4311,f4315,f4319,f4323,f4327,f4331,f4335,f4339,f4343,f4347,f4351,f4355,f4359,f4363,f4367,f4371,f4375,f4379,f4383,f4387,f4391,f4395,f4399,f4403,f4407,f4411,f4415,f4419,f4423,f4427,f4431,f4435,f4439,f4443,f4447,f4451,f4455,f4459,f4463,f4467,f4471,f4475,f4479,f4483,f4487,f4491,f4495,f4499,f4503,f4507,f4511,f4515,f4519,f4523,f4527,f4531,f4535,f4539,f4543,f4547,f4551,f4555,f4559,f4563,f4567,f4571,f4575,f4579,f4583,f4587,f4591,f4595,f4599,f4603,f4607,f4611,f4615,f4619,f4623,f4627,f4631,f4635,f4639,f4643,f4647,f4651,f4655,f4659,f4663,f4667,f4671,f4675,f4679,f4683,f4687,f4691,f4695,f4699,f4703,f4707,f4711,f4715,f4719,f4723,f4727,f4731,f4735,f4739,f4743,f4747,f4751,f4755,f4759,f4763,f4767,f4771,f4775,f4779,f4783,f4787,f4791,f4795,f4799,f4803,f4807,f4811,f4815,f4819,f4823,f4827,f4831,f4835,f4839,f4843,f4847,f4851,f4855,f4859,f4863,f4867,f4871,f4875,f4879,f4883,f4887,f4891,f4895,f4899,f4903,f4907,f4911,f4915,f4919,f4923,f4927,f4931,f4935,f4939,f4943,f4947,f4951,f4955,f4959,f4963,f4967,f4971,f4975,f4979,f4983,f4987,f4991,f4995,f4999,f5003,f5007,f5011,f5015,f5019,f5023,f5027,f5031,f5035,f5039,f5043,f5047,f5051,f5055,f5059,f5063,f5067,f5071,f5075,f5079,f5083,f5087,f5091,f5095,f5099,f5103,f5107,f5111,f5115,f5119,f5123,f5127,f5131,f5135,f5139,f5143,f5147,f5151,f5155,f5159,f5163,f5167,f5171,f5175,f5179,f5183,f5187,f5191,f5195,f5199,f5203,f5207,f5211,f5215,f5219,f5223,f5227,f5231,f5235,f5239,f5243,f5247,f5251,f5255,f5259,f5263,f5267,f5271,f5275,f5279,f5283,f5287,f5291,f5295,f5299,f5303,f5307,f5311,f5315,f5319,f5323,f5327,f5331,f5335,f5339,f5343,f5347,f5351,f5355,f5359,f5363,f5367,f5371,f5375,f5379,f5383,f5387,f5391,f5395,f5399,f5403,f5407,f5411,f5415,f5419,f5423,f5427,f5431,f5435,f5439,f5443,f5447,f5451,f5455,f5459,f5463,f5467,f5471,f5475,f5479,f5483,f5487,f5491,f5495,f5499,f5503,f5507,f5511,f5515,f5519,f5523,f5527,f5531,f5535,f5539,f5543,f5547,f5551,f5555,f5559,f5563,f5567,f5571,f5575,f5579,f5583,f5587,f5591,f5595,f5599,f5603,f5607,f5611,f5615,f5619,f5623,f5627,f5631,f5635,f5639,f5643,f5647,f5651,f5655,f5659,f5663,f5667,f5671,f5675,f5679,f5683,f5687,f5691,f5695,f5699,f5703,f5707,f5711,f5715,f5719,f5723,f5727,f5731,f5735,f5739,f5743,f5747,f5751,f5755,f5759,f5763,f5767,f5771,f5775,f5779,f5783,f5787,f5791,f5795,f5799,f5803,f5807,f5811,f5815,f5819,f5823,f5827,f5831,f5835,f5839,f5843,f5847,f5851,f5855,f5859,f5863,f5867,f5871,f5875,f5879,f5883,f5887,f5891,f5895,f5899,f5903,f5907,f5911,f5915,f5919,f5923,f5927,f5931,f5935,f5939,f5943,f5947,f5951,f5955,f5959,f5963,f5967,f5971,f5975,f5979,f5983,f5987,f5991,f5995,f5999,f6003,f6007,f6011,f6015,f6019,f6023,f6027,f6031,f6035,f6039,f6043,f6047,f6051,f6055,f6059,f6063,f6067,f6071,f6075,f6079,f6083,f6087,f6091,f6095,f6099,f6103,f6107,f6111,f6115,f6119,f6123,f6127,f6131,f6135,f6139,f6143,f6147,f6151,f6155,f6159,f6163,f6167,f6171,f6175,f6179,f6183,f6187,f6191,f6195,f6199,f6203,f6207,f6211,f6215,f6219,f6223,f6227,f6231,f6235,f6239,f6243,f6247,f6251,f6255,f6259,f6263,f6267,f6271,f6275,f6279,f6283,f6287,f6291,f6295,f6299,f6303,f6307,f6311,f6315,f6319,f6323,f6327,f6331,f6335,f6339,f6343,f6347,f6351,f6355,f6359,f6363,f6367,f6371,f6375,f6379,f6383,f6387,f6391,f6395,f6399,f6403,f6407,f6411,f6415,f6419,f6423,f6427,f6431,f6435,f6439,f6443,f6447,f6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,f21865,f21869,f21882,f21886,f21890,f21894,f21898,f21902,f21906,f21910,f21914,f21918,f21922,f21926,f21930,f21934,f21938,f21942,f21946,f21950,f21954,f21958,f21962,f21966,f21970,f21975,f21981,f21986,f22159,f22266,f22634,f22841,f22845,f22849,f22853,f22857,f22861,f22865,f22869,f22875,f22881,f22885,f22889,f22893,f22897,f22901,f22905,f22910,f22914,f22918,f22922,f22926,f22930,f22934,f22938,f22942,f22946,f22950,f22954,f22958,f22962,f22966,f22970,f22974,f22978,f22982,f22986,f22990,f22994,f22998,f23002,f23006,f23193,f23197,f23430,f23464,f23935,f24257,f24261,f24265,f24269,f24273,f24278,f24282,f24286,f24291,f24295,f24296,f24300,f24304,f24308,f24312,f24316,f24320,f24324,f24328,f24332,f24336,f24340,f24344,f24348,f24352,f24356,f24360,f24364,f24368,f24372,f24376,f24383,f24387,f24391,f24395,f24399,f24403,f24407,f24411,f24415,f24419,f24428,f24432,f24436,f24440,f24444,f24448,f24452,f24457,f24468,f24472,f24476,f24480,f24489,f24493,f24497,f24503,f24514,f24520,f24546,f24550,f24554,f24560,f24621,f24626,f24659,f25020,f25217,f25336,f25340,f25344,f25422,f25426,f25430,f25434,f25438,f25442,f25446,f25450,f25454,f25458,f25463,f25467,f25471,f25475,f25479,f25483,f25487,f25491,f25495,f25499,f25503,f25507,f25511,f25515,f25519,f25523,f25528,f25537,f25543,f25565,f26074,f26078,f26082,f26115,f26119,f26123,f26127,f26131,f26135,f26139,f26143,f26147,f26151,f26159,f26163,f26167,f26171,f26175,f26179,f26183,f26187,f26191,f26195,f26199,f26203,f26207,f26211,f26215,f26219,f26223,f26227,f26231,f26235,f26239,f26244,f26248,f26252,f26256,f26260,f26264,f26268,f26272,f26276,f26280,f26284,f26291,f26295,f26299,f26303,f26307,f26311,f26315,f26319,f26323,f26327,f26336,f26340,f26344,f26348,f26352,f26356,f26360,f26364,f26368,f26372,f26376,f26382,f26386,f26392,f26407,f26747,f26756,f27304,f27308,f27312,f27316,f27320,f27324,f27328,f27332,f27336,f27340,f27344,f27348,f27352,f27356,f27360,f27364,f27368,f27372,f27376,f27380,f27384,f27390,f27394,f27398,f27402,f27406,f27410,f27414,f27418,f27422,f27426,f27432,f27436,f27440,f27444,f27448,f27452,f27456,f27460,f27890,f28209,f28213,f28217,f28221,f28226,f28230,f28234,f28238,f28242,f28246,f28250,f28254,f28258,f28262,f28266,f28278,f28282,f28286,f28290,f28294,f28298,f28302,f28306,f28310,f28314,f28319,f28323,f28328,f28849,f28942,f28946,f28950,f28974,f28978,f28982,f28986,f28990,f28995,f29000,f29004,f29008,f29012,f29017,f29021,f29025,f29029,f29033,f29037,f29041,f29045,f29161,f29165,f29315,f29554,f29569,f29573,f29577,f29581,f29585,f29589,f29593,f29597,f29601,f29605,f29610,f29614,f29618,f29622,f29626,f29630,f29634,f29638,f29642,f29646,f29650,f29655,f29659,f29663,f29667,f30022,f30187,f30191,f30195,f30199,f30203,f30207,f30211,f30215,f30219,f30223,f30488,f30492,f30496,f30514,f30518,f30522,f30526,f30530,f30534,f30538,f30542,f30605,f30787,f30802,f30806,f30810,f30814,f30818,f30822,f30826,f30830,f30834,f30838,f30843,f30847,f30851,f30855,f30859,f30863,f30867,f30871,f30875,f30879,f30883,f30888,f30892,f30896,f30900,f30904,f30909,f31625,f31630,f31634,f31646,f31650,f31655,f31666,f31670,f31689,f31693,f31697,f31701,f31705,f31709,f31713,f31717,f31721,f31725,f31729,f31733,f31737,f32219,f32223,f32227,f32231,f32240,f32244,f32248,f32252,f32256,f32260,f32643,f32647,f32651,f32655,f32728,f32732,f32736,f32740,f32869,f32873,f32877,f32881,f32886,f32891,f32896,f32901,f32905,f32909,f32913,f32949,f32953,f32957,f32961,f32965,f32988,f32992,f32996,f33001,f33005,f33354,f33370,f33374,f33378,f33382,f33386,f33390,f33394,f33534,f33539,f33542,f33546,f33550,f33554,f33558,f33562,f33566,f33570,f33574,f33578,f33878,f33883,f33887,f33891,f33895,f34074,f34078,f34082,f34089,f34093,f34099,f34107,f34113,f34121,f34127,f34136,f34140,f34146,f34231,f34235,f34239,f34254,f34404,f34408,f34412,f34417,f34424,f34448,f34481,f34488,f34511,f34516,f34547,f34584,f34589,f34602,f34606,f34610,f34627,f34657,f34661,f34665,f34669,f34790,f34830,f34863,f34867,f34885,f34906,f34929,f34933,f34937,f34979,f35002,f35021,f35026,f35037,f35065,f35077,f35081,f35111,f35119,f35123,f35127,f35131,f35135,f35139,f35410,f35438,f35442,f35446,f35451,f35455,f35460,f35464,f35468,f35472,f35476,f35484,f35489,f35494,f35498,f35503,f35507,f35511,f35515,f35519,f35523,f35527,f35531,f35539,f35543,f35547,f35551,f35555,f35563,f35567,f35571,f35575,f35576,f35580,f35584,f35588,f35592,f35596,f35600,f35604,f35608,f35612,f35616,f35620,f35624,f35631,f35636,f35640,f35644,f35648,f35652,f35704,f36402]) ).
fof(f36402,plain,
( spl0_1722
| spl0_2918
| ~ spl0_2410
| ~ spl0_2901 ),
inference(avatar_split_clause,[],[f35030,f35018,f22984,f35448,f12481]) ).
fof(f12481,plain,
( spl0_1722
<=> c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1722])]) ).
fof(f35448,plain,
( spl0_2918
<=> c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_H,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2918])]) ).
fof(f22984,plain,
( spl0_2410
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2410])]) ).
fof(f35018,plain,
( spl0_2901
<=> c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2901])]) ).
fof(f35030,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_H,tc_Message_Omsg)
| c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_2410
| ~ spl0_2901 ),
inference(resolution,[],[f35020,f22985]) ).
fof(f22985,plain,
( ! [X91,X88,X86] :
( ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) )
| ~ spl0_2410 ),
inference(avatar_component_clause,[],[f22984]) ).
fof(f35020,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_2901 ),
inference(avatar_component_clause,[],[f35018]) ).
fof(f35704,plain,
( spl0_2967
| spl0_2918
| ~ spl0_2411
| ~ spl0_2901 ),
inference(avatar_split_clause,[],[f35029,f35018,f22988,f35448,f35701]) ).
fof(f35701,plain,
( spl0_2967
<=> c_in(c_Message_Omsg_OKey(v_K),v_H,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2967])]) ).
fof(f22988,plain,
( spl0_2411
<=> ! [X86,X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2411])]) ).
fof(f35029,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_H,tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(v_K),v_H,tc_Message_Omsg)
| ~ spl0_2411
| ~ spl0_2901 ),
inference(resolution,[],[f35020,f22989]) ).
fof(f22989,plain,
( ! [X91,X88,X86] :
( ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg) )
| ~ spl0_2411 ),
inference(avatar_component_clause,[],[f22988]) ).
fof(f35652,plain,
( spl0_2966
| ~ spl0_141
| ~ spl0_2307 ),
inference(avatar_split_clause,[],[f22063,f21717,f3701,f35650]) ).
fof(f35650,plain,
( spl0_2966
<=> ! [X48,X47,X49] : c_in(X47,c_Relation_ORange(c_UNIV,X48,X49),X49) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2966])]) ).
fof(f3701,plain,
( spl0_141
<=> ! [X0,X1] : c_in(X0,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_141])]) ).
fof(f21717,plain,
( spl0_2307
<=> ! [X5,X18,X27,X2,X1] :
( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2307])]) ).
fof(f22063,plain,
( ! [X48,X49,X47] : c_in(X47,c_Relation_ORange(c_UNIV,X48,X49),X49)
| ~ spl0_141
| ~ spl0_2307 ),
inference(resolution,[],[f21718,f3702]) ).
fof(f3702,plain,
( ! [X0,X1] : c_in(X0,c_UNIV,X1)
| ~ spl0_141 ),
inference(avatar_component_clause,[],[f3701]) ).
fof(f21718,plain,
( ! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
| c_in(X27,c_Relation_ORange(X5,X1,X2),X2) )
| ~ spl0_2307 ),
inference(avatar_component_clause,[],[f21717]) ).
fof(f35648,plain,
( spl0_2965
| ~ spl0_141
| ~ spl0_2304 ),
inference(avatar_split_clause,[],[f22012,f21705,f3701,f35646]) ).
fof(f35646,plain,
( spl0_2965
<=> ! [X48,X47,X49] : c_in(X47,c_Relation_ODomain(c_UNIV,X48,X49),X48) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2965])]) ).
fof(f21705,plain,
( spl0_2304
<=> ! [X18,X5,X27,X2,X1] :
( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2304])]) ).
fof(f22012,plain,
( ! [X48,X49,X47] : c_in(X47,c_Relation_ODomain(c_UNIV,X48,X49),X48)
| ~ spl0_141
| ~ spl0_2304 ),
inference(resolution,[],[f21706,f3702]) ).
fof(f21706,plain,
( ! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2))
| c_in(X18,c_Relation_ODomain(X5,X1,X2),X1) )
| ~ spl0_2304 ),
inference(avatar_component_clause,[],[f21705]) ).
fof(f35644,plain,
( spl0_2964
| ~ spl0_1057
| ~ spl0_1157
| ~ spl0_1206
| ~ spl0_2114 ),
inference(avatar_split_clause,[],[f18656,f18214,f9197,f9000,f7368,f35642]) ).
fof(f35642,plain,
( spl0_2964
<=> ! [X3] : c_0 = c_Binomial_Obinomial(c_1,c_Suc(c_Suc(X3))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2964])]) ).
fof(f7368,plain,
( spl0_1057
<=> c_Suc(c_0) = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1057])]) ).
fof(f9000,plain,
( spl0_1157
<=> ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1157])]) ).
fof(f9197,plain,
( spl0_1206
<=> ! [X3] : c_plus(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1206])]) ).
fof(f18214,plain,
( spl0_2114
<=> ! [X16,X21] : c_Binomial_Obinomial(c_Suc(X21),c_Suc(X16)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Suc(X16)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2114])]) ).
fof(f18656,plain,
( ! [X3] : c_0 = c_Binomial_Obinomial(c_1,c_Suc(c_Suc(X3)))
| ~ spl0_1057
| ~ spl0_1157
| ~ spl0_1206
| ~ spl0_2114 ),
inference(forward_demodulation,[],[f18655,f7370]) ).
fof(f7370,plain,
( c_Suc(c_0) = c_1
| ~ spl0_1057 ),
inference(avatar_component_clause,[],[f7368]) ).
fof(f18655,plain,
( ! [X3] : c_0 = c_Binomial_Obinomial(c_Suc(c_0),c_Suc(c_Suc(X3)))
| ~ spl0_1157
| ~ spl0_1206
| ~ spl0_2114 ),
inference(forward_demodulation,[],[f18654,f9001]) ).
fof(f9001,plain,
( ! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16))
| ~ spl0_1157 ),
inference(avatar_component_clause,[],[f9000]) ).
fof(f18654,plain,
( ! [X3] : c_Binomial_Obinomial(c_Suc(c_0),c_Suc(c_Suc(X3))) = c_Binomial_Obinomial(c_0,c_Suc(c_Suc(X3)))
| ~ spl0_1157
| ~ spl0_1206
| ~ spl0_2114 ),
inference(forward_demodulation,[],[f18616,f9198]) ).
fof(f9198,plain,
( ! [X3] : c_plus(c_0,X3,tc_nat) = X3
| ~ spl0_1206 ),
inference(avatar_component_clause,[],[f9197]) ).
fof(f18616,plain,
( ! [X3] : c_Binomial_Obinomial(c_Suc(c_0),c_Suc(c_Suc(X3))) = c_plus(c_0,c_Binomial_Obinomial(c_0,c_Suc(c_Suc(X3))),tc_nat)
| ~ spl0_1157
| ~ spl0_2114 ),
inference(superposition,[],[f18215,f9001]) ).
fof(f18215,plain,
( ! [X21,X16] : c_Binomial_Obinomial(c_Suc(X21),c_Suc(X16)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Suc(X16)),tc_nat)
| ~ spl0_2114 ),
inference(avatar_component_clause,[],[f18214]) ).
fof(f35640,plain,
( spl0_2963
| ~ spl0_1229
| ~ spl0_1496
| ~ spl0_2094 ),
inference(avatar_split_clause,[],[f17995,f16773,f10595,f9291,f35638]) ).
fof(f35638,plain,
( spl0_2963
<=> ! [X0] : c_emptyset = c_Inter(c_Pow(c_emptyset,X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2963])]) ).
fof(f9291,plain,
( spl0_1229
<=> ! [X13,X1] : c_emptyset = c_inter(c_emptyset,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1229])]) ).
fof(f10595,plain,
( spl0_1496
<=> ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1496])]) ).
fof(f16773,plain,
( spl0_2094
<=> ! [X13,X18,X1] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_inter(X18,c_Inter(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2094])]) ).
fof(f17995,plain,
( ! [X0] : c_emptyset = c_Inter(c_Pow(c_emptyset,X0),X0)
| ~ spl0_1229
| ~ spl0_1496
| ~ spl0_2094 ),
inference(forward_demodulation,[],[f17991,f9292]) ).
fof(f9292,plain,
( ! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1)
| ~ spl0_1229 ),
inference(avatar_component_clause,[],[f9291]) ).
fof(f17991,plain,
( ! [X0] : c_inter(c_emptyset,c_Inter(c_emptyset,X0),X0) = c_Inter(c_Pow(c_emptyset,X0),X0)
| ~ spl0_1496
| ~ spl0_2094 ),
inference(superposition,[],[f16774,f10596]) ).
fof(f10596,plain,
( ! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1))
| ~ spl0_1496 ),
inference(avatar_component_clause,[],[f10595]) ).
fof(f16774,plain,
( ! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_inter(X18,c_Inter(X13,X1),X1)
| ~ spl0_2094 ),
inference(avatar_component_clause,[],[f16773]) ).
fof(f35636,plain,
( spl0_2962
| ~ spl0_1059
| ~ spl0_1199
| ~ spl0_2037 ),
inference(avatar_split_clause,[],[f17114,f16513,f9169,f7377,f35633]) ).
fof(f35633,plain,
( spl0_2962
<=> c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2962])]) ).
fof(f7377,plain,
( spl0_1059
<=> c_less(c_0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1059])]) ).
fof(f9169,plain,
( spl0_1199
<=> ! [X15] : c_0 = c_minus(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1199])]) ).
fof(f16513,plain,
( spl0_2037
<=> ! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2037])]) ).
fof(f17114,plain,
( c_0 = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_1059
| ~ spl0_1199
| ~ spl0_2037 ),
inference(forward_demodulation,[],[f17090,f9170]) ).
fof(f9170,plain,
( ! [X15] : c_0 = c_minus(X15,X15,tc_nat)
| ~ spl0_1199 ),
inference(avatar_component_clause,[],[f9169]) ).
fof(f17090,plain,
( c_minus(c_1,c_1,tc_nat) = c_List_Olast(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_1059
| ~ spl0_2037 ),
inference(resolution,[],[f16514,f7379]) ).
fof(f7379,plain,
( c_less(c_0,c_1,tc_nat)
| ~ spl0_1059 ),
inference(avatar_component_clause,[],[f7377]) ).
fof(f16514,plain,
( ! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) )
| ~ spl0_2037 ),
inference(avatar_component_clause,[],[f16513]) ).
fof(f35631,plain,
( spl0_2960
| spl0_2961
| ~ spl0_1081
| ~ spl0_2030 ),
inference(avatar_split_clause,[],[f17012,f16485,f8652,f35629,f35626]) ).
fof(f35626,plain,
( spl0_2960
<=> ! [X3] : ~ class_Ring__and__Field_Oordered__idom(tc_set(X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2960])]) ).
fof(f35629,plain,
( spl0_2961
<=> ! [X2] : c_lessequals(X2,X2,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2961])]) ).
fof(f8652,plain,
( spl0_1081
<=> ! [X12,X1] : c_lessequals(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1081])]) ).
fof(f16485,plain,
( spl0_2030
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2030])]) ).
fof(f17012,plain,
( ! [X2,X3] :
( c_lessequals(X2,X2,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_set(X3)) )
| ~ spl0_1081
| ~ spl0_2030 ),
inference(resolution,[],[f16486,f8653]) ).
fof(f8653,plain,
( ! [X1,X12] : c_lessequals(X12,X12,tc_set(X1))
| ~ spl0_1081 ),
inference(avatar_component_clause,[],[f8652]) ).
fof(f16486,plain,
( ! [X48,X11,X1] :
( ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_2030 ),
inference(avatar_component_clause,[],[f16485]) ).
fof(f35624,plain,
( spl0_2959
| ~ spl0_1248
| ~ spl0_1999 ),
inference(avatar_split_clause,[],[f16342,f14730,f9367,f35622]) ).
fof(f35622,plain,
( spl0_2959
<=> ! [X0] : c_lessequals(X0,c_Message_Osynth(c_Message_Osynth(X0)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2959])]) ).
fof(f9367,plain,
( spl0_1248
<=> ! [X88] : c_lessequals(X88,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1248])]) ).
fof(f14730,plain,
( spl0_1999
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1999])]) ).
fof(f16342,plain,
( ! [X0] : c_lessequals(X0,c_Message_Osynth(c_Message_Osynth(X0)),tc_set(tc_Message_Omsg))
| ~ spl0_1248
| ~ spl0_1999 ),
inference(resolution,[],[f14731,f9368]) ).
fof(f9368,plain,
( ! [X88] : c_lessequals(X88,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ spl0_1248 ),
inference(avatar_component_clause,[],[f9367]) ).
fof(f14731,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1999 ),
inference(avatar_component_clause,[],[f14730]) ).
fof(f35620,plain,
( spl0_2958
| ~ spl0_1623
| ~ spl0_1949 ),
inference(avatar_split_clause,[],[f15869,f14517,f11621,f35618]) ).
fof(f35618,plain,
( spl0_2958
<=> ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2958])]) ).
fof(f11621,plain,
( spl0_1623
<=> ! [X2,X27,X1,X18] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1623])]) ).
fof(f14517,plain,
( spl0_1949
<=> ! [X2,X1,X3] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1949])]) ).
fof(f15869,plain,
( ! [X2,X0,X1] : c_0 = c_Nat_Osize(X0,tc_prod(X1,X2))
| ~ spl0_1623
| ~ spl0_1949 ),
inference(superposition,[],[f11622,f14518]) ).
fof(f14518,plain,
( ! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3
| ~ spl0_1949 ),
inference(avatar_component_clause,[],[f14517]) ).
fof(f11622,plain,
( ! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2))
| ~ spl0_1623 ),
inference(avatar_component_clause,[],[f11621]) ).
fof(f35616,plain,
( spl0_2957
| ~ spl0_1187
| ~ spl0_1907 ),
inference(avatar_split_clause,[],[f15101,f14323,f9121,f35614]) ).
fof(f35614,plain,
( spl0_2957
<=> ! [X6,X8,X7] : ~ c_List_Onull(c_List_Oreplicate(c_Suc(X7),X6,X8),X8) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2957])]) ).
fof(f9121,plain,
( spl0_1187
<=> ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1187])]) ).
fof(f14323,plain,
( spl0_1907
<=> ! [X41,X0,X21] : c_List_Oreplicate(c_Suc(X21),X0,X41) = c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1907])]) ).
fof(f15101,plain,
( ! [X8,X6,X7] : ~ c_List_Onull(c_List_Oreplicate(c_Suc(X7),X6,X8),X8)
| ~ spl0_1187
| ~ spl0_1907 ),
inference(superposition,[],[f9122,f14324]) ).
fof(f14324,plain,
( ! [X21,X41,X0] : c_List_Oreplicate(c_Suc(X21),X0,X41) = c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41)
| ~ spl0_1907 ),
inference(avatar_component_clause,[],[f14323]) ).
fof(f9122,plain,
( ! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ spl0_1187 ),
inference(avatar_component_clause,[],[f9121]) ).
fof(f35612,plain,
( spl0_2956
| ~ spl0_1184
| ~ spl0_1907 ),
inference(avatar_split_clause,[],[f15099,f14323,f9109,f35610]) ).
fof(f35610,plain,
( spl0_2956
<=> ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_Suc(X1),X0,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2956])]) ).
fof(f9109,plain,
( spl0_1184
<=> ! [X42,X1,X63] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1184])]) ).
fof(f15099,plain,
( ! [X2,X0,X1] : c_List_Olist_ONil != c_List_Oreplicate(c_Suc(X1),X0,X2)
| ~ spl0_1184
| ~ spl0_1907 ),
inference(superposition,[],[f9110,f14324]) ).
fof(f9110,plain,
( ! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1)
| ~ spl0_1184 ),
inference(avatar_component_clause,[],[f9109]) ).
fof(f35608,plain,
( spl0_2955
| ~ spl0_1264
| ~ spl0_2004 ),
inference(avatar_split_clause,[],[f14765,f14756,f9447,f35606]) ).
fof(f35606,plain,
( spl0_2955
<=> ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2955])]) ).
fof(f9447,plain,
( spl0_1264
<=> ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1264])]) ).
fof(f14756,plain,
( spl0_2004
<=> ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Suc(c_1),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2004])]) ).
fof(f14765,plain,
( ! [X0] : c_lessequals(X0,c_plus(X0,X0,tc_nat),tc_nat)
| ~ spl0_1264
| ~ spl0_2004 ),
inference(superposition,[],[f9448,f14757]) ).
fof(f14757,plain,
( ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Suc(c_1),tc_nat) = X3
| ~ spl0_2004 ),
inference(avatar_component_clause,[],[f14756]) ).
fof(f9448,plain,
( ! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat)
| ~ spl0_1264 ),
inference(avatar_component_clause,[],[f9447]) ).
fof(f35604,plain,
( spl0_2954
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1289
| ~ spl0_1864 ),
inference(avatar_split_clause,[],[f14122,f13076,f9547,f9197,f7368,f35602]) ).
fof(f35602,plain,
( spl0_2954
<=> ! [X1] : ~ c_less(c_Suc(c_Suc(X1)),c_Suc(c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2954])]) ).
fof(f9547,plain,
( spl0_1289
<=> ! [X43,X59] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1289])]) ).
fof(f13076,plain,
( spl0_1864
<=> ! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1864])]) ).
fof(f14122,plain,
( ! [X1] : ~ c_less(c_Suc(c_Suc(X1)),c_Suc(c_1),tc_nat)
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1289
| ~ spl0_1864 ),
inference(forward_demodulation,[],[f14104,f14121]) ).
fof(f14121,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_Suc(c_1)
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864 ),
inference(forward_demodulation,[],[f14101,f7370]) ).
fof(f14101,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat) = c_Suc(c_Suc(c_0))
| ~ spl0_1206
| ~ spl0_1864 ),
inference(superposition,[],[f13077,f9198]) ).
fof(f13077,plain,
( ! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1864 ),
inference(avatar_component_clause,[],[f13076]) ).
fof(f14104,plain,
( ! [X1] : ~ c_less(c_Suc(c_Suc(X1)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_1289
| ~ spl0_1864 ),
inference(superposition,[],[f9548,f13077]) ).
fof(f9548,plain,
( ! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat)
| ~ spl0_1289 ),
inference(avatar_component_clause,[],[f9547]) ).
fof(f35600,plain,
( spl0_2953
| ~ spl0_1231
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f13982,f13036,f9299,f35598]) ).
fof(f35598,plain,
( spl0_2953
<=> ! [X2] : c_Transitive__Closure_Ortrancl(c_UNIV,X2) = c_Transitive__Closure_Otrancl(c_UNIV,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2953])]) ).
fof(f9299,plain,
( spl0_1231
<=> ! [X13,X1] : c_UNIV = c_union(c_UNIV,X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1231])]) ).
fof(f13036,plain,
( spl0_1854
<=> ! [X5,X1] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1854])]) ).
fof(f13982,plain,
( ! [X2] : c_Transitive__Closure_Ortrancl(c_UNIV,X2) = c_Transitive__Closure_Otrancl(c_UNIV,X2)
| ~ spl0_1231
| ~ spl0_1854 ),
inference(superposition,[],[f13037,f9300]) ).
fof(f9300,plain,
( ! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1)
| ~ spl0_1231 ),
inference(avatar_component_clause,[],[f9299]) ).
fof(f13037,plain,
( ! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1)
| ~ spl0_1854 ),
inference(avatar_component_clause,[],[f13036]) ).
fof(f35596,plain,
( spl0_2952
| ~ spl0_1135
| ~ spl0_1229
| ~ spl0_1809 ),
inference(avatar_split_clause,[],[f13650,f12842,f9291,f8893,f35594]) ).
fof(f35594,plain,
( spl0_2952
<=> ! [X0,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X1,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2952])]) ).
fof(f8893,plain,
( spl0_1135
<=> ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1135])]) ).
fof(f12842,plain,
( spl0_1809
<=> ! [X13,X12,X1] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1809])]) ).
fof(f13650,plain,
( ! [X0,X1] : c_emptyset = c_Relation_OImage(c_emptyset,X1,X0,X0)
| ~ spl0_1135
| ~ spl0_1229
| ~ spl0_1809 ),
inference(forward_demodulation,[],[f13647,f9292]) ).
fof(f13647,plain,
( ! [X0,X1] : c_inter(c_emptyset,X1,X0) = c_Relation_OImage(c_emptyset,X1,X0,X0)
| ~ spl0_1135
| ~ spl0_1809 ),
inference(superposition,[],[f12843,f8894]) ).
fof(f8894,plain,
( ! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1)
| ~ spl0_1135 ),
inference(avatar_component_clause,[],[f8893]) ).
fof(f12843,plain,
( ! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1)
| ~ spl0_1809 ),
inference(avatar_component_clause,[],[f12842]) ).
fof(f35592,plain,
( spl0_2951
| ~ spl0_1057
| ~ spl0_1203
| ~ spl0_1777 ),
inference(avatar_split_clause,[],[f13455,f12707,f9185,f7368,f35590]) ).
fof(f35590,plain,
( spl0_2951
<=> ! [X0] : c_1 = c_Orderings_Omin(c_Suc(X0),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2951])]) ).
fof(f9185,plain,
( spl0_1203
<=> ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1203])]) ).
fof(f12707,plain,
( spl0_1777
<=> ! [X21,X15] : c_Orderings_Omin(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omin(X15,X21,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1777])]) ).
fof(f13455,plain,
( ! [X0] : c_1 = c_Orderings_Omin(c_Suc(X0),c_1,tc_nat)
| ~ spl0_1057
| ~ spl0_1203
| ~ spl0_1777 ),
inference(forward_demodulation,[],[f13454,f7370]) ).
fof(f13454,plain,
( ! [X0] : c_Suc(c_0) = c_Orderings_Omin(c_Suc(X0),c_1,tc_nat)
| ~ spl0_1057
| ~ spl0_1203
| ~ spl0_1777 ),
inference(forward_demodulation,[],[f13451,f9186]) ).
fof(f9186,plain,
( ! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat)
| ~ spl0_1203 ),
inference(avatar_component_clause,[],[f9185]) ).
fof(f13451,plain,
( ! [X0] : c_Suc(c_Orderings_Omin(X0,c_0,tc_nat)) = c_Orderings_Omin(c_Suc(X0),c_1,tc_nat)
| ~ spl0_1057
| ~ spl0_1777 ),
inference(superposition,[],[f12708,f7370]) ).
fof(f12708,plain,
( ! [X21,X15] : c_Orderings_Omin(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omin(X15,X21,tc_nat))
| ~ spl0_1777 ),
inference(avatar_component_clause,[],[f12707]) ).
fof(f35588,plain,
( spl0_2950
| ~ spl0_1057
| ~ spl0_1202
| ~ spl0_1777 ),
inference(avatar_split_clause,[],[f13453,f12707,f9181,f7368,f35586]) ).
fof(f35586,plain,
( spl0_2950
<=> ! [X0] : c_1 = c_Orderings_Omin(c_1,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2950])]) ).
fof(f9181,plain,
( spl0_1202
<=> ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1202])]) ).
fof(f13453,plain,
( ! [X0] : c_1 = c_Orderings_Omin(c_1,c_Suc(X0),tc_nat)
| ~ spl0_1057
| ~ spl0_1202
| ~ spl0_1777 ),
inference(forward_demodulation,[],[f13452,f7370]) ).
fof(f13452,plain,
( ! [X0] : c_Suc(c_0) = c_Orderings_Omin(c_1,c_Suc(X0),tc_nat)
| ~ spl0_1057
| ~ spl0_1202
| ~ spl0_1777 ),
inference(forward_demodulation,[],[f13450,f9182]) ).
fof(f9182,plain,
( ! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat)
| ~ spl0_1202 ),
inference(avatar_component_clause,[],[f9181]) ).
fof(f13450,plain,
( ! [X0] : c_Suc(c_Orderings_Omin(c_0,X0,tc_nat)) = c_Orderings_Omin(c_1,c_Suc(X0),tc_nat)
| ~ spl0_1057
| ~ spl0_1777 ),
inference(superposition,[],[f12708,f7370]) ).
fof(f35584,plain,
( spl0_2949
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1239
| ~ spl0_1660
| ~ spl0_1707 ),
inference(avatar_split_clause,[],[f12448,f11958,f11770,f9331,f9161,f7368,f35582]) ).
fof(f35582,plain,
( spl0_2949
<=> ! [X5] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X5)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2949])]) ).
fof(f9161,plain,
( spl0_1197
<=> ! [X3] : c_plus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1197])]) ).
fof(f9331,plain,
( spl0_1239
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1239])]) ).
fof(f11770,plain,
( spl0_1660
<=> ! [X21,X15] : c_plus(X15,c_Suc(X21),tc_nat) = c_Suc(c_plus(X15,X21,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1660])]) ).
fof(f11958,plain,
( spl0_1707
<=> ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1707])]) ).
fof(f12448,plain,
( ! [X5] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X5)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1239
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12447,f7370]) ).
fof(f12447,plain,
( ! [X5] : c_Suc(c_0) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X5)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1239
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12433,f12162]) ).
fof(f12162,plain,
( ! [X0] : c_Suc(X0) = c_plus(X0,c_1,tc_nat)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1660 ),
inference(forward_demodulation,[],[f12155,f9162]) ).
fof(f9162,plain,
( ! [X3] : c_plus(X3,c_0,tc_nat) = X3
| ~ spl0_1197 ),
inference(avatar_component_clause,[],[f9161]) ).
fof(f12155,plain,
( ! [X0] : c_Suc(c_plus(X0,c_0,tc_nat)) = c_plus(X0,c_1,tc_nat)
| ~ spl0_1057
| ~ spl0_1660 ),
inference(superposition,[],[f11771,f7370]) ).
fof(f11771,plain,
( ! [X21,X15] : c_plus(X15,c_Suc(X21),tc_nat) = c_Suc(c_plus(X15,X21,tc_nat))
| ~ spl0_1660 ),
inference(avatar_component_clause,[],[f11770]) ).
fof(f12433,plain,
( ! [X5] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONumber(X5)),tc_Message_Omsg)
| ~ spl0_1239
| ~ spl0_1707 ),
inference(superposition,[],[f11959,f9332]) ).
fof(f9332,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg)
| ~ spl0_1239 ),
inference(avatar_component_clause,[],[f9331]) ).
fof(f11959,plain,
( ! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_1707 ),
inference(avatar_component_clause,[],[f11958]) ).
fof(f35580,plain,
( spl0_2948
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1240
| ~ spl0_1660
| ~ spl0_1707 ),
inference(avatar_split_clause,[],[f12446,f11958,f11770,f9335,f9161,f7368,f35578]) ).
fof(f35578,plain,
( spl0_2948
<=> ! [X4] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X4)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2948])]) ).
fof(f9335,plain,
( spl0_1240
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1240])]) ).
fof(f12446,plain,
( ! [X4] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X4)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1240
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12445,f7370]) ).
fof(f12445,plain,
( ! [X4] : c_Suc(c_0) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X4)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1240
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12432,f12162]) ).
fof(f12432,plain,
( ! [X4] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_ONonce(X4)),tc_Message_Omsg)
| ~ spl0_1240
| ~ spl0_1707 ),
inference(superposition,[],[f11959,f9336]) ).
fof(f9336,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg)
| ~ spl0_1240 ),
inference(avatar_component_clause,[],[f9335]) ).
fof(f35576,plain,
( ~ spl0_2792
| ~ spl0_1525
| ~ spl0_2806 ),
inference(avatar_split_clause,[],[f33601,f32866,f10968,f32237]) ).
fof(f32237,plain,
( spl0_2792
<=> c_lessequals(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2792])]) ).
fof(f10968,plain,
( spl0_1525
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1525])]) ).
fof(f32866,plain,
( spl0_2806
<=> c_less(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2806])]) ).
fof(f33601,plain,
( ~ c_lessequals(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg))
| ~ spl0_1525
| ~ spl0_2806 ),
inference(resolution,[],[f32868,f10969]) ).
fof(f10969,plain,
( ! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) )
| ~ spl0_1525 ),
inference(avatar_component_clause,[],[f10968]) ).
fof(f32868,plain,
( c_less(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_2806 ),
inference(avatar_component_clause,[],[f32866]) ).
fof(f35575,plain,
( spl0_2947
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1241
| ~ spl0_1660
| ~ spl0_1707 ),
inference(avatar_split_clause,[],[f12444,f11958,f11770,f9339,f9161,f7368,f35573]) ).
fof(f35573,plain,
( spl0_2947
<=> ! [X3] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X3)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2947])]) ).
fof(f9339,plain,
( spl0_1241
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1241])]) ).
fof(f12444,plain,
( ! [X3] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X3)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1241
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12443,f7370]) ).
fof(f12443,plain,
( ! [X3] : c_Suc(c_0) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X3)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1241
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12431,f12162]) ).
fof(f12431,plain,
( ! [X3] : c_plus(c_0,c_1,tc_nat) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OKey(X3)),tc_Message_Omsg)
| ~ spl0_1241
| ~ spl0_1707 ),
inference(superposition,[],[f11959,f9340]) ).
fof(f9340,plain,
( ! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg)
| ~ spl0_1241 ),
inference(avatar_component_clause,[],[f9339]) ).
fof(f35571,plain,
( spl0_2946
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1238
| ~ spl0_1660
| ~ spl0_1707 ),
inference(avatar_split_clause,[],[f12441,f11958,f11770,f9327,f9161,f7368,f35569]) ).
fof(f35569,plain,
( spl0_2946
<=> ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2946])]) ).
fof(f9327,plain,
( spl0_1238
<=> ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1238])]) ).
fof(f12441,plain,
( ! [X0] : c_1 = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1238
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12440,f7370]) ).
fof(f12440,plain,
( ! [X0] : c_Suc(c_0) = c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg)
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1238
| ~ spl0_1660
| ~ spl0_1707 ),
inference(forward_demodulation,[],[f12429,f12162]) ).
fof(f12429,plain,
( ! [X0] : c_Nat_Osize(c_Message_Omsg_OHash(c_Message_Omsg_OAgent(X0)),tc_Message_Omsg) = c_plus(c_0,c_1,tc_nat)
| ~ spl0_1238
| ~ spl0_1707 ),
inference(superposition,[],[f11959,f9328]) ).
fof(f9328,plain,
( ! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg)
| ~ spl0_1238 ),
inference(avatar_component_clause,[],[f9327]) ).
fof(f35567,plain,
( spl0_2945
| ~ spl0_1289
| ~ spl0_1707 ),
inference(avatar_split_clause,[],[f12438,f11958,f9547,f35565]) ).
fof(f35565,plain,
( spl0_2945
<=> ! [X4] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X4),tc_Message_Omsg),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2945])]) ).
fof(f12438,plain,
( ! [X4] : ~ c_less(c_Nat_Osize(c_Message_Omsg_OHash(X4),tc_Message_Omsg),c_1,tc_nat)
| ~ spl0_1289
| ~ spl0_1707 ),
inference(superposition,[],[f9548,f11959]) ).
fof(f35563,plain,
( spl0_2943
| ~ spl0_2944
| ~ spl0_139
| ~ spl0_1676 ),
inference(avatar_split_clause,[],[f12241,f11834,f3693,f35560,f35557]) ).
fof(f35557,plain,
( spl0_2943
<=> ! [X0] : c_HOL_Oabs(X0,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2943])]) ).
fof(f35560,plain,
( spl0_2944
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2944])]) ).
fof(f3693,plain,
( spl0_139
<=> ! [X21] : c_lessequals(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_139])]) ).
fof(f11834,plain,
( spl0_1676
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1676])]) ).
fof(f12241,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(tc_nat)
| c_HOL_Oabs(X0,tc_nat) = X0 )
| ~ spl0_139
| ~ spl0_1676 ),
inference(resolution,[],[f11835,f3694]) ).
fof(f3694,plain,
( ! [X21] : c_lessequals(c_0,X21,tc_nat)
| ~ spl0_139 ),
inference(avatar_component_clause,[],[f3693]) ).
fof(f11835,plain,
( ! [X3,X1] :
( ~ c_lessequals(c_0,X3,X1)
| ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X3,X1) = X3 )
| ~ spl0_1676 ),
inference(avatar_component_clause,[],[f11834]) ).
fof(f35555,plain,
( spl0_2942
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1667 ),
inference(avatar_split_clause,[],[f12202,f11798,f9197,f7368,f35553]) ).
fof(f35553,plain,
( spl0_2942
<=> ! [X0] : c_Suc(X0) = c_plus(c_1,X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2942])]) ).
fof(f11798,plain,
( spl0_1667
<=> ! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1667])]) ).
fof(f12202,plain,
( ! [X0] : c_Suc(X0) = c_plus(c_1,X0,tc_nat)
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1667 ),
inference(forward_demodulation,[],[f12191,f9198]) ).
fof(f12191,plain,
( ! [X0] : c_Suc(c_plus(c_0,X0,tc_nat)) = c_plus(c_1,X0,tc_nat)
| ~ spl0_1057
| ~ spl0_1667 ),
inference(superposition,[],[f11799,f7370]) ).
fof(f11799,plain,
( ! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat)
| ~ spl0_1667 ),
inference(avatar_component_clause,[],[f11798]) ).
fof(f35551,plain,
( spl0_2941
| ~ spl0_1057
| ~ spl0_1207
| ~ spl0_1664 ),
inference(avatar_split_clause,[],[f12184,f11786,f9201,f7368,f35549]) ).
fof(f35549,plain,
( spl0_2941
<=> ! [X0] : c_minus(c_Suc(X0),c_1,tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2941])]) ).
fof(f9201,plain,
( spl0_1207
<=> ! [X3] : c_minus(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1207])]) ).
fof(f11786,plain,
( spl0_1664
<=> ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Suc(X15),c_Suc(X21),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1664])]) ).
fof(f12184,plain,
( ! [X0] : c_minus(c_Suc(X0),c_1,tc_nat) = X0
| ~ spl0_1057
| ~ spl0_1207
| ~ spl0_1664 ),
inference(forward_demodulation,[],[f12178,f9202]) ).
fof(f9202,plain,
( ! [X3] : c_minus(X3,c_0,tc_nat) = X3
| ~ spl0_1207 ),
inference(avatar_component_clause,[],[f9201]) ).
fof(f12178,plain,
( ! [X0] : c_minus(X0,c_0,tc_nat) = c_minus(c_Suc(X0),c_1,tc_nat)
| ~ spl0_1057
| ~ spl0_1664 ),
inference(superposition,[],[f11787,f7370]) ).
fof(f11787,plain,
( ! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Suc(X15),c_Suc(X21),tc_nat)
| ~ spl0_1664 ),
inference(avatar_component_clause,[],[f11786]) ).
fof(f35547,plain,
( spl0_2940
| ~ spl0_1057
| ~ spl0_1198
| ~ spl0_1664 ),
inference(avatar_split_clause,[],[f12183,f11786,f9165,f7368,f35545]) ).
fof(f35545,plain,
( spl0_2940
<=> ! [X0] : c_0 = c_minus(c_1,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2940])]) ).
fof(f9165,plain,
( spl0_1198
<=> ! [X21] : c_0 = c_minus(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1198])]) ).
fof(f12183,plain,
( ! [X0] : c_0 = c_minus(c_1,c_Suc(X0),tc_nat)
| ~ spl0_1057
| ~ spl0_1198
| ~ spl0_1664 ),
inference(forward_demodulation,[],[f12177,f9166]) ).
fof(f9166,plain,
( ! [X21] : c_0 = c_minus(c_0,X21,tc_nat)
| ~ spl0_1198 ),
inference(avatar_component_clause,[],[f9165]) ).
fof(f12177,plain,
( ! [X0] : c_minus(c_0,X0,tc_nat) = c_minus(c_1,c_Suc(X0),tc_nat)
| ~ spl0_1057
| ~ spl0_1664 ),
inference(superposition,[],[f11787,f7370]) ).
fof(f35543,plain,
( spl0_2939
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1660 ),
inference(avatar_split_clause,[],[f12162,f11770,f9161,f7368,f35541]) ).
fof(f35541,plain,
( spl0_2939
<=> ! [X0] : c_Suc(X0) = c_plus(X0,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2939])]) ).
fof(f35539,plain,
( spl0_2938
| ~ spl0_1059
| ~ spl0_1644 ),
inference(avatar_split_clause,[],[f12071,f11706,f7377,f35536]) ).
fof(f35536,plain,
( spl0_2938
<=> c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2938])]) ).
fof(f11706,plain,
( spl0_1644
<=> ! [X59,X3] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1644])]) ).
fof(f12071,plain,
( c_0 = c_List_Ohd(c_List_Oupt(c_0,c_1),tc_nat)
| ~ spl0_1059
| ~ spl0_1644 ),
inference(resolution,[],[f11707,f7379]) ).
fof(f11707,plain,
( ! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 )
| ~ spl0_1644 ),
inference(avatar_component_clause,[],[f11706]) ).
fof(f35531,plain,
( spl0_2937
| ~ spl0_1207
| ~ spl0_1575 ),
inference(avatar_split_clause,[],[f11506,f11174,f9201,f35529]) ).
fof(f35529,plain,
( spl0_2937
<=> ! [X2] :
( c_0 != X2
| c_lessequals(X2,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2937])]) ).
fof(f11174,plain,
( spl0_1575
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1575])]) ).
fof(f11506,plain,
( ! [X2] :
( c_0 != X2
| c_lessequals(X2,c_0,tc_nat) )
| ~ spl0_1207
| ~ spl0_1575 ),
inference(superposition,[],[f11175,f9202]) ).
fof(f11175,plain,
( ! [X21,X15] :
( c_0 != c_minus(X15,X21,tc_nat)
| c_lessequals(X15,X21,tc_nat) )
| ~ spl0_1575 ),
inference(avatar_component_clause,[],[f11174]) ).
fof(f35527,plain,
( spl0_2936
| ~ spl0_1078
| ~ spl0_1539 ),
inference(avatar_split_clause,[],[f11371,f11024,f8640,f35525]) ).
fof(f35525,plain,
( spl0_2936
<=> ! [X0] : c_Divides_Oop_Amod(X0,c_Suc(X0),tc_nat) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2936])]) ).
fof(f8640,plain,
( spl0_1078
<=> ! [X21] : c_less(X21,c_Suc(X21),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1078])]) ).
fof(f11024,plain,
( spl0_1539
<=> ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1539])]) ).
fof(f11371,plain,
( ! [X0] : c_Divides_Oop_Amod(X0,c_Suc(X0),tc_nat) = X0
| ~ spl0_1078
| ~ spl0_1539 ),
inference(resolution,[],[f11025,f8641]) ).
fof(f8641,plain,
( ! [X21] : c_less(X21,c_Suc(X21),tc_nat)
| ~ spl0_1078 ),
inference(avatar_component_clause,[],[f8640]) ).
fof(f11025,plain,
( ! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 )
| ~ spl0_1539 ),
inference(avatar_component_clause,[],[f11024]) ).
fof(f35523,plain,
( spl0_2935
| ~ spl0_1078
| ~ spl0_1537 ),
inference(avatar_split_clause,[],[f11358,f11016,f8640,f35521]) ).
fof(f35521,plain,
( spl0_2935
<=> ! [X0] : c_0 = c_div(X0,c_Suc(X0),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2935])]) ).
fof(f11016,plain,
( spl0_1537
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1537])]) ).
fof(f11358,plain,
( ! [X0] : c_0 = c_div(X0,c_Suc(X0),tc_nat)
| ~ spl0_1078
| ~ spl0_1537 ),
inference(resolution,[],[f11017,f8641]) ).
fof(f11017,plain,
( ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) )
| ~ spl0_1537 ),
inference(avatar_component_clause,[],[f11016]) ).
fof(f35519,plain,
( spl0_2934
| ~ spl0_1313
| ~ spl0_1496 ),
inference(avatar_split_clause,[],[f10912,f10595,f9643,f35517]) ).
fof(f35517,plain,
( spl0_2934
<=> ! [X1] : c_in(c_emptyset,c_Pow(c_emptyset,X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2934])]) ).
fof(f9643,plain,
( spl0_1313
<=> ! [X12,X0,X1] : c_in(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1313])]) ).
fof(f10912,plain,
( ! [X1] : c_in(c_emptyset,c_Pow(c_emptyset,X1),tc_set(X1))
| ~ spl0_1313
| ~ spl0_1496 ),
inference(superposition,[],[f9644,f10596]) ).
fof(f9644,plain,
( ! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1)
| ~ spl0_1313 ),
inference(avatar_component_clause,[],[f9643]) ).
fof(f35515,plain,
( spl0_2933
| ~ spl0_109
| ~ spl0_1486 ),
inference(avatar_split_clause,[],[f10886,f10555,f3553,f35513]) ).
fof(f35513,plain,
( spl0_2933
<=> ! [X1] : c_0 = c_Nat_Opower(c_0,c_Suc(X1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2933])]) ).
fof(f3553,plain,
( spl0_109
<=> class_Power_Orecpower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_109])]) ).
fof(f10555,plain,
( spl0_1486
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1486])]) ).
fof(f10886,plain,
( ! [X1] : c_0 = c_Nat_Opower(c_0,c_Suc(X1),tc_nat)
| ~ spl0_109
| ~ spl0_1486 ),
inference(resolution,[],[f10556,f3555]) ).
fof(f3555,plain,
( class_Power_Orecpower(tc_nat)
| ~ spl0_109 ),
inference(avatar_component_clause,[],[f3553]) ).
fof(f10556,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) )
| ~ spl0_1486 ),
inference(avatar_component_clause,[],[f10555]) ).
fof(f35511,plain,
( spl0_2932
| ~ spl0_62
| ~ spl0_1486 ),
inference(avatar_split_clause,[],[f10885,f10555,f3318,f35509]) ).
fof(f35509,plain,
( spl0_2932
<=> ! [X0] : c_0 = c_Nat_Opower(c_0,c_Suc(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2932])]) ).
fof(f3318,plain,
( spl0_62
<=> class_Power_Orecpower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_62])]) ).
fof(f10885,plain,
( ! [X0] : c_0 = c_Nat_Opower(c_0,c_Suc(X0),tc_IntDef_Oint)
| ~ spl0_62
| ~ spl0_1486 ),
inference(resolution,[],[f10556,f3320]) ).
fof(f3320,plain,
( class_Power_Orecpower(tc_IntDef_Oint)
| ~ spl0_62 ),
inference(avatar_component_clause,[],[f3318]) ).
fof(f35507,plain,
( spl0_2931
| ~ spl0_11
| ~ spl0_1479 ),
inference(avatar_split_clause,[],[f10874,f10527,f3063,f35505]) ).
fof(f35505,plain,
( spl0_2931
<=> ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2931])]) ).
fof(f3063,plain,
( spl0_11
<=> class_OrderedGroup_Oab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f10527,plain,
( spl0_1479
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1479])]) ).
fof(f10874,plain,
( ! [X0] : c_uminus(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) = X0
| ~ spl0_11
| ~ spl0_1479 ),
inference(resolution,[],[f10528,f3065]) ).
fof(f3065,plain,
( class_OrderedGroup_Oab__group__add(tc_IntDef_Oint)
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f3063]) ).
fof(f10528,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 )
| ~ spl0_1479 ),
inference(avatar_component_clause,[],[f10527]) ).
fof(f35503,plain,
( spl0_2930
| ~ spl0_59
| ~ spl0_1473 ),
inference(avatar_split_clause,[],[f10850,f10503,f3303,f35500]) ).
fof(f35500,plain,
( spl0_2930
<=> c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2930])]) ).
fof(f3303,plain,
( spl0_59
<=> class_Numeral_Onumber__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_59])]) ).
fof(f10503,plain,
( spl0_1473
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1473])]) ).
fof(f10850,plain,
( c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint) = c_uminus(c_1,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1473 ),
inference(resolution,[],[f10504,f3305]) ).
fof(f3305,plain,
( class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_59 ),
inference(avatar_component_clause,[],[f3303]) ).
fof(f10504,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) )
| ~ spl0_1473 ),
inference(avatar_component_clause,[],[f10503]) ).
fof(f35498,plain,
( spl0_2929
| ~ spl0_1313
| ~ spl0_1462 ),
inference(avatar_split_clause,[],[f10818,f10458,f9643,f35496]) ).
fof(f35496,plain,
( spl0_2929
<=> ! [X1] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2929])]) ).
fof(f10458,plain,
( spl0_1462
<=> ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1462])]) ).
fof(f10818,plain,
( ! [X1] : c_in(c_List_Olist_ONil,c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1))
| ~ spl0_1313
| ~ spl0_1462 ),
inference(superposition,[],[f9644,f10459]) ).
fof(f10459,plain,
( ! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41))
| ~ spl0_1462 ),
inference(avatar_component_clause,[],[f10458]) ).
fof(f35494,plain,
( spl0_2928
| ~ spl0_1051
| ~ spl0_1057
| ~ spl0_1423 ),
inference(avatar_split_clause,[],[f10698,f10298,f7368,f7341,f35492]) ).
fof(f35492,plain,
( spl0_2928
<=> ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2928])]) ).
fof(f7341,plain,
( spl0_1051
<=> c_1 = c_IntDef_Oint(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1051])]) ).
fof(f10298,plain,
( spl0_1423
<=> ! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1423])]) ).
fof(f10698,plain,
( ! [X0] : c_less(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1057
| ~ spl0_1423 ),
inference(forward_demodulation,[],[f10695,f7343]) ).
fof(f7343,plain,
( c_1 = c_IntDef_Oint(c_1)
| ~ spl0_1051 ),
inference(avatar_component_clause,[],[f7341]) ).
fof(f10695,plain,
( ! [X0] : c_less(c_uminus(c_IntDef_Oint(c_1),tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1057
| ~ spl0_1423 ),
inference(superposition,[],[f10299,f7370]) ).
fof(f10299,plain,
( ! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1423 ),
inference(avatar_component_clause,[],[f10298]) ).
fof(f35489,plain,
( spl0_2927
| ~ spl0_1402
| ~ spl0_1404 ),
inference(avatar_split_clause,[],[f10270,f10088,f10079,f35486]) ).
fof(f35486,plain,
( spl0_2927
<=> c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2927])]) ).
fof(f10079,plain,
( spl0_1402
<=> c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1402])]) ).
fof(f10088,plain,
( spl0_1404
<=> ! [X1,X3] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1404])]) ).
fof(f10270,plain,
( c_0 = c_Set_Ocontents(c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_1402
| ~ spl0_1404 ),
inference(superposition,[],[f10089,f10081]) ).
fof(f10081,plain,
( c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat)
| ~ spl0_1402 ),
inference(avatar_component_clause,[],[f10079]) ).
fof(f10089,plain,
( ! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3
| ~ spl0_1404 ),
inference(avatar_component_clause,[],[f10088]) ).
fof(f35484,plain,
( spl0_2925
| ~ spl0_2926
| ~ spl0_1286
| ~ spl0_1381 ),
inference(avatar_split_clause,[],[f10234,f9995,f9535,f35481,f35478]) ).
fof(f35478,plain,
( spl0_2925
<=> ! [X0] : c_0 = c_OrderedGroup_Onprt(X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2925])]) ).
fof(f35481,plain,
( spl0_2926
<=> class_OrderedGroup_Olordered__ab__group(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2926])]) ).
fof(f9535,plain,
( spl0_1286
<=> ! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1286])]) ).
fof(f9995,plain,
( spl0_1381
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1381])]) ).
fof(f10234,plain,
( ! [X0] :
( ~ class_OrderedGroup_Olordered__ab__group(tc_nat)
| c_0 = c_OrderedGroup_Onprt(X0,tc_nat) )
| ~ spl0_1286
| ~ spl0_1381 ),
inference(resolution,[],[f9996,f9536]) ).
fof(f9536,plain,
( ! [X43] :
( ~ c_lessequals(X43,c_0,tc_nat)
| c_0 = X43 )
| ~ spl0_1286 ),
inference(avatar_component_clause,[],[f9535]) ).
fof(f9996,plain,
( ! [X18,X1] :
( c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1)
| ~ class_OrderedGroup_Olordered__ab__group(X1) )
| ~ spl0_1381 ),
inference(avatar_component_clause,[],[f9995]) ).
fof(f35476,plain,
( spl0_2924
| ~ spl0_1057
| ~ spl0_1367 ),
inference(avatar_split_clause,[],[f10205,f9938,f7368,f35474]) ).
fof(f35474,plain,
( spl0_2924
<=> ! [X0] :
( c_1 != c_Suc(X0)
| c_0 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2924])]) ).
fof(f9938,plain,
( spl0_1367
<=> ! [X21,X15] :
( X15 = X21
| c_Suc(X21) != c_Suc(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1367])]) ).
fof(f10205,plain,
( ! [X0] :
( c_1 != c_Suc(X0)
| c_0 = X0 )
| ~ spl0_1057
| ~ spl0_1367 ),
inference(superposition,[],[f9939,f7370]) ).
fof(f9939,plain,
( ! [X21,X15] :
( c_Suc(X21) != c_Suc(X15)
| X15 = X21 )
| ~ spl0_1367 ),
inference(avatar_component_clause,[],[f9938]) ).
fof(f35472,plain,
( spl0_2923
| ~ spl0_1051
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f10175,f9840,f7341,f35470]) ).
fof(f35470,plain,
( spl0_2923
<=> ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2923])]) ).
fof(f9840,plain,
( spl0_1343
<=> ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1343])]) ).
fof(f10175,plain,
( ! [X0] : ~ c_less(c_IntDef_Oint(X0),c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1343 ),
inference(superposition,[],[f9841,f7343]) ).
fof(f9841,plain,
( ! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1343 ),
inference(avatar_component_clause,[],[f9840]) ).
fof(f35468,plain,
( spl0_2922
| ~ spl0_1052
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f10174,f9840,f7346,f35466]) ).
fof(f35466,plain,
( spl0_2922
<=> ! [X1] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2922])]) ).
fof(f7346,plain,
( spl0_1052
<=> c_0 = c_IntDef_Oint(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1052])]) ).
fof(f10174,plain,
( ! [X1] : ~ c_less(c_0,c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1052
| ~ spl0_1343 ),
inference(superposition,[],[f9841,f7348]) ).
fof(f7348,plain,
( c_0 = c_IntDef_Oint(c_0)
| ~ spl0_1052 ),
inference(avatar_component_clause,[],[f7346]) ).
fof(f35464,plain,
( spl0_2921
| ~ spl0_1051
| ~ spl0_1343 ),
inference(avatar_split_clause,[],[f10173,f9840,f7341,f35462]) ).
fof(f35462,plain,
( spl0_2921
<=> ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2921])]) ).
fof(f10173,plain,
( ! [X0] : ~ c_less(c_1,c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1343 ),
inference(superposition,[],[f9841,f7343]) ).
fof(f35460,plain,
( spl0_127
| ~ spl0_2920
| ~ spl0_1051
| ~ spl0_1341 ),
inference(avatar_split_clause,[],[f10169,f9832,f7341,f35457,f3638]) ).
fof(f3638,plain,
( spl0_127
<=> c_0 = c_1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_127])]) ).
fof(f35457,plain,
( spl0_2920
<=> c_lessequals(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2920])]) ).
fof(f9832,plain,
( spl0_1341
<=> ! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1341])]) ).
fof(f10169,plain,
( ~ c_lessequals(c_1,c_0,tc_IntDef_Oint)
| c_0 = c_1
| ~ spl0_1051
| ~ spl0_1341 ),
inference(superposition,[],[f9833,f7343]) ).
fof(f9833,plain,
( ! [X21] :
( ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_1341 ),
inference(avatar_component_clause,[],[f9832]) ).
fof(f35455,plain,
( spl0_2919
| ~ spl0_1051
| ~ spl0_1340 ),
inference(avatar_split_clause,[],[f10164,f9828,f7341,f35453]) ).
fof(f35453,plain,
( spl0_2919
<=> ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2919])]) ).
fof(f9828,plain,
( spl0_1340
<=> ! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1340])]) ).
fof(f10164,plain,
( ! [X0] :
( c_1 != c_IntDef_Oint(X0)
| c_1 = X0 )
| ~ spl0_1051
| ~ spl0_1340 ),
inference(superposition,[],[f9829,f7343]) ).
fof(f9829,plain,
( ! [X21,X15] :
( c_IntDef_Oint(X21) != c_IntDef_Oint(X15)
| X15 = X21 )
| ~ spl0_1340 ),
inference(avatar_component_clause,[],[f9828]) ).
fof(f35451,plain,
( ~ spl0_2918
| ~ spl0_1511
| spl0_2900 ),
inference(avatar_split_clause,[],[f35027,f35014,f10656,f35448]) ).
fof(f10656,plain,
( spl0_1511
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1511])]) ).
fof(f35014,plain,
( spl0_2900
<=> c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2900])]) ).
fof(f35027,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,v_X),v_H,tc_Message_Omsg)
| ~ spl0_1511
| spl0_2900 ),
inference(resolution,[],[f35015,f10657]) ).
fof(f10657,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1511 ),
inference(avatar_component_clause,[],[f10656]) ).
fof(f35015,plain,
( ~ c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(v_H),tc_Message_Omsg)
| spl0_2900 ),
inference(avatar_component_clause,[],[f35014]) ).
fof(f35446,plain,
( spl0_2917
| ~ spl0_1052
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10151,f9745,f7346,f35444]) ).
fof(f35444,plain,
( spl0_2917
<=> ! [X1] : c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2917])]) ).
fof(f9745,plain,
( spl0_1320
<=> ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1320])]) ).
fof(f10151,plain,
( ! [X1] : c_lessequals(c_uminus(c_IntDef_Oint(X1),tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ spl0_1052
| ~ spl0_1320 ),
inference(superposition,[],[f9746,f7348]) ).
fof(f9746,plain,
( ! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1320 ),
inference(avatar_component_clause,[],[f9745]) ).
fof(f35442,plain,
( spl0_2916
| ~ spl0_1051
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10150,f9745,f7341,f35440]) ).
fof(f35440,plain,
( spl0_2916
<=> ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2916])]) ).
fof(f10150,plain,
( ! [X0] : c_lessequals(c_uminus(c_IntDef_Oint(X0),tc_IntDef_Oint),c_1,tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1320 ),
inference(superposition,[],[f9746,f7343]) ).
fof(f35438,plain,
( spl0_2915
| ~ spl0_1051
| ~ spl0_1320 ),
inference(avatar_split_clause,[],[f10148,f9745,f7341,f35436]) ).
fof(f35436,plain,
( spl0_2915
<=> ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2915])]) ).
fof(f10148,plain,
( ! [X0] : c_lessequals(c_uminus(c_1,tc_IntDef_Oint),c_IntDef_Oint(X0),tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1320 ),
inference(superposition,[],[f9746,f7343]) ).
fof(f35410,plain,
( spl0_2914
| ~ spl0_118
| ~ spl0_2408 ),
inference(avatar_split_clause,[],[f23918,f22976,f3598,f35408]) ).
fof(f35408,plain,
( spl0_2914
<=> ! [X318] : c_minus(X318,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) = c_minus(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),X318,tc_Message_Omsg),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2914])]) ).
fof(f3598,plain,
( spl0_118
<=> c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_118])]) ).
fof(f22976,plain,
( spl0_2408
<=> ! [X13,X0,X12,X1] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2408])]) ).
fof(f23918,plain,
( ! [X318] : c_minus(X318,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) = c_minus(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),X318,tc_Message_Omsg),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg))
| ~ spl0_118
| ~ spl0_2408 ),
inference(resolution,[],[f22977,f3600]) ).
fof(f3600,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| ~ spl0_118 ),
inference(avatar_component_clause,[],[f3598]) ).
fof(f22977,plain,
( ! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) )
| ~ spl0_2408 ),
inference(avatar_component_clause,[],[f22976]) ).
fof(f35139,plain,
( spl0_2913
| ~ spl0_1231
| ~ spl0_2183 ),
inference(avatar_split_clause,[],[f19657,f18510,f9299,f35137]) ).
fof(f35137,plain,
( spl0_2913
<=> ! [X18,X17] : c_UNIV = c_insert(X18,c_UNIV,X17) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2913])]) ).
fof(f18510,plain,
( spl0_2183
<=> ! [X18,X13,X12,X1] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2183])]) ).
fof(f19657,plain,
( ! [X18,X17] : c_UNIV = c_insert(X18,c_UNIV,X17)
| ~ spl0_1231
| ~ spl0_2183 ),
inference(forward_demodulation,[],[f19622,f9300]) ).
fof(f19622,plain,
( ! [X18,X16,X17] : c_union(c_UNIV,c_insert(X18,X16,X17),X17) = c_insert(X18,c_UNIV,X17)
| ~ spl0_1231
| ~ spl0_2183 ),
inference(superposition,[],[f18511,f9300]) ).
fof(f18511,plain,
( ! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1)
| ~ spl0_2183 ),
inference(avatar_component_clause,[],[f18510]) ).
fof(f35135,plain,
( spl0_2912
| ~ spl0_1081
| ~ spl0_2175 ),
inference(avatar_split_clause,[],[f19508,f18478,f8652,f35133]) ).
fof(f35133,plain,
( spl0_2912
<=> ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2912])]) ).
fof(f18478,plain,
( spl0_2175
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2175])]) ).
fof(f19508,plain,
( ! [X0,X1] :
( c_lessequals(X0,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_1081
| ~ spl0_2175 ),
inference(resolution,[],[f18479,f8653]) ).
fof(f18479,plain,
( ! [X3,X0,X1] :
( ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1))
| c_lessequals(X3,X0,X1)
| ~ class_Orderings_Olinorder(X1) )
| ~ spl0_2175 ),
inference(avatar_component_clause,[],[f18478]) ).
fof(f35131,plain,
( spl0_2911
| ~ spl0_1164
| ~ spl0_2134 ),
inference(avatar_split_clause,[],[f19073,f18294,f9028,f35129]) ).
fof(f35129,plain,
( spl0_2911
<=> ! [X2,X3] : c_List_Orotate(c_0,X2,X3) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2911])]) ).
fof(f9028,plain,
( spl0_1164
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1164])]) ).
fof(f18294,plain,
( spl0_2134
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2134])]) ).
fof(f19073,plain,
( ! [X2,X3] : c_List_Orotate(c_0,X2,X3) = X2
| ~ spl0_1164
| ~ spl0_2134 ),
inference(trivial_inequality_removal,[],[f19063]) ).
fof(f19063,plain,
( ! [X2,X3] :
( c_0 != c_0
| c_List_Orotate(c_0,X2,X3) = X2 )
| ~ spl0_1164
| ~ spl0_2134 ),
inference(superposition,[],[f18295,f9029]) ).
fof(f9029,plain,
( ! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat)
| ~ spl0_1164 ),
inference(avatar_component_clause,[],[f9028]) ).
fof(f18295,plain,
( ! [X21,X3,X1] :
( c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Orotate(X21,X3,X1) = X3 )
| ~ spl0_2134 ),
inference(avatar_component_clause,[],[f18294]) ).
fof(f35127,plain,
( spl0_2910
| ~ spl0_1126
| ~ spl0_1127
| ~ spl0_1129
| ~ spl0_1212
| ~ spl0_2001 ),
inference(avatar_split_clause,[],[f16365,f14738,f9222,f8867,f8859,f8854,f35125]) ).
fof(f35125,plain,
( spl0_2910
<=> ! [X1] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X1) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2910])]) ).
fof(f8854,plain,
( spl0_1126
<=> c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1126])]) ).
fof(f8859,plain,
( spl0_1127
<=> ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1127])]) ).
fof(f8867,plain,
( spl0_1129
<=> ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1129])]) ).
fof(f9222,plain,
( spl0_1212
<=> c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1212])]) ).
fof(f14738,plain,
( spl0_2001
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2001])]) ).
fof(f16365,plain,
( ! [X1] : c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X1) = X1
| ~ spl0_1126
| ~ spl0_1127
| ~ spl0_1129
| ~ spl0_1212
| ~ spl0_2001 ),
inference(forward_demodulation,[],[f16364,f8860]) ).
fof(f8860,plain,
( ! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3
| ~ spl0_1127 ),
inference(avatar_component_clause,[],[f8859]) ).
fof(f16364,plain,
( ! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ spl0_1126
| ~ spl0_1129
| ~ spl0_1212
| ~ spl0_2001 ),
inference(forward_demodulation,[],[f16363,f9224]) ).
fof(f9224,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls)
| ~ spl0_1212 ),
inference(avatar_component_clause,[],[f9222]) ).
fof(f16363,plain,
( ! [X1] : c_Numeral_Obin__add(c_Numeral_OPls,X1) = c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1)
| ~ spl0_1126
| ~ spl0_1129
| ~ spl0_2001 ),
inference(forward_demodulation,[],[f16353,f8868]) ).
fof(f8868,plain,
( ! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11)
| ~ spl0_1129 ),
inference(avatar_component_clause,[],[f8867]) ).
fof(f16353,plain,
( ! [X1] : c_Numeral_Obin__mult(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OPls,X1),X1)
| ~ spl0_1126
| ~ spl0_2001 ),
inference(superposition,[],[f14739,f8856]) ).
fof(f8856,plain,
( c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0)
| ~ spl0_1126 ),
inference(avatar_component_clause,[],[f8854]) ).
fof(f14739,plain,
( ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11)
| ~ spl0_2001 ),
inference(avatar_component_clause,[],[f14738]) ).
fof(f35123,plain,
( spl0_2909
| ~ spl0_1081
| ~ spl0_1997 ),
inference(avatar_split_clause,[],[f16316,f14722,f8652,f35121]) ).
fof(f35121,plain,
( spl0_2909
<=> ! [X2] : c_lessequals(X2,c_Message_Oparts(X2),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2909])]) ).
fof(f14722,plain,
( spl0_1997
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1997])]) ).
fof(f16316,plain,
( ! [X2] : c_lessequals(X2,c_Message_Oparts(X2),tc_set(tc_Message_Omsg))
| ~ spl0_1081
| ~ spl0_1997 ),
inference(resolution,[],[f14723,f8653]) ).
fof(f14723,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1997 ),
inference(avatar_component_clause,[],[f14722]) ).
fof(f35119,plain,
( spl0_2908
| ~ spl0_1081
| ~ spl0_1989 ),
inference(avatar_split_clause,[],[f16197,f14685,f8652,f35117]) ).
fof(f35117,plain,
( spl0_2908
<=> ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2908])]) ).
fof(f14685,plain,
( spl0_1989
<=> ! [X20,X88] :
( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1989])]) ).
fof(f16197,plain,
( ! [X0] : c_lessequals(X0,c_Message_Oanalz(X0),tc_set(tc_Message_Omsg))
| ~ spl0_1081
| ~ spl0_1989 ),
inference(resolution,[],[f14686,f8653]) ).
fof(f14686,plain,
( ! [X88,X20] :
( ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) )
| ~ spl0_1989 ),
inference(avatar_component_clause,[],[f14685]) ).
fof(f35111,plain,
( spl0_2907
| ~ spl0_1187
| ~ spl0_1900 ),
inference(avatar_split_clause,[],[f15042,f14280,f9121,f35109]) ).
fof(f35109,plain,
( spl0_2907
<=> ! [X4,X5] :
( ~ c_List_Onull(X4,X5)
| c_List_Olist_ONil = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2907])]) ).
fof(f14280,plain,
( spl0_1900
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1900])]) ).
fof(f15042,plain,
( ! [X4,X5] :
( ~ c_List_Onull(X4,X5)
| c_List_Olist_ONil = X4 )
| ~ spl0_1187
| ~ spl0_1900 ),
inference(superposition,[],[f9122,f14281]) ).
fof(f14281,plain,
( ! [X3,X1] :
( c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3
| c_List_Olist_ONil = X3 )
| ~ spl0_1900 ),
inference(avatar_component_clause,[],[f14280]) ).
fof(f35081,plain,
( spl0_2906
| spl0_117
| ~ spl0_2405 ),
inference(avatar_split_clause,[],[f23749,f22964,f3593,f35079]) ).
fof(f35079,plain,
( spl0_2906
<=> ! [X301] : c_minus(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),X301,tc_set(tc_Message_Omsg)) = c_minus(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_insert(v_X,X301,tc_Message_Omsg),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2906])]) ).
fof(f3593,plain,
( spl0_117
<=> c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_117])]) ).
fof(f22964,plain,
( spl0_2405
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2405])]) ).
fof(f23749,plain,
( ! [X301] : c_minus(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),X301,tc_set(tc_Message_Omsg)) = c_minus(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),c_insert(v_X,X301,tc_Message_Omsg),tc_set(tc_Message_Omsg))
| spl0_117
| ~ spl0_2405 ),
inference(resolution,[],[f22965,f3595]) ).
fof(f3595,plain,
( ~ c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| spl0_117 ),
inference(avatar_component_clause,[],[f3593]) ).
fof(f22965,plain,
( ! [X0,X1,X12,X13] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) )
| ~ spl0_2405 ),
inference(avatar_component_clause,[],[f22964]) ).
fof(f35077,plain,
( ~ spl0_2904
| spl0_2905
| ~ spl0_118
| ~ spl0_2016 ),
inference(avatar_split_clause,[],[f16887,f16400,f3598,f35075,f35071]) ).
fof(f35071,plain,
( spl0_2904
<=> c_Infinite__Set_Oatmost__one(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2904])]) ).
fof(f35075,plain,
( spl0_2905
<=> ! [X174] :
( c_Message_Omsg_OCrypt(v_K,v_X) = X174
| ~ c_in(X174,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2905])]) ).
fof(f16400,plain,
( spl0_2016
<=> ! [X0,X3,X22,X1] :
( ~ c_Infinite__Set_Oatmost__one(X22,X1)
| X0 = X3
| ~ c_in(X0,X22,X1)
| ~ c_in(X3,X22,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2016])]) ).
fof(f16887,plain,
( ! [X174] :
( c_Message_Omsg_OCrypt(v_K,v_X) = X174
| ~ c_in(X174,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)
| ~ c_Infinite__Set_Oatmost__one(c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) )
| ~ spl0_118
| ~ spl0_2016 ),
inference(resolution,[],[f16401,f3600]) ).
fof(f16401,plain,
( ! [X3,X0,X1,X22] :
( ~ c_in(X3,X22,X1)
| X0 = X3
| ~ c_in(X0,X22,X1)
| ~ c_Infinite__Set_Oatmost__one(X22,X1) )
| ~ spl0_2016 ),
inference(avatar_component_clause,[],[f16400]) ).
fof(f35065,plain,
( spl0_2903
| ~ spl0_1727
| ~ spl0_1984 ),
inference(avatar_split_clause,[],[f16112,f14665,f12502,f35063]) ).
fof(f35063,plain,
( spl0_2903
<=> ! [X2,X1] : ~ c_Wellfounded__Recursion_Owf(c_Transitive__Closure_Ortrancl(X1,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2903])]) ).
fof(f12502,plain,
( spl0_1727
<=> ! [X18,X5,X1] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1727])]) ).
fof(f14665,plain,
( spl0_1984
<=> ! [X18,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1984])]) ).
fof(f16112,plain,
( ! [X2,X1] : ~ c_Wellfounded__Recursion_Owf(c_Transitive__Closure_Ortrancl(X1,X2),X2)
| ~ spl0_1727
| ~ spl0_1984 ),
inference(resolution,[],[f14666,f12503]) ).
fof(f12503,plain,
( ! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1))
| ~ spl0_1727 ),
inference(avatar_component_clause,[],[f12502]) ).
fof(f14666,plain,
( ! [X18,X1,X5] :
( ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1))
| ~ c_Wellfounded__Recursion_Owf(X5,X1) )
| ~ spl0_1984 ),
inference(avatar_component_clause,[],[f14665]) ).
fof(f35037,plain,
( spl0_2902
| ~ spl0_1
| ~ spl0_2408 ),
inference(avatar_split_clause,[],[f23916,f22976,f3013,f35035]) ).
fof(f35035,plain,
( spl0_2902
<=> ! [X316] : c_minus(X316,c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) = c_minus(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),X316,tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2902])]) ).
fof(f3013,plain,
( spl0_1
<=> c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f23916,plain,
( ! [X316] : c_minus(X316,c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)) = c_minus(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),X316,tc_Message_Omsg),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ spl0_1
| ~ spl0_2408 ),
inference(resolution,[],[f22977,f3015]) ).
fof(f3015,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f3013]) ).
fof(f35026,plain,
( spl0_1720
| ~ spl0_1862
| ~ spl0_2900 ),
inference(avatar_split_clause,[],[f35022,f35014,f13068,f12419]) ).
fof(f12419,plain,
( spl0_1720
<=> c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1720])]) ).
fof(f13068,plain,
( spl0_1862
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1862])]) ).
fof(f35022,plain,
( c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ spl0_1862
| ~ spl0_2900 ),
inference(resolution,[],[f35016,f13069]) ).
fof(f13069,plain,
( ! [X91,X88,X86] :
( ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) )
| ~ spl0_1862 ),
inference(avatar_component_clause,[],[f13068]) ).
fof(f35016,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ spl0_2900 ),
inference(avatar_component_clause,[],[f35014]) ).
fof(f35021,plain,
( spl0_2900
| spl0_2901
| ~ spl0_118
| ~ spl0_2182 ),
inference(avatar_split_clause,[],[f19600,f18506,f3598,f35018,f35014]) ).
fof(f18506,plain,
( spl0_2182
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2182])]) ).
fof(f19600,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(v_H),tc_Message_Omsg)
| ~ spl0_118
| ~ spl0_2182 ),
inference(resolution,[],[f18507,f3600]) ).
fof(f18507,plain,
( ! [X1,X4,X12,X13] :
( ~ c_in(X4,c_union(X12,X13,X1),X1)
| c_in(X4,X13,X1)
| c_in(X4,X12,X1) )
| ~ spl0_2182 ),
inference(avatar_component_clause,[],[f18506]) ).
fof(f35002,plain,
spl0_2899,
inference(avatar_split_clause,[],[f6,f35000]) ).
fof(f35000,plain,
( spl0_2899
<=> ! [X5,X10,X9,X7,X8,X6,X2,X1] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2899])]) ).
fof(f6,axiom,
! [X2,X10,X1,X8,X6,X9,X7,X5] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_OScons(X10,X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdprodI_0) ).
fof(f34979,plain,
spl0_2898,
inference(avatar_split_clause,[],[f10,f34977]) ).
fof(f34977,plain,
( spl0_2898
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2898])]) ).
fof(f10,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdsumE_3) ).
fof(f34937,plain,
spl0_2897,
inference(avatar_split_clause,[],[f9,f34935]) ).
fof(f34935,plain,
( spl0_2897
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2897])]) ).
fof(f9,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__1(X5,X11,X1,X2),c_Main_OdsumE__2(X5,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdsumE_2) ).
fof(f34933,plain,
spl0_2896,
inference(avatar_split_clause,[],[f8,f34931]) ).
fof(f34931,plain,
( spl0_2896
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2896])]) ).
fof(f8,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_in(c_Pair(c_Main_OdsumE__3(X6,X11,X1,X2),c_Main_OdsumE__4(X6,X11,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdsumE_1) ).
fof(f34929,plain,
( spl0_2895
| ~ spl0_1243
| ~ spl0_2791 ),
inference(avatar_split_clause,[],[f32928,f32233,f9347,f34927]) ).
fof(f34927,plain,
( spl0_2895
<=> ! [X3] : c_in(c_Message_Omsg_ONumber(X3),v_H,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2895])]) ).
fof(f9347,plain,
( spl0_1243
<=> ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1243])]) ).
fof(f32233,plain,
( spl0_2791
<=> v_H = c_Message_Osynth(c_Message_Oparts(c_UNIV)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2791])]) ).
fof(f32928,plain,
( ! [X3] : c_in(c_Message_Omsg_ONumber(X3),v_H,tc_Message_Omsg)
| ~ spl0_1243
| ~ spl0_2791 ),
inference(superposition,[],[f9348,f32235]) ).
fof(f32235,plain,
( v_H = c_Message_Osynth(c_Message_Oparts(c_UNIV))
| ~ spl0_2791 ),
inference(avatar_component_clause,[],[f32233]) ).
fof(f9348,plain,
( ! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1243 ),
inference(avatar_component_clause,[],[f9347]) ).
fof(f34906,plain,
spl0_2894,
inference(avatar_split_clause,[],[f7,f34904]) ).
fof(f34904,plain,
( spl0_2894
<=> ! [X5,X11,X6,X2,X1] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2894])]) ).
fof(f7,axiom,
! [X2,X11,X1,X6,X5] :
( ~ c_in(X11,c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OIn1(c_Main_OdsumE__3(X6,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn1(c_Main_OdsumE__4(X6,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11
| c_Pair(c_Datatype__Universe_OIn0(c_Main_OdsumE__1(X5,X11,X1,X2),X1,X2),c_Datatype__Universe_OIn0(c_Main_OdsumE__2(X5,X11,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X11 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdsumE_0) ).
fof(f34885,plain,
spl0_2893,
inference(avatar_split_clause,[],[f3,f34883]) ).
fof(f34883,plain,
( spl0_2893
<=> ! [X5,X4,X6,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2893])]) ).
fof(f3,axiom,
! [X2,X1,X6,X4,X5] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_Pair(c_Datatype__Universe_OScons(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__2(X4,X5,X6,X1,X2),X1,X2),c_Datatype__Universe_OScons(c_Main_OdprodE__3(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdprodE_0) ).
fof(f34867,plain,
spl0_2892,
inference(avatar_split_clause,[],[f12,f34865]) ).
fof(f34865,plain,
( spl0_2892
<=> ! [X5,X7,X8,X6,X2,X1] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2892])]) ).
fof(f12,axiom,
! [X2,X1,X8,X6,X7,X5] :
( ~ c_in(c_Pair(X7,X8,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_OIn1(X8,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Odsum__In1I_0) ).
fof(f34863,plain,
spl0_2891,
inference(avatar_split_clause,[],[f11,f34861]) ).
fof(f34861,plain,
( spl0_2891
<=> ! [X6,X9,X10,X5,X2,X1] :
( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2891])]) ).
fof(f11,axiom,
! [X2,X10,X1,X6,X9,X5] :
( ~ c_in(c_Pair(X9,X10,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_OIn0(X10,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Odsum__In0I_0) ).
fof(f34830,plain,
( spl0_2890
| ~ spl0_59
| ~ spl0_2245
| ~ spl0_2246
| ~ spl0_2889 ),
inference(avatar_split_clause,[],[f34792,f34788,f20086,f20082,f3303,f34828]) ).
fof(f34828,plain,
( spl0_2890
<=> ! [X11,X47] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2890])]) ).
fof(f20082,plain,
( spl0_2245
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2245])]) ).
fof(f20086,plain,
( spl0_2246
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2246])]) ).
fof(f34788,plain,
( spl0_2889
<=> ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2889])]) ).
fof(f34792,plain,
( ! [X11,X47] :
( c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2245
| ~ spl0_2246
| ~ spl0_2889 ),
inference(forward_demodulation,[],[f34791,f20821]) ).
fof(f20821,plain,
( ! [X0,X1] : c_plus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,X1),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_2245 ),
inference(resolution,[],[f20083,f3305]) ).
fof(f20083,plain,
( ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) )
| ~ spl0_2245 ),
inference(avatar_component_clause,[],[f20082]) ).
fof(f34791,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2889 ),
inference(forward_demodulation,[],[f34789,f20822]) ).
fof(f20822,plain,
( ! [X0,X1] : c_times(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X1,tc_IntDef_Oint),tc_IntDef_Oint) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X0,X1),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_2246 ),
inference(resolution,[],[f20087,f3305]) ).
fof(f20087,plain,
( ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) )
| ~ spl0_2246 ),
inference(avatar_component_clause,[],[f20086]) ).
fof(f34789,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2889 ),
inference(avatar_component_clause,[],[f34788]) ).
fof(f34790,plain,
spl0_2889,
inference(avatar_split_clause,[],[f2984,f34788]) ).
fof(f2984,plain,
! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2983,f2156]) ).
fof(f2156,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OPls),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__succ__Pls_0) ).
fof(f2983,plain,
! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2982,f2154]) ).
fof(f2154,axiom,
! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__succ__1_0) ).
fof(f2982,plain,
! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1452,f2156]) ).
fof(f1452,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OnegDivAlg__eqn__number__of_1) ).
fof(f34669,plain,
spl0_2888,
inference(avatar_split_clause,[],[f1620,f34667]) ).
fof(f34667,plain,
( spl0_2888
<=> ! [X5,X18,X3,X0,X27,X1] :
( c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X0,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2888])]) ).
fof(f1620,axiom,
! [X3,X0,X18,X1,X27,X5] :
( c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X0,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__cons__cons_1) ).
fof(f34665,plain,
spl0_2887,
inference(avatar_split_clause,[],[f1501,f34663]) ).
fof(f34663,plain,
( spl0_2887
<=> ! [X3,X23,X0,X5,X25,X1] :
( c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2887])]) ).
fof(f1501,axiom,
! [X3,X0,X1,X5,X25,X23] :
( c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OCons__in__lex_1) ).
fof(f34661,plain,
spl0_2886,
inference(avatar_split_clause,[],[f5,f34659]) ).
fof(f34659,plain,
( spl0_2886
<=> ! [X5,X4,X6,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2886])]) ).
fof(f5,axiom,
! [X2,X1,X6,X4,X5] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__1(X4,X5,X6,X1,X2),c_Main_OdprodE__3(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X5,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdprodE_2) ).
fof(f34657,plain,
spl0_2885,
inference(avatar_split_clause,[],[f4,f34655]) ).
fof(f34655,plain,
( spl0_2885
<=> ! [X5,X4,X6,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2885])]) ).
fof(f4,axiom,
! [X2,X1,X6,X4,X5] :
( ~ c_in(X4,c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))))
| c_in(c_Pair(c_Main_OdprodE__2(X4,X5,X6,X1,X2),c_Main_OdprodE__4(X4,X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X6,tc_prod(tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2)))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OdprodE_1) ).
fof(f34627,plain,
( spl0_2884
| ~ spl0_2462
| ~ spl0_1817
| ~ spl0_2806 ),
inference(avatar_split_clause,[],[f33602,f32866,f12874,f24425,f34624]) ).
fof(f34624,plain,
( spl0_2884
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2884])]) ).
fof(f24425,plain,
( spl0_2462
<=> class_Orderings_Oorder(tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2462])]) ).
fof(f12874,plain,
( spl0_1817
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1817])]) ).
fof(f33602,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_emptyset = c_SetInterval_OatLeastAtMost(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg))
| ~ spl0_1817
| ~ spl0_2806 ),
inference(resolution,[],[f32868,f12875]) ).
fof(f12875,plain,
( ! [X21,X1,X15] :
( ~ c_less(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) )
| ~ spl0_1817 ),
inference(avatar_component_clause,[],[f12874]) ).
fof(f34610,plain,
spl0_2883,
inference(avatar_split_clause,[],[f1503,f34608]) ).
fof(f34608,plain,
( spl0_2883
<=> ! [X3,X23,X0,X5,X25,X1] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2883])]) ).
fof(f1503,axiom,
! [X3,X0,X1,X5,X25,X23] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OCons__in__lex_3) ).
fof(f34606,plain,
spl0_2882,
inference(avatar_split_clause,[],[f1369,f34604]) ).
fof(f34604,plain,
( spl0_2882
<=> ! [X0,X3] :
( ~ c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2882])]) ).
fof(f1369,axiom,
! [X3,X0] :
( ~ c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) = c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oequiv__intrel__iff_1) ).
fof(f34602,plain,
spl0_2881,
inference(avatar_split_clause,[],[f1368,f34600]) ).
fof(f34600,plain,
( spl0_2881
<=> ! [X0,X3] :
( c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2881])]) ).
fof(f1368,axiom,
! [X3,X0] :
( c_in(c_Pair(X0,X3,tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)))
| c_Relation_OImage(c_IntDef_Ointrel,c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) != c_Relation_OImage(c_IntDef_Ointrel,c_insert(X3,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oequiv__intrel__iff_0) ).
fof(f34589,plain,
( spl0_2880
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2879 ),
inference(avatar_split_clause,[],[f34585,f34582,f20086,f3303,f34587]) ).
fof(f34587,plain,
( spl0_2880
<=> ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2880])]) ).
fof(f34582,plain,
( spl0_2879
<=> ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2879])]) ).
fof(f34585,plain,
( ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2879 ),
inference(forward_demodulation,[],[f34583,f20822]) ).
fof(f34583,plain,
( ! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2879 ),
inference(avatar_component_clause,[],[f34582]) ).
fof(f34584,plain,
spl0_2879,
inference(avatar_split_clause,[],[f2978,f34582]) ).
fof(f2978,plain,
! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2977,f2156]) ).
fof(f2977,plain,
! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2976,f2154]) ).
fof(f2976,plain,
! [X11,X47] :
( c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1461,f2156]) ).
fof(f1461,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OposDivAlg__eqn__number__of_1) ).
fof(f34547,plain,
spl0_2878,
inference(avatar_split_clause,[],[f1791,f34545]) ).
fof(f34545,plain,
( spl0_2878
<=> ! [X52,X53,X23,X25,X2,X1] :
( c_Nat_Osize(X25,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X2))
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X52,tc_List_Olist(X2))
| c_List_Ozip(c_append(X23,X25,X1),c_append(X52,X53,X2),X1,X2) = c_append(c_List_Ozip(X23,X52,X1,X2),c_List_Ozip(X25,X53,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2878])]) ).
fof(f1791,axiom,
! [X2,X1,X52,X53,X25,X23] :
( c_Nat_Osize(X25,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X2))
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X52,tc_List_Olist(X2))
| c_List_Ozip(c_append(X23,X25,X1),c_append(X52,X53,X2),X1,X2) = c_append(c_List_Ozip(X23,X52,X1,X2),c_List_Ozip(X25,X53,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ozip__append_0) ).
fof(f34516,plain,
( spl0_2877
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2876 ),
inference(avatar_split_clause,[],[f34512,f34509,f20086,f3303,f34514]) ).
fof(f34514,plain,
( spl0_2877
<=> ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2877])]) ).
fof(f34509,plain,
( spl0_2876
<=> ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2876])]) ).
fof(f34512,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2876 ),
inference(forward_demodulation,[],[f34510,f20822]) ).
fof(f34510,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2876 ),
inference(avatar_component_clause,[],[f34509]) ).
fof(f34511,plain,
spl0_2876,
inference(avatar_split_clause,[],[f2981,f34509]) ).
fof(f2981,plain,
! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2980,f2156]) ).
fof(f2980,plain,
! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2979,f2154]) ).
fof(f2979,plain,
! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1450,f2156]) ).
fof(f1450,axiom,
! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OnegDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OnegDivAlg__eqn__1__number__of_1) ).
fof(f34488,plain,
( spl0_2875
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_2245
| ~ spl0_2874 ),
inference(avatar_split_clause,[],[f34484,f34479,f20082,f10503,f3303,f34486]) ).
fof(f34486,plain,
( spl0_2875
<=> ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2875])]) ).
fof(f34479,plain,
( spl0_2874
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2874])]) ).
fof(f34484,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_2245
| ~ spl0_2874 ),
inference(forward_demodulation,[],[f34483,f10850]) ).
fof(f34483,plain,
( ! [X11,X47] :
( c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2245
| ~ spl0_2874 ),
inference(forward_demodulation,[],[f34482,f20821]) ).
fof(f34482,plain,
( ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__add(X11,X47),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2245
| ~ spl0_2874 ),
inference(forward_demodulation,[],[f34480,f20821]) ).
fof(f34480,plain,
( ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2874 ),
inference(avatar_component_clause,[],[f34479]) ).
fof(f34481,plain,
spl0_2874,
inference(avatar_split_clause,[],[f1451,f34479]) ).
fof(f1451,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OnegDivAlg__eqn__number__of_0) ).
fof(f34448,plain,
spl0_2873,
inference(avatar_split_clause,[],[f1504,f34446]) ).
fof(f34446,plain,
( spl0_2873
<=> ! [X3,X23,X0,X5,X25,X1] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2873])]) ).
fof(f1504,axiom,
! [X3,X0,X1,X5,X25,X23] :
( c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OCons__in__lex_4) ).
fof(f34424,plain,
( spl0_2872
| ~ spl0_1225
| ~ spl0_2270
| ~ spl0_2677 ),
inference(avatar_split_clause,[],[f29122,f29014,f20190,f9275,f34421]) ).
fof(f34421,plain,
( spl0_2872
<=> c_UNIV = c_union(c_uminus(c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2872])]) ).
fof(f9275,plain,
( spl0_1225
<=> ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1225])]) ).
fof(f20190,plain,
( spl0_2270
<=> ! [X13,X12,X1] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2270])]) ).
fof(f29014,plain,
( spl0_2677
<=> c_emptyset = c_minus(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2677])]) ).
fof(f29122,plain,
( c_UNIV = c_union(c_uminus(c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_1225
| ~ spl0_2270
| ~ spl0_2677 ),
inference(forward_demodulation,[],[f29111,f9276]) ).
fof(f9276,plain,
( ! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1))
| ~ spl0_1225 ),
inference(avatar_component_clause,[],[f9275]) ).
fof(f29111,plain,
( c_uminus(c_emptyset,tc_set(tc_Message_Omsg)) = c_union(c_uminus(c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_2270
| ~ spl0_2677 ),
inference(superposition,[],[f20191,f29016]) ).
fof(f29016,plain,
( c_emptyset = c_minus(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_2677 ),
inference(avatar_component_clause,[],[f29014]) ).
fof(f20191,plain,
( ! [X1,X12,X13] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1)
| ~ spl0_2270 ),
inference(avatar_component_clause,[],[f20190]) ).
fof(f34417,plain,
( spl0_2871
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2870 ),
inference(avatar_split_clause,[],[f34413,f34410,f20086,f3303,f34415]) ).
fof(f34415,plain,
( spl0_2871
<=> ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2871])]) ).
fof(f34410,plain,
( spl0_2870
<=> ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2870])]) ).
fof(f34413,plain,
( ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(c_Numeral_Obin__mult(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X11),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_2246
| ~ spl0_2870 ),
inference(forward_demodulation,[],[f34411,f20822]) ).
fof(f34411,plain,
( ! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2870 ),
inference(avatar_component_clause,[],[f34410]) ).
fof(f34412,plain,
spl0_2870,
inference(avatar_split_clause,[],[f2975,f34410]) ).
fof(f2975,plain,
! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2974,f2156]) ).
fof(f2974,plain,
! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2973,f2154]) ).
fof(f2973,plain,
! [X11] :
( c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1459,f2156]) ).
fof(f1459,axiom,
! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_IntDiv_Oadjust(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_IntDiv_OposDivAlg(c_Pair(c_1,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OposDivAlg__eqn__1__number__of_1) ).
fof(f34408,plain,
spl0_2869,
inference(avatar_split_clause,[],[f54,f34406]) ).
fof(f34406,plain,
( spl0_2869
<=> ! [X3,X23,X5,X25,X1] :
( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2869])]) ).
fof(f54,axiom,
! [X3,X1,X5,X25,X23] :
( ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Cons2_1) ).
fof(f34404,plain,
spl0_2868,
inference(avatar_split_clause,[],[f51,f34402]) ).
fof(f34402,plain,
( spl0_2868
<=> ! [X3,X23,X5,X25,X1] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2868])]) ).
fof(f51,axiom,
! [X3,X1,X5,X25,X23] :
( ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(X25,c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Cons1_1) ).
fof(f34254,plain,
spl0_2867,
inference(avatar_split_clause,[],[f1957,f34252]) ).
fof(f34252,plain,
( spl0_2867
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2867])]) ).
fof(f1957,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_8) ).
fof(f34239,plain,
spl0_2866,
inference(avatar_split_clause,[],[f1941,f34237]) ).
fof(f34237,plain,
( spl0_2866
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2866])]) ).
fof(f1941,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_8) ).
fof(f34235,plain,
spl0_2865,
inference(avatar_split_clause,[],[f1920,f34233]) ).
fof(f34233,plain,
( spl0_2865
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2865])]) ).
fof(f1920,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_8) ).
fof(f34231,plain,
spl0_2864,
inference(avatar_split_clause,[],[f1904,f34229]) ).
fof(f34229,plain,
( spl0_2864
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2864])]) ).
fof(f1904,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_8) ).
fof(f34146,plain,
( spl0_2863
| ~ spl0_59
| ~ spl0_1591
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2862 ),
inference(avatar_split_clause,[],[f34142,f34138,f14521,f12723,f11238,f3303,f34144]) ).
fof(f34144,plain,
( spl0_2863
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2863])]) ).
fof(f11238,plain,
( spl0_1591
<=> ! [X2,X18,X1,X3] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1591])]) ).
fof(f12723,plain,
( spl0_1781
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1781])]) ).
fof(f14521,plain,
( spl0_1950
<=> ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1950])]) ).
fof(f34138,plain,
( spl0_2862
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2862])]) ).
fof(f34142,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1591
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2862 ),
inference(forward_demodulation,[],[f34141,f13480]) ).
fof(f13480,plain,
( ! [X0] : c_Numeral_Onumber__of(c_Numeral_Obin__minus(X0),tc_IntDef_Oint) = c_uminus(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1781 ),
inference(resolution,[],[f12724,f3305]) ).
fof(f12724,plain,
( ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) )
| ~ spl0_1781 ),
inference(avatar_component_clause,[],[f12723]) ).
fof(f34141,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2862 ),
inference(forward_demodulation,[],[f34139,f15874]) ).
fof(f15874,plain,
( ! [X2,X0,X1] : c_Main_Osurj__pair__2(X0,X1,X2) = c_snd(X0,X1,X2)
| ~ spl0_1591
| ~ spl0_1950 ),
inference(superposition,[],[f11239,f14522]) ).
fof(f14522,plain,
( ! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48
| ~ spl0_1950 ),
inference(avatar_component_clause,[],[f14521]) ).
fof(f11239,plain,
( ! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3
| ~ spl0_1591 ),
inference(avatar_component_clause,[],[f11238]) ).
fof(f34139,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2862 ),
inference(avatar_component_clause,[],[f34138]) ).
fof(f34140,plain,
spl0_2862,
inference(avatar_split_clause,[],[f2972,f34138]) ).
fof(f2972,plain,
! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1446,f1456]) ).
fof(f1456,axiom,
! [X49,X5] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OnegateSnd__eq_0) ).
fof(f1446,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__pos__neg__number__of_0) ).
fof(f34136,plain,
( spl0_2861
| ~ spl0_2462
| ~ spl0_1818
| ~ spl0_2660 ),
inference(avatar_split_clause,[],[f28603,f28316,f12878,f24425,f34133]) ).
fof(f34133,plain,
( spl0_2861
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2861])]) ).
fof(f12878,plain,
( spl0_1818
<=> ! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1818])]) ).
fof(f28316,plain,
( spl0_2660
<=> c_lessequals(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2660])]) ).
fof(f28603,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_emptyset = c_SetInterval_OatLeastLessThan(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg))
| ~ spl0_1818
| ~ spl0_2660 ),
inference(resolution,[],[f28318,f12879]) ).
fof(f12879,plain,
( ! [X21,X1,X15] :
( ~ c_lessequals(X21,X15,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) )
| ~ spl0_1818 ),
inference(avatar_component_clause,[],[f12878]) ).
fof(f28318,plain,
( c_lessequals(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_2660 ),
inference(avatar_component_clause,[],[f28316]) ).
fof(f34127,plain,
( spl0_2860
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2859 ),
inference(avatar_split_clause,[],[f34123,f34119,f14521,f12723,f11234,f3303,f34125]) ).
fof(f34125,plain,
( spl0_2860
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2860])]) ).
fof(f11234,plain,
( spl0_1590
<=> ! [X3,X27,X2,X1] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1590])]) ).
fof(f34119,plain,
( spl0_2859
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2859])]) ).
fof(f34123,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2859 ),
inference(forward_demodulation,[],[f34122,f13480]) ).
fof(f34122,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2859 ),
inference(forward_demodulation,[],[f34120,f15875]) ).
fof(f15875,plain,
( ! [X3,X4,X5] : c_fst(X3,X4,X5) = c_Main_Osurj__pair__1(X3,X4,X5)
| ~ spl0_1590
| ~ spl0_1950 ),
inference(superposition,[],[f11235,f14522]) ).
fof(f11235,plain,
( ! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3
| ~ spl0_1590 ),
inference(avatar_component_clause,[],[f11234]) ).
fof(f34120,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2859 ),
inference(avatar_component_clause,[],[f34119]) ).
fof(f34121,plain,
spl0_2859,
inference(avatar_split_clause,[],[f2971,f34119]) ).
fof(f2971,plain,
! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1436,f1456]) ).
fof(f1436,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odiv__pos__neg__number__of_0) ).
fof(f34113,plain,
( spl0_2858
| ~ spl0_59
| ~ spl0_1591
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2857 ),
inference(avatar_split_clause,[],[f34109,f34105,f14521,f12723,f11238,f3303,f34111]) ).
fof(f34111,plain,
( spl0_2858
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2858])]) ).
fof(f34105,plain,
( spl0_2857
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2857])]) ).
fof(f34109,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1591
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2857 ),
inference(forward_demodulation,[],[f34108,f13480]) ).
fof(f34108,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2857 ),
inference(forward_demodulation,[],[f34106,f15874]) ).
fof(f34106,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2857 ),
inference(avatar_component_clause,[],[f34105]) ).
fof(f34107,plain,
spl0_2857,
inference(avatar_split_clause,[],[f2970,f34105]) ).
fof(f2970,plain,
! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1443,f1456]) ).
fof(f1443,axiom,
! [X11,X47] :
( ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__neg__neg__number__of_0) ).
fof(f34099,plain,
( spl0_2856
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2855 ),
inference(avatar_split_clause,[],[f34095,f34091,f14521,f12723,f11234,f3303,f34097]) ).
fof(f34097,plain,
( spl0_2856
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2856])]) ).
fof(f34091,plain,
( spl0_2855
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2855])]) ).
fof(f34095,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1590
| ~ spl0_1781
| ~ spl0_1950
| ~ spl0_2855 ),
inference(forward_demodulation,[],[f34094,f13480]) ).
fof(f34094,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2855 ),
inference(forward_demodulation,[],[f34092,f15875]) ).
fof(f34092,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2855 ),
inference(avatar_component_clause,[],[f34091]) ).
fof(f34093,plain,
spl0_2855,
inference(avatar_split_clause,[],[f2969,f34091]) ).
fof(f2969,plain,
! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1433,f1456]) ).
fof(f1433,axiom,
! [X11,X47] :
( ~ c_lessequals(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OposDivAlg(c_Pair(c_uminus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odiv__neg__neg__number__of_0) ).
fof(f34089,plain,
spl0_2854,
inference(avatar_split_clause,[],[f1622,f34087]) ).
fof(f34087,plain,
( spl0_2854
<=> ! [X62,X3,X0,X5,X1] :
( ~ c_in(c_Pair(X62,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X62,X1),c_List_Olist_OCons(X0,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2854])]) ).
fof(f1622,axiom,
! [X3,X0,X1,X62,X5] :
( ~ c_in(c_Pair(X62,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X62,X1),c_List_Olist_OCons(X0,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__cons__cons_3) ).
fof(f34082,plain,
spl0_2853,
inference(avatar_split_clause,[],[f1505,f34080]) ).
fof(f34080,plain,
( spl0_2853
<=> ! [X23,X0,X5,X25,X1] :
( ~ c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X0,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2853])]) ).
fof(f1505,axiom,
! [X0,X1,X5,X25,X23] :
( ~ c_in(c_Pair(X23,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1)))
| c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X0,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OCons__in__lex_5) ).
fof(f34078,plain,
spl0_2852,
inference(avatar_split_clause,[],[f1188,f34076]) ).
fof(f34076,plain,
( spl0_2852
<=> ! [X5,X6,X2,X1] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2852])]) ).
fof(f1188,axiom,
! [X2,X1,X6,X5] : c_Relation_ODomain(c_Datatype__Universe_Odsum(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ousum(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_ODomain__dsum_0) ).
fof(f34074,plain,
spl0_2851,
inference(avatar_split_clause,[],[f1187,f34072]) ).
fof(f34072,plain,
( spl0_2851
<=> ! [X5,X6,X2,X1] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2851])]) ).
fof(f1187,axiom,
! [X2,X1,X6,X5] : c_Relation_ODomain(c_Datatype__Universe_Odprod(X5,X6,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))) = c_Datatype__Universe_Ouprod(c_Relation_ODomain(X5,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),c_Relation_ODomain(X6,tc_set(tc_Datatype__Universe_Onode(X1,X2)),tc_set(tc_Datatype__Universe_Onode(X1,X2))),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_ODomain__dprod_0) ).
fof(f33895,plain,
spl0_2850,
inference(avatar_split_clause,[],[f1958,f33893]) ).
fof(f33893,plain,
( spl0_2850
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2850])]) ).
fof(f1958,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_9) ).
fof(f33891,plain,
spl0_2849,
inference(avatar_split_clause,[],[f1942,f33889]) ).
fof(f33889,plain,
( spl0_2849
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2849])]) ).
fof(f1942,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_9) ).
fof(f33887,plain,
spl0_2848,
inference(avatar_split_clause,[],[f1921,f33885]) ).
fof(f33885,plain,
( spl0_2848
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2848])]) ).
fof(f1921,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_9) ).
fof(f33883,plain,
( spl0_2847
| ~ spl0_2462
| ~ spl0_1829
| ~ spl0_2660 ),
inference(avatar_split_clause,[],[f28602,f28316,f12928,f24425,f33880]) ).
fof(f33880,plain,
( spl0_2847
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2847])]) ).
fof(f12928,plain,
( spl0_1829
<=> ! [X16,X1,X26] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1829])]) ).
fof(f28602,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg))
| ~ spl0_1829
| ~ spl0_2660 ),
inference(resolution,[],[f28318,f12929]) ).
fof(f12929,plain,
( ! [X1,X26,X16] :
( ~ c_lessequals(X26,X16,X1)
| ~ class_Orderings_Oorder(X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) )
| ~ spl0_1829 ),
inference(avatar_component_clause,[],[f12928]) ).
fof(f33878,plain,
spl0_2846,
inference(avatar_split_clause,[],[f1905,f33876]) ).
fof(f33876,plain,
( spl0_2846
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2846])]) ).
fof(f1905,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_9) ).
fof(f33578,plain,
( spl0_2845
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_2835 ),
inference(avatar_split_clause,[],[f33535,f33532,f10503,f3303,f33576]) ).
fof(f33576,plain,
( spl0_2845
<=> ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2845])]) ).
fof(f33532,plain,
( spl0_2835
<=> ! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2835])]) ).
fof(f33535,plain,
( ! [X11] :
( c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_2835 ),
inference(forward_demodulation,[],[f33533,f10850]) ).
fof(f33533,plain,
( ! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2835 ),
inference(avatar_component_clause,[],[f33532]) ).
fof(f33574,plain,
spl0_2844,
inference(avatar_split_clause,[],[f1953,f33572]) ).
fof(f33572,plain,
( spl0_2844
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2844])]) ).
fof(f1953,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_4) ).
fof(f33570,plain,
spl0_2843,
inference(avatar_split_clause,[],[f1950,f33568]) ).
fof(f33568,plain,
( spl0_2843
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2843])]) ).
fof(f1950,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_1) ).
fof(f33566,plain,
spl0_2842,
inference(avatar_split_clause,[],[f1937,f33564]) ).
fof(f33564,plain,
( spl0_2842
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2842])]) ).
fof(f1937,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_4) ).
fof(f33562,plain,
spl0_2841,
inference(avatar_split_clause,[],[f1934,f33560]) ).
fof(f33560,plain,
( spl0_2841
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2841])]) ).
fof(f1934,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_1) ).
fof(f33558,plain,
spl0_2840,
inference(avatar_split_clause,[],[f1916,f33556]) ).
fof(f33556,plain,
( spl0_2840
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2840])]) ).
fof(f1916,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_4) ).
fof(f33554,plain,
spl0_2839,
inference(avatar_split_clause,[],[f1913,f33552]) ).
fof(f33552,plain,
( spl0_2839
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2839])]) ).
fof(f1913,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_1) ).
fof(f33550,plain,
spl0_2838,
inference(avatar_split_clause,[],[f1900,f33548]) ).
fof(f33548,plain,
( spl0_2838
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2838])]) ).
fof(f1900,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_4) ).
fof(f33546,plain,
spl0_2837,
inference(avatar_split_clause,[],[f1897,f33544]) ).
fof(f33544,plain,
( spl0_2837
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2837])]) ).
fof(f1897,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_1) ).
fof(f33542,plain,
( ~ spl0_1081
| spl0_2825 ),
inference(avatar_contradiction_clause,[],[f33540]) ).
fof(f33540,plain,
( $false
| ~ spl0_1081
| spl0_2825 ),
inference(resolution,[],[f33000,f8653]) ).
fof(f33000,plain,
( ~ c_lessequals(v_H,v_H,tc_set(tc_Message_Omsg))
| spl0_2825 ),
inference(avatar_component_clause,[],[f32998]) ).
fof(f32998,plain,
( spl0_2825
<=> c_lessequals(v_H,v_H,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2825])]) ).
fof(f33539,plain,
spl0_2836,
inference(avatar_split_clause,[],[f1705,f33537]) ).
fof(f33537,plain,
( spl0_2836
<=> ! [X43,X23,X25,X2,X1] :
( ~ c_less(X43,c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat)
| ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Ozip(X23,X25,X1,X2),X43,tc_prod(X1,X2)) = c_Pair(c_List_Onth(X23,X43,X1),c_List_Onth(X25,X43,X2),X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2836])]) ).
fof(f1705,axiom,
! [X2,X1,X25,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat)
| ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Ozip(X23,X25,X1,X2),X43,tc_prod(X1,X2)) = c_Pair(c_List_Onth(X23,X43,X1),c_List_Onth(X25,X43,X2),X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__zip_0) ).
fof(f33534,plain,
spl0_2835,
inference(avatar_split_clause,[],[f1449,f33532]) ).
fof(f1449,axiom,
! [X11] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OnegDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_plus(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OnegDivAlg__eqn__1__number__of_0) ).
fof(f33394,plain,
spl0_2834,
inference(avatar_split_clause,[],[f1619,f33392]) ).
fof(f33392,plain,
( spl0_2834
<=> ! [X18,X3,X0,X5,X27,X1] :
( X18 = X27
| c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2834])]) ).
fof(f1619,axiom,
! [X3,X0,X18,X1,X27,X5] :
( X18 = X27
| c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__cons__cons_0) ).
fof(f33390,plain,
spl0_2833,
inference(avatar_split_clause,[],[f1500,f33388]) ).
fof(f33388,plain,
( spl0_2833
<=> ! [X3,X23,X0,X5,X25,X1] :
( X0 = X3
| c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2833])]) ).
fof(f1500,axiom,
! [X3,X0,X1,X5,X25,X23] :
( X0 = X3
| c_in(c_Pair(X0,X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OCons__in__lex_0) ).
fof(f33386,plain,
spl0_2832,
inference(avatar_split_clause,[],[f1383,f33384]) ).
fof(f33384,plain,
( spl0_2832
<=> ! [X47,X0,X14,X3] :
( c_plus(X0,X47,tc_nat) != c_plus(X14,X3,tc_nat)
| c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2832])]) ).
fof(f1383,axiom,
! [X3,X0,X47,X14] :
( c_plus(X0,X47,tc_nat) != c_plus(X14,X3,tc_nat)
| c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ointrel__iff_1) ).
fof(f33382,plain,
spl0_2831,
inference(avatar_split_clause,[],[f1382,f33380]) ).
fof(f33380,plain,
( spl0_2831
<=> ! [X47,X0,X14,X3] :
( c_plus(X0,X47,tc_nat) = c_plus(X14,X3,tc_nat)
| ~ c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2831])]) ).
fof(f1382,axiom,
! [X3,X0,X47,X14] :
( c_plus(X0,X47,tc_nat) = c_plus(X14,X3,tc_nat)
| ~ c_in(c_Pair(c_Pair(X0,X3,tc_nat,tc_nat),c_Pair(X14,X47,tc_nat,tc_nat),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_Ointrel,tc_prod(tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ointrel__iff_0) ).
fof(f33378,plain,
spl0_2830,
inference(avatar_split_clause,[],[f85,f33376]) ).
fof(f33376,plain,
( spl0_2830
<=> ! [X31,X4,X18,X6,X5,X27,X2,X1] :
( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
| ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
| c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2830])]) ).
fof(f85,axiom,
! [X2,X31,X18,X1,X6,X27,X4,X5] :
( ~ c_in(c_Pair(X27,X4,X2,X31),X5,tc_prod(X2,X31))
| ~ c_in(c_Pair(X18,X27,X1,X2),X6,tc_prod(X1,X2))
| c_in(c_Pair(X18,X4,X1,X31),c_Relation_Orel__comp(X5,X6,X2,X31,X1),tc_prod(X1,X31)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Orel__compI_0) ).
fof(f33374,plain,
spl0_2829,
inference(avatar_split_clause,[],[f53,f33372]) ).
fof(f33372,plain,
( spl0_2829
<=> ! [X5,X3,X23,X25,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2829])]) ).
fof(f53,axiom,
! [X3,X1,X5,X25,X23] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons2__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Cons2_0) ).
fof(f33370,plain,
spl0_2828,
inference(avatar_split_clause,[],[f50,f33368]) ).
fof(f33368,plain,
( spl0_2828
<=> ! [X5,X3,X23,X25,X1] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2828])]) ).
fof(f50,axiom,
! [X3,X1,X5,X25,X23] :
( c_List_Olist_OCons(c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),c_Main_Olistrel__Cons1__2(X5,X23,X3,X25,X1),X1) = X23
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Cons1_0) ).
fof(f33354,plain,
( spl0_2827
| ~ spl0_1242
| ~ spl0_2791 ),
inference(avatar_split_clause,[],[f32927,f32233,f9343,f33352]) ).
fof(f33352,plain,
( spl0_2827
<=> ! [X2] : c_in(c_Message_Omsg_OAgent(X2),v_H,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2827])]) ).
fof(f9343,plain,
( spl0_1242
<=> ! [X12,X88] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1242])]) ).
fof(f32927,plain,
( ! [X2] : c_in(c_Message_Omsg_OAgent(X2),v_H,tc_Message_Omsg)
| ~ spl0_1242
| ~ spl0_2791 ),
inference(superposition,[],[f9344,f32235]) ).
fof(f9344,plain,
( ! [X88,X12] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ spl0_1242 ),
inference(avatar_component_clause,[],[f9343]) ).
fof(f33005,plain,
( spl0_2826
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2812 ),
inference(avatar_split_clause,[],[f32897,f32894,f14521,f11238,f33003]) ).
fof(f33003,plain,
( spl0_2826
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2826])]) ).
fof(f32894,plain,
( spl0_2812
<=> ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2812])]) ).
fof(f32897,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2812 ),
inference(forward_demodulation,[],[f32895,f15874]) ).
fof(f32895,plain,
( ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2812 ),
inference(avatar_component_clause,[],[f32894]) ).
fof(f33001,plain,
( ~ spl0_2825
| ~ spl0_2791
| spl0_2792 ),
inference(avatar_split_clause,[],[f32926,f32237,f32233,f32998]) ).
fof(f32926,plain,
( ~ c_lessequals(v_H,v_H,tc_set(tc_Message_Omsg))
| ~ spl0_2791
| spl0_2792 ),
inference(superposition,[],[f32239,f32235]) ).
fof(f32239,plain,
( ~ c_lessequals(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg))
| spl0_2792 ),
inference(avatar_component_clause,[],[f32237]) ).
fof(f32996,plain,
( spl0_2824
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2811 ),
inference(avatar_split_clause,[],[f32892,f32889,f14521,f11238,f32994]) ).
fof(f32994,plain,
( spl0_2824
<=> ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2824])]) ).
fof(f32889,plain,
( spl0_2811
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2811])]) ).
fof(f32892,plain,
( ! [X11,X47] :
( c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2811 ),
inference(forward_demodulation,[],[f32890,f15874]) ).
fof(f32890,plain,
( ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2811 ),
inference(avatar_component_clause,[],[f32889]) ).
fof(f32992,plain,
( spl0_2823
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2810 ),
inference(avatar_split_clause,[],[f32887,f32884,f14521,f11234,f32990]) ).
fof(f32990,plain,
( spl0_2823
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2823])]) ).
fof(f32884,plain,
( spl0_2810
<=> ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2810])]) ).
fof(f32887,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2810 ),
inference(forward_demodulation,[],[f32885,f15875]) ).
fof(f32885,plain,
( ! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2810 ),
inference(avatar_component_clause,[],[f32884]) ).
fof(f32988,plain,
( spl0_2822
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2809 ),
inference(avatar_split_clause,[],[f32882,f32879,f14521,f11234,f32986]) ).
fof(f32986,plain,
( spl0_2822
<=> ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2822])]) ).
fof(f32879,plain,
( spl0_2809
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2809])]) ).
fof(f32882,plain,
( ! [X11,X47] :
( c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2809 ),
inference(forward_demodulation,[],[f32880,f15875]) ).
fof(f32880,plain,
( ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2809 ),
inference(avatar_component_clause,[],[f32879]) ).
fof(f32965,plain,
spl0_2821,
inference(avatar_split_clause,[],[f1956,f32963]) ).
fof(f32963,plain,
( spl0_2821
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2821])]) ).
fof(f1956,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_7) ).
fof(f32961,plain,
spl0_2820,
inference(avatar_split_clause,[],[f1954,f32959]) ).
fof(f32959,plain,
( spl0_2820
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2820])]) ).
fof(f1954,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_5) ).
fof(f32957,plain,
spl0_2819,
inference(avatar_split_clause,[],[f1940,f32955]) ).
fof(f32955,plain,
( spl0_2819
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2819])]) ).
fof(f1940,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_7) ).
fof(f32953,plain,
spl0_2818,
inference(avatar_split_clause,[],[f1938,f32951]) ).
fof(f32951,plain,
( spl0_2818
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2818])]) ).
fof(f1938,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_5) ).
fof(f32949,plain,
spl0_2817,
inference(avatar_split_clause,[],[f1919,f32947]) ).
fof(f32947,plain,
( spl0_2817
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2817])]) ).
fof(f1919,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_7) ).
fof(f32913,plain,
spl0_2816,
inference(avatar_split_clause,[],[f1917,f32911]) ).
fof(f32911,plain,
( spl0_2816
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2816])]) ).
fof(f1917,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_5) ).
fof(f32909,plain,
spl0_2815,
inference(avatar_split_clause,[],[f1903,f32907]) ).
fof(f32907,plain,
( spl0_2815
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2815])]) ).
fof(f1903,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_7) ).
fof(f32905,plain,
spl0_2814,
inference(avatar_split_clause,[],[f1901,f32903]) ).
fof(f32903,plain,
( spl0_2814
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2814])]) ).
fof(f1901,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_5) ).
fof(f32901,plain,
spl0_2813,
inference(avatar_split_clause,[],[f1502,f32899]) ).
fof(f32899,plain,
( spl0_2813
<=> ! [X5,X23,X0,X3,X25,X1] :
( X0 = X3
| c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2813])]) ).
fof(f1502,axiom,
! [X3,X0,X1,X5,X25,X23] :
( X0 = X3
| c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(X25,tc_List_Olist(X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OCons__in__lex_2) ).
fof(f32896,plain,
spl0_2812,
inference(avatar_split_clause,[],[f1448,f32894]) ).
fof(f1448,axiom,
! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__pos__pos__number__of_0) ).
fof(f32891,plain,
spl0_2811,
inference(avatar_split_clause,[],[f1444,f32889]) ).
fof(f1444,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__neg__pos__number__of_0) ).
fof(f32886,plain,
spl0_2810,
inference(avatar_split_clause,[],[f1438,f32884]) ).
fof(f1438,axiom,
! [X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odiv__pos__pos__number__of_0) ).
fof(f32881,plain,
spl0_2809,
inference(avatar_split_clause,[],[f1434,f32879]) ).
fof(f1434,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odiv__neg__pos__number__of_0) ).
fof(f32877,plain,
spl0_2808,
inference(avatar_split_clause,[],[f55,f32875]) ).
fof(f32875,plain,
( spl0_2808
<=> ! [X3,X23,X5,X25,X1] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2808])]) ).
fof(f55,axiom,
! [X3,X1,X5,X25,X23] :
( c_in(c_Pair(c_Main_Olistrel__Cons2__1(X5,X23,X3,X25,X1),X3,X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(X23,c_List_Olist_OCons(X3,X25,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Cons2_2) ).
fof(f32873,plain,
spl0_2807,
inference(avatar_split_clause,[],[f52,f32871]) ).
fof(f32871,plain,
( spl0_2807
<=> ! [X3,X23,X5,X25,X1] :
( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2807])]) ).
fof(f52,axiom,
! [X3,X1,X5,X25,X23] :
( c_in(c_Pair(X3,c_Main_Olistrel__Cons1__1(X5,X23,X3,X25,X1),X1,X1),X5,tc_prod(X1,X1))
| ~ c_in(c_Pair(c_List_Olist_OCons(X3,X25,X1),X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Cons1_2) ).
fof(f32869,plain,
( spl0_2806
| spl0_2791
| ~ spl0_1880
| ~ spl0_2660 ),
inference(avatar_split_clause,[],[f28599,f28316,f14198,f32233,f32866]) ).
fof(f14198,plain,
( spl0_1880
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1880])]) ).
fof(f28599,plain,
( v_H = c_Message_Osynth(c_Message_Oparts(c_UNIV))
| c_less(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_1880
| ~ spl0_2660 ),
inference(resolution,[],[f28318,f14199]) ).
fof(f14199,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13
| c_less(X12,X13,tc_set(X1)) )
| ~ spl0_1880 ),
inference(avatar_component_clause,[],[f14198]) ).
fof(f32740,plain,
spl0_2805,
inference(avatar_split_clause,[],[f1470,f32738]) ).
fof(f32738,plain,
( spl0_2805
<=> ! [X11,X27,X47] :
( c_Numeral_Obit_OB0 = X27
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2805])]) ).
fof(f1470,axiom,
! [X11,X47,X27] :
( c_Numeral_Obit_OB0 = X27
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_plus(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__number__of__BIT_2) ).
fof(f32736,plain,
spl0_2804,
inference(avatar_split_clause,[],[f83,f32734]) ).
fof(f32734,plain,
( spl0_2804
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2804])]) ).
fof(f83,axiom,
! [X31,X2,X1,X6,X5,X30] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),X1,X31),X6,tc_prod(X1,X31)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Orel__compE_1) ).
fof(f32732,plain,
spl0_2803,
inference(avatar_split_clause,[],[f82,f32730]) ).
fof(f32730,plain,
( spl0_2803
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2803])]) ).
fof(f82,axiom,
! [X31,X2,X1,X6,X5,X30] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_Orel__compE__2(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X31,X2),X5,tc_prod(X31,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Orel__compE_0) ).
fof(f32728,plain,
spl0_2802,
inference(avatar_split_clause,[],[f20,f32726]) ).
fof(f32726,plain,
( spl0_2802
<=> ! [X13,X14,X12,X2,X1] :
( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2802])]) ).
fof(f20,axiom,
! [X2,X1,X14,X12,X13] :
( ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OusumE_3) ).
fof(f32655,plain,
spl0_2801,
inference(avatar_split_clause,[],[f1621,f32653]) ).
fof(f32653,plain,
( spl0_2801
<=> ! [X5,X18,X3,X0,X27,X1] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2801])]) ).
fof(f1621,axiom,
! [X3,X0,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(c_List_Olist_OCons(X18,X0,X1),c_List_Olist_OCons(X27,X3,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__cons__cons_2) ).
fof(f32651,plain,
spl0_2800,
inference(avatar_split_clause,[],[f1460,f32649]) ).
fof(f32649,plain,
( spl0_2800
<=> ! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2800])]) ).
fof(f1460,axiom,
! [X11,X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OposDivAlg__eqn__number__of_0) ).
fof(f32647,plain,
spl0_2799,
inference(avatar_split_clause,[],[f19,f32645]) ).
fof(f32645,plain,
( spl0_2799
<=> ! [X13,X14,X12,X2,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2799])]) ).
fof(f19,axiom,
! [X2,X1,X14,X12,X13] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__1(X12,X14,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OusumE_2) ).
fof(f32643,plain,
spl0_2798,
inference(avatar_split_clause,[],[f18,f32641]) ).
fof(f32641,plain,
( spl0_2798
<=> ! [X14,X13,X12,X2,X1] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2798])]) ).
fof(f18,axiom,
! [X2,X1,X14,X12,X13] :
( c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OusumE__2(X13,X14,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OusumE_1) ).
fof(f32260,plain,
spl0_2797,
inference(avatar_split_clause,[],[f1952,f32258]) ).
fof(f32258,plain,
( spl0_2797
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2797])]) ).
fof(f1952,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_3) ).
fof(f32256,plain,
spl0_2796,
inference(avatar_split_clause,[],[f1951,f32254]) ).
fof(f32254,plain,
( spl0_2796
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2796])]) ).
fof(f1951,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_2) ).
fof(f32252,plain,
spl0_2795,
inference(avatar_split_clause,[],[f1936,f32250]) ).
fof(f32250,plain,
( spl0_2795
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2795])]) ).
fof(f1936,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_3) ).
fof(f32248,plain,
spl0_2794,
inference(avatar_split_clause,[],[f1935,f32246]) ).
fof(f32246,plain,
( spl0_2794
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2794])]) ).
fof(f1935,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_2) ).
fof(f32244,plain,
spl0_2793,
inference(avatar_split_clause,[],[f1915,f32242]) ).
fof(f32242,plain,
( spl0_2793
<=> ! [X2,X27,X11,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2793])]) ).
fof(f1915,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_3) ).
fof(f32240,plain,
( spl0_2791
| ~ spl0_2792
| ~ spl0_1882
| ~ spl0_2660 ),
inference(avatar_split_clause,[],[f28597,f28316,f14206,f32237,f32233]) ).
fof(f14206,plain,
( spl0_1882
<=> ! [X13,X12,X1] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1882])]) ).
fof(f28597,plain,
( ~ c_lessequals(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_set(tc_Message_Omsg))
| v_H = c_Message_Osynth(c_Message_Oparts(c_UNIV))
| ~ spl0_1882
| ~ spl0_2660 ),
inference(resolution,[],[f28318,f14207]) ).
fof(f14207,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(X12,X13,tc_set(X1))
| X12 = X13 )
| ~ spl0_1882 ),
inference(avatar_component_clause,[],[f14206]) ).
fof(f32231,plain,
spl0_2790,
inference(avatar_split_clause,[],[f1914,f32229]) ).
fof(f32229,plain,
( spl0_2790
<=> ! [X2,X27,X11,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2790])]) ).
fof(f1914,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_2) ).
fof(f32227,plain,
spl0_2789,
inference(avatar_split_clause,[],[f1899,f32225]) ).
fof(f32225,plain,
( spl0_2789
<=> ! [X2,X27,X11,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2789])]) ).
fof(f1899,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_3) ).
fof(f32223,plain,
spl0_2788,
inference(avatar_split_clause,[],[f1898,f32221]) ).
fof(f32221,plain,
( spl0_2788
<=> ! [X2,X27,X11,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2788])]) ).
fof(f1898,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_2) ).
fof(f32219,plain,
spl0_2787,
inference(avatar_split_clause,[],[f17,f32217]) ).
fof(f32217,plain,
( spl0_2787
<=> ! [X13,X14,X12,X2,X1] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2787])]) ).
fof(f17,axiom,
! [X2,X1,X14,X12,X13] :
( c_Datatype__Universe_OIn1(c_Main_OusumE__2(X13,X14,X1,X2),X1,X2) = X14
| c_Datatype__Universe_OIn0(c_Main_OusumE__1(X12,X14,X1,X2),X1,X2) = X14
| ~ c_in(X14,c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OusumE_0) ).
fof(f31737,plain,
spl0_2786,
inference(avatar_split_clause,[],[f1998,f31735]) ).
fof(f31735,plain,
( spl0_2786
<=> ! [X2,X27,X18,X47] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2786])]) ).
fof(f1998,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__right__number__of_2) ).
fof(f31733,plain,
spl0_2785,
inference(avatar_split_clause,[],[f1992,f31731]) ).
fof(f31731,plain,
( spl0_2785
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2785])]) ).
fof(f1992,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__left__number__of_2) ).
fof(f31729,plain,
( spl0_2784
| ~ spl0_1863
| ~ spl0_2634 ),
inference(avatar_split_clause,[],[f28076,f27888,f13072,f31727]) ).
fof(f31727,plain,
( spl0_2784
<=> ! [X1] :
( c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_UNIV,X1,tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2784])]) ).
fof(f13072,plain,
( spl0_1863
<=> ! [X20,X88] :
( ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1863])]) ).
fof(f27888,plain,
( spl0_2634
<=> ! [X2] :
( ~ c_lessequals(c_Message_Oparts(c_UNIV),X2,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),X2,tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2634])]) ).
fof(f28076,plain,
( ! [X1] :
( c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(X1),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_UNIV,X1,tc_set(tc_Message_Omsg)) )
| ~ spl0_1863
| ~ spl0_2634 ),
inference(resolution,[],[f27889,f13073]) ).
fof(f13073,plain,
( ! [X88,X20] :
( c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg)) )
| ~ spl0_1863 ),
inference(avatar_component_clause,[],[f13072]) ).
fof(f27889,plain,
( ! [X2] :
( ~ c_lessequals(c_Message_Oparts(c_UNIV),X2,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),X2,tc_set(tc_Message_Omsg)) )
| ~ spl0_2634 ),
inference(avatar_component_clause,[],[f27888]) ).
fof(f31725,plain,
spl0_2783,
inference(avatar_split_clause,[],[f1986,f31723]) ).
fof(f31723,plain,
( spl0_2783
<=> ! [X2,X27,X18,X47] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2783])]) ).
fof(f1986,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__right__number__of_2) ).
fof(f31721,plain,
spl0_2782,
inference(avatar_split_clause,[],[f1980,f31719]) ).
fof(f31719,plain,
( spl0_2782
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2782])]) ).
fof(f1980,axiom,
! [X2,X47,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__left__number__of_2) ).
fof(f31717,plain,
spl0_2781,
inference(avatar_split_clause,[],[f1955,f31715]) ).
fof(f31715,plain,
( spl0_2781
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2781])]) ).
fof(f1955,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_6) ).
fof(f31713,plain,
spl0_2780,
inference(avatar_split_clause,[],[f1949,f31711]) ).
fof(f31711,plain,
( spl0_2780
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2780])]) ).
fof(f1949,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__divide__eq__number__of_0) ).
fof(f31709,plain,
spl0_2779,
inference(avatar_split_clause,[],[f1939,f31707]) ).
fof(f31707,plain,
( spl0_2779
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2779])]) ).
fof(f1939,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2)
| c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_6) ).
fof(f31705,plain,
spl0_2778,
inference(avatar_split_clause,[],[f1933,f31703]) ).
fof(f31703,plain,
( spl0_2778
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2778])]) ).
fof(f1933,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X18,c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X27,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__divide__eq__number__of_0) ).
fof(f31701,plain,
spl0_2777,
inference(avatar_split_clause,[],[f1918,f31699]) ).
fof(f31699,plain,
( spl0_2777
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2777])]) ).
fof(f1918,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_6) ).
fof(f31697,plain,
spl0_2776,
inference(avatar_split_clause,[],[f1912,f31695]) ).
fof(f31695,plain,
( spl0_2776
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2776])]) ).
fof(f1912,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_less(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__eq__number__of_0) ).
fof(f31693,plain,
spl0_2775,
inference(avatar_split_clause,[],[f1902,f31691]) ).
fof(f31691,plain,
( spl0_2775
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2775])]) ).
fof(f1902,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2)
| c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_6) ).
fof(f31689,plain,
spl0_2774,
inference(avatar_split_clause,[],[f1896,f31687]) ).
fof(f31687,plain,
( spl0_2774
<=> ! [X18,X11,X27,X2] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2774])]) ).
fof(f1896,axiom,
! [X2,X11,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_divide(X27,c_Numeral_Onumber__of(X11,X2),X2),X18,X2)
| c_lessequals(X27,c_times(X18,c_Numeral_Onumber__of(X11,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__eq__number__of_0) ).
fof(f31670,plain,
spl0_2773,
inference(avatar_split_clause,[],[f115,f31668]) ).
fof(f31668,plain,
( spl0_2773
<=> ! [X13,X14,X12,X2,X1] :
( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2773])]) ).
fof(f115,axiom,
! [X2,X1,X14,X12,X13] :
( ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OPlusE_0) ).
fof(f31666,plain,
spl0_2772,
inference(avatar_split_clause,[],[f84,f31664]) ).
fof(f31664,plain,
( spl0_2772
<=> ! [X5,X31,X30,X6,X2,X1] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2772])]) ).
fof(f84,axiom,
! [X31,X2,X1,X6,X5,X30] :
( ~ c_in(X30,c_Relation_Orel__comp(X5,X6,X31,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_Orel__compE__1(X5,X6,X30,X31,X2,X1),c_Main_Orel__compE__3(X5,X6,X30,X31,X2,X1),X1,X2) = X30 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Orel__compE_2) ).
fof(f31655,plain,
( spl0_2771
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2770 ),
inference(avatar_split_clause,[],[f31651,f31648,f13076,f9197,f7368,f31653]) ).
fof(f31653,plain,
( spl0_2771
<=> ! [X18,X21,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Suc(c_1),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Suc(c_1),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2771])]) ).
fof(f31648,plain,
( spl0_2770
<=> ! [X18,X21,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2770])]) ).
fof(f31651,plain,
( ! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Suc(c_1),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Suc(c_1),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2770 ),
inference(forward_demodulation,[],[f31649,f14121]) ).
fof(f31649,plain,
( ! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) )
| ~ spl0_2770 ),
inference(avatar_component_clause,[],[f31648]) ).
fof(f31650,plain,
spl0_2770,
inference(avatar_split_clause,[],[f2966,f31648]) ).
fof(f2966,plain,
! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(forward_demodulation,[],[f2965,f2156]) ).
fof(f2965,plain,
! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(forward_demodulation,[],[f2964,f2154]) ).
fof(f2964,plain,
! [X21,X18,X1] :
( c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1) ),
inference(forward_demodulation,[],[f1875,f2156]) ).
fof(f1875,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Nat_Opower(c_uminus(X18,X1),c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) = c_Nat_Opower(X18,c_times(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Opower__minus__even_0) ).
fof(f31646,plain,
spl0_2769,
inference(avatar_split_clause,[],[f16,f31644]) ).
fof(f31644,plain,
( spl0_2769
<=> ! [X9,X13,X7,X12,X2,X1] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2769])]) ).
fof(f16,axiom,
! [X2,X1,X9,X7,X12,X13] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OScons(X9,X7,X1,X2),c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OuprodI_0) ).
fof(f31634,plain,
( spl0_2768
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2765 ),
inference(avatar_split_clause,[],[f30910,f30907,f14521,f11238,f31632]) ).
fof(f31632,plain,
( spl0_2768
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2768])]) ).
fof(f30907,plain,
( spl0_2765
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2765])]) ).
fof(f30910,plain,
( ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2765 ),
inference(forward_demodulation,[],[f30908,f15874]) ).
fof(f30908,plain,
( ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2765 ),
inference(avatar_component_clause,[],[f30907]) ).
fof(f31630,plain,
( spl0_2767
| ~ spl0_1225
| ~ spl0_2270
| ~ spl0_2663 ),
inference(avatar_split_clause,[],[f28970,f28846,f20190,f9275,f31627]) ).
fof(f31627,plain,
( spl0_2767
<=> c_UNIV = c_union(c_uminus(v_H,tc_set(tc_Message_Omsg)),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2767])]) ).
fof(f28846,plain,
( spl0_2663
<=> c_emptyset = c_minus(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2663])]) ).
fof(f28970,plain,
( c_UNIV = c_union(c_uminus(v_H,tc_set(tc_Message_Omsg)),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_1225
| ~ spl0_2270
| ~ spl0_2663 ),
inference(forward_demodulation,[],[f28959,f9276]) ).
fof(f28959,plain,
( c_uminus(c_emptyset,tc_set(tc_Message_Omsg)) = c_union(c_uminus(v_H,tc_set(tc_Message_Omsg)),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_2270
| ~ spl0_2663 ),
inference(superposition,[],[f20191,f28848]) ).
fof(f28848,plain,
( c_emptyset = c_minus(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_2663 ),
inference(avatar_component_clause,[],[f28846]) ).
fof(f31625,plain,
( spl0_2766
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2764 ),
inference(avatar_split_clause,[],[f30905,f30902,f14521,f11234,f31623]) ).
fof(f31623,plain,
( spl0_2766
<=> ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2766])]) ).
fof(f30902,plain,
( spl0_2764
<=> ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2764])]) ).
fof(f30905,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2764 ),
inference(forward_demodulation,[],[f30903,f15875]) ).
fof(f30903,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) )
| ~ spl0_2764 ),
inference(avatar_component_clause,[],[f30902]) ).
fof(f30909,plain,
spl0_2765,
inference(avatar_split_clause,[],[f2923,f30907]) ).
fof(f2923,plain,
! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1445,f1456]) ).
fof(f1445,axiom,
! [X11] :
( ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__pos__neg__1__number__of_0) ).
fof(f30904,plain,
spl0_2764,
inference(avatar_split_clause,[],[f2922,f30902]) ).
fof(f2922,plain,
! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_IntDiv_OnegateSnd(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)))),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1435,f1456]) ).
fof(f1435,axiom,
! [X11] :
( ~ c_less(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),c_0,tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OnegateSnd(c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_uminus(c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint))),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odiv__pos__neg__1__number__of_0) ).
fof(f30900,plain,
spl0_2763,
inference(avatar_split_clause,[],[f2003,f30898]) ).
fof(f30898,plain,
( spl0_2763
<=> ! [X4,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_plus(X27,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2763])]) ).
fof(f2003,axiom,
! [X2,X47,X27,X4] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_plus(X27,X4,X2),X2) = c_plus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oright__distrib__number__of_0) ).
fof(f30896,plain,
spl0_2762,
inference(avatar_split_clause,[],[f2002,f30894]) ).
fof(f30894,plain,
( spl0_2762
<=> ! [X4,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_minus(X27,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2762])]) ).
fof(f2002,axiom,
! [X2,X47,X27,X4] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_Numeral_Onumber__of(X47,X2),c_minus(X27,X4,X2),X2) = c_minus(c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),c_times(c_Numeral_Onumber__of(X47,X2),X4,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oright__diff__distrib__number__of_0) ).
fof(f30892,plain,
spl0_2761,
inference(avatar_split_clause,[],[f2000,f30890]) ).
fof(f30890,plain,
( spl0_2761
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2761])]) ).
fof(f2000,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__right__number__of_4) ).
fof(f30888,plain,
( spl0_2760
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2677 ),
inference(avatar_split_clause,[],[f29121,f29014,f14629,f9315,f30885]) ).
fof(f30885,plain,
( spl0_2760
<=> c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),c_Message_Osynth(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2760])]) ).
fof(f9315,plain,
( spl0_1235
<=> ! [X1,X3] : c_union(X3,c_emptyset,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1235])]) ).
fof(f14629,plain,
( spl0_1976
<=> ! [X13,X12,X1] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1976])]) ).
fof(f29121,plain,
( c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2677 ),
inference(forward_demodulation,[],[f29108,f9316]) ).
fof(f9316,plain,
( ! [X3,X1] : c_union(X3,c_emptyset,X1) = X3
| ~ spl0_1235 ),
inference(avatar_component_clause,[],[f9315]) ).
fof(f29108,plain,
( c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),c_emptyset,tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_1976
| ~ spl0_2677 ),
inference(superposition,[],[f14630,f29016]) ).
fof(f14630,plain,
( ! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1)
| ~ spl0_1976 ),
inference(avatar_component_clause,[],[f14629]) ).
fof(f30883,plain,
spl0_2759,
inference(avatar_split_clause,[],[f1999,f30881]) ).
fof(f30881,plain,
( spl0_2759
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2759])]) ).
fof(f1999,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__right__number__of_3) ).
fof(f30879,plain,
spl0_2758,
inference(avatar_split_clause,[],[f1997,f30877]) ).
fof(f30877,plain,
( spl0_2758
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2758])]) ).
fof(f1997,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__right__number__of_1) ).
fof(f30875,plain,
spl0_2757,
inference(avatar_split_clause,[],[f1996,f30873]) ).
fof(f30873,plain,
( spl0_2757
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2757])]) ).
fof(f1996,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__right__number__of_0) ).
fof(f30871,plain,
spl0_2756,
inference(avatar_split_clause,[],[f1994,f30869]) ).
fof(f30869,plain,
( spl0_2756
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2756])]) ).
fof(f1994,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__left__number__of_4) ).
fof(f30867,plain,
spl0_2755,
inference(avatar_split_clause,[],[f1993,f30865]) ).
fof(f30865,plain,
( spl0_2755
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2755])]) ).
fof(f1993,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,X18,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__left__number__of_3) ).
fof(f30863,plain,
spl0_2754,
inference(avatar_split_clause,[],[f1991,f30861]) ).
fof(f30861,plain,
( spl0_2754
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2754])]) ).
fof(f1991,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,X18,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__left__number__of_1) ).
fof(f30859,plain,
spl0_2753,
inference(avatar_split_clause,[],[f1990,f30857]) ).
fof(f30857,plain,
( spl0_2753
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2753])]) ).
fof(f1990,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X18,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__left__number__of_0) ).
fof(f30855,plain,
spl0_2752,
inference(avatar_split_clause,[],[f1988,f30853]) ).
fof(f30853,plain,
( spl0_2752
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2752])]) ).
fof(f1988,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__right__number__of_4) ).
fof(f30851,plain,
spl0_2751,
inference(avatar_split_clause,[],[f1987,f30849]) ).
fof(f30849,plain,
( spl0_2751
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2751])]) ).
fof(f1987,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__right__number__of_3) ).
fof(f30847,plain,
spl0_2750,
inference(avatar_split_clause,[],[f1985,f30845]) ).
fof(f30845,plain,
( spl0_2750
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2750])]) ).
fof(f1985,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__right__number__of_1) ).
fof(f30843,plain,
( spl0_2749
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2677 ),
inference(avatar_split_clause,[],[f29120,f29014,f14625,f9311,f30840]) ).
fof(f30840,plain,
( spl0_2749
<=> c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2749])]) ).
fof(f9311,plain,
( spl0_1234
<=> ! [X1,X3] : c_union(c_emptyset,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1234])]) ).
fof(f14625,plain,
( spl0_1975
<=> ! [X13,X12,X1] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1975])]) ).
fof(f29120,plain,
( c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2677 ),
inference(forward_demodulation,[],[f29107,f9312]) ).
fof(f9312,plain,
( ! [X3,X1] : c_union(c_emptyset,X3,X1) = X3
| ~ spl0_1234 ),
inference(avatar_component_clause,[],[f9311]) ).
fof(f29107,plain,
( c_union(c_emptyset,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg) = c_union(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_1975
| ~ spl0_2677 ),
inference(superposition,[],[f14626,f29016]) ).
fof(f14626,plain,
( ! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1)
| ~ spl0_1975 ),
inference(avatar_component_clause,[],[f14625]) ).
fof(f30838,plain,
spl0_2748,
inference(avatar_split_clause,[],[f1984,f30836]) ).
fof(f30836,plain,
( spl0_2748
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2748])]) ).
fof(f1984,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__right__number__of_0) ).
fof(f30834,plain,
spl0_2747,
inference(avatar_split_clause,[],[f1982,f30832]) ).
fof(f30832,plain,
( spl0_2747
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2747])]) ).
fof(f1982,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__left__number__of_4) ).
fof(f30830,plain,
spl0_2746,
inference(avatar_split_clause,[],[f1981,f30828]) ).
fof(f30828,plain,
( spl0_2746
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2746])]) ).
fof(f1981,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,X18,X2)
| c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__left__number__of_3) ).
fof(f30826,plain,
spl0_2745,
inference(avatar_split_clause,[],[f1979,f30824]) ).
fof(f30824,plain,
( spl0_2745
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2745])]) ).
fof(f1979,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,X18,X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_0,X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__left__number__of_1) ).
fof(f30822,plain,
spl0_2744,
inference(avatar_split_clause,[],[f1978,f30820]) ).
fof(f30820,plain,
( spl0_2744
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2744])]) ).
fof(f1978,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X18,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X47,X2),X2)
| ~ c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__left__number__of_0) ).
fof(f30818,plain,
spl0_2743,
inference(avatar_split_clause,[],[f1948,f30816]) ).
fof(f30816,plain,
( spl0_2743
<=> ! [X18,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_plus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_plus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2743])]) ).
fof(f1948,axiom,
! [X2,X18,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Osemiring(X2)
| c_times(c_plus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_plus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oleft__distrib__number__of_0) ).
fof(f30814,plain,
spl0_2742,
inference(avatar_split_clause,[],[f1947,f30812]) ).
fof(f30812,plain,
( spl0_2742
<=> ! [X18,X47,X27,X2] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_minus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_minus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2742])]) ).
fof(f1947,axiom,
! [X2,X18,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_Ring__and__Field_Oring(X2)
| c_times(c_minus(X18,X27,X2),c_Numeral_Onumber__of(X47,X2),X2) = c_minus(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oleft__diff__distrib__number__of_0) ).
fof(f30810,plain,
spl0_2741,
inference(avatar_split_clause,[],[f1862,f30808]) ).
fof(f30808,plain,
( spl0_2741
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2741])]) ).
fof(f1862,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Omod__nat__number__of_2) ).
fof(f30806,plain,
spl0_2740,
inference(avatar_split_clause,[],[f117,f30804]) ).
fof(f30804,plain,
( spl0_2740
<=> ! [X2,X14,X13,X12,X1] :
( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2740])]) ).
fof(f117,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInr(c_Main_OPlusE__2(X13,X14,X2,X1),X2,X1) = X14 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OPlusE_2) ).
fof(f30802,plain,
spl0_2739,
inference(avatar_split_clause,[],[f116,f30800]) ).
fof(f30800,plain,
( spl0_2739
<=> ! [X13,X14,X12,X2,X1] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2739])]) ).
fof(f116,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2))
| c_Sum__Type_OInl(c_Main_OPlusE__1(X12,X14,X1,X2),X1,X2) = X14 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OPlusE_1) ).
fof(f30787,plain,
spl0_2738,
inference(avatar_split_clause,[],[f13,f30785]) ).
fof(f30785,plain,
( spl0_2738
<=> ! [X4,X13,X12,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2738])]) ).
fof(f13,axiom,
! [X2,X1,X4,X12,X13] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_Datatype__Universe_OScons(c_Main_OuprodE__1(X12,X13,X4,X1,X2),c_Main_OuprodE__2(X12,X13,X4,X1,X2),X1,X2) = X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OuprodE_0) ).
fof(f30605,plain,
( spl0_2737
| ~ spl0_1881
| ~ spl0_2639 ),
inference(avatar_split_clause,[],[f28269,f28223,f14202,f30603]) ).
fof(f30603,plain,
( spl0_2737
<=> ! [X0] :
( c_in(X0,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Osynth(v_H),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2737])]) ).
fof(f14202,plain,
( spl0_1881
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1881])]) ).
fof(f28223,plain,
( spl0_2639
<=> c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2639])]) ).
fof(f28269,plain,
( ! [X0] :
( c_in(X0,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Osynth(v_H),tc_Message_Omsg) )
| ~ spl0_1881
| ~ spl0_2639 ),
inference(resolution,[],[f28225,f14203]) ).
fof(f14203,plain,
( ! [X1,X4,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1) )
| ~ spl0_1881 ),
inference(avatar_component_clause,[],[f14202]) ).
fof(f28225,plain,
( c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_2639 ),
inference(avatar_component_clause,[],[f28223]) ).
fof(f30542,plain,
spl0_2736,
inference(avatar_split_clause,[],[f2724,f30540]) ).
fof(f30540,plain,
( spl0_2736
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2736])]) ).
fof(f2724,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Owf__insert_2) ).
fof(f30538,plain,
spl0_2735,
inference(avatar_split_clause,[],[f2721,f30536]) ).
fof(f30536,plain,
( spl0_2735
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2735])]) ).
fof(f2721,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Oacyclic__insert_2) ).
fof(f30534,plain,
spl0_2734,
inference(avatar_split_clause,[],[f2331,f30532]) ).
fof(f30532,plain,
( spl0_2734
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2734])]) ).
fof(f2331,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__eq__number__of_0) ).
fof(f30530,plain,
spl0_2733,
inference(avatar_split_clause,[],[f2321,f30528]) ).
fof(f30528,plain,
( spl0_2733
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2733])]) ).
fof(f2321,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__le__zero__eq__number__of_4) ).
fof(f30526,plain,
spl0_2732,
inference(avatar_split_clause,[],[f2010,f30524]) ).
fof(f30524,plain,
( spl0_2732
<=> ! [X2,X27,X11] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2732])]) ).
fof(f2010,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__less__divide__iff__number__of_0) ).
fof(f30522,plain,
spl0_2731,
inference(avatar_split_clause,[],[f2004,f30520]) ).
fof(f30520,plain,
( spl0_2731
<=> ! [X2,X27,X11] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2731])]) ).
fof(f2004,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__le__divide__iff__number__of_0) ).
fof(f30518,plain,
spl0_2730,
inference(avatar_split_clause,[],[f1906,f30516]) ).
fof(f30516,plain,
( spl0_2730
<=> ! [X2,X27,X11] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2730])]) ).
fof(f1906,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__0__iff__number__of_0) ).
fof(f30514,plain,
spl0_2729,
inference(avatar_split_clause,[],[f1890,f30512]) ).
fof(f30512,plain,
( spl0_2729
<=> ! [X2,X27,X11] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2729])]) ).
fof(f1890,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__0__iff__number__of_0) ).
fof(f30496,plain,
spl0_2728,
inference(avatar_split_clause,[],[f1768,f30494]) ).
fof(f30494,plain,
( spl0_2728
<=> ! [X47,X0,X23,X1] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2728])]) ).
fof(f1768,axiom,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Otake(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__Cons__number__of_1) ).
fof(f30492,plain,
spl0_2727,
inference(avatar_split_clause,[],[f1469,f30490]) ).
fof(f30490,plain,
( spl0_2727
<=> ! [X27,X11,X47] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2727])]) ).
fof(f1469,axiom,
! [X11,X47,X27] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,X27),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__number__of__BIT_1) ).
fof(f30488,plain,
spl0_2726,
inference(avatar_split_clause,[],[f77,f30486]) ).
fof(f30486,plain,
( spl0_2726
<=> ! [X5,X29,X2,X1] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2726])]) ).
fof(f77,axiom,
! [X2,X29,X1,X5] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_in(c_Pair(c_Main_OconverseE__1(X5,X29,X2,X1),c_Main_OconverseE__2(X5,X29,X2,X1),X2,X1),X5,tc_prod(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OconverseE_0) ).
fof(f30223,plain,
spl0_2725,
inference(avatar_split_clause,[],[f2001,f30221]) ).
fof(f30221,plain,
( spl0_2725
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2725])]) ).
fof(f2001,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__right__number__of_5) ).
fof(f30219,plain,
spl0_2724,
inference(avatar_split_clause,[],[f1995,f30217]) ).
fof(f30217,plain,
( spl0_2724
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2724])]) ).
fof(f1995,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X18,X27,X2)
| ~ c_less(X27,X18,X2)
| c_less(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__less__cancel__left__number__of_5) ).
fof(f30215,plain,
spl0_2723,
inference(avatar_split_clause,[],[f1989,f30213]) ).
fof(f30213,plain,
( spl0_2723
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2723])]) ).
fof(f1989,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(X18,c_Numeral_Onumber__of(X47,X2),X2),c_times(X27,c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__right__number__of_5) ).
fof(f30211,plain,
spl0_2722,
inference(avatar_split_clause,[],[f1983,f30209]) ).
fof(f30209,plain,
( spl0_2722
<=> ! [X18,X47,X27,X2] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2722])]) ).
fof(f1983,axiom,
! [X2,X18,X47,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X18,X27,X2)
| ~ c_lessequals(X27,X18,X2)
| c_lessequals(c_times(c_Numeral_Onumber__of(X47,X2),X18,X2),c_times(c_Numeral_Onumber__of(X47,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omult__le__cancel__left__number__of_5) ).
fof(f30207,plain,
spl0_2721,
inference(avatar_split_clause,[],[f1794,f30205]) ).
fof(f30205,plain,
( spl0_2721
<=> ! [X0,X23,X25,X2,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2721])]) ).
fof(f1794,axiom,
! [X2,X0,X1,X25,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone = c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Map_Omap__of__zip__is__None_1) ).
fof(f30203,plain,
spl0_2720,
inference(avatar_split_clause,[],[f1793,f30201]) ).
fof(f30201,plain,
( spl0_2720
<=> ! [X0,X23,X25,X2,X1] :
( ~ c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2720])]) ).
fof(f1793,axiom,
! [X2,X0,X1,X25,X23] :
( ~ c_in(X0,c_List_Oset(X23,X1),X1)
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X2))
| c_Datatype_Ooption_ONone != c_Map_Omap__of(c_List_Ozip(X23,X25,X1,X2),X0,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Map_Omap__of__zip__is__None_0) ).
fof(f30199,plain,
spl0_2719,
inference(avatar_split_clause,[],[f1789,f30197]) ).
fof(f30197,plain,
( spl0_2719
<=> ! [X3,X0,X23,X25,X2,X1] : c_List_Ozip(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X2),X1,X2) = c_List_Olist_OCons(c_Pair(X0,X3,X1,X2),c_List_Ozip(X23,X25,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2719])]) ).
fof(f1789,axiom,
! [X2,X3,X0,X1,X25,X23] : c_List_Ozip(c_List_Olist_OCons(X0,X23,X1),c_List_Olist_OCons(X3,X25,X2),X1,X2) = c_List_Olist_OCons(c_Pair(X0,X3,X1,X2),c_List_Ozip(X23,X25,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ozip__Cons__Cons_0) ).
fof(f30195,plain,
spl0_2718,
inference(avatar_split_clause,[],[f1616,f30193]) ).
fof(f30193,plain,
( spl0_2718
<=> ! [X5,X1,X3] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X3,X1),c_Main_Olexord__Nil__left__2(X3,X1),X1) = X3
| ~ c_in(c_Pair(c_List_Olist_ONil,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2718])]) ).
fof(f1616,axiom,
! [X3,X1,X5] :
( c_List_Olist_OCons(c_Main_Olexord__Nil__left__1(X3,X1),c_Main_Olexord__Nil__left__2(X3,X1),X1) = X3
| ~ c_in(c_Pair(c_List_Olist_ONil,X3,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__Nil__left_0) ).
fof(f30191,plain,
spl0_2717,
inference(avatar_split_clause,[],[f1458,f30189]) ).
fof(f30189,plain,
( spl0_2717
<=> ! [X11] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2717])]) ).
fof(f1458,axiom,
! [X11] :
( ~ c_less(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_1,tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OposDivAlg__eqn__1__number__of_0) ).
fof(f30187,plain,
spl0_2716,
inference(avatar_split_clause,[],[f118,f30185]) ).
fof(f30185,plain,
( spl0_2716
<=> ! [X13,X14,X12,X2,X1] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2716])]) ).
fof(f118,axiom,
! [X2,X1,X14,X12,X13] :
( c_in(c_Main_OPlusE__2(X13,X14,X2,X1),X13,X2)
| c_in(c_Main_OPlusE__1(X12,X14,X1,X2),X12,X1)
| ~ c_in(X14,c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OPlusE_3) ).
fof(f30022,plain,
( spl0_2714
| ~ spl0_2715
| ~ spl0_1497
| ~ spl0_2699 ),
inference(avatar_split_clause,[],[f29808,f29607,f10599,f30019,f30015]) ).
fof(f30015,plain,
( spl0_2714
<=> c_emptyset = v_H ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2714])]) ).
fof(f30019,plain,
( spl0_2715
<=> c_emptyset = c_Message_Osynth(c_Message_Oparts(c_UNIV)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2715])]) ).
fof(f10599,plain,
( spl0_1497
<=> ! [X13,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1497])]) ).
fof(f29607,plain,
( spl0_2699
<=> c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2699])]) ).
fof(f29808,plain,
( c_emptyset != c_Message_Osynth(c_Message_Oparts(c_UNIV))
| c_emptyset = v_H
| ~ spl0_1497
| ~ spl0_2699 ),
inference(superposition,[],[f10600,f29609]) ).
fof(f29609,plain,
( c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_2699 ),
inference(avatar_component_clause,[],[f29607]) ).
fof(f10600,plain,
( ! [X1,X12,X13] :
( c_emptyset != c_union(X12,X13,X1)
| c_emptyset = X12 )
| ~ spl0_1497 ),
inference(avatar_component_clause,[],[f10599]) ).
fof(f29667,plain,
spl0_2713,
inference(avatar_split_clause,[],[f2788,f29665]) ).
fof(f29665,plain,
( spl0_2713
<=> ! [X86,X91,X88] :
( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2713])]) ).
fof(f2788,axiom,
! [X91,X88,X86] :
( ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__Crypt__if_0) ).
fof(f29663,plain,
spl0_2712,
inference(avatar_split_clause,[],[f2015,f29661]) ).
fof(f29661,plain,
( spl0_2712
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,c_0,X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2712])]) ).
fof(f2015,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,c_0,X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__less__divide__iff__number__of_5) ).
fof(f29659,plain,
spl0_2711,
inference(avatar_split_clause,[],[f2014,f29657]) ).
fof(f29657,plain,
( spl0_2711
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2711])]) ).
fof(f2014,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X27,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__less__divide__iff__number__of_4) ).
fof(f29655,plain,
( spl0_2710
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2663 ),
inference(avatar_split_clause,[],[f28969,f28846,f14629,f9315,f29652]) ).
fof(f29652,plain,
( spl0_2710
<=> c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2710])]) ).
fof(f28969,plain,
( c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_Message_Omsg)
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2663 ),
inference(forward_demodulation,[],[f28956,f9316]) ).
fof(f28956,plain,
( c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),v_H,tc_Message_Omsg) = c_union(c_Message_Osynth(c_Message_Oparts(c_UNIV)),c_emptyset,tc_Message_Omsg)
| ~ spl0_1976
| ~ spl0_2663 ),
inference(superposition,[],[f14630,f28848]) ).
fof(f29650,plain,
spl0_2709,
inference(avatar_split_clause,[],[f2012,f29648]) ).
fof(f29648,plain,
( spl0_2709
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,X27,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2709])]) ).
fof(f2012,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,X27,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__less__divide__iff__number__of_2) ).
fof(f29646,plain,
spl0_2708,
inference(avatar_split_clause,[],[f2011,f29644]) ).
fof(f29644,plain,
( spl0_2708
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2708])]) ).
fof(f2011,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__less__divide__iff__number__of_1) ).
fof(f29642,plain,
spl0_2707,
inference(avatar_split_clause,[],[f2009,f29640]) ).
fof(f29640,plain,
( spl0_2707
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,c_0,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2707])]) ).
fof(f2009,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,c_0,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__le__divide__iff__number__of_5) ).
fof(f29638,plain,
spl0_2706,
inference(avatar_split_clause,[],[f2008,f29636]) ).
fof(f29636,plain,
( spl0_2706
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2706])]) ).
fof(f2008,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__le__divide__iff__number__of_4) ).
fof(f29634,plain,
spl0_2705,
inference(avatar_split_clause,[],[f2006,f29632]) ).
fof(f29632,plain,
( spl0_2705
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2705])]) ).
fof(f2006,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,X27,X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__le__divide__iff__number__of_2) ).
fof(f29630,plain,
spl0_2704,
inference(avatar_split_clause,[],[f2005,f29628]) ).
fof(f29628,plain,
( spl0_2704
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2704])]) ).
fof(f2005,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__le__divide__iff__number__of_1) ).
fof(f29626,plain,
spl0_2703,
inference(avatar_split_clause,[],[f1911,f29624]) ).
fof(f29624,plain,
( spl0_2703
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X27,X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2703])]) ).
fof(f1911,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(c_0,X27,X2)
| ~ c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__0__iff__number__of_5) ).
fof(f29622,plain,
spl0_2702,
inference(avatar_split_clause,[],[f1910,f29620]) ).
fof(f29620,plain,
( spl0_2702
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,c_0,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2702])]) ).
fof(f1910,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_less(X27,c_0,X2)
| ~ c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__0__iff__number__of_4) ).
fof(f29618,plain,
spl0_2701,
inference(avatar_split_clause,[],[f1908,f29616]) ).
fof(f29616,plain,
( spl0_2701
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2701])]) ).
fof(f1908,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__0__iff__number__of_2) ).
fof(f29614,plain,
spl0_2700,
inference(avatar_split_clause,[],[f1907,f29612]) ).
fof(f29612,plain,
( spl0_2700
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,X27,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2700])]) ).
fof(f1907,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(c_0,X27,X2)
| c_less(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__0__iff__number__of_1) ).
fof(f29610,plain,
( spl0_2699
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2663 ),
inference(avatar_split_clause,[],[f28968,f28846,f14625,f9311,f29607]) ).
fof(f28968,plain,
( c_Message_Osynth(c_Message_Oparts(c_UNIV)) = c_union(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2663 ),
inference(forward_demodulation,[],[f28955,f9312]) ).
fof(f28955,plain,
( c_union(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg) = c_union(c_emptyset,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ spl0_1975
| ~ spl0_2663 ),
inference(superposition,[],[f14626,f28848]) ).
fof(f29605,plain,
spl0_2698,
inference(avatar_split_clause,[],[f1895,f29603]) ).
fof(f29603,plain,
( spl0_2698
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2698])]) ).
fof(f1895,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__0__iff__number__of_5) ).
fof(f29601,plain,
spl0_2697,
inference(avatar_split_clause,[],[f1894,f29599]) ).
fof(f29599,plain,
( spl0_2697
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,c_0,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2697])]) ).
fof(f1894,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| ~ c_lessequals(X27,c_0,X2)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__0__iff__number__of_4) ).
fof(f29597,plain,
spl0_2696,
inference(avatar_split_clause,[],[f1892,f29595]) ).
fof(f29595,plain,
( spl0_2696
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2696])]) ).
fof(f1892,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_Numeral_Onumber__of(X11,X2),c_0,X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__0__iff__number__of_2) ).
fof(f29593,plain,
spl0_2695,
inference(avatar_split_clause,[],[f1891,f29591]) ).
fof(f29591,plain,
( spl0_2695
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,X27,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2695])]) ).
fof(f1891,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(c_0,X27,X2)
| c_lessequals(c_0,c_Numeral_Onumber__of(X11,X2),X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__0__iff__number__of_1) ).
fof(f29589,plain,
spl0_2694,
inference(avatar_split_clause,[],[f1846,f29587]) ).
fof(f29587,plain,
( spl0_2694
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2694])]) ).
fof(f1846,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_9) ).
fof(f29585,plain,
spl0_2693,
inference(avatar_split_clause,[],[f1844,f29583]) ).
fof(f29583,plain,
( spl0_2693
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2693])]) ).
fof(f1844,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_7) ).
fof(f29581,plain,
spl0_2692,
inference(avatar_split_clause,[],[f1842,f29579]) ).
fof(f29579,plain,
( spl0_2692
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2692])]) ).
fof(f1842,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_5) ).
fof(f29577,plain,
spl0_2691,
inference(avatar_split_clause,[],[f1840,f29575]) ).
fof(f29575,plain,
( spl0_2691
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2691])]) ).
fof(f1840,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_3) ).
fof(f29573,plain,
spl0_2690,
inference(avatar_split_clause,[],[f1839,f29571]) ).
fof(f29571,plain,
( spl0_2690
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2690])]) ).
fof(f1839,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_2) ).
fof(f29569,plain,
spl0_2689,
inference(avatar_split_clause,[],[f1792,f29567]) ).
fof(f29567,plain,
( spl0_2689
<=> ! [X59,X43,X0,X3,X2,X1] : c_List_Ozip(c_List_Oreplicate(X43,X0,X1),c_List_Oreplicate(X59,X3,X2),X1,X2) = c_List_Oreplicate(c_Orderings_Omin(X43,X59,tc_nat),c_Pair(X0,X3,X1,X2),tc_prod(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2689])]) ).
fof(f1792,axiom,
! [X2,X3,X0,X59,X1,X43] : c_List_Ozip(c_List_Oreplicate(X43,X0,X1),c_List_Oreplicate(X59,X3,X2),X1,X2) = c_List_Oreplicate(c_Orderings_Omin(X43,X59,tc_nat),c_Pair(X0,X3,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ozip__replicate_0) ).
fof(f29554,plain,
spl0_2688,
inference(avatar_split_clause,[],[f1698,f29552]) ).
fof(f29552,plain,
( spl0_2688
<=> ! [X43,X23,X21,X1] :
( ~ c_lessequals(c_plus(X21,X43,tc_nat),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Odrop(X21,X23,X1),X43,X1) = c_List_Onth(X23,c_plus(X21,X43,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2688])]) ).
fof(f1698,axiom,
! [X21,X1,X23,X43] :
( ~ c_lessequals(c_plus(X21,X43,tc_nat),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Odrop(X21,X23,X1),X43,X1) = c_List_Onth(X23,c_plus(X21,X43,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__drop_0) ).
fof(f29315,plain,
( spl0_2687
| ~ spl0_1881
| ~ spl0_2660 ),
inference(avatar_split_clause,[],[f28598,f28316,f14202,f29313]) ).
fof(f29313,plain,
( spl0_2687
<=> ! [X0] :
( c_in(X0,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ c_in(X0,v_H,tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2687])]) ).
fof(f28598,plain,
( ! [X0] :
( c_in(X0,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_Message_Omsg)
| ~ c_in(X0,v_H,tc_Message_Omsg) )
| ~ spl0_1881
| ~ spl0_2660 ),
inference(resolution,[],[f28318,f14203]) ).
fof(f29165,plain,
( spl0_2686
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2672 ),
inference(avatar_split_clause,[],[f28996,f28993,f14521,f11238,f29163]) ).
fof(f29163,plain,
( spl0_2686
<=> ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2686])]) ).
fof(f28993,plain,
( spl0_2672
<=> ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2672])]) ).
fof(f28996,plain,
( ! [X11] :
( c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__2(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1591
| ~ spl0_1950
| ~ spl0_2672 ),
inference(forward_demodulation,[],[f28994,f15874]) ).
fof(f28994,plain,
( ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2672 ),
inference(avatar_component_clause,[],[f28993]) ).
fof(f29161,plain,
( spl0_2685
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2671 ),
inference(avatar_split_clause,[],[f28991,f28988,f14521,f11234,f29159]) ).
fof(f29159,plain,
( spl0_2685
<=> ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2685])]) ).
fof(f28988,plain,
( spl0_2671
<=> ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2671])]) ).
fof(f28991,plain,
( ! [X11] :
( c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_Main_Osurj__pair__1(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1590
| ~ spl0_1950
| ~ spl0_2671 ),
inference(forward_demodulation,[],[f28989,f15875]) ).
fof(f28989,plain,
( ! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) )
| ~ spl0_2671 ),
inference(avatar_component_clause,[],[f28988]) ).
fof(f29045,plain,
spl0_2684,
inference(avatar_split_clause,[],[f2882,f29043]) ).
fof(f29043,plain,
( spl0_2684
<=> ! [X15,X47] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2684])]) ).
fof(f2882,plain,
! [X47,X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f1880,f2156]) ).
fof(f1880,axiom,
! [X47,X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_Divides_Oop_Amod(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_OSuc__mod__eq__add3__mod__number__of_0) ).
fof(f29041,plain,
spl0_2683,
inference(avatar_split_clause,[],[f2881,f29039]) ).
fof(f29039,plain,
( spl0_2683
<=> ! [X15,X47] : c_div(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2683])]) ).
fof(f2881,plain,
! [X47,X15] : c_div(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
inference(forward_demodulation,[],[f1879,f2156]) ).
fof(f1879,axiom,
! [X47,X15] : c_div(c_Suc(c_Suc(c_Suc(X15))),c_Numeral_Onumber__of(X47,tc_nat),tc_nat) = c_div(c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X15,tc_nat),c_Numeral_Onumber__of(X47,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_OSuc__div__eq__add3__div__number__of_0) ).
fof(f29037,plain,
spl0_2682,
inference(avatar_split_clause,[],[f2723,f29035]) ).
fof(f29035,plain,
( spl0_2682
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2682])]) ).
fof(f2723,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Owf__insert_1) ).
fof(f29033,plain,
spl0_2681,
inference(avatar_split_clause,[],[f2720,f29031]) ).
fof(f29031,plain,
( spl0_2681
<=> ! [X3,X0,X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2681])]) ).
fof(f2720,axiom,
! [X3,X0,X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1)
| ~ c_in(c_Pair(X0,X3,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Oacyclic__insert_1) ).
fof(f29029,plain,
spl0_2680,
inference(avatar_split_clause,[],[f2316,f29027]) ).
fof(f29027,plain,
( spl0_2680
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X0,X1),c_Numeral_Onumber__of(X11,tc_nat),X1) = c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2680])]) ).
fof(f2316,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_Nat_Opower(c_HOL_Oabs(X0,X1),c_Numeral_Onumber__of(X11,tc_nat),X1) = c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__even__abs__number__of_0) ).
fof(f29025,plain,
spl0_2679,
inference(avatar_split_clause,[],[f1826,f29023]) ).
fof(f29023,plain,
( spl0_2679
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X83),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2679])]) ).
fof(f1826,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X83),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oadd__nat__number__of_2) ).
fof(f29021,plain,
spl0_2678,
inference(avatar_split_clause,[],[f1771,f29019]) ).
fof(f29019,plain,
( spl0_2678
<=> ! [X21,X23,X25,X1] : c_List_Otake(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Otake(X21,X23,X1),c_List_Otake(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2678])]) ).
fof(f1771,axiom,
! [X21,X1,X25,X23] : c_List_Otake(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Otake(X21,X23,X1),c_List_Otake(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__append_0) ).
fof(f29017,plain,
( spl0_2677
| ~ spl0_1838
| ~ spl0_2639 ),
inference(avatar_split_clause,[],[f28271,f28223,f12970,f29014]) ).
fof(f12970,plain,
( spl0_1838
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1838])]) ).
fof(f28271,plain,
( c_emptyset = c_minus(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_1838
| ~ spl0_2639 ),
inference(resolution,[],[f28225,f12971]) ).
fof(f12971,plain,
( ! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) )
| ~ spl0_1838 ),
inference(avatar_component_clause,[],[f12970]) ).
fof(f29012,plain,
spl0_2676,
inference(avatar_split_clause,[],[f1695,f29010]) ).
fof(f29010,plain,
( spl0_2676
<=> ! [X0,X1,X23,X47] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Numeral_Onumber__of(X47,tc_nat),X1) = c_List_Onth(X23,c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2676])]) ).
fof(f1695,axiom,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Numeral_Onumber__of(X47,tc_nat),X1) = c_List_Onth(X23,c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__Cons__number__of_1) ).
fof(f29008,plain,
spl0_2675,
inference(avatar_split_clause,[],[f1573,f29006]) ).
fof(f29006,plain,
( spl0_2675
<=> ! [X21,X23,X25,X1] : c_List_Odrop(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Odrop(X21,X23,X1),c_List_Odrop(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2675])]) ).
fof(f1573,axiom,
! [X21,X1,X25,X23] : c_List_Odrop(X21,c_append(X23,X25,X1),X1) = c_append(c_List_Odrop(X21,X23,X1),c_List_Odrop(c_minus(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),X25,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__append_0) ).
fof(f29004,plain,
spl0_2674,
inference(avatar_split_clause,[],[f1571,f29002]) ).
fof(f29002,plain,
( spl0_2674
<=> ! [X47,X0,X23,X1] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2674])]) ).
fof(f1571,axiom,
! [X0,X47,X1,X23] :
( c_0 = c_Numeral_Onumber__of(X47,tc_nat)
| c_List_Odrop(c_Numeral_Onumber__of(X47,tc_nat),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(c_minus(c_Numeral_Onumber__of(X47,tc_nat),c_1,tc_nat),X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__Cons__number__of_1) ).
fof(f29000,plain,
spl0_2673,
inference(avatar_split_clause,[],[f1526,f28998]) ).
fof(f28998,plain,
( spl0_2673
<=> ! [X23,X12,X25,X1] :
( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2673])]) ).
fof(f1526,axiom,
! [X1,X25,X12,X23] :
( ~ c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__in__lists__conv_2) ).
fof(f28995,plain,
spl0_2672,
inference(avatar_split_clause,[],[f1447,f28993]) ).
fof(f1447,axiom,
! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_snd(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__pos__pos__1__number__of_0) ).
fof(f28990,plain,
spl0_2671,
inference(avatar_split_clause,[],[f1437,f28988]) ).
fof(f1437,axiom,
! [X11] :
( ~ c_lessequals(c_0,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_fst(c_IntDiv_OposDivAlg(c_Pair(c_1,c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)),tc_IntDef_Oint,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odiv__pos__pos__1__number__of_0) ).
fof(f28986,plain,
spl0_2670,
inference(avatar_split_clause,[],[f1381,f28984]) ).
fof(f28984,plain,
( spl0_2670
<=> ! [X0,X3] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X0,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2670])]) ).
fof(f1381,axiom,
! [X3,X0] : c_in(c_Relation_OImage(c_IntDef_Ointrel,c_insert(c_Pair(X0,X3,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat),tc_prod(tc_nat,tc_nat)),c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ointrel_A_96_96_A_123_Ix1_M_Ay1_J_125_A_58_AInteg_A_61_61_ATrue_0) ).
fof(f28982,plain,
spl0_2669,
inference(avatar_split_clause,[],[f1269,f28980]) ).
fof(f28980,plain,
( spl0_2669
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(X0,c_Finite__Set_OMin(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2669])]) ).
fof(f1269,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(X0,c_Finite__Set_OMin(X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__gr__iff_0) ).
fof(f28978,plain,
spl0_2668,
inference(avatar_split_clause,[],[f1266,f28976]) ).
fof(f28976,plain,
( spl0_2668
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2668])]) ).
fof(f1266,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X0,X24,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__ge__iff_0) ).
fof(f28974,plain,
spl0_2667,
inference(avatar_split_clause,[],[f1262,f28972]) ).
fof(f28972,plain,
( spl0_2667
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(c_Finite__Set_OMax(X12,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2667])]) ).
fof(f1262,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_less(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_less(c_Finite__Set_OMax(X12,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__less__iff_0) ).
fof(f28950,plain,
spl0_2666,
inference(avatar_split_clause,[],[f1259,f28948]) ).
fof(f28948,plain,
( spl0_2666
<=> ! [X24,X0,X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2666])]) ).
fof(f1259,axiom,
! [X0,X1,X24,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X24,X12,X1)
| c_lessequals(X24,X0,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__le__iff_0) ).
fof(f28946,plain,
spl0_2665,
inference(avatar_split_clause,[],[f1208,f28944]) ).
fof(f28944,plain,
( spl0_2665
<=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2665])]) ).
fof(f1208,axiom,
! [X2,X1,X9,X16,X7] : c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OScons(X9,X7,X1,X2),X1,X2) = c_Datatype__Universe_OScons(c_Datatype__Universe_Ontrunc(X16,X9,X1,X2),c_Datatype__Universe_Ontrunc(X16,X7,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__Scons_0) ).
fof(f28942,plain,
spl0_2664,
inference(avatar_split_clause,[],[f78,f28940]) ).
fof(f28940,plain,
( spl0_2664
<=> ! [X5,X29,X2,X1] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2664])]) ).
fof(f78,axiom,
! [X2,X29,X1,X5] :
( ~ c_in(X29,c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2))
| c_Pair(c_Main_OconverseE__2(X5,X29,X2,X1),c_Main_OconverseE__1(X5,X29,X2,X1),X1,X2) = X29 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OconverseE_1) ).
fof(f28849,plain,
( spl0_2663
| ~ spl0_1838
| ~ spl0_2660 ),
inference(avatar_split_clause,[],[f28600,f28316,f12970,f28846]) ).
fof(f28600,plain,
( c_emptyset = c_minus(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_1838
| ~ spl0_2660 ),
inference(resolution,[],[f28318,f12971]) ).
fof(f28328,plain,
( spl0_2662
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2661 ),
inference(avatar_split_clause,[],[f28324,f28321,f13076,f9197,f7368,f28326]) ).
fof(f28326,plain,
( spl0_2662
<=> ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Suc(c_1),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2662])]) ).
fof(f28321,plain,
( spl0_2661
<=> ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2661])]) ).
fof(f28324,plain,
( ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Suc(c_1),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) )
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2661 ),
inference(forward_demodulation,[],[f28322,f14121]) ).
fof(f28322,plain,
( ! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) )
| ~ spl0_2661 ),
inference(avatar_component_clause,[],[f28321]) ).
fof(f28323,plain,
spl0_2661,
inference(avatar_split_clause,[],[f2963,f28321]) ).
fof(f2963,plain,
! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f2962,f2156]) ).
fof(f2962,plain,
! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f2961,f2154]) ).
fof(f2961,plain,
! [X2,X11] :
( c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) = c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X2)
| ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2) ),
inference(forward_demodulation,[],[f1874,f2156]) ).
fof(f1874,axiom,
! [X2,X11] :
( ~ class_Power_Orecpower(X2)
| ~ class_Numeral_Onumber(X2)
| c_Nat_Opower(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X2) = c_times(c_Numeral_Onumber__of(X11,X2),c_Numeral_Onumber__of(X11,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Opower2__eq__square__number__of_0) ).
fof(f28319,plain,
( spl0_2660
| ~ spl0_1999
| ~ spl0_2639 ),
inference(avatar_split_clause,[],[f28267,f28223,f14730,f28316]) ).
fof(f28267,plain,
( c_lessequals(v_H,c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_1999
| ~ spl0_2639 ),
inference(resolution,[],[f28225,f14731]) ).
fof(f28314,plain,
spl0_2659,
inference(avatar_split_clause,[],[f2385,f28312]) ).
fof(f28312,plain,
( spl0_2659
<=> ! [X18,X5,X27,X2,X1] :
( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2659])]) ).
fof(f2385,axiom,
! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Oconverse__iff_1) ).
fof(f28310,plain,
spl0_2658,
inference(avatar_split_clause,[],[f2384,f28308]) ).
fof(f28308,plain,
( spl0_2658
<=> ! [X18,X5,X27,X2,X1] :
( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2658])]) ).
fof(f2384,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(c_Pair(X27,X18,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(c_Pair(X18,X27,X1,X2),c_Relation_Oconverse(X5,X2,X1),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Oconverse__iff_0) ).
fof(f28306,plain,
spl0_2657,
inference(avatar_split_clause,[],[f2332,f28304]) ).
fof(f28304,plain,
( spl0_2657
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2657])]) ).
fof(f2332,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__eq__number__of_1) ).
fof(f28302,plain,
spl0_2656,
inference(avatar_split_clause,[],[f2322,f28300]) ).
fof(f28300,plain,
( spl0_2656
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2656])]) ).
fof(f2322,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_lessequals(c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__le__zero__eq__number__of_5) ).
fof(f28298,plain,
spl0_2655,
inference(avatar_split_clause,[],[f2107,f28296]) ).
fof(f28296,plain,
( spl0_2655
<=> ! [X4,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2655])]) ).
fof(f2107,axiom,
! [X11,X1,X47,X4] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_minus(X4,c_Numeral_Onumber__of(X11,X1),X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1),X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Oadd__number__of__diff2_0) ).
fof(f28294,plain,
spl0_2654,
inference(avatar_split_clause,[],[f2013,f28292]) ).
fof(f28292,plain,
( spl0_2654
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_0,X27,X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2654])]) ).
fof(f2013,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_0,X27,X2)
| ~ c_less(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__less__divide__iff__number__of_3) ).
fof(f28290,plain,
spl0_2653,
inference(avatar_split_clause,[],[f2007,f28288]) ).
fof(f28288,plain,
( spl0_2653
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2653])]) ).
fof(f2007,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_0,c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ozero__le__divide__iff__number__of_3) ).
fof(f28286,plain,
spl0_2652,
inference(avatar_split_clause,[],[f1909,f28284]) ).
fof(f28284,plain,
( spl0_2652
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_0,X27,X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2652])]) ).
fof(f1909,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_less(X27,c_0,X2)
| c_less(c_0,X27,X2)
| ~ c_less(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__less__0__iff__number__of_3) ).
fof(f28282,plain,
spl0_2651,
inference(avatar_split_clause,[],[f1893,f28280]) ).
fof(f28280,plain,
( spl0_2651
<=> ! [X11,X2,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2651])]) ).
fof(f1893,axiom,
! [X2,X11,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Oordered__field(X2)
| ~ class_Numeral_Onumber(X2)
| c_lessequals(X27,c_0,X2)
| c_lessequals(c_0,X27,X2)
| ~ c_lessequals(c_divide(c_Numeral_Onumber__of(X11,X2),X27,X2),c_0,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__le__0__iff__number__of_3) ).
fof(f28278,plain,
spl0_2650,
inference(avatar_split_clause,[],[f1877,f28276]) ).
fof(f28276,plain,
( spl0_2650
<=> ! [X11,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_nat),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2650])]) ).
fof(f1877,axiom,
! [X11,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_IntDef_Onat(c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_nat),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Opower__nat__number__of__number__of_1) ).
fof(f28266,plain,
spl0_2649,
inference(avatar_split_clause,[],[f1828,f28264]) ).
fof(f28264,plain,
( spl0_2649
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2649])]) ).
fof(f1828,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Odiv__nat__number__of_1) ).
fof(f28262,plain,
spl0_2648,
inference(avatar_split_clause,[],[f1273,f28260]) ).
fof(f28260,plain,
( spl0_2648
<=> ! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMin(c_insert(X0,X12,X2),X2) = c_Orderings_Omin(X0,c_Finite__Set_OMin(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2648])]) ).
fof(f1273,axiom,
! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMin(c_insert(X0,X12,X2),X2) = c_Orderings_Omin(X0,c_Finite__Set_OMin(X12,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__insert_0) ).
fof(f28258,plain,
spl0_2647,
inference(avatar_split_clause,[],[f1271,f28256]) ).
fof(f28256,plain,
( spl0_2647
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2647])]) ).
fof(f1271,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_less(X0,c_Main_OMin__gr__iff__1(X12,X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__gr__iff_2) ).
fof(f28254,plain,
spl0_2646,
inference(avatar_split_clause,[],[f1270,f28252]) ).
fof(f28252,plain,
( spl0_2646
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__gr__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2646])]) ).
fof(f1270,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__gr__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__gr__iff_1) ).
fof(f28250,plain,
spl0_2645,
inference(avatar_split_clause,[],[f1268,f28248]) ).
fof(f28248,plain,
( spl0_2645
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_lessequals(X0,c_Main_OMin__ge__iff__1(X12,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2645])]) ).
fof(f1268,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| ~ c_lessequals(X0,c_Main_OMin__ge__iff__1(X12,X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__ge__iff_2) ).
fof(f28246,plain,
spl0_2644,
inference(avatar_split_clause,[],[f1267,f28244]) ).
fof(f28244,plain,
( spl0_2644
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__ge__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2644])]) ).
fof(f1267,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMin(X12,X1),X1)
| c_in(c_Main_OMin__ge__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__ge__iff_1) ).
fof(f28242,plain,
spl0_2643,
inference(avatar_split_clause,[],[f1264,f28240]) ).
fof(f28240,plain,
( spl0_2643
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_less(c_Main_OMax__less__iff__1(X12,X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2643])]) ).
fof(f1264,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_less(c_Main_OMax__less__iff__1(X12,X0,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__less__iff_2) ).
fof(f28238,plain,
spl0_2642,
inference(avatar_split_clause,[],[f1263,f28236]) ).
fof(f28236,plain,
( spl0_2642
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__less__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2642])]) ).
fof(f1263,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_less(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__less__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__less__iff_1) ).
fof(f28234,plain,
spl0_2641,
inference(avatar_split_clause,[],[f1261,f28232]) ).
fof(f28232,plain,
( spl0_2641
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X12,X0,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2641])]) ).
fof(f1261,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| ~ c_lessequals(c_Main_OMax__le__iff__1(X12,X0,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__le__iff_2) ).
fof(f28230,plain,
spl0_2640,
inference(avatar_split_clause,[],[f1260,f28228]) ).
fof(f28228,plain,
( spl0_2640
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__le__iff__1(X12,X0,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2640])]) ).
fof(f1260,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMax(X12,X1),X0,X1)
| c_in(c_Main_OMax__le__iff__1(X12,X0,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__le__iff_1) ).
fof(f28226,plain,
( spl0_2639
| ~ spl0_1248
| ~ spl0_2634 ),
inference(avatar_split_clause,[],[f28077,f27888,f9367,f28223]) ).
fof(f28077,plain,
( c_lessequals(c_Message_Osynth(v_H),c_Message_Osynth(c_Message_Oparts(c_UNIV)),tc_set(tc_Message_Omsg))
| ~ spl0_1248
| ~ spl0_2634 ),
inference(resolution,[],[f27889,f9368]) ).
fof(f28221,plain,
spl0_2638,
inference(avatar_split_clause,[],[f1258,f28219]) ).
fof(f28219,plain,
( spl0_2638
<=> ! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMax(c_insert(X0,X12,X2),X2) = c_Orderings_Omax(X0,c_Finite__Set_OMax(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2638])]) ).
fof(f1258,axiom,
! [X2,X0,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Finite__Set_OMax(c_insert(X0,X12,X2),X2) = c_Orderings_Omax(X0,c_Finite__Set_OMax(X12,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__insert_0) ).
fof(f28217,plain,
spl0_2637,
inference(avatar_split_clause,[],[f73,f28215]) ).
fof(f28215,plain,
( spl0_2637
<=> ! [X12,X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2637])]) ).
fof(f73,axiom,
! [X2,X1,X27,X5,X12] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Pair(c_Main_OImageE__1(X12,X27,X5,X2,X1),X27,X2,X1),X5,tc_prod(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImageE_1) ).
fof(f28213,plain,
spl0_2636,
inference(avatar_split_clause,[],[f15,f28211]) ).
fof(f28211,plain,
( spl0_2636
<=> ! [X4,X13,X12,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2636])]) ).
fof(f15,axiom,
! [X2,X1,X4,X12,X13] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__1(X12,X13,X4,X1,X2),X12,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OuprodE_2) ).
fof(f28209,plain,
spl0_2635,
inference(avatar_split_clause,[],[f14,f28207]) ).
fof(f28207,plain,
( spl0_2635
<=> ! [X4,X13,X12,X2,X1] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2635])]) ).
fof(f14,axiom,
! [X2,X1,X4,X12,X13] :
( ~ c_in(X4,c_Datatype__Universe_Ouprod(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Main_OuprodE__2(X12,X13,X4,X1,X2),X13,tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OuprodE_1) ).
fof(f27890,plain,
( spl0_2634
| ~ spl0_1977
| ~ spl0_2202 ),
inference(avatar_split_clause,[],[f19399,f19126,f14633,f27888]) ).
fof(f14633,plain,
( spl0_1977
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1977])]) ).
fof(f19126,plain,
( spl0_2202
<=> c_Message_Oparts(c_UNIV) = c_union(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2202])]) ).
fof(f19399,plain,
( ! [X2] :
( ~ c_lessequals(c_Message_Oparts(c_UNIV),X2,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(v_H),X2,tc_set(tc_Message_Omsg)) )
| ~ spl0_1977
| ~ spl0_2202 ),
inference(superposition,[],[f14634,f19128]) ).
fof(f19128,plain,
( c_Message_Oparts(c_UNIV) = c_union(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_2202 ),
inference(avatar_component_clause,[],[f19126]) ).
fof(f14634,plain,
( ! [X1,X12,X32,X13] :
( ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1))
| c_lessequals(X12,X32,tc_set(X1)) )
| ~ spl0_1977 ),
inference(avatar_component_clause,[],[f14633]) ).
fof(f27460,plain,
spl0_2633,
inference(avatar_split_clause,[],[f2789,f27458]) ).
fof(f27458,plain,
( spl0_2633
<=> ! [X86,X91,X88] :
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2633])]) ).
fof(f2789,axiom,
! [X91,X88,X86] :
( c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__Crypt__if_1) ).
fof(f27456,plain,
spl0_2632,
inference(avatar_split_clause,[],[f2562,f27454]) ).
fof(f27454,plain,
( spl0_2632
<=> ! [X15,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X43,X21,X1)
| c_minus(c_SetInterval_OatLeastLessThan(X43,X15,X1),c_SetInterval_OatLeastLessThan(X43,X21,X1),tc_set(X1)) = c_SetInterval_OatLeastLessThan(X21,X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2632])]) ).
fof(f2562,axiom,
! [X21,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X43,X21,X1)
| c_minus(c_SetInterval_OatLeastLessThan(X43,X15,X1),c_SetInterval_OatLeastLessThan(X43,X21,X1),tc_set(X1)) = c_SetInterval_OatLeastLessThan(X21,X15,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Oivl__diff_0) ).
fof(f27452,plain,
spl0_2631,
inference(avatar_split_clause,[],[f2487,f27450]) ).
fof(f27450,plain,
( spl0_2631
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(X18,X27,X1) = c_divide(c_times(X18,X4,X1),c_times(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2631])]) ).
fof(f2487,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(X18,X27,X1) = c_divide(c_times(X18,X4,X1),c_times(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__right__if_1) ).
fof(f27448,plain,
spl0_2630,
inference(avatar_split_clause,[],[f2481,f27446]) ).
fof(f27446,plain,
( spl0_2630
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(X18,X27,X1) = c_divide(c_times(X4,X18,X1),c_times(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2630])]) ).
fof(f2481,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(X18,X27,X1) = c_divide(c_times(X4,X18,X1),c_times(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__left__if_1) ).
fof(f27444,plain,
spl0_2629,
inference(avatar_split_clause,[],[f2445,f27442]) ).
fof(f27442,plain,
( spl0_2629
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(X18,c_0,X1)
| ~ c_less(X27,c_0,X1)
| c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2629])]) ).
fof(f2445,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(X18,c_0,X1)
| ~ c_less(X27,c_0,X1)
| c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__less__iff__less__neg_1) ).
fof(f27440,plain,
spl0_2628,
inference(avatar_split_clause,[],[f2444,f27438]) ).
fof(f27438,plain,
( spl0_2628
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| ~ c_less(X18,c_0,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2628])]) ).
fof(f2444,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| ~ c_less(X18,c_0,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__less__iff__less__neg_0) ).
fof(f27436,plain,
spl0_2627,
inference(avatar_split_clause,[],[f2443,f27434]) ).
fof(f27434,plain,
( spl0_2627
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(c_0,X18,X1)
| ~ c_less(c_0,X27,X1)
| c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2627])]) ).
fof(f2443,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(c_0,X18,X1)
| ~ c_less(c_0,X27,X1)
| c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__less__iff__less_1) ).
fof(f27432,plain,
spl0_2626,
inference(avatar_split_clause,[],[f2442,f27430]) ).
fof(f27430,plain,
( spl0_2626
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| ~ c_less(c_0,X18,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2626])]) ).
fof(f2442,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| ~ c_less(c_0,X18,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__less__iff__less_0) ).
fof(f27426,plain,
spl0_2625,
inference(avatar_split_clause,[],[f2441,f27424]) ).
fof(f27424,plain,
( spl0_2625
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| ~ c_less(X18,c_0,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2625])]) ).
fof(f2441,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| ~ c_less(X18,c_0,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__le__iff__le__neg_1) ).
fof(f27422,plain,
spl0_2624,
inference(avatar_split_clause,[],[f2440,f27420]) ).
fof(f27420,plain,
( spl0_2624
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| ~ c_less(X18,c_0,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2624])]) ).
fof(f2440,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| ~ c_less(X18,c_0,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__le__iff__le__neg_0) ).
fof(f27418,plain,
spl0_2623,
inference(avatar_split_clause,[],[f2439,f27416]) ).
fof(f27416,plain,
( spl0_2623
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| ~ c_less(c_0,X18,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2623])]) ).
fof(f2439,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| ~ c_less(c_0,X18,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__le__iff__le_1) ).
fof(f27414,plain,
spl0_2622,
inference(avatar_split_clause,[],[f2438,f27412]) ).
fof(f27412,plain,
( spl0_2622
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| ~ c_less(c_0,X18,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2622])]) ).
fof(f2438,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| ~ c_less(c_0,X18,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__le__iff__le_0) ).
fof(f27410,plain,
spl0_2621,
inference(avatar_split_clause,[],[f2356,f27408]) ).
fof(f27408,plain,
( spl0_2621
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2621])]) ).
fof(f2356,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__strict__increasing__iff_1) ).
fof(f27406,plain,
spl0_2620,
inference(avatar_split_clause,[],[f2355,f27404]) ).
fof(f27404,plain,
( spl0_2620
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_less(X0,X3,tc_nat)
| ~ c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2620])]) ).
fof(f2355,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_less(X0,X3,tc_nat)
| ~ c_less(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__strict__increasing__iff_0) ).
fof(f27402,plain,
spl0_2619,
inference(avatar_split_clause,[],[f2351,f27400]) ).
fof(f27400,plain,
( spl0_2619
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2619])]) ).
fof(f2351,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X0,X3,tc_nat)
| ~ c_less(c_1,X27,X1)
| c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__increasing__iff_1) ).
fof(f27398,plain,
spl0_2618,
inference(avatar_split_clause,[],[f2350,f27396]) ).
fof(f27396,plain,
( spl0_2618
<=> ! [X3,X0,X27,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2618])]) ).
fof(f2350,axiom,
! [X3,X0,X1,X27] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,X27,X1)
| c_lessequals(X0,X3,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X27,X0,X1),c_Nat_Opower(X27,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__increasing__iff_0) ).
fof(f27394,plain,
spl0_2617,
inference(avatar_split_clause,[],[f2336,f27392]) ).
fof(f27392,plain,
( spl0_2617
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2617])]) ).
fof(f2336,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__eq__number__of_5) ).
fof(f27390,plain,
spl0_2616,
inference(avatar_split_clause,[],[f2333,f27388]) ).
fof(f27388,plain,
( spl0_2616
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2616])]) ).
fof(f2333,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_0,X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__eq__number__of_2) ).
fof(f27384,plain,
spl0_2615,
inference(avatar_split_clause,[],[f2330,f27382]) ).
fof(f27382,plain,
( spl0_2615
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2615])]) ).
fof(f2330,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__le__power__eq__number__of_2) ).
fof(f27380,plain,
spl0_2614,
inference(avatar_split_clause,[],[f2328,f27378]) ).
fof(f27378,plain,
( spl0_2614
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2614])]) ).
fof(f2328,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__le__power__eq__number__of_0) ).
fof(f27376,plain,
spl0_2613,
inference(avatar_split_clause,[],[f2325,f27374]) ).
fof(f27374,plain,
( spl0_2613
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2613])]) ).
fof(f2325,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__less__zero__eq__number__of_2) ).
fof(f27372,plain,
spl0_2612,
inference(avatar_split_clause,[],[f2319,f27370]) ).
fof(f27370,plain,
( spl0_2612
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2612])]) ).
fof(f2319,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X0,c_0,X1)
| c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__le__zero__eq__number__of_2) ).
fof(f27368,plain,
spl0_2611,
inference(avatar_split_clause,[],[f2168,f27366]) ).
fof(f27366,plain,
( spl0_2611
<=> ! [X48,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2611])]) ).
fof(f2168,axiom,
! [X48,X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_times(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1),X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Omult__number__of__left_0) ).
fof(f27364,plain,
spl0_2610,
inference(avatar_split_clause,[],[f2108,f27362]) ).
fof(f27362,plain,
( spl0_2610
<=> ! [X48,X47,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2610])]) ).
fof(f2108,axiom,
! [X48,X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_plus(c_Numeral_Onumber__of(X11,X1),X48,X1),X1) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1),X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Oadd__number__of__left_0) ).
fof(f27360,plain,
spl0_2609,
inference(avatar_split_clause,[],[f1861,f27358]) ).
fof(f27358,plain,
( spl0_2609
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2609])]) ).
fof(f1861,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Omod__nat__number__of_1) ).
fof(f27356,plain,
spl0_2608,
inference(avatar_split_clause,[],[f1859,f27354]) ).
fof(f27354,plain,
( spl0_2608
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2608])]) ).
fof(f1859,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__nat__number__of_4) ).
fof(f27352,plain,
spl0_2607,
inference(avatar_split_clause,[],[f1834,f27350]) ).
fof(f27350,plain,
( spl0_2607
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2607])]) ).
fof(f1834,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) != c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_0) ).
fof(f27348,plain,
spl0_2606,
inference(avatar_split_clause,[],[f1825,f27346]) ).
fof(f27346,plain,
( spl0_2606
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2606])]) ).
fof(f1825,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oadd__nat__number__of_1) ).
fof(f27344,plain,
( spl0_2605
| ~ spl0_2185
| ~ spl0_2577 ),
inference(avatar_split_clause,[],[f26749,f26329,f18519,f27342]) ).
fof(f27342,plain,
( spl0_2605
<=> ! [X1] :
( ~ c_in(X1,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(X1,c_Union(c_Finite__Set_OFinites,tc_Message_Omsg),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2605])]) ).
fof(f18519,plain,
( spl0_2185
<=> ! [X24,X12,X32,X1] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2185])]) ).
fof(f26329,plain,
( spl0_2577
<=> c_in(c_Message_Osynth(v_H),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2577])]) ).
fof(f26749,plain,
( ! [X1] :
( ~ c_in(X1,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(X1,c_Union(c_Finite__Set_OFinites,tc_Message_Omsg),tc_Message_Omsg) )
| ~ spl0_2185
| ~ spl0_2577 ),
inference(resolution,[],[f26331,f18520]) ).
fof(f18520,plain,
( ! [X1,X24,X12,X32] :
( ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,X24,X1)
| c_in(X12,c_Union(X32,X1),X1) )
| ~ spl0_2185 ),
inference(avatar_component_clause,[],[f18519]) ).
fof(f26331,plain,
( c_in(c_Message_Osynth(v_H),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ spl0_2577 ),
inference(avatar_component_clause,[],[f26329]) ).
fof(f27340,plain,
spl0_2604,
inference(avatar_split_clause,[],[f1635,f27338]) ).
fof(f27338,plain,
( spl0_2604
<=> ! [X43,X23,X0,X3,X1] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X23,X43,X0,X1),X43,X3,X1) = c_List_Olist__update(X23,X43,X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2604])]) ).
fof(f1635,axiom,
! [X3,X0,X1,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(c_List_Olist__update(X23,X43,X0,X1),X43,X3,X1) = c_List_Olist__update(X23,X43,X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__update__overwrite_0) ).
fof(f27336,plain,
spl0_2603,
inference(avatar_split_clause,[],[f1634,f27334]) ).
fof(f27334,plain,
( spl0_2603
<=> ! [X3,X0,X23,X25,X1] : c_List_Olist__update(c_append(X23,c_List_Olist_OCons(X0,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X3,X1) = c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2603])]) ).
fof(f1634,axiom,
! [X3,X0,X1,X25,X23] : c_List_Olist__update(c_append(X23,c_List_Olist_OCons(X0,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X3,X1) = c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__update__length_0) ).
fof(f27332,plain,
spl0_2602,
inference(avatar_split_clause,[],[f1558,f27330]) ).
fof(f27330,plain,
( spl0_2602
<=> ! [X25,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(X25,X1)
| c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset != c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2602])]) ).
fof(f1558,axiom,
! [X1,X25,X23] :
( ~ c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(X25,X1)
| c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset != c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__append_3) ).
fof(f27328,plain,
spl0_2601,
inference(avatar_split_clause,[],[f1355,f27326]) ).
fof(f27326,plain,
( spl0_2601
<=> ! [X0,X3] :
( X0 = X3
| c_IntDef_OAbs__Integ(X0) != c_IntDef_OAbs__Integ(X3)
| ~ c_in(X0,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2601])]) ).
fof(f1355,axiom,
! [X3,X0] :
( X0 = X3
| c_IntDef_OAbs__Integ(X0) != c_IntDef_OAbs__Integ(X3)
| ~ c_in(X0,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat)))
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInteg_OAbs__Integ__inject_0) ).
fof(f27324,plain,
spl0_2600,
inference(avatar_split_clause,[],[f1294,f27322]) ).
fof(f27322,plain,
( spl0_2600
<=> ! [X2,X12,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2600])]) ).
fof(f1294,axiom,
! [X2,X3,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omax(X3,c_Finite__Set_OMin(X12,X2),X2) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Osup__Inf__absorb_0) ).
fof(f27320,plain,
spl0_2599,
inference(avatar_split_clause,[],[f1293,f27318]) ).
fof(f27318,plain,
( spl0_2599
<=> ! [X2,X12,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2599])]) ).
fof(f1293,axiom,
! [X2,X3,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X3,X12,X2)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_Orderings_Omin(X3,c_Finite__Set_OMax(X12,X2),X2) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_Oinf__Sup__absorb_0) ).
fof(f27316,plain,
spl0_2598,
inference(avatar_split_clause,[],[f1222,f27314]) ).
fof(f27314,plain,
( spl0_2598
<=> ! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) = c_div(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2598])]) ).
fof(f1222,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) = c_div(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__mult__self2_0) ).
fof(f27312,plain,
spl0_2597,
inference(avatar_split_clause,[],[f1220,f27310]) ).
fof(f27310,plain,
( spl0_2597
<=> ! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) = c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2597])]) ).
fof(f1220,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) = c_plus(X16,c_div(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__mult__self1_0) ).
fof(f27308,plain,
spl0_2596,
inference(avatar_split_clause,[],[f121,f27306]) ).
fof(f27306,plain,
( spl0_2596
<=> ! [X5,X18,X27,X1] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2596])]) ).
fof(f121,axiom,
! [X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X1,X1),X5,tc_prod(X1,X1))
| c_in(c_Pair(X18,X27,X1,X1),c_Transitive__Closure_Otrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Otrancl_Or__into__trancl_0) ).
fof(f27304,plain,
spl0_2595,
inference(avatar_split_clause,[],[f74,f27302]) ).
fof(f27302,plain,
( spl0_2595
<=> ! [X5,X18,X12,X27,X2,X1] :
( ~ c_in(X18,X12,X1)
| c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2595])]) ).
fof(f74,axiom,
! [X2,X18,X1,X27,X5,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X27,c_Relation_OImage(X5,X12,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImageI_0) ).
fof(f26756,plain,
( spl0_2594
| ~ spl0_1542
| spl0_2578 ),
inference(avatar_split_clause,[],[f26509,f26333,f11039,f26753]) ).
fof(f26753,plain,
( spl0_2594
<=> c_0 = c_Finite__Set_Ocard(c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2594])]) ).
fof(f11039,plain,
( spl0_1542
<=> ! [X12,X1] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1542])]) ).
fof(f26333,plain,
( spl0_2578
<=> c_in(c_Message_Oparts(c_UNIV),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2578])]) ).
fof(f26509,plain,
( c_0 = c_Finite__Set_Ocard(c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1542
| spl0_2578 ),
inference(resolution,[],[f26335,f11040]) ).
fof(f11040,plain,
( ! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_0 = c_Finite__Set_Ocard(X12,X1) )
| ~ spl0_1542 ),
inference(avatar_component_clause,[],[f11039]) ).
fof(f26335,plain,
( ~ c_in(c_Message_Oparts(c_UNIV),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| spl0_2578 ),
inference(avatar_component_clause,[],[f26333]) ).
fof(f26747,plain,
( spl0_2593
| ~ spl0_1542
| spl0_2577 ),
inference(avatar_split_clause,[],[f26377,f26329,f11039,f26744]) ).
fof(f26744,plain,
( spl0_2593
<=> c_0 = c_Finite__Set_Ocard(c_Message_Osynth(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2593])]) ).
fof(f26377,plain,
( c_0 = c_Finite__Set_Ocard(c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_1542
| spl0_2577 ),
inference(resolution,[],[f26330,f11040]) ).
fof(f26330,plain,
( ~ c_in(c_Message_Osynth(v_H),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| spl0_2577 ),
inference(avatar_component_clause,[],[f26329]) ).
fof(f26407,plain,
spl0_2592,
inference(avatar_split_clause,[],[f3009,f26405]) ).
fof(f26405,plain,
( spl0_2592
<=> ! [X5,X1] :
( c_less(c_0,c_divide(X5,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1),X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ c_less(c_0,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2592])]) ).
fof(f3009,plain,
! [X1,X5] :
( c_less(c_0,c_divide(X5,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1),X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ c_less(c_0,X5,X1) ),
inference(forward_demodulation,[],[f3008,f2156]) ).
fof(f3008,plain,
! [X1,X5] :
( c_less(c_0,c_divide(X5,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1),X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ c_less(c_0,X5,X1) ),
inference(forward_demodulation,[],[f3007,f2154]) ).
fof(f3007,plain,
! [X1,X5] :
( c_less(c_0,c_divide(X5,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1),X1),X1)
| ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ c_less(c_0,X5,X1) ),
inference(forward_demodulation,[],[f1931,f2156]) ).
fof(f1931,axiom,
! [X1,X5] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ c_less(c_0,X5,X1)
| c_less(c_0,c_divide(X5,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ohalf__gt__zero_0) ).
fof(f26392,plain,
( spl0_2591
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2590 ),
inference(avatar_split_clause,[],[f26388,f26384,f13076,f9197,f7368,f26390]) ).
fof(f26390,plain,
( spl0_2591
<=> ! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2591])]) ).
fof(f26384,plain,
( spl0_2590
<=> ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2590])]) ).
fof(f26388,plain,
( ! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat),tc_nat) )
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2590 ),
inference(forward_demodulation,[],[f26387,f14121]) ).
fof(f26387,plain,
( ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2590 ),
inference(forward_demodulation,[],[f26385,f14121]) ).
fof(f26385,plain,
( ! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) )
| ~ spl0_2590 ),
inference(avatar_component_clause,[],[f26384]) ).
fof(f26386,plain,
spl0_2590,
inference(avatar_split_clause,[],[f2949,f26384]) ).
fof(f2949,plain,
! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2948,f2156]) ).
fof(f2948,plain,
! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2947,f2154]) ).
fof(f2947,plain,
! [X15] :
( ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat)
| c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2946,f2156]) ).
fof(f2946,plain,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2945,f2156]) ).
fof(f2945,plain,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f2944,f2154]) ).
fof(f2944,plain,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
inference(forward_demodulation,[],[f1975,f2156]) ).
fof(f1975,axiom,
! [X15] :
( c_1 = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)
| ~ c_less(c_0,c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omod2__gr__0_0) ).
fof(f26382,plain,
spl0_2589,
inference(avatar_split_clause,[],[f2810,f26380]) ).
fof(f26380,plain,
( spl0_2589
<=> ! [X87,X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2589])]) ).
fof(f2810,axiom,
! [X88,X86,X87] : c_Message_Oparts(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__MPair_0) ).
fof(f26376,plain,
spl0_2588,
inference(avatar_split_clause,[],[f2796,f26374]) ).
fof(f26374,plain,
( spl0_2588
<=> ! [X87,X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2588])]) ).
fof(f2796,axiom,
! [X88,X86,X87] : c_Message_Oanalz(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(c_insert(X86,c_insert(X87,X88,tc_Message_Omsg),tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__insert__MPair_0) ).
fof(f26372,plain,
spl0_2587,
inference(avatar_split_clause,[],[f2566,f26370]) ).
fof(f26370,plain,
( spl0_2587
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X15,X43,X1)
| ~ c_lessequals(X59,X21,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2587])]) ).
fof(f2566,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X15,X43,X1)
| ~ c_lessequals(X59,X21,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Oivl__subset_3) ).
fof(f26368,plain,
spl0_2586,
inference(avatar_split_clause,[],[f2564,f26366]) ).
fof(f26366,plain,
( spl0_2586
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X59,X21,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2586])]) ).
fof(f2564,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X59,X21,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Oivl__subset_1) ).
fof(f26364,plain,
spl0_2585,
inference(avatar_split_clause,[],[f2563,f26362]) ).
fof(f26362,plain,
( spl0_2585
<=> ! [X59,X43,X21,X15,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X15,X43,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2585])]) ).
fof(f2563,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X59,X43,X1)
| c_lessequals(X15,X43,X1)
| ~ c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Oivl__subset_0) ).
fof(f26360,plain,
spl0_2584,
inference(avatar_split_clause,[],[f2391,f26358]) ).
fof(f26358,plain,
( spl0_2584
<=> ! [X41,X21,X85] : c_Nat_Opower(X85,c_Suc(X21),tc_set(tc_prod(X41,X41))) = c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2584])]) ).
fof(f2391,axiom,
! [X21,X41,X85] : c_Nat_Opower(X85,c_Suc(X21),tc_set(tc_prod(X41,X41))) = c_Relation_Orel__comp(X85,c_Nat_Opower(X85,X21,tc_set(tc_prod(X41,X41))),X41,X41,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation__Power_Orelpow_Osimps__2_0) ).
fof(f26356,plain,
spl0_2583,
inference(avatar_split_clause,[],[f2376,f26354]) ).
fof(f26354,plain,
( spl0_2583
<=> ! [X5,X18,X27,X2,X1] :
( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2583])]) ).
fof(f2376,axiom,
! [X2,X18,X1,X27,X5] :
( ~ c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImage__singleton__iff_1) ).
fof(f26352,plain,
spl0_2582,
inference(avatar_split_clause,[],[f2375,f26350]) ).
fof(f26350,plain,
( spl0_2582
<=> ! [X5,X18,X27,X2,X1] :
( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2582])]) ).
fof(f2375,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(c_Pair(X18,X27,X2,X1),X5,tc_prod(X2,X1))
| ~ c_in(X27,c_Relation_OImage(X5,c_insert(X18,c_emptyset,X2),X2,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImage__singleton__iff_0) ).
fof(f26348,plain,
spl0_2581,
inference(avatar_split_clause,[],[f2335,f26346]) ).
fof(f26346,plain,
( spl0_2581
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2581])]) ).
fof(f2335,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__eq__number__of_4) ).
fof(f26344,plain,
spl0_2580,
inference(avatar_split_clause,[],[f2318,f26342]) ).
fof(f26342,plain,
( spl0_2580
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2580])]) ).
fof(f2318,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__le__zero__eq__number__of_1) ).
fof(f26340,plain,
spl0_2579,
inference(avatar_split_clause,[],[f2174,f26338]) ).
fof(f26338,plain,
( spl0_2579
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2579])]) ).
fof(f2174,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) = c_HOL_Oabs(c_plus(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__add__abs_0) ).
fof(f26336,plain,
( spl0_2577
| ~ spl0_2578
| ~ spl0_1888
| ~ spl0_2202 ),
inference(avatar_split_clause,[],[f19397,f19126,f14230,f26333,f26329]) ).
fof(f14230,plain,
( spl0_1888
<=> ! [X20,X1,X19] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1888])]) ).
fof(f19397,plain,
( ~ c_in(c_Message_Oparts(c_UNIV),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| c_in(c_Message_Osynth(v_H),c_Finite__Set_OFinites,tc_set(tc_Message_Omsg))
| ~ spl0_1888
| ~ spl0_2202 ),
inference(superposition,[],[f14231,f19128]) ).
fof(f14231,plain,
( ! [X1,X19,X20] :
( ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(X19,c_Finite__Set_OFinites,tc_set(X1)) )
| ~ spl0_1888 ),
inference(avatar_component_clause,[],[f14230]) ).
fof(f26327,plain,
spl0_2576,
inference(avatar_split_clause,[],[f2121,f26325]) ).
fof(f26325,plain,
( spl0_2576
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) = c_uminus(c_Numeral_Onumber__of(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2576])]) ).
fof(f2121,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) = c_uminus(c_Numeral_Onumber__of(X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__6_0) ).
fof(f26323,plain,
spl0_2575,
inference(avatar_split_clause,[],[f1857,f26321]) ).
fof(f26321,plain,
( spl0_2575
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2575])]) ).
fof(f1857,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__nat__number__of_2) ).
fof(f26319,plain,
spl0_2574,
inference(avatar_split_clause,[],[f1856,f26317]) ).
fof(f26317,plain,
( spl0_2574
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2574])]) ).
fof(f1856,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X83)),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__nat__number__of_1) ).
fof(f26315,plain,
spl0_2573,
inference(avatar_split_clause,[],[f1810,f26313]) ).
fof(f26313,plain,
( spl0_2573
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_lessequals(X21,X15,tc_nat)
| c_NatArith_Oof__nat(c_minus(X15,X21,tc_nat),X1) = c_minus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2573])]) ).
fof(f1810,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_lessequals(X21,X15,tc_nat)
| c_NatArith_Oof__nat(c_minus(X15,X21,tc_nat),X1) = c_minus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__diff_0) ).
fof(f26311,plain,
spl0_2572,
inference(avatar_split_clause,[],[f1798,f26309]) ).
fof(f26309,plain,
( spl0_2572
<=> ! [X16,X59,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(c_Suc(c_minus(X59,X16,tc_nat)),X15,tc_nat) = c_minus(c_Suc(X59),c_plus(X16,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2572])]) ).
fof(f1798,axiom,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(c_Suc(c_minus(X59,X16,tc_nat)),X15,tc_nat) = c_minus(c_Suc(X59),c_plus(X16,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Odiff__Suc__diff__eq2_0) ).
fof(f26307,plain,
spl0_2571,
inference(avatar_split_clause,[],[f1797,f26305]) ).
fof(f26305,plain,
( spl0_2571
<=> ! [X16,X59,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X15,c_Suc(c_minus(X59,X16,tc_nat)),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Suc(X59),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2571])]) ).
fof(f1797,axiom,
! [X59,X16,X15] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X15,c_Suc(c_minus(X59,X16,tc_nat)),tc_nat) = c_minus(c_plus(X15,X16,tc_nat),c_Suc(X59),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Odiff__Suc__diff__eq1_0) ).
fof(f26303,plain,
spl0_2570,
inference(avatar_split_clause,[],[f1672,f26301]) ).
fof(f26301,plain,
( spl0_2570
<=> ! [X45,X3,X70,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2570])]) ).
fof(f1672,axiom,
! [X72,X70,X3,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__9_0) ).
fof(f26299,plain,
spl0_2569,
inference(avatar_split_clause,[],[f1671,f26297]) ).
fof(f26297,plain,
( spl0_2569
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2569])]) ).
fof(f1671,axiom,
! [X3,X70,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__8_0) ).
fof(f26295,plain,
spl0_2568,
inference(avatar_split_clause,[],[f1670,f26293]) ).
fof(f26293,plain,
( spl0_2568
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2568])]) ).
fof(f1670,axiom,
! [X3,X70,X72,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__7_0) ).
fof(f26291,plain,
spl0_2567,
inference(avatar_split_clause,[],[f1669,f26289]) ).
fof(f26289,plain,
( spl0_2567
<=> ! [X45,X3,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2567])]) ).
fof(f1669,axiom,
! [X3,X72,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__6_0) ).
fof(f26284,plain,
spl0_2566,
inference(avatar_split_clause,[],[f1668,f26282]) ).
fof(f26282,plain,
( spl0_2566
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2566])]) ).
fof(f1668,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X79,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__5_0) ).
fof(f26280,plain,
spl0_2565,
inference(avatar_split_clause,[],[f1667,f26278]) ).
fof(f26278,plain,
( spl0_2565
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2565])]) ).
fof(f1667,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__4_0) ).
fof(f26276,plain,
spl0_2564,
inference(avatar_split_clause,[],[f1666,f26274]) ).
fof(f26274,plain,
( spl0_2564
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2564])]) ).
fof(f1666,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__3_0) ).
fof(f26272,plain,
spl0_2563,
inference(avatar_split_clause,[],[f1665,f26270]) ).
fof(f26270,plain,
( spl0_2563
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2563])]) ).
fof(f1665,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X79,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__2_0) ).
fof(f26268,plain,
spl0_2562,
inference(avatar_split_clause,[],[f1664,f26266]) ).
fof(f26266,plain,
( spl0_2562
<=> ! [X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2562])]) ).
fof(f1664,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X76,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__1_0) ).
fof(f26264,plain,
spl0_2561,
inference(avatar_split_clause,[],[f1663,f26262]) ).
fof(f26262,plain,
( spl0_2561
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X72,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2561])]) ).
fof(f1663,axiom,
! [X72,X70,X73,X71,X80,X78,X3,X1,X68,X44,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__16_0) ).
fof(f26260,plain,
spl0_2560,
inference(avatar_split_clause,[],[f1662,f26258]) ).
fof(f26258,plain,
( spl0_2560
<=> ! [X45,X3,X70,X73,X80,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2560])]) ).
fof(f1662,axiom,
! [X72,X70,X73,X71,X80,X3,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__15_0) ).
fof(f26256,plain,
spl0_2559,
inference(avatar_split_clause,[],[f1661,f26254]) ).
fof(f26254,plain,
( spl0_2559
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2559])]) ).
fof(f1661,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__14_0) ).
fof(f26252,plain,
spl0_2558,
inference(avatar_split_clause,[],[f1660,f26250]) ).
fof(f26250,plain,
( spl0_2558
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X71,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2558])]) ).
fof(f1660,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__13_0) ).
fof(f26248,plain,
spl0_2557,
inference(avatar_split_clause,[],[f1659,f26246]) ).
fof(f26246,plain,
( spl0_2557
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2557])]) ).
fof(f1659,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__12_0) ).
fof(f26244,plain,
( spl0_2556
| ~ spl0_2462
| ~ spl0_1817
| ~ spl0_2420 ),
inference(avatar_split_clause,[],[f24379,f23932,f12874,f24425,f26241]) ).
fof(f26241,plain,
( spl0_2556
<=> c_emptyset = c_SetInterval_OatLeastAtMost(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2556])]) ).
fof(f23932,plain,
( spl0_2420
<=> c_less(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2420])]) ).
fof(f24379,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_emptyset = c_SetInterval_OatLeastAtMost(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| ~ spl0_1817
| ~ spl0_2420 ),
inference(resolution,[],[f23934,f12875]) ).
fof(f23934,plain,
( c_less(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_2420 ),
inference(avatar_component_clause,[],[f23932]) ).
fof(f26239,plain,
spl0_2555,
inference(avatar_split_clause,[],[f1658,f26237]) ).
fof(f26237,plain,
( spl0_2555
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X44,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2555])]) ).
fof(f1658,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__11_0) ).
fof(f26235,plain,
spl0_2554,
inference(avatar_split_clause,[],[f1657,f26233]) ).
fof(f26233,plain,
( spl0_2554
<=> ! [X45,X3,X70,X73,X71,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2554])]) ).
fof(f1657,axiom,
! [X72,X70,X73,X71,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__rec(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Orecs__10_0) ).
fof(f26231,plain,
spl0_2553,
inference(avatar_split_clause,[],[f1656,f26229]) ).
fof(f26229,plain,
( spl0_2553
<=> ! [X45,X3,X70,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2553])]) ).
fof(f1656,axiom,
! [X72,X70,X3,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X3,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble8,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__9_0) ).
fof(f26227,plain,
spl0_2552,
inference(avatar_split_clause,[],[f1655,f26225]) ).
fof(f26225,plain,
( spl0_2552
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2552])]) ).
fof(f1655,axiom,
! [X3,X70,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X3,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble7,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__8_0) ).
fof(f26223,plain,
spl0_2551,
inference(avatar_split_clause,[],[f1654,f26221]) ).
fof(f26221,plain,
( spl0_2551
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2551])]) ).
fof(f1654,axiom,
! [X3,X70,X72,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X3,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble6,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__7_0) ).
fof(f26219,plain,
spl0_2550,
inference(avatar_split_clause,[],[f1653,f26217]) ).
fof(f26217,plain,
( spl0_2550
<=> ! [X45,X3,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2550])]) ).
fof(f1653,axiom,
! [X3,X72,X73,X71,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X3,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble5,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__6_0) ).
fof(f26215,plain,
spl0_2549,
inference(avatar_split_clause,[],[f1652,f26213]) ).
fof(f26213,plain,
( spl0_2549
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2549])]) ).
fof(f1652,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X79,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X3,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble4,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__5_0) ).
fof(f26211,plain,
spl0_2548,
inference(avatar_split_clause,[],[f1651,f26209]) ).
fof(f26209,plain,
( spl0_2548
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2548])]) ).
fof(f1651,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X3,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__4_0) ).
fof(f26207,plain,
spl0_2547,
inference(avatar_split_clause,[],[f1650,f26205]) ).
fof(f26205,plain,
( spl0_2547
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2547])]) ).
fof(f1650,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X45,X76,X77,X79,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X3,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble2,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__3_0) ).
fof(f26203,plain,
spl0_2546,
inference(avatar_split_clause,[],[f1649,f26201]) ).
fof(f26201,plain,
( spl0_2546
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2546])]) ).
fof(f1649,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X79,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X3,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__2_0) ).
fof(f26199,plain,
spl0_2545,
inference(avatar_split_clause,[],[f1648,f26197]) ).
fof(f26197,plain,
( spl0_2545
<=> ! [X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2545])]) ).
fof(f1648,axiom,
! [X3,X70,X72,X71,X73,X80,X78,X1,X68,X44,X69,X76,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X3,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble0,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__1_0) ).
fof(f26195,plain,
spl0_2544,
inference(avatar_split_clause,[],[f1647,f26193]) ).
fof(f26193,plain,
( spl0_2544
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X72,X69,X76,X77,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2544])]) ).
fof(f1647,axiom,
! [X72,X70,X73,X71,X80,X78,X3,X1,X68,X44,X69,X45,X76,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X78,X3,c_List_Onibble_ONibbleF,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__16_0) ).
fof(f26191,plain,
spl0_2543,
inference(avatar_split_clause,[],[f1646,f26189]) ).
fof(f26189,plain,
( spl0_2543
<=> ! [X45,X3,X70,X73,X80,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2543])]) ).
fof(f1646,axiom,
! [X72,X70,X73,X71,X80,X3,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X77,X3,X79,c_List_Onibble_ONibbleE,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__15_0) ).
fof(f26187,plain,
spl0_2542,
inference(avatar_split_clause,[],[f1645,f26185]) ).
fof(f26185,plain,
( spl0_2542
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X72,X71,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2542])]) ).
fof(f1645,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X76,X3,X78,X79,c_List_Onibble_ONibbleD,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__14_0) ).
fof(f26183,plain,
spl0_2541,
inference(avatar_split_clause,[],[f1644,f26181]) ).
fof(f26181,plain,
( spl0_2541
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X71,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2541])]) ).
fof(f1644,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X79,X77,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X75,X3,X77,X78,X79,c_List_Onibble_ONibbleC,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__13_0) ).
fof(f26179,plain,
spl0_2540,
inference(avatar_split_clause,[],[f1643,f26177]) ).
fof(f26177,plain,
( spl0_2540
<=> ! [X45,X3,X70,X73,X80,X78,X44,X1,X68,X79,X69,X76,X77,X72,X71,X67,X74] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2540])]) ).
fof(f1643,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X74,X3,X76,X77,X78,X79,c_List_Onibble_ONibbleB,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__12_0) ).
fof(f26175,plain,
spl0_2539,
inference(avatar_split_clause,[],[f1642,f26173]) ).
fof(f26173,plain,
( spl0_2539
<=> ! [X45,X3,X70,X73,X80,X78,X1,X68,X79,X69,X76,X77,X72,X71,X67,X44,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2539])]) ).
fof(f1642,axiom,
! [X72,X70,X73,X71,X80,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X80,X3,X75,X76,X77,X78,X79,c_List_Onibble_ONibbleA,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__11_0) ).
fof(f26171,plain,
spl0_2538,
inference(avatar_split_clause,[],[f1641,f26169]) ).
fof(f26169,plain,
( spl0_2538
<=> ! [X45,X3,X70,X73,X71,X78,X44,X1,X68,X79,X69,X76,X77,X72,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2538])]) ).
fof(f1641,axiom,
! [X72,X70,X73,X71,X3,X78,X1,X68,X44,X69,X45,X76,X77,X79,X67,X74,X75] : c_List_Onibble_Onibble__case(X45,X44,X67,X68,X69,X70,X71,X72,X73,X3,X74,X75,X76,X77,X78,X79,c_List_Onibble_ONibble9,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Ocases__10_0) ).
fof(f26167,plain,
spl0_2537,
inference(avatar_split_clause,[],[f1629,f26165]) ).
fof(f26165,plain,
( spl0_2537
<=> ! [X41,X60,X18,X65] :
( ~ c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist_OCons(X18,c_List_Olist__inter(X60,X65,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2537])]) ).
fof(f1629,axiom,
! [X65,X41,X18,X60] :
( ~ c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist_OCons(X18,c_List_Olist__inter(X60,X65,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__inter_Osimps__2_0) ).
fof(f26163,plain,
spl0_2536,
inference(avatar_split_clause,[],[f1614,f26161]) ).
fof(f26161,plain,
( spl0_2536
<=> ! [X23,X25,X2,X1] : c_Nat_Osize(c_List_Ozip(X23,X25,X1,X2),tc_List_Olist(tc_prod(X1,X2))) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2536])]) ).
fof(f1614,axiom,
! [X2,X1,X25,X23] : c_Nat_Osize(c_List_Ozip(X23,X25,X1,X2),tc_List_Olist(tc_prod(X1,X2))) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X2)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__zip_0) ).
fof(f26159,plain,
( ~ spl0_2534
| spl0_2535
| ~ spl0_2016
| ~ spl0_2302 ),
inference(avatar_split_clause,[],[f21741,f21696,f16400,f26157,f26153]) ).
fof(f26153,plain,
( spl0_2534
<=> c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2534])]) ).
fof(f26157,plain,
( spl0_2535
<=> ! [X0] :
( v_X = X0
| ~ c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2535])]) ).
fof(f21696,plain,
( spl0_2302
<=> c_in(v_X,c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2302])]) ).
fof(f21741,plain,
( ! [X0] :
( v_X = X0
| ~ c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_UNIV),tc_Message_Omsg) )
| ~ spl0_2016
| ~ spl0_2302 ),
inference(resolution,[],[f21698,f16401]) ).
fof(f21698,plain,
( c_in(v_X,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_2302 ),
inference(avatar_component_clause,[],[f21696]) ).
fof(f26151,plain,
spl0_2533,
inference(avatar_split_clause,[],[f1523,f26149]) ).
fof(f26149,plain,
( spl0_2533
<=> ! [X53,X23,X25,X52,X1] :
( X52 = X53
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2533])]) ).
fof(f1523,axiom,
! [X1,X52,X53,X25,X23] :
( X52 = X53
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__eq__append__conv_3) ).
fof(f26147,plain,
spl0_2532,
inference(avatar_split_clause,[],[f1522,f26145]) ).
fof(f26145,plain,
( spl0_2532
<=> ! [X52,X53,X23,X25,X1] :
( X23 = X25
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2532])]) ).
fof(f1522,axiom,
! [X1,X52,X53,X25,X23] :
( X23 = X25
| c_Nat_Osize(X52,tc_List_Olist(X1)) != c_Nat_Osize(X53,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__eq__append__conv_2) ).
fof(f26143,plain,
spl0_2531,
inference(avatar_split_clause,[],[f1521,f26141]) ).
fof(f26141,plain,
( spl0_2531
<=> ! [X53,X23,X25,X52,X1] :
( X52 = X53
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2531])]) ).
fof(f1521,axiom,
! [X1,X52,X53,X25,X23] :
( X52 = X53
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__eq__append__conv_1) ).
fof(f26139,plain,
spl0_2530,
inference(avatar_split_clause,[],[f1520,f26137]) ).
fof(f26137,plain,
( spl0_2530
<=> ! [X52,X53,X23,X25,X1] :
( X23 = X25
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2530])]) ).
fof(f1520,axiom,
! [X1,X52,X53,X25,X23] :
( X23 = X25
| c_Nat_Osize(X23,tc_List_Olist(X1)) != c_Nat_Osize(X25,tc_List_Olist(X1))
| c_append(X23,X52,X1) != c_append(X25,X53,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__eq__append__conv_0) ).
fof(f26135,plain,
spl0_2529,
inference(avatar_split_clause,[],[f1468,f26133]) ).
fof(f26133,plain,
( spl0_2529
<=> ! [X11,X47] : c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2529])]) ).
fof(f1468,axiom,
! [X11,X47] : c_div(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(c_Numeral_Onumber__of(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__number__of__BIT_0) ).
fof(f26131,plain,
spl0_2528,
inference(avatar_split_clause,[],[f1283,f26129]) ).
fof(f26129,plain,
( spl0_2528
<=> ! [X18,X13,X12,X1] :
( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2528])]) ).
fof(f1283,axiom,
! [X1,X18,X12,X13] :
( ~ c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Diff__insert_1) ).
fof(f26127,plain,
spl0_2527,
inference(avatar_split_clause,[],[f1282,f26125]) ).
fof(f26125,plain,
( spl0_2527
<=> ! [X18,X13,X12,X1] :
( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2527])]) ).
fof(f1282,axiom,
! [X1,X18,X12,X13] :
( c_in(c_minus(X12,X13,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_minus(X12,c_insert(X18,X13,X1),tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Diff__insert_0) ).
fof(f26123,plain,
spl0_2526,
inference(avatar_split_clause,[],[f79,f26121]) ).
fof(f26121,plain,
( spl0_2526
<=> ! [X12,X1,X4] :
( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
| c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2526])]) ).
fof(f79,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1))
| c_Pair(c_Main_OdiagE__1(X12,X4,X1),c_Main_OdiagE__1(X12,X4,X1),X1,X1) = X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OdiagE_0) ).
fof(f26119,plain,
spl0_2525,
inference(avatar_split_clause,[],[f75,f26117]) ).
fof(f26117,plain,
( spl0_2525
<=> ! [X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
| c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2525])]) ).
fof(f75,axiom,
! [X2,X1,X27,X5] :
( ~ c_in(X27,c_Relation_ORange(X5,X2,X1),X1)
| c_in(c_Pair(c_Main_ORangeE__1(X27,X5,X1,X2),X27,X2,X1),X5,tc_prod(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ORangeE_0) ).
fof(f26115,plain,
spl0_2524,
inference(avatar_split_clause,[],[f69,f26113]) ).
fof(f26113,plain,
( spl0_2524
<=> ! [X18,X5,X2,X1] :
( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2524])]) ).
fof(f69,axiom,
! [X2,X18,X1,X5] :
( ~ c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| c_in(c_Pair(X18,c_Main_ODomainE__1(X18,X5,X1,X2),X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ODomainE_0) ).
fof(f26082,plain,
spl0_2523,
inference(avatar_split_clause,[],[f60,f26080]) ).
fof(f26080,plain,
( spl0_2523
<=> ! [X18,X12,X1,X26] :
( ~ c_in(X18,X12,X1)
| ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2523])]) ).
fof(f60,axiom,
! [X18,X1,X26,X12] :
( ~ c_in(X18,X12,X1)
| ~ c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_List_Olist_OCons(X18,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olists_OCons_0) ).
fof(f26078,plain,
spl0_2522,
inference(avatar_split_clause,[],[f22,f26076]) ).
fof(f26076,plain,
( spl0_2522
<=> ! [X13,X7,X12,X2,X1] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2522])]) ).
fof(f22,axiom,
! [X2,X1,X7,X12,X13] :
( ~ c_in(X7,X13,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn1(X7,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ousum__In1I_0) ).
fof(f26074,plain,
spl0_2521,
inference(avatar_split_clause,[],[f21,f26072]) ).
fof(f26072,plain,
( spl0_2521
<=> ! [X13,X12,X9,X2,X1] :
( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2521])]) ).
fof(f21,axiom,
! [X2,X1,X9,X12,X13] :
( ~ c_in(X9,X12,tc_set(tc_Datatype__Universe_Onode(X1,X2)))
| c_in(c_Datatype__Universe_OIn0(X9,X1,X2),c_Datatype__Universe_Ousum(X12,X13,X1,X2),tc_set(tc_Datatype__Universe_Onode(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ousum__In0I_0) ).
fof(f25565,plain,
( spl0_2520
| ~ spl0_1068
| ~ spl0_1874
| ~ spl0_2204 ),
inference(avatar_split_clause,[],[f25398,f19439,f14164,f7418,f25562]) ).
fof(f25562,plain,
( spl0_2520
<=> c_in(v_X,c_emptyset,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2520])]) ).
fof(f7418,plain,
( spl0_1068
<=> c_emptyset = c_Message_Oparts(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1068])]) ).
fof(f14164,plain,
( spl0_1874
<=> c_in(v_X,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1874])]) ).
fof(f19439,plain,
( spl0_2204
<=> c_emptyset = c_Message_Osynth(v_H) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2204])]) ).
fof(f25398,plain,
( c_in(v_X,c_emptyset,tc_Message_Omsg)
| ~ spl0_1068
| ~ spl0_1874
| ~ spl0_2204 ),
inference(forward_demodulation,[],[f25349,f7420]) ).
fof(f7420,plain,
( c_emptyset = c_Message_Oparts(c_emptyset)
| ~ spl0_1068 ),
inference(avatar_component_clause,[],[f7418]) ).
fof(f25349,plain,
( c_in(v_X,c_Message_Oparts(c_emptyset),tc_Message_Omsg)
| ~ spl0_1874
| ~ spl0_2204 ),
inference(superposition,[],[f14166,f19441]) ).
fof(f19441,plain,
( c_emptyset = c_Message_Osynth(v_H)
| ~ spl0_2204 ),
inference(avatar_component_clause,[],[f19439]) ).
fof(f14166,plain,
( c_in(v_X,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ spl0_1874 ),
inference(avatar_component_clause,[],[f14164]) ).
fof(f25543,plain,
( spl0_2519
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2518 ),
inference(avatar_split_clause,[],[f25539,f25535,f13084,f10339,f7341,f3303,f25541]) ).
fof(f25541,plain,
( spl0_2519
<=> ! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2519])]) ).
fof(f10339,plain,
( spl0_1433
<=> ! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1433])]) ).
fof(f13084,plain,
( spl0_1866
<=> ! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1866])]) ).
fof(f25535,plain,
( spl0_2518
<=> ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2518])]) ).
fof(f25539,plain,
( ! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2518 ),
inference(forward_demodulation,[],[f25538,f14162]) ).
fof(f14162,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint) = c_IntDef_Oint(c_Suc(c_1))
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866 ),
inference(forward_demodulation,[],[f14161,f10726]) ).
fof(f10726,plain,
( c_IntDef_Oint(c_Suc(c_1)) = c_plus(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1433 ),
inference(superposition,[],[f10340,f7343]) ).
fof(f10340,plain,
( ! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1433 ),
inference(avatar_component_clause,[],[f10339]) ).
fof(f14161,plain,
( c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint) = c_plus(c_1,c_1,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1866 ),
inference(resolution,[],[f13085,f3305]) ).
fof(f13085,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1) )
| ~ spl0_1866 ),
inference(avatar_component_clause,[],[f13084]) ).
fof(f25538,plain,
( ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2518 ),
inference(forward_demodulation,[],[f25536,f14162]) ).
fof(f25536,plain,
( ! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2518 ),
inference(avatar_component_clause,[],[f25535]) ).
fof(f25537,plain,
spl0_2518,
inference(avatar_split_clause,[],[f2943,f25535]) ).
fof(f2943,plain,
! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2942,f2156]) ).
fof(f2942,plain,
! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2941,f2154]) ).
fof(f2941,plain,
! [X0] :
( c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2940,f2156]) ).
fof(f2940,plain,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2939,f2156]) ).
fof(f2939,plain,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2938,f2154]) ).
fof(f2938,plain,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2308,f2156]) ).
fof(f2308,axiom,
! [X0] :
( c_1 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(X0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oneq__one__mod__two_0) ).
fof(f25528,plain,
( spl0_2517
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2516 ),
inference(avatar_split_clause,[],[f25524,f25521,f13076,f9197,f7368,f25526]) ).
fof(f25526,plain,
( spl0_2517
<=> ! [X15] : c_div(c_Suc(c_Suc(X15)),c_Suc(c_1),tc_nat) = c_Suc(c_div(X15,c_Suc(c_1),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2517])]) ).
fof(f25521,plain,
( spl0_2516
<=> ! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2516])]) ).
fof(f25524,plain,
( ! [X15] : c_div(c_Suc(c_Suc(X15)),c_Suc(c_1),tc_nat) = c_Suc(c_div(X15,c_Suc(c_1),tc_nat))
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2516 ),
inference(forward_demodulation,[],[f25522,f14121]) ).
fof(f25522,plain,
( ! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat))
| ~ spl0_2516 ),
inference(avatar_component_clause,[],[f25521]) ).
fof(f25523,plain,
spl0_2516,
inference(avatar_split_clause,[],[f2880,f25521]) ).
fof(f2880,plain,
! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)),
inference(forward_demodulation,[],[f2879,f2156]) ).
fof(f2879,plain,
! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat)),
inference(forward_demodulation,[],[f2878,f2154]) ).
fof(f2878,plain,
! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
inference(forward_demodulation,[],[f1884,f2156]) ).
fof(f1884,axiom,
! [X15] : c_div(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Suc(c_div(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odiv2__Suc__Suc_0) ).
fof(f25519,plain,
spl0_2515,
inference(avatar_split_clause,[],[f2874,f25517]) ).
fof(f25517,plain,
( spl0_2515
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2515])]) ).
fof(f2874,plain,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
inference(forward_demodulation,[],[f1977,f2156]) ).
fof(f1977,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_Divides_Oop_Amod(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omod__Suc__eq__mod__add3_0) ).
fof(f25515,plain,
spl0_2514,
inference(avatar_split_clause,[],[f2873,f25513]) ).
fof(f25513,plain,
( spl0_2514
<=> ! [X21,X15] : c_div(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2514])]) ).
fof(f2873,plain,
! [X21,X15] : c_div(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
inference(forward_demodulation,[],[f1885,f2156]) ).
fof(f1885,axiom,
! [X21,X15] : c_div(X15,c_Suc(c_Suc(c_Suc(X21))),tc_nat) = c_div(X15,c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB1),tc_nat),X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odiv__Suc__eq__div__add3_0) ).
fof(f25511,plain,
spl0_2513,
inference(avatar_split_clause,[],[f2352,f25509]) ).
fof(f25509,plain,
( spl0_2513
<=> ! [X15,X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| ~ c_less(c_1,X18,X1)
| c_Nat_Opower(X18,X21,X1) != c_Nat_Opower(X18,X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2513])]) ).
fof(f2352,axiom,
! [X21,X1,X18,X15] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| ~ c_less(c_1,X18,X1)
| c_Nat_Opower(X18,X21,X1) != c_Nat_Opower(X18,X15,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__inject__exp_0) ).
fof(f25507,plain,
spl0_2512,
inference(avatar_split_clause,[],[f2327,f25505]) ).
fof(f25505,plain,
( spl0_2512
<=> ! [X21,X1,X0] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_uminus(c_Nat_Opower(X0,X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2512])]) ).
fof(f2327,axiom,
! [X21,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_uminus(c_Nat_Opower(X0,X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__minus__odd_0) ).
fof(f25503,plain,
spl0_2511,
inference(avatar_split_clause,[],[f2320,f25501]) ).
fof(f25501,plain,
( spl0_2511
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| c_lessequals(X0,c_0,X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2511])]) ).
fof(f2320,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X0
| c_lessequals(X0,c_0,X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__le__zero__eq__number__of_3) ).
fof(f25499,plain,
spl0_2510,
inference(avatar_split_clause,[],[f2149,f25497]) ).
fof(f25497,plain,
( spl0_2510
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2510])]) ).
fof(f2149,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__6_1) ).
fof(f25495,plain,
spl0_2509,
inference(avatar_split_clause,[],[f2148,f25493]) ).
fof(f25493,plain,
( spl0_2509
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2509])]) ).
fof(f2148,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__6_0) ).
fof(f25491,plain,
spl0_2508,
inference(avatar_split_clause,[],[f2140,f25489]) ).
fof(f25489,plain,
( spl0_2508
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2508])]) ).
fof(f2140,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__13_1) ).
fof(f25487,plain,
spl0_2507,
inference(avatar_split_clause,[],[f2139,f25485]) ).
fof(f25485,plain,
( spl0_2507
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2507])]) ).
fof(f2139,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(X0)),X1),X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_Numeral_Onumber__of(X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__13_0) ).
fof(f25483,plain,
spl0_2506,
inference(avatar_split_clause,[],[f1973,f25481]) ).
fof(f25481,plain,
( spl0_2506
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2506])]) ).
fof(f1973,axiom,
! [X2,X47,X18] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__less__iff__number__of_1) ).
fof(f25479,plain,
spl0_2505,
inference(avatar_split_clause,[],[f1972,f25477]) ).
fof(f25477,plain,
( spl0_2505
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2505])]) ).
fof(f1972,axiom,
! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_less(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__less__iff__number__of_0) ).
fof(f25475,plain,
spl0_2504,
inference(avatar_split_clause,[],[f1969,f25473]) ).
fof(f25473,plain,
( spl0_2504
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2504])]) ).
fof(f1969,axiom,
! [X2,X47,X18] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__le__iff__number__of_1) ).
fof(f25471,plain,
spl0_2503,
inference(avatar_split_clause,[],[f1968,f25469]) ).
fof(f25469,plain,
( spl0_2503
<=> ! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2503])]) ).
fof(f1968,axiom,
! [X2,X18,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_Numeral_Onumber__of(X47,X2),X2)
| c_lessequals(c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__le__iff__number__of_0) ).
fof(f25467,plain,
spl0_2502,
inference(avatar_split_clause,[],[f1962,f25465]) ).
fof(f25465,plain,
( spl0_2502
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2502])]) ).
fof(f1962,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__minus__iff__number__of_1) ).
fof(f25463,plain,
( ~ spl0_2501
| ~ spl0_1068
| spl0_2105
| ~ spl0_2204 ),
inference(avatar_split_clause,[],[f25403,f19439,f16985,f7418,f25460]) ).
fof(f25460,plain,
( spl0_2501
<=> c_Infinite__Set_Oatmost__one(c_emptyset,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2501])]) ).
fof(f16985,plain,
( spl0_2105
<=> c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2105])]) ).
fof(f25403,plain,
( ~ c_Infinite__Set_Oatmost__one(c_emptyset,tc_Message_Omsg)
| ~ spl0_1068
| spl0_2105
| ~ spl0_2204 ),
inference(forward_demodulation,[],[f25354,f7420]) ).
fof(f25354,plain,
( ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_emptyset),tc_Message_Omsg)
| spl0_2105
| ~ spl0_2204 ),
inference(superposition,[],[f16987,f19441]) ).
fof(f16987,plain,
( ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| spl0_2105 ),
inference(avatar_component_clause,[],[f16985]) ).
fof(f25458,plain,
spl0_2500,
inference(avatar_split_clause,[],[f1961,f25456]) ).
fof(f25456,plain,
( spl0_2500
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2500])]) ).
fof(f1961,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_less(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__minus__iff__number__of_0) ).
fof(f25454,plain,
spl0_2499,
inference(avatar_split_clause,[],[f1946,f25452]) ).
fof(f25452,plain,
( spl0_2499
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2499])]) ).
fof(f1946,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2)
| c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__minus__iff__number__of_1) ).
fof(f25450,plain,
spl0_2498,
inference(avatar_split_clause,[],[f1945,f25448]) ).
fof(f25448,plain,
( spl0_2498
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2498])]) ).
fof(f1945,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ c_lessequals(c_Numeral_Onumber__of(X47,X2),c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_Numeral_Onumber__of(X47,X2),X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__minus__iff__number__of_0) ).
fof(f25446,plain,
spl0_2497,
inference(avatar_split_clause,[],[f1876,f25444]) ).
fof(f25444,plain,
( spl0_2497
<=> ! [X11,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2497])]) ).
fof(f1876,axiom,
! [X11,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Nat_Opower(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X11,tc_nat),tc_nat) = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Opower__nat__number__of__number__of_0) ).
fof(f25442,plain,
spl0_2496,
inference(avatar_split_clause,[],[f1777,f25440]) ).
fof(f25440,plain,
( spl0_2496
<=> ! [X21,X43,X15] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Otake(X15,c_List_Oupt(X43,X21),tc_nat) = c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2496])]) ).
fof(f1777,axiom,
! [X21,X15,X43] :
( ~ c_lessequals(c_plus(X43,X15,tc_nat),X21,tc_nat)
| c_List_Otake(X15,c_List_Oupt(X43,X21),tc_nat) = c_List_Oupt(X43,c_plus(X43,X15,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__upt_0) ).
fof(f25438,plain,
spl0_2495,
inference(avatar_split_clause,[],[f1755,f25436]) ).
fof(f25436,plain,
( spl0_2495
<=> ! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Oset(c_List_Oremove1(X0,X23,X1),X1) = c_minus(c_List_Oset(X23,X1),c_insert(X0,c_emptyset,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2495])]) ).
fof(f1755,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Oset(c_List_Oremove1(X0,X23,X1),X1) = c_minus(c_List_Oset(X23,X1),c_insert(X0,c_emptyset,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__remove1__eq_0) ).
fof(f25434,plain,
spl0_2494,
inference(avatar_split_clause,[],[f1280,f25432]) ).
fof(f25432,plain,
( spl0_2494
<=> ! [X12,X0,X1] :
( c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Suc(c_Finite__Set_Ocard(X12,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2494])]) ).
fof(f1280,axiom,
! [X0,X1,X12] :
( c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_Finite__Set_Ocard(c_insert(X0,X12,X1),X1) = c_Suc(c_Finite__Set_Ocard(X12,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ocard__insert__disjoint_0) ).
fof(f25430,plain,
spl0_2493,
inference(avatar_split_clause,[],[f1274,f25428]) ).
fof(f25428,plain,
( spl0_2493
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMin(X12,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2493])]) ).
fof(f1274,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(c_Finite__Set_OMin(X12,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__le_0) ).
fof(f25426,plain,
spl0_2492,
inference(avatar_split_clause,[],[f1256,f25424]) ).
fof(f25424,plain,
( spl0_2492
<=> ! [X12,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMax(X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2492])]) ).
fof(f1256,axiom,
! [X0,X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X0,X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_lessequals(X0,c_Finite__Set_OMax(X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__ge_0) ).
fof(f25422,plain,
spl0_2491,
inference(avatar_split_clause,[],[f1205,f25420]) ).
fof(f25420,plain,
( spl0_2491
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2491])]) ).
fof(f1205,axiom,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn1(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__In1_0) ).
fof(f25344,plain,
spl0_2490,
inference(avatar_split_clause,[],[f1204,f25342]) ).
fof(f25342,plain,
( spl0_2490
<=> ! [X9,X16,X2,X1] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2490])]) ).
fof(f1204,axiom,
! [X2,X1,X9,X16] : c_Datatype__Universe_Ontrunc(c_Suc(c_Suc(X16)),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) = c_Datatype__Universe_OIn0(c_Datatype__Universe_Ontrunc(c_Suc(X16),X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__In0_0) ).
fof(f25340,plain,
spl0_2489,
inference(avatar_split_clause,[],[f33,f25338]) ).
fof(f25338,plain,
( spl0_2489
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2489])]) ).
fof(f33,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| ~ c_in(c_Main_Ofinite__Union__1(X12,X1),c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Union_1) ).
fof(f25336,plain,
spl0_2488,
inference(avatar_split_clause,[],[f32,f25334]) ).
fof(f25334,plain,
( spl0_2488
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2488])]) ).
fof(f32,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(tc_set(X1)))
| c_in(c_Main_Ofinite__Union__1(X12,X1),X12,tc_set(X1))
| c_in(c_Union(X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Union_0) ).
fof(f25217,plain,
( spl0_2204
| spl0_2487
| ~ spl0_1499
| ~ spl0_2236 ),
inference(avatar_split_clause,[],[f20181,f20046,f10607,f25214,f19439]) ).
fof(f25214,plain,
( spl0_2487
<=> c_in(c_Main_Oall__not__in__conv__1(c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2487])]) ).
fof(f10607,plain,
( spl0_1499
<=> ! [X12,X1] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1499])]) ).
fof(f20046,plain,
( spl0_2236
<=> ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Osynth(v_H),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2236])]) ).
fof(f20181,plain,
( c_in(c_Main_Oall__not__in__conv__1(c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| c_emptyset = c_Message_Osynth(v_H)
| ~ spl0_1499
| ~ spl0_2236 ),
inference(resolution,[],[f20047,f10608]) ).
fof(f10608,plain,
( ! [X1,X12] :
( c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1)
| c_emptyset = X12 )
| ~ spl0_1499 ),
inference(avatar_component_clause,[],[f10607]) ).
fof(f20047,plain,
( ! [X0] :
( ~ c_in(X0,c_Message_Osynth(v_H),tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg) )
| ~ spl0_2236 ),
inference(avatar_component_clause,[],[f20046]) ).
fof(f25020,plain,
( spl0_2486
| ~ spl0_1225
| ~ spl0_2215
| ~ spl0_2270 ),
inference(avatar_split_clause,[],[f21404,f20190,f19942,f9275,f25017]) ).
fof(f25017,plain,
( spl0_2486
<=> c_UNIV = c_union(c_uminus(c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2486])]) ).
fof(f19942,plain,
( spl0_2215
<=> c_emptyset = c_minus(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2215])]) ).
fof(f21404,plain,
( c_UNIV = c_union(c_uminus(c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1225
| ~ spl0_2215
| ~ spl0_2270 ),
inference(forward_demodulation,[],[f21363,f9276]) ).
fof(f21363,plain,
( c_uminus(c_emptyset,tc_set(tc_Message_Omsg)) = c_union(c_uminus(c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg)),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_2215
| ~ spl0_2270 ),
inference(superposition,[],[f20191,f19944]) ).
fof(f19944,plain,
( c_emptyset = c_minus(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_2215 ),
inference(avatar_component_clause,[],[f19942]) ).
fof(f24659,plain,
( spl0_2485
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2428 ),
inference(avatar_split_clause,[],[f24287,f24284,f14323,f9129,f7368,f24657]) ).
fof(f24657,plain,
( spl0_2485
<=> ! [X3,X23,X25,X1] :
( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
| c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2485])]) ).
fof(f9129,plain,
( spl0_1189
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1189])]) ).
fof(f24284,plain,
( spl0_2428
<=> ! [X3,X23,X25,X1] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2428])]) ).
fof(f24287,plain,
( ! [X3,X1,X25,X23] :
( c_append(c_List_Orev(X25,X1),c_List_Oreplicate(c_1,X3,X1),X1) = X23
| c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1) )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2428 ),
inference(forward_demodulation,[],[f24285,f15117]) ).
fof(f15117,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_1,X0,X1)
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907 ),
inference(forward_demodulation,[],[f15098,f7370]) ).
fof(f15098,plain,
( ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Oreplicate(c_Suc(c_0),X0,X1)
| ~ spl0_1189
| ~ spl0_1907 ),
inference(superposition,[],[f14324,f9130]) ).
fof(f9130,plain,
( ! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41)
| ~ spl0_1189 ),
inference(avatar_component_clause,[],[f9129]) ).
fof(f24285,plain,
( ! [X3,X1,X25,X23] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 )
| ~ spl0_2428 ),
inference(avatar_component_clause,[],[f24284]) ).
fof(f24626,plain,
( spl0_2484
| ~ spl0_2462
| ~ spl0_1818
| ~ spl0_2184 ),
inference(avatar_split_clause,[],[f18576,f18514,f12878,f24425,f24623]) ).
fof(f24623,plain,
( spl0_2484
<=> c_emptyset = c_SetInterval_OatLeastLessThan(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2484])]) ).
fof(f18514,plain,
( spl0_2184
<=> c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2184])]) ).
fof(f18576,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_emptyset = c_SetInterval_OatLeastLessThan(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| ~ spl0_1818
| ~ spl0_2184 ),
inference(resolution,[],[f18516,f12879]) ).
fof(f18516,plain,
( c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_2184 ),
inference(avatar_component_clause,[],[f18514]) ).
fof(f24621,plain,
( spl0_2483
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_2425 ),
inference(avatar_split_clause,[],[f24274,f24271,f10503,f3303,f24619]) ).
fof(f24619,plain,
( spl0_2483
<=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2483])]) ).
fof(f24271,plain,
( spl0_2425
<=> ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2425])]) ).
fof(f24274,plain,
( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_uminus(c_1,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_uminus(c_1,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_2425 ),
inference(forward_demodulation,[],[f24272,f10850]) ).
fof(f24272,plain,
( ! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint)
| ~ spl0_2425 ),
inference(avatar_component_clause,[],[f24271]) ).
fof(f24560,plain,
( spl0_2482
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2481 ),
inference(avatar_split_clause,[],[f24556,f24552,f11543,f9209,f24558]) ).
fof(f24558,plain,
( spl0_2482
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2482])]) ).
fof(f9209,plain,
( spl0_1209
<=> ! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1209])]) ).
fof(f11543,plain,
( spl0_1619
<=> c_Numeral_OMin = c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1619])]) ).
fof(f24552,plain,
( spl0_2481
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2481])]) ).
fof(f24556,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2481 ),
inference(forward_demodulation,[],[f24555,f9210]) ).
fof(f9210,plain,
( ! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin)
| ~ spl0_1209 ),
inference(avatar_component_clause,[],[f9209]) ).
fof(f24555,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1619
| ~ spl0_2481 ),
inference(forward_demodulation,[],[f24553,f11545]) ).
fof(f11545,plain,
( c_Numeral_OMin = c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1619 ),
inference(avatar_component_clause,[],[f11543]) ).
fof(f24553,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_2481 ),
inference(avatar_component_clause,[],[f24552]) ).
fof(f24554,plain,
spl0_2481,
inference(avatar_split_clause,[],[f3002,f24552]) ).
fof(f3002,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f1319,f2156]) ).
fof(f1319,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__13_1) ).
fof(f24550,plain,
spl0_2480,
inference(avatar_split_clause,[],[f3000,f24548]) ).
fof(f24548,plain,
( spl0_2480
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2480])]) ).
fof(f3000,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1315,f2156]) ).
fof(f1315,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__11_1) ).
fof(f24546,plain,
spl0_2479,
inference(avatar_split_clause,[],[f2998,f24544]) ).
fof(f24544,plain,
( spl0_2479
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2479])]) ).
fof(f2998,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f1327,f2156]) ).
fof(f1327,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__17_1) ).
fof(f24520,plain,
( spl0_2478
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2477 ),
inference(avatar_split_clause,[],[f24516,f24512,f11543,f9209,f24518]) ).
fof(f24518,plain,
( spl0_2478
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2478])]) ).
fof(f24512,plain,
( spl0_2477
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2477])]) ).
fof(f24516,plain,
( ! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2477 ),
inference(forward_demodulation,[],[f24515,f9210]) ).
fof(f24515,plain,
( ! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1619
| ~ spl0_2477 ),
inference(forward_demodulation,[],[f24513,f11545]) ).
fof(f24513,plain,
( ! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_2477 ),
inference(avatar_component_clause,[],[f24512]) ).
fof(f24514,plain,
spl0_2477,
inference(avatar_split_clause,[],[f2995,f24512]) ).
fof(f2995,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1323,f2156]) ).
fof(f1323,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__15_1) ).
fof(f24503,plain,
( spl0_2476
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2475 ),
inference(avatar_split_clause,[],[f24499,f24495,f11543,f9209,f24501]) ).
fof(f24501,plain,
( spl0_2476
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2476])]) ).
fof(f24495,plain,
( spl0_2475
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2475])]) ).
fof(f24499,plain,
( ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2475 ),
inference(forward_demodulation,[],[f24498,f9210]) ).
fof(f24498,plain,
( ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_1619
| ~ spl0_2475 ),
inference(forward_demodulation,[],[f24496,f11545]) ).
fof(f24496,plain,
( ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) )
| ~ spl0_2475 ),
inference(avatar_component_clause,[],[f24495]) ).
fof(f24497,plain,
spl0_2475,
inference(avatar_split_clause,[],[f2992,f24495]) ).
fof(f2992,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f1318,f2156]) ).
fof(f1318,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__13_0) ).
fof(f24493,plain,
spl0_2474,
inference(avatar_split_clause,[],[f2990,f24491]) ).
fof(f24491,plain,
( spl0_2474
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2474])]) ).
fof(f2990,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1314,f2156]) ).
fof(f1314,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__11_0) ).
fof(f24489,plain,
spl0_2473,
inference(avatar_split_clause,[],[f2988,f24487]) ).
fof(f24487,plain,
( spl0_2473
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2473])]) ).
fof(f2988,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X0)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1) ),
inference(forward_demodulation,[],[f1326,f2156]) ).
fof(f1326,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_1,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__17_0) ).
fof(f24480,plain,
( spl0_2472
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2471 ),
inference(avatar_split_clause,[],[f24474,f24470,f11543,f9209,f24478]) ).
fof(f24478,plain,
( spl0_2472
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2472])]) ).
fof(f24470,plain,
( spl0_2471
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2471])]) ).
fof(f24474,plain,
( ! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2471 ),
inference(forward_demodulation,[],[f24473,f9210]) ).
fof(f24473,plain,
( ! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_1619
| ~ spl0_2471 ),
inference(forward_demodulation,[],[f24471,f11545]) ).
fof(f24471,plain,
( ! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) )
| ~ spl0_2471 ),
inference(avatar_component_clause,[],[f24470]) ).
fof(f24476,plain,
( ~ spl0_124
| spl0_2462 ),
inference(avatar_contradiction_clause,[],[f24475]) ).
fof(f24475,plain,
( $false
| ~ spl0_124
| spl0_2462 ),
inference(resolution,[],[f24427,f3626]) ).
fof(f3626,plain,
( ! [X37] : class_Orderings_Oorder(tc_set(X37))
| ~ spl0_124 ),
inference(avatar_component_clause,[],[f3625]) ).
fof(f3625,plain,
( spl0_124
<=> ! [X37] : class_Orderings_Oorder(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_124])]) ).
fof(f24427,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| spl0_2462 ),
inference(avatar_component_clause,[],[f24425]) ).
fof(f24472,plain,
spl0_2471,
inference(avatar_split_clause,[],[f2985,f24470]) ).
fof(f2985,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1322,f2156]) ).
fof(f1322,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_1,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__15_0) ).
fof(f24468,plain,
spl0_2470,
inference(avatar_split_clause,[],[f2916,f24466]) ).
fof(f24466,plain,
( spl0_2470
<=> ! [X83] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2470])]) ).
fof(f2916,plain,
! [X83] :
( c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1872,f2016]) ).
fof(f2016,axiom,
c_Suc(c_0) = c_1,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OOne__nat__def_0) ).
fof(f1872,axiom,
! [X83] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oone__mod__nat__number__of_1) ).
fof(f24457,plain,
( spl0_2469
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2468 ),
inference(avatar_split_clause,[],[f24453,f24450,f13076,f9197,f7368,f24455]) ).
fof(f24455,plain,
( spl0_2469
<=> ! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Suc(c_1),tc_nat) = c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2469])]) ).
fof(f24450,plain,
( spl0_2468
<=> ! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2468])]) ).
fof(f24453,plain,
( ! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Suc(c_1),tc_nat) = c_Divides_Oop_Amod(X15,c_Suc(c_1),tc_nat)
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2468 ),
inference(forward_demodulation,[],[f24451,f14121]) ).
fof(f24451,plain,
( ! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat)
| ~ spl0_2468 ),
inference(avatar_component_clause,[],[f24450]) ).
fof(f24452,plain,
spl0_2468,
inference(avatar_split_clause,[],[f2877,f24450]) ).
fof(f2877,plain,
! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2876,f2156]) ).
fof(f2876,plain,
! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2875,f2154]) ).
fof(f2875,plain,
! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),
inference(forward_demodulation,[],[f1974,f2156]) ).
fof(f1974,axiom,
! [X15] : c_Divides_Oop_Amod(c_Suc(c_Suc(X15)),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = c_Divides_Oop_Amod(X15,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Omod2__Suc__Suc_0) ).
fof(f24448,plain,
spl0_2467,
inference(avatar_split_clause,[],[f2795,f24446]) ).
fof(f24446,plain,
( spl0_2467
<=> ! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2467])]) ).
fof(f2795,axiom,
! [X91,X88] :
( c_in(X91,c_Message_OkeysFor(c_Message_Oanalz(X88)),tc_nat)
| c_Message_Oanalz(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__insert__Key_0) ).
fof(f24444,plain,
spl0_2466,
inference(avatar_split_clause,[],[f2786,f24442]) ).
fof(f24442,plain,
( spl0_2466
<=> ! [X86,X91,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2466])]) ).
fof(f2786,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(c_Message_OinvKey(X91)),c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz_ODecrypt__dest_0) ).
fof(f24440,plain,
spl0_2465,
inference(avatar_split_clause,[],[f2682,f24438]) ).
fof(f24438,plain,
( spl0_2465
<=> ! [X18,X13,X12,X1] :
( c_in(X18,X13,X1)
| c_emptyset != c_inter(X12,X13,X1)
| c_emptyset = c_inter(c_insert(X18,X12,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2465])]) ).
fof(f2682,axiom,
! [X18,X1,X12,X13] :
( c_in(X18,X13,X1)
| c_emptyset != c_inter(X12,X13,X1)
| c_emptyset = c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__disjoint__2_2) ).
fof(f24436,plain,
spl0_2464,
inference(avatar_split_clause,[],[f2663,f24434]) ).
fof(f24434,plain,
( spl0_2464
<=> ! [X18,X13,X12,X1] :
( c_in(X18,X13,X1)
| c_emptyset != c_inter(X13,X12,X1)
| c_emptyset = c_inter(X13,c_insert(X18,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2464])]) ).
fof(f2663,axiom,
! [X18,X1,X12,X13] :
( c_in(X18,X13,X1)
| c_emptyset != c_inter(X13,X12,X1)
| c_emptyset = c_inter(X13,c_insert(X18,X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Odisjoint__insert__1_2) ).
fof(f24432,plain,
spl0_2463,
inference(avatar_split_clause,[],[f2483,f24430]) ).
fof(f24430,plain,
( spl0_2463
<=> ! [X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_1,X27,X1) = c_divide(X4,c_times(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2463])]) ).
fof(f2483,axiom,
! [X1,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_1,X27,X1) = c_divide(X4,c_times(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__right__if1_1) ).
fof(f24428,plain,
( spl0_2461
| ~ spl0_2462
| ~ spl0_1829
| ~ spl0_2184 ),
inference(avatar_split_clause,[],[f18575,f18514,f12928,f24425,f24421]) ).
fof(f24421,plain,
( spl0_2461
<=> c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2461])]) ).
fof(f18575,plain,
( ~ class_Orderings_Oorder(tc_set(tc_Message_Omsg))
| c_emptyset = c_SetInterval_OgreaterThanAtMost(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| ~ spl0_1829
| ~ spl0_2184 ),
inference(resolution,[],[f18516,f12929]) ).
fof(f24419,plain,
spl0_2460,
inference(avatar_split_clause,[],[f2477,f24417]) ).
fof(f24417,plain,
( spl0_2460
<=> ! [X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_1,X27,X1) = c_divide(X4,c_times(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2460])]) ).
fof(f2477,axiom,
! [X1,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_1,X27,X1) = c_divide(X4,c_times(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__left__if1_1) ).
fof(f24415,plain,
spl0_2459,
inference(avatar_split_clause,[],[f2465,f24413]) ).
fof(f24413,plain,
( spl0_2459
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,X27,X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2459])]) ).
fof(f2465,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,X27,X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oless__divide__eq__1__pos_1) ).
fof(f24411,plain,
spl0_2458,
inference(avatar_split_clause,[],[f2464,f24409]) ).
fof(f24409,plain,
( spl0_2458
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_less(X18,X27,X1)
| ~ c_less(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2458])]) ).
fof(f2464,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_less(X18,X27,X1)
| ~ c_less(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oless__divide__eq__1__pos_0) ).
fof(f24407,plain,
spl0_2457,
inference(avatar_split_clause,[],[f2463,f24405]) ).
fof(f24405,plain,
( spl0_2457
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2457])]) ).
fof(f2463,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oless__divide__eq__1__neg_1) ).
fof(f24403,plain,
spl0_2456,
inference(avatar_split_clause,[],[f2462,f24401]) ).
fof(f24401,plain,
( spl0_2456
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2456])]) ).
fof(f2462,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oless__divide__eq__1__neg_0) ).
fof(f24399,plain,
spl0_2455,
inference(avatar_split_clause,[],[f2461,f24397]) ).
fof(f24397,plain,
( spl0_2455
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2455])]) ).
fof(f2461,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ole__divide__eq__1__pos_1) ).
fof(f24395,plain,
spl0_2454,
inference(avatar_split_clause,[],[f2460,f24393]) ).
fof(f24393,plain,
( spl0_2454
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2454])]) ).
fof(f2460,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ole__divide__eq__1__pos_0) ).
fof(f24391,plain,
spl0_2453,
inference(avatar_split_clause,[],[f2459,f24389]) ).
fof(f24389,plain,
( spl0_2453
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2453])]) ).
fof(f2459,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ole__divide__eq__1__neg_1) ).
fof(f24387,plain,
spl0_2452,
inference(avatar_split_clause,[],[f2458,f24385]) ).
fof(f24385,plain,
( spl0_2452
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_1,c_divide(X27,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2452])]) ).
fof(f2458,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_1,c_divide(X27,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ole__divide__eq__1__neg_0) ).
fof(f24383,plain,
spl0_2451,
inference(avatar_split_clause,[],[f2447,f24381]) ).
fof(f24381,plain,
( spl0_2451
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse(c_times(X18,X27,X1),X1) = c_times(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2451])]) ).
fof(f2447,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse(c_times(X18,X27,X1),X1) = c_times(c_HOL_Oinverse(X18,X1),c_HOL_Oinverse(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__mult__distrib_0) ).
fof(f24376,plain,
spl0_2450,
inference(avatar_split_clause,[],[f2421,f24374]) ).
fof(f24374,plain,
( spl0_2450
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2450])]) ).
fof(f2421,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,X18,X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__less__eq__1__pos_1) ).
fof(f24372,plain,
spl0_2449,
inference(avatar_split_clause,[],[f2420,f24370]) ).
fof(f24370,plain,
( spl0_2449
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2449])]) ).
fof(f2420,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_less(X27,X18,X1)
| ~ c_less(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__less__eq__1__pos_0) ).
fof(f24368,plain,
spl0_2448,
inference(avatar_split_clause,[],[f2419,f24366]) ).
fof(f24366,plain,
( spl0_2448
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,X27,X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2448])]) ).
fof(f2419,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,X27,X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__less__eq__1__neg_1) ).
fof(f24364,plain,
spl0_2447,
inference(avatar_split_clause,[],[f2418,f24362]) ).
fof(f24362,plain,
( spl0_2447
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_less(X18,X27,X1)
| ~ c_less(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2447])]) ).
fof(f2418,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_less(X18,X27,X1)
| ~ c_less(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__less__eq__1__neg_0) ).
fof(f24360,plain,
spl0_2446,
inference(avatar_split_clause,[],[f2415,f24358]) ).
fof(f24358,plain,
( spl0_2446
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2446])]) ).
fof(f2415,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| ~ c_lessequals(X27,X18,X1)
| c_lessequals(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__le__eq__1__pos_1) ).
fof(f24356,plain,
spl0_2445,
inference(avatar_split_clause,[],[f2414,f24354]) ).
fof(f24354,plain,
( spl0_2445
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2445])]) ).
fof(f2414,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_lessequals(X27,X18,X1)
| ~ c_lessequals(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__le__eq__1__pos_0) ).
fof(f24352,plain,
spl0_2444,
inference(avatar_split_clause,[],[f2413,f24350]) ).
fof(f24350,plain,
( spl0_2444
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2444])]) ).
fof(f2413,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__le__eq__1__neg_1) ).
fof(f24348,plain,
spl0_2443,
inference(avatar_split_clause,[],[f2412,f24346]) ).
fof(f24346,plain,
( spl0_2443
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_divide(X27,X18,X1),c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2443])]) ).
fof(f2412,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_divide(X27,X18,X1),c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__le__eq__1__neg_0) ).
fof(f24344,plain,
spl0_2442,
inference(avatar_split_clause,[],[f2402,f24342]) ).
fof(f24342,plain,
( spl0_2442
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X18,c_divide(X27,X4,X1),X1) = c_divide(c_times(X18,X4,X1),X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2442])]) ).
fof(f2402,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X18,c_divide(X27,X4,X1),X1) = c_divide(c_times(X18,X4,X1),X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__divide__eq__right_0) ).
fof(f24340,plain,
spl0_2441,
inference(avatar_split_clause,[],[f2401,f24338]) ).
fof(f24338,plain,
( spl0_2441
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(c_divide(X18,X27,X1),X4,X1) = c_divide(X18,c_times(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2441])]) ).
fof(f2401,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(c_divide(X18,X27,X1),X4,X1) = c_divide(X18,c_times(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__divide__eq__left_0) ).
fof(f24336,plain,
spl0_2440,
inference(avatar_split_clause,[],[f2399,f24334]) ).
fof(f24334,plain,
( spl0_2440
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_divide(X18,X4,X1) != c_divide(X27,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2440])]) ).
fof(f2399,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_divide(X18,X4,X1) != c_divide(X27,X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__cancel__right_0) ).
fof(f24332,plain,
spl0_2439,
inference(avatar_split_clause,[],[f2397,f24330]) ).
fof(f24330,plain,
( spl0_2439
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_divide(X4,X18,X1) != c_divide(X4,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2439])]) ).
fof(f2397,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_divide(X4,X18,X1) != c_divide(X4,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__cancel__left_0) ).
fof(f24328,plain,
spl0_2438,
inference(avatar_split_clause,[],[f2392,f24326]) ).
fof(f24326,plain,
( spl0_2438
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oabs(c_divide(X18,X27,X1),X1) = c_divide(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2438])]) ).
fof(f2392,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oabs(c_divide(X18,X27,X1),X1) = c_divide(c_HOL_Oabs(X18,X1),c_HOL_Oabs(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oabs__divide_0) ).
fof(f24324,plain,
spl0_2437,
inference(avatar_split_clause,[],[f2122,f24322]) ).
fof(f24322,plain,
( spl0_2437
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2437])]) ).
fof(f2122,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_Numeral_Onumber__of(X0,X1) = c_HOL_Oabs(c_Numeral_Onumber__of(X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__6_1) ).
fof(f24320,plain,
spl0_2436,
inference(avatar_split_clause,[],[f1963,f24318]) ).
fof(f24318,plain,
( spl0_2436
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) = c_uminus(c_divide(c_1,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2436])]) ).
fof(f1963,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_divide(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) = c_uminus(c_divide(c_1,X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus1__divide_0) ).
fof(f24316,plain,
spl0_2435,
inference(avatar_split_clause,[],[f1926,f24314]) ).
fof(f24314,plain,
( spl0_2435
<=> ! [X2,X11] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Numeral_Onumber(X2)
| c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(X11,X2),X2),c_Numeral_Onumber__of(X11,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2435])]) ).
fof(f1926,axiom,
! [X2,X11] :
( ~ class_Ring__and__Field_Odivision__by__zero(X2)
| ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Numeral_Onumber(X2)
| c_0 = c_divide(c_times(c_0,c_Numeral_Onumber__of(X11,X2),X2),c_Numeral_Onumber__of(X11,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oeq__divide__eq__number__of_4) ).
fof(f24312,plain,
spl0_2434,
inference(avatar_split_clause,[],[f1864,f24310]) ).
fof(f24310,plain,
( spl0_2434
<=> ! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2434])]) ).
fof(f1864,axiom,
! [X83,X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X83),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Omult__nat__number__of_1) ).
fof(f24308,plain,
spl0_2433,
inference(avatar_split_clause,[],[f1858,f24306]) ).
fof(f24306,plain,
( spl0_2433
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2433])]) ).
fof(f1858,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__nat__number__of_3) ).
fof(f24304,plain,
spl0_2432,
inference(avatar_split_clause,[],[f1855,f24302]) ).
fof(f24302,plain,
( spl0_2432
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2432])]) ).
fof(f1855,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X83),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_less(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__nat__number__of_0) ).
fof(f24300,plain,
spl0_2431,
inference(avatar_split_clause,[],[f1800,f24298]) ).
fof(f24298,plain,
( spl0_2431
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2431])]) ).
fof(f1800,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_minus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X16,tc_nat),X59,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Odiff__diff__right_0) ).
fof(f24296,plain,
( spl0_1722
| ~ spl0_2302
| ~ spl0_2345 ),
inference(avatar_split_clause,[],[f24214,f21875,f21696,f12481]) ).
fof(f21875,plain,
( spl0_2345
<=> c_Message_Osynth(v_H) = c_Message_Oparts(c_UNIV) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2345])]) ).
fof(f24214,plain,
( c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_2302
| ~ spl0_2345 ),
inference(superposition,[],[f21698,f21877]) ).
fof(f21877,plain,
( c_Message_Osynth(v_H) = c_Message_Oparts(c_UNIV)
| ~ spl0_2345 ),
inference(avatar_component_clause,[],[f21875]) ).
fof(f24295,plain,
spl0_2430,
inference(avatar_split_clause,[],[f1796,f24293]) ).
fof(f24293,plain,
( spl0_2430
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2430])]) ).
fof(f1796,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(X43,c_minus(X59,X16,tc_nat),tc_nat) = c_minus(c_plus(X43,X59,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oadd__diff__assoc_0) ).
fof(f24291,plain,
spl0_2429,
inference(avatar_split_clause,[],[f1795,f24289]) ).
fof(f24289,plain,
( spl0_2429
<=> ! [X16,X59,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2429])]) ).
fof(f1795,axiom,
! [X59,X16,X43] :
( ~ c_lessequals(X16,X59,tc_nat)
| c_plus(c_minus(X59,X16,tc_nat),X43,tc_nat) = c_minus(c_plus(X59,X43,tc_nat),X16,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oadd__diff__assoc2_0) ).
fof(f24286,plain,
spl0_2428,
inference(avatar_split_clause,[],[f1726,f24284]) ).
fof(f1726,axiom,
! [X3,X1,X25,X23] :
( c_List_Olist_OCons(X3,X25,X1) != c_List_Orev(X23,X1)
| c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) = X23 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__eq__Cons__iff_0) ).
fof(f24282,plain,
spl0_2427,
inference(avatar_split_clause,[],[f1714,f24280]) ).
fof(f24280,plain,
( spl0_2427
<=> ! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2427])]) ).
fof(f1714,axiom,
! [X41,X0,X23] :
( c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Oremdups(X23,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremdups_Osimps__2_1) ).
fof(f24278,plain,
spl0_2426,
inference(avatar_split_clause,[],[f1617,f24276]) ).
fof(f24276,plain,
( spl0_2426
<=> ! [X61,X5,X1,X24] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2426])]) ).
fof(f1617,axiom,
! [X1,X24,X5,X61] : c_in(c_Pair(c_List_Olist_ONil,c_List_Olist_OCons(X24,X61,X1),tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__Nil__left_1) ).
fof(f24273,plain,
spl0_2425,
inference(avatar_split_clause,[],[f1453,f24271]) ).
fof(f1453,axiom,
! [X27] : c_IntDiv_OnegDivAlg(c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),c_minus(X27,c_1,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OnegDivAlg__minus1_0) ).
fof(f24269,plain,
spl0_2424,
inference(avatar_split_clause,[],[f1219,f24267]) ).
fof(f24267,plain,
( spl0_2424
<=> ! [X4,X27,X18] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2424])]) ).
fof(f1219,axiom,
! [X18,X27,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(X18,X27,tc_nat) = c_div(c_times(X18,X4,tc_nat),c_times(X27,X4,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__mult__mult2_0) ).
fof(f24265,plain,
spl0_2423,
inference(avatar_split_clause,[],[f1218,f24263]) ).
fof(f24263,plain,
( spl0_2423
<=> ! [X4,X27,X18] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2423])]) ).
fof(f1218,axiom,
! [X18,X27,X4] :
( ~ c_less(c_0,X4,tc_nat)
| c_div(c_times(X4,X18,tc_nat),c_times(X4,X27,tc_nat),tc_nat) = c_div(X18,X27,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__mult__mult1_0) ).
fof(f24261,plain,
spl0_2422,
inference(avatar_split_clause,[],[f57,f24259]) ).
fof(f24259,plain,
( spl0_2422
<=> ! [X5,X1,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2422])]) ).
fof(f57,axiom,
! [X1,X5,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Nil2_0) ).
fof(f24257,plain,
spl0_2421,
inference(avatar_split_clause,[],[f56,f24255]) ).
fof(f24255,plain,
( spl0_2421
<=> ! [X5,X1,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2421])]) ).
fof(f56,axiom,
! [X1,X5,X23] :
( c_List_Olist_ONil = X23
| ~ c_in(c_Pair(c_List_Olist_ONil,X23,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olistrel(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Nil1_0) ).
fof(f23935,plain,
( spl0_2420
| spl0_2345
| ~ spl0_1880
| ~ spl0_2184 ),
inference(avatar_split_clause,[],[f18573,f18514,f14198,f21875,f23932]) ).
fof(f18573,plain,
( c_Message_Osynth(v_H) = c_Message_Oparts(c_UNIV)
| c_less(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_1880
| ~ spl0_2184 ),
inference(resolution,[],[f18516,f14199]) ).
fof(f23464,plain,
( spl0_2419
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2390 ),
inference(avatar_split_clause,[],[f22906,f22903,f14323,f9129,f7368,f23462]) ).
fof(f23462,plain,
( spl0_2419
<=> ! [X59,X43] :
( c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
| ~ c_lessequals(X43,X59,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2419])]) ).
fof(f22903,plain,
( spl0_2390
<=> ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2390])]) ).
fof(f22906,plain,
( ! [X59,X43] :
( c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Oreplicate(c_1,X59,tc_nat),tc_nat)
| ~ c_lessequals(X43,X59,tc_nat) )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2390 ),
inference(forward_demodulation,[],[f22904,f15117]) ).
fof(f22904,plain,
( ! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) )
| ~ spl0_2390 ),
inference(avatar_component_clause,[],[f22903]) ).
fof(f23430,plain,
( spl0_2345
| ~ spl0_2418
| ~ spl0_1882
| ~ spl0_2184 ),
inference(avatar_split_clause,[],[f18571,f18514,f14206,f23427,f21875]) ).
fof(f23427,plain,
( spl0_2418
<=> c_lessequals(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2418])]) ).
fof(f18571,plain,
( ~ c_lessequals(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_set(tc_Message_Omsg))
| c_Message_Osynth(v_H) = c_Message_Oparts(c_UNIV)
| ~ spl0_1882
| ~ spl0_2184 ),
inference(resolution,[],[f18516,f14207]) ).
fof(f23197,plain,
( spl0_2417
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2383 ),
inference(avatar_split_clause,[],[f22877,f22873,f14323,f9129,f7368,f23195]) ).
fof(f23195,plain,
( spl0_2417
<=> ! [X3,X0,X23,X25,X1] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X0 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2417])]) ).
fof(f22873,plain,
( spl0_2383
<=> ! [X23,X0,X3,X25,X1] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2383])]) ).
fof(f22877,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X0 = X3 )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2383 ),
inference(forward_demodulation,[],[f22876,f15117]) ).
fof(f22876,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
| X0 = X3 )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2383 ),
inference(forward_demodulation,[],[f22874,f15117]) ).
fof(f22874,plain,
( ! [X3,X0,X1,X25,X23] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
| ~ spl0_2383 ),
inference(avatar_component_clause,[],[f22873]) ).
fof(f23193,plain,
( spl0_2416
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2382 ),
inference(avatar_split_clause,[],[f22871,f22867,f14323,f9129,f7368,f23191]) ).
fof(f23191,plain,
( spl0_2416
<=> ! [X3,X0,X23,X25,X1] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X23 = X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2416])]) ).
fof(f22867,plain,
( spl0_2382
<=> ! [X3,X0,X23,X25,X1] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2382])]) ).
fof(f22871,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1) != c_append(X23,c_List_Oreplicate(c_1,X0,X1),X1)
| X23 = X25 )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2382 ),
inference(forward_demodulation,[],[f22870,f15117]) ).
fof(f22870,plain,
( ! [X3,X0,X1,X25,X23] :
( c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Oreplicate(c_1,X3,X1),X1)
| X23 = X25 )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2382 ),
inference(forward_demodulation,[],[f22868,f15117]) ).
fof(f22868,plain,
( ! [X3,X0,X1,X25,X23] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) )
| ~ spl0_2382 ),
inference(avatar_component_clause,[],[f22867]) ).
fof(f23006,plain,
spl0_2415,
inference(avatar_split_clause,[],[f2807,f23004]) ).
fof(f23004,plain,
( spl0_2415
<=> ! [X86,X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2415])]) ).
fof(f2807,axiom,
! [X91,X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__Crypt_0) ).
fof(f23002,plain,
spl0_2414,
inference(avatar_split_clause,[],[f2802,f23000]) ).
fof(f23000,plain,
( spl0_2414
<=> ! [X20,X88,X4] :
( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
| c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2414])]) ).
fof(f2802,axiom,
! [X88,X4,X20] :
( c_in(X4,c_Message_Oparts(X20),tc_Message_Omsg)
| c_in(X4,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(X4,c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oin__parts__UnE_0) ).
fof(f22998,plain,
spl0_2413,
inference(avatar_split_clause,[],[f2782,f22996]) ).
fof(f22996,plain,
( spl0_2413
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2413])]) ).
fof(f2782,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OMPair__synth_1) ).
fof(f22994,plain,
spl0_2412,
inference(avatar_split_clause,[],[f2781,f22992]) ).
fof(f22992,plain,
( spl0_2412
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2412])]) ).
fof(f2781,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OMPair__synth_0) ).
fof(f22990,plain,
spl0_2411,
inference(avatar_split_clause,[],[f2774,f22988]) ).
fof(f2774,axiom,
! [X91,X88,X86] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OCrypt__synth__eq_0) ).
fof(f22986,plain,
spl0_2410,
inference(avatar_split_clause,[],[f2773,f22984]) ).
fof(f2773,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OCrypt__synth_1) ).
fof(f22982,plain,
spl0_2409,
inference(avatar_split_clause,[],[f2686,f22980]) ).
fof(f22980,plain,
( spl0_2409
<=> ! [X18,X13,X12,X1] : c_inter(c_insert(X18,X12,X1),c_insert(X18,X13,X1),X1) = c_insert(X18,c_inter(X12,X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2409])]) ).
fof(f2686,axiom,
! [X18,X1,X12,X13] : c_inter(c_insert(X18,X12,X1),c_insert(X18,X13,X1),X1) = c_insert(X18,c_inter(X12,X13,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__inter__insert_0) ).
fof(f22978,plain,
spl0_2408,
inference(avatar_split_clause,[],[f2674,f22976]) ).
fof(f2674,axiom,
! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__Diff1_0) ).
fof(f22974,plain,
spl0_2407,
inference(avatar_split_clause,[],[f2647,f22972]) ).
fof(f22972,plain,
( spl0_2407
<=> ! [X13,X12,X32,X1] :
( ~ c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2407])]) ).
fof(f2647,axiom,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(X12,X32,tc_set(X1))
| c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__subset__iff_2) ).
fof(f22970,plain,
spl0_2406,
inference(avatar_split_clause,[],[f2611,f22968]) ).
fof(f22968,plain,
( spl0_2406
<=> ! [X13,X12,X32,X1] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2406])]) ).
fof(f2611,axiom,
! [X1,X12,X32,X13] :
( ~ c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,X12,tc_set(X1))
| c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__subset__iff_2) ).
fof(f22966,plain,
spl0_2405,
inference(avatar_split_clause,[],[f2597,f22964]) ).
fof(f2597,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X12,X1)
| c_minus(X12,X13,tc_set(X1)) = c_minus(X12,c_insert(X0,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__insert0_0) ).
fof(f22962,plain,
spl0_2404,
inference(avatar_split_clause,[],[f2577,f22960]) ).
fof(f22960,plain,
( spl0_2404
<=> ! [X13,X12,X1] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_inter(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2404])]) ).
fof(f2577,axiom,
! [X1,X12,X13] : c_uminus(c_union(X12,X13,X1),tc_set(X1)) = c_inter(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__Un_0) ).
fof(f22958,plain,
spl0_2403,
inference(avatar_split_clause,[],[f2575,f22956]) ).
fof(f22956,plain,
( spl0_2403
<=> ! [X13,X12,X1] : c_uminus(c_inter(X12,X13,X1),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2403])]) ).
fof(f2575,axiom,
! [X1,X12,X13] : c_uminus(c_inter(X12,X13,X1),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__Int_0) ).
fof(f22954,plain,
spl0_2402,
inference(avatar_split_clause,[],[f2337,f22952]) ).
fof(f22952,plain,
( spl0_2402
<=> ! [X0,X11] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2402])]) ).
fof(f2337,axiom,
! [X0,X11] :
( c_less(c_0,X0,tc_nat)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__nat__eq__number__of_0) ).
fof(f22950,plain,
spl0_2401,
inference(avatar_split_clause,[],[f2329,f22948]) ).
fof(f22948,plain,
( spl0_2401
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2401])]) ).
fof(f2329,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| c_lessequals(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__le__power__eq__number__of_1) ).
fof(f22946,plain,
spl0_2400,
inference(avatar_split_clause,[],[f2326,f22944]) ).
fof(f22944,plain,
( spl0_2400
<=> ! [X21,X1,X0] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2400])]) ).
fof(f2326,axiom,
! [X21,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X21,tc_nat)
| c_Nat_Opower(c_uminus(X0,X1),X21,X1) = c_Nat_Opower(X0,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__minus__even_0) ).
fof(f22942,plain,
spl0_2399,
inference(avatar_split_clause,[],[f2323,f22940]) ).
fof(f22940,plain,
( spl0_2399
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2399])]) ).
fof(f2323,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X11,tc_nat),tc_nat)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__less__zero__eq__number__of_0) ).
fof(f22938,plain,
spl0_2398,
inference(avatar_split_clause,[],[f2165,f22936]) ).
fof(f22936,plain,
( spl0_2398
<=> ! [X11,X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2398])]) ).
fof(f2165,axiom,
! [X48,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_uminus(c_Numeral_Onumber__of(X11,X1),X1),X48,X1) = c_times(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1),X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Ominus__number__of__mult_0) ).
fof(f22934,plain,
spl0_2397,
inference(avatar_split_clause,[],[f2077,f22932]) ).
fof(f22932,plain,
( spl0_2397
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2397])]) ).
fof(f2077,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__less__cancel2_2) ).
fof(f22930,plain,
spl0_2396,
inference(avatar_split_clause,[],[f2074,f22928]) ).
fof(f22928,plain,
( spl0_2396
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2396])]) ).
fof(f2074,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| ~ c_less(c_0,X16,tc_nat)
| c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__less__cancel1_2) ).
fof(f22926,plain,
spl0_2395,
inference(avatar_split_clause,[],[f2069,f22924]) ).
fof(f22924,plain,
( spl0_2395
<=> ! [X16,X21,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2395])]) ).
fof(f2069,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__le__cancel2_0) ).
fof(f22922,plain,
spl0_2394,
inference(avatar_split_clause,[],[f2066,f22920]) ).
fof(f22920,plain,
( spl0_2394
<=> ! [X16,X21,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2394])]) ).
fof(f2066,axiom,
! [X21,X16,X15] :
( ~ c_less(c_0,X16,tc_nat)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__le__cancel1_0) ).
fof(f22918,plain,
spl0_2393,
inference(avatar_split_clause,[],[f1929,f22916]) ).
fof(f22916,plain,
( spl0_2393
<=> ! [X2,X27,X47] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
| c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2393])]) ).
fof(f1929,axiom,
! [X2,X47,X27] :
( ~ class_Numeral_Onumber(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_uminus(X27,X2) != c_Numeral_Onumber__of(X47,X2)
| c_uminus(c_Numeral_Onumber__of(X47,X2),X2) = X27 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oequation__minus__iff__number__of_0) ).
fof(f22914,plain,
spl0_2392,
inference(avatar_split_clause,[],[f1830,f22912]) ).
fof(f22912,plain,
( spl0_2392
<=> ! [X0,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2392])]) ).
fof(f1830,axiom,
! [X3,X0] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Odvd__eq__mod__eq__0__number__of_1) ).
fof(f22910,plain,
spl0_2391,
inference(avatar_split_clause,[],[f1829,f22908]) ).
fof(f22908,plain,
( spl0_2391
<=> ! [X0,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2391])]) ).
fof(f1829,axiom,
! [X3,X0] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_nat),c_Numeral_Onumber__of(X3,tc_nat),tc_nat)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_nat),c_Numeral_Onumber__of(X0,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Odvd__eq__mod__eq__0__number__of_0) ).
fof(f22905,plain,
spl0_2390,
inference(avatar_split_clause,[],[f1782,f22903]) ).
fof(f1782,axiom,
! [X59,X43] :
( ~ c_lessequals(X43,X59,tc_nat)
| c_List_Oupt(X43,c_Suc(X59)) = c_append(c_List_Oupt(X43,X59),c_List_Olist_OCons(X59,c_List_Olist_ONil,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oupt_Oupt__Suc_0) ).
fof(f22901,plain,
spl0_2389,
inference(avatar_split_clause,[],[f1721,f22899]) ).
fof(f22899,plain,
( spl0_2389
<=> ! [X41,X0,X23,X3] :
( X0 = X3
| c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2389])]) ).
fof(f1721,axiom,
! [X3,X41,X0,X23] :
( X0 = X3
| c_List_Oremove1(X0,c_List_Olist_OCons(X3,X23,X41),X41) = c_List_Olist_OCons(X3,c_List_Oremove1(X0,X23,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremove1_Osimps__2_1) ).
fof(f22897,plain,
spl0_2388,
inference(avatar_split_clause,[],[f1704,f22895]) ).
fof(f22895,plain,
( spl0_2388
<=> ! [X16,X59,X43] :
( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
| c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2388])]) ).
fof(f1704,axiom,
! [X59,X16,X43] :
( ~ c_less(c_plus(X43,X16,tc_nat),X59,tc_nat)
| c_plus(X43,X16,tc_nat) = c_List_Onth(c_List_Oupt(X43,X59),X16,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__upt_0) ).
fof(f22893,plain,
( spl0_2387
| ~ spl0_1862
| ~ spl0_2297 ),
inference(avatar_split_clause,[],[f20751,f20598,f13068,f22891]) ).
fof(f22891,plain,
( spl0_2387
<=> ! [X9,X10] :
( ~ c_in(c_Message_Omsg_OCrypt(X9,X10),v_H,tc_Message_Omsg)
| c_in(X10,c_Message_Oparts(c_UNIV),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2387])]) ).
fof(f20598,plain,
( spl0_2297
<=> ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,v_H,tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2297])]) ).
fof(f20751,plain,
( ! [X10,X9] :
( ~ c_in(c_Message_Omsg_OCrypt(X9,X10),v_H,tc_Message_Omsg)
| c_in(X10,c_Message_Oparts(c_UNIV),tc_Message_Omsg) )
| ~ spl0_1862
| ~ spl0_2297 ),
inference(resolution,[],[f20599,f13069]) ).
fof(f20599,plain,
( ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,v_H,tc_Message_Omsg) )
| ~ spl0_2297 ),
inference(avatar_component_clause,[],[f20598]) ).
fof(f22889,plain,
spl0_2386,
inference(avatar_split_clause,[],[f1697,f22887]) ).
fof(f22887,plain,
( spl0_2386
<=> ! [X21,X23,X25,X1] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2386])]) ).
fof(f1697,axiom,
! [X21,X1,X25,X23] : c_List_Onth(c_append(X23,X25,X1),c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),X1) = c_List_Onth(X25,X21,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__append__length__plus_0) ).
fof(f22885,plain,
spl0_2385,
inference(avatar_split_clause,[],[f1630,f22883]) ).
fof(f22883,plain,
( spl0_2385
<=> ! [X41,X60,X18,X65] :
( c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2385])]) ).
fof(f1630,axiom,
! [X65,X41,X18,X60] :
( c_in(X18,c_List_Oset(X65,X41),X41)
| c_List_Olist__inter(c_List_Olist_OCons(X18,X60,X41),X65,X41) = c_List_Olist__inter(X60,X65,X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__inter_Osimps__2_1) ).
fof(f22881,plain,
spl0_2384,
inference(avatar_split_clause,[],[f1599,f22879]) ).
fof(f22879,plain,
( spl0_2384
<=> ! [X25,X1,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2384])]) ).
fof(f1599,axiom,
! [X1,X25,X23] : c_Nat_Osize(c_append(X23,X25,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_Nat_Osize(X25,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__append_0) ).
fof(f22875,plain,
spl0_2383,
inference(avatar_split_clause,[],[f1517,f22873]) ).
fof(f1517,axiom,
! [X3,X0,X1,X25,X23] :
( X0 = X3
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend1__eq__conv_1) ).
fof(f22869,plain,
spl0_2382,
inference(avatar_split_clause,[],[f1516,f22867]) ).
fof(f1516,axiom,
! [X3,X0,X1,X25,X23] :
( X23 = X25
| c_append(X23,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) != c_append(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend1__eq__conv_0) ).
fof(f22865,plain,
spl0_2381,
inference(avatar_split_clause,[],[f1481,f22863]) ).
fof(f22863,plain,
( spl0_2381
<=> ! [X0,X3] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2381])]) ).
fof(f1481,axiom,
! [X3,X0] :
( c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_1) ).
fof(f22861,plain,
spl0_2380,
inference(avatar_split_clause,[],[f1480,f22859]) ).
fof(f22859,plain,
( spl0_2380
<=> ! [X0,X3] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2380])]) ).
fof(f1480,axiom,
! [X3,X0] :
( ~ c_Divides_Oop_Advd(c_Numeral_Onumber__of(X0,tc_IntDef_Oint),c_Numeral_Onumber__of(X3,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X3,tc_IntDef_Oint),c_Numeral_Onumber__of(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__iff__zmod__eq__0__number__of_0) ).
fof(f22857,plain,
spl0_2379,
inference(avatar_split_clause,[],[f1473,f22855]) ).
fof(f22855,plain,
( spl0_2379
<=> ! [X18,X27] :
( c_0 = X18
| c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2379])]) ).
fof(f1473,axiom,
! [X18,X27] :
( c_0 = X18
| c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) = c_div(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__zadd__self2_0) ).
fof(f22853,plain,
spl0_2378,
inference(avatar_split_clause,[],[f1472,f22851]) ).
fof(f22851,plain,
( spl0_2378
<=> ! [X18,X27] :
( c_0 = X18
| c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2378])]) ).
fof(f1472,axiom,
! [X18,X27] :
( c_0 = X18
| c_div(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_plus(c_div(X27,X18,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__zadd__self1_0) ).
fof(f22849,plain,
spl0_2377,
inference(avatar_split_clause,[],[f1292,f22847]) ).
fof(f22847,plain,
( spl0_2377
<=> ! [X2,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2377])]) ).
fof(f1292,axiom,
! [X2,X12] :
( ~ class_Orderings_Olinorder(X2)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X2))
| c_lessequals(c_Finite__Set_OMin(X12,X2),c_Finite__Set_OMax(X12,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Omin__max_Obelow__inf__sup__Inf__Sup_OInf__le__Sup_0) ).
fof(f22845,plain,
( spl0_2376
| ~ spl0_1855
| ~ spl0_2297 ),
inference(avatar_split_clause,[],[f20750,f20598,f13040,f22843]) ).
fof(f22843,plain,
( spl0_2376
<=> ! [X8,X7] :
( ~ c_in(c_Message_Omsg_OMPair(X7,X8),v_H,tc_Message_Omsg)
| c_in(X8,c_Message_Oparts(c_UNIV),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2376])]) ).
fof(f13040,plain,
( spl0_1855
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1855])]) ).
fof(f20750,plain,
( ! [X8,X7] :
( ~ c_in(c_Message_Omsg_OMPair(X7,X8),v_H,tc_Message_Omsg)
| c_in(X8,c_Message_Oparts(c_UNIV),tc_Message_Omsg) )
| ~ spl0_1855
| ~ spl0_2297 ),
inference(resolution,[],[f20599,f13041]) ).
fof(f13041,plain,
( ! [X88,X86,X87] :
( ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg)
| c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg) )
| ~ spl0_1855 ),
inference(avatar_component_clause,[],[f13040]) ).
fof(f22841,plain,
spl0_2375,
inference(avatar_split_clause,[],[f1288,f22839]) ).
fof(f22839,plain,
( spl0_2375
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2375])]) ).
fof(f1288,axiom,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Un_2) ).
fof(f22634,plain,
( spl0_2374
| ~ spl0_1856
| ~ spl0_2297 ),
inference(avatar_split_clause,[],[f20749,f20598,f13044,f22632]) ).
fof(f22632,plain,
( spl0_2374
<=> ! [X6,X5] :
( ~ c_in(c_Message_Omsg_OMPair(X5,X6),v_H,tc_Message_Omsg)
| c_in(X5,c_Message_Oparts(c_UNIV),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2374])]) ).
fof(f13044,plain,
( spl0_1856
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1856])]) ).
fof(f20749,plain,
( ! [X6,X5] :
( ~ c_in(c_Message_Omsg_OMPair(X5,X6),v_H,tc_Message_Omsg)
| c_in(X5,c_Message_Oparts(c_UNIV),tc_Message_Omsg) )
| ~ spl0_1856
| ~ spl0_2297 ),
inference(resolution,[],[f20599,f13045]) ).
fof(f13045,plain,
( ! [X88,X86,X87] :
( ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) )
| ~ spl0_1856 ),
inference(avatar_component_clause,[],[f13044]) ).
fof(f22266,plain,
( spl0_2373
| ~ spl0_1225
| ~ spl0_2201
| ~ spl0_2270 ),
inference(avatar_split_clause,[],[f21403,f20190,f18609,f9275,f22263]) ).
fof(f22263,plain,
( spl0_2373
<=> c_UNIV = c_union(c_uminus(c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2373])]) ).
fof(f18609,plain,
( spl0_2201
<=> c_emptyset = c_minus(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2201])]) ).
fof(f21403,plain,
( c_UNIV = c_union(c_uminus(c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1225
| ~ spl0_2201
| ~ spl0_2270 ),
inference(forward_demodulation,[],[f21362,f9276]) ).
fof(f21362,plain,
( c_union(c_uminus(c_Message_Osynth(v_H),tc_set(tc_Message_Omsg)),c_Message_Oparts(c_UNIV),tc_Message_Omsg) = c_uminus(c_emptyset,tc_set(tc_Message_Omsg))
| ~ spl0_2201
| ~ spl0_2270 ),
inference(superposition,[],[f20191,f18611]) ).
fof(f18611,plain,
( c_emptyset = c_minus(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_2201 ),
inference(avatar_component_clause,[],[f18609]) ).
fof(f22159,plain,
( spl0_2372
| ~ spl0_1704
| ~ spl0_2236 ),
inference(avatar_split_clause,[],[f20183,f20046,f11946,f22157]) ).
fof(f22157,plain,
( spl0_2372
<=> ! [X3] :
( c_in(c_Message_Omsg_OHash(X3),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X3,c_Message_Osynth(v_H),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2372])]) ).
fof(f11946,plain,
( spl0_1704
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1704])]) ).
fof(f20183,plain,
( ! [X3] :
( c_in(c_Message_Omsg_OHash(X3),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X3,c_Message_Osynth(v_H),tc_Message_Omsg) )
| ~ spl0_1704
| ~ spl0_2236 ),
inference(resolution,[],[f20047,f11947]) ).
fof(f11947,plain,
( ! [X88,X86] :
( c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) )
| ~ spl0_1704 ),
inference(avatar_component_clause,[],[f11946]) ).
fof(f21986,plain,
( spl0_2371
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2370 ),
inference(avatar_split_clause,[],[f21982,f21979,f13084,f10339,f7341,f3303,f21984]) ).
fof(f21984,plain,
( spl0_2371
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2371])]) ).
fof(f21979,plain,
( spl0_2370
<=> ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2370])]) ).
fof(f21982,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2370 ),
inference(forward_demodulation,[],[f21980,f14162]) ).
fof(f21980,plain,
( ! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2370 ),
inference(avatar_component_clause,[],[f21979]) ).
fof(f21981,plain,
spl0_2370,
inference(avatar_split_clause,[],[f2919,f21979]) ).
fof(f2919,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2918,f2156]) ).
fof(f2918,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2917,f2154]) ).
fof(f2917,plain,
! [X47] :
( c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2273,f2156]) ).
fof(f2273,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 != c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_1) ).
fof(f21975,plain,
( spl0_2369
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2368 ),
inference(avatar_split_clause,[],[f21971,f21968,f13084,f10339,f7341,f3303,f21973]) ).
fof(f21973,plain,
( spl0_2369
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2369])]) ).
fof(f21968,plain,
( spl0_2368
<=> ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2368])]) ).
fof(f21971,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_IntDef_Oint(c_Suc(c_1)),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_59
| ~ spl0_1051
| ~ spl0_1433
| ~ spl0_1866
| ~ spl0_2368 ),
inference(forward_demodulation,[],[f21969,f14162]) ).
fof(f21969,plain,
( ! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_2368 ),
inference(avatar_component_clause,[],[f21968]) ).
fof(f21970,plain,
spl0_2368,
inference(avatar_split_clause,[],[f2915,f21968]) ).
fof(f2915,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2914,f2156]) ).
fof(f2914,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2913,f2154]) ).
fof(f2913,plain,
! [X47] :
( c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f2272,f2156]) ).
fof(f2272,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Anumber__of_Av_Amod_A2_A_61_A0_0) ).
fof(f21966,plain,
spl0_2367,
inference(avatar_split_clause,[],[f2871,f21964]) ).
fof(f21964,plain,
( spl0_2367
<=> ! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2367])]) ).
fof(f2871,plain,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_1,tc_nat),
inference(forward_demodulation,[],[f2765,f2016]) ).
fof(f2765,axiom,
! [X98,X99] : c_Nat_Osize(c_Message_Omsg_OMPair(X98,X99),tc_Message_Omsg) = c_plus(c_plus(c_Nat_Osize(X98,tc_Message_Omsg),c_Nat_Osize(X99,tc_Message_Omsg),tc_nat),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__6_0) ).
fof(f21962,plain,
spl0_2366,
inference(avatar_split_clause,[],[f2870,f21960]) ).
fof(f21960,plain,
( spl0_2366
<=> ! [X16,X21,X15] : c_minus(c_minus(c_Suc(X15),X21,tc_nat),c_Suc(X16),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2366])]) ).
fof(f2870,plain,
! [X21,X16,X15] : c_minus(c_minus(c_Suc(X15),X21,tc_nat),c_Suc(X16),tc_nat) = c_minus(X15,c_plus(X21,X16,tc_nat),tc_nat),
inference(forward_demodulation,[],[f2018,f2037]) ).
fof(f2037,axiom,
! [X59,X16,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__diff__left_0) ).
fof(f2018,axiom,
! [X21,X16,X15] : c_minus(c_minus(c_Suc(X15),X21,tc_nat),c_Suc(X16),tc_nat) = c_minus(c_minus(X15,X21,tc_nat),X16,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__diff__diff_0) ).
fof(f21958,plain,
spl0_2365,
inference(avatar_split_clause,[],[f2819,f21956]) ).
fof(f21956,plain,
( spl0_2365
<=> ! [X87,X86,X88] :
( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2365])]) ).
fof(f2819,axiom,
! [X88,X86,X87] :
( ~ c_in(X87,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth_OMPair_0) ).
fof(f21954,plain,
spl0_2364,
inference(avatar_split_clause,[],[f2816,f21952]) ).
fof(f21952,plain,
( spl0_2364
<=> ! [X86,X91,X88] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2364])]) ).
fof(f2816,axiom,
! [X91,X88,X86] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth_OCrypt_0) ).
fof(f21950,plain,
spl0_2363,
inference(avatar_split_clause,[],[f2697,f21948]) ).
fof(f21948,plain,
( spl0_2363
<=> ! [X12,X0,X1] :
( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
| c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2363])]) ).
fof(f2697,axiom,
! [X0,X1,X12] :
( ~ c_lessequals(X12,c_insert(X0,c_emptyset,X1),tc_set(X1))
| c_insert(X0,X12,X1) = c_insert(X0,c_emptyset,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osingleton__insert__inj__eq_H_2) ).
fof(f21946,plain,
spl0_2362,
inference(avatar_split_clause,[],[f2693,f21944]) ).
fof(f21944,plain,
( spl0_2362
<=> ! [X12,X27,X1,X18] :
( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2362])]) ).
fof(f2693,axiom,
! [X1,X18,X27,X12] :
( c_lessequals(X12,c_insert(X27,c_emptyset,X1),tc_set(X1))
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osingleton__insert__inj__eq_1) ).
fof(f21942,plain,
spl0_2361,
inference(avatar_split_clause,[],[f2690,f21940]) ).
fof(f21940,plain,
( spl0_2361
<=> ! [X13,X0,X12,X1] :
( ~ c_in(X0,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2361])]) ).
fof(f2690,axiom,
! [X0,X1,X12,X13] :
( ~ c_in(X0,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__subset_2) ).
fof(f21938,plain,
spl0_2360,
inference(avatar_split_clause,[],[f2573,f21936]) ).
fof(f21936,plain,
( spl0_2360
<=> ! [X16,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2360])]) ).
fof(f2573,axiom,
! [X1,X16] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X16,c_emptyset,X1) = c_minus(c_insert(X16,c_emptyset,X1),c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Osingle__Diff__lessThan_0) ).
fof(f21934,plain,
spl0_2359,
inference(avatar_split_clause,[],[f2565,f21932]) ).
fof(f21932,plain,
( spl0_2359
<=> ! [X15,X59,X43,X21,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X59,X43,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2359])]) ).
fof(f2565,axiom,
! [X21,X59,X1,X15,X43] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X59,X43,X1)
| c_lessequals(c_SetInterval_OatLeastLessThan(X43,X59,X1),c_SetInterval_OatLeastLessThan(X15,X21,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Oivl__subset_2) ).
fof(f21930,plain,
spl0_2358,
inference(avatar_split_clause,[],[f2556,f21928]) ).
fof(f21928,plain,
( spl0_2358
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2358])]) ).
fof(f2556,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanLessThan__iff_2) ).
fof(f21926,plain,
spl0_2357,
inference(avatar_split_clause,[],[f2553,f21924]) ).
fof(f21924,plain,
( spl0_2357
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X14,X1)
| ~ c_less(X26,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2357])]) ).
fof(f2553,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X14,X1)
| ~ c_less(X26,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanAtMost__iff_2) ).
fof(f21922,plain,
spl0_2356,
inference(avatar_split_clause,[],[f2526,f21920]) ).
fof(f21920,plain,
( spl0_2356
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2356])]) ).
fof(f2526,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_less(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastLessThan__iff_2) ).
fof(f21918,plain,
spl0_2355,
inference(avatar_split_clause,[],[f2521,f21916]) ).
fof(f21916,plain,
( spl0_2355
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_lessequals(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2355])]) ).
fof(f2521,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X26,X43,X1)
| ~ c_lessequals(X43,X14,X1)
| c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastAtMost__iff_2) ).
fof(f21914,plain,
spl0_2354,
inference(avatar_split_clause,[],[f2502,f21912]) ).
fof(f21912,plain,
( spl0_2354
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_divide(X27,X4,X1),X18,X1) = c_divide(c_times(X27,X18,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2354])]) ).
fof(f2502,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_divide(X27,X4,X1),X18,X1) = c_divide(c_times(X27,X18,X1),X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Otimes__divide__eq__2_0) ).
fof(f21910,plain,
spl0_2353,
inference(avatar_split_clause,[],[f2501,f21908]) ).
fof(f21908,plain,
( spl0_2353
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X18,c_divide(X27,X4,X1),X1) = c_divide(c_times(X18,X27,X1),X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2353])]) ).
fof(f2501,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X18,c_divide(X27,X4,X1),X1) = c_divide(c_times(X18,X27,X1),X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Otimes__divide__eq__1_0) ).
fof(f21906,plain,
spl0_2352,
inference(avatar_split_clause,[],[f2466,f21904]) ).
fof(f21904,plain,
( spl0_2352
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X18,X27,X1) = c_divide(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2352])]) ).
fof(f2466,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X18,X27,X1) = c_divide(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ominus__divide__divide_0) ).
fof(f21902,plain,
spl0_2351,
inference(avatar_split_clause,[],[f2431,f21900]) ).
fof(f21900,plain,
( spl0_2351
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_times(X27,X4,X1) != c_times(X18,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2351])]) ).
fof(f2431,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_times(X27,X4,X1) != c_times(X18,X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ofield__mult__cancel__right_0) ).
fof(f21898,plain,
spl0_2350,
inference(avatar_split_clause,[],[f2429,f21896]) ).
fof(f21896,plain,
( spl0_2350
<=> ! [X18,X4,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_times(X4,X18,X1) != c_times(X4,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2350])]) ).
fof(f2429,axiom,
! [X1,X18,X27,X4] :
( ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_0 = X4
| c_times(X4,X18,X1) != c_times(X4,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ofield__mult__cancel__left_0) ).
fof(f21894,plain,
spl0_2349,
inference(avatar_split_clause,[],[f2423,f21892]) ).
fof(f21892,plain,
( spl0_2349
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_uminus(c_divide(X18,X27,X1),X1) = c_divide(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2349])]) ).
fof(f2423,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_uminus(c_divide(X18,X27,X1),X1) = c_divide(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__minus__right_0) ).
fof(f21890,plain,
spl0_2348,
inference(avatar_split_clause,[],[f2324,f21888]) ).
fof(f21888,plain,
( spl0_2348
<=> ! [X11,X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X0,c_0,X1)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2348])]) ).
fof(f2324,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X0,c_0,X1)
| ~ c_less(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__less__zero__eq__number__of_1) ).
fof(f21886,plain,
spl0_2347,
inference(avatar_split_clause,[],[f2307,f21884]) ).
fof(f21884,plain,
( spl0_2347
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2347])]) ).
fof(f2307,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oneg__one__odd__power_0) ).
fof(f21882,plain,
( ~ spl0_2344
| spl0_2345
| ~ spl0_2346
| ~ spl0_1677
| ~ spl0_2201 ),
inference(avatar_split_clause,[],[f18860,f18609,f11838,f21879,f21875,f21871]) ).
fof(f21871,plain,
( spl0_2344
<=> class_OrderedGroup_Oab__group__add(tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2344])]) ).
fof(f21879,plain,
( spl0_2346
<=> c_0 = c_emptyset ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2346])]) ).
fof(f11838,plain,
( spl0_1677
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1677])]) ).
fof(f18860,plain,
( c_0 != c_emptyset
| c_Message_Osynth(v_H) = c_Message_Oparts(c_UNIV)
| ~ class_OrderedGroup_Oab__group__add(tc_set(tc_Message_Omsg))
| ~ spl0_1677
| ~ spl0_2201 ),
inference(superposition,[],[f11839,f18611]) ).
fof(f11839,plain,
( ! [X18,X1,X27] :
( c_0 != c_minus(X18,X27,X1)
| X18 = X27
| ~ class_OrderedGroup_Oab__group__add(X1) )
| ~ spl0_1677 ),
inference(avatar_component_clause,[],[f11838]) ).
fof(f21869,plain,
spl0_2343,
inference(avatar_split_clause,[],[f2305,f21867]) ).
fof(f21867,plain,
( spl0_2343
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2343])]) ).
fof(f2305,axiom,
! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_Parity_Oeven(X0,tc_nat)
| c_uminus(c_1,X1) = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ominus__one__odd__power_0) ).
fof(f21865,plain,
spl0_2342,
inference(avatar_split_clause,[],[f2266,f21863]) ).
fof(f21863,plain,
( spl0_2342
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X48,X2)
| ~ c_lessequals(X3,X48,X2)
| c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2342])]) ).
fof(f2266,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X48,X2)
| ~ c_lessequals(X3,X48,X2)
| c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_2) ).
fof(f21861,plain,
spl0_2341,
inference(avatar_split_clause,[],[f2261,f21859]) ).
fof(f21859,plain,
( spl0_2341
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X48,X2)
| c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2341])]) ).
fof(f2261,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| ~ c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,X48,X2)
| c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_2) ).
fof(f21857,plain,
spl0_2340,
inference(avatar_split_clause,[],[f2258,f21855]) ).
fof(f21855,plain,
( spl0_2340
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X48,X0,X1)
| ~ c_less(X48,X3,X1)
| c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2340])]) ).
fof(f2258,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X48,X0,X1)
| ~ c_less(X48,X3,X1)
| c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__less__iff__conj_2) ).
fof(f21853,plain,
spl0_2339,
inference(avatar_split_clause,[],[f2255,f21851]) ).
fof(f21851,plain,
( spl0_2339
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X0,X48,X1)
| ~ c_less(X3,X48,X1)
| c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2339])]) ).
fof(f2255,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_less(X0,X48,X1)
| ~ c_less(X3,X48,X1)
| c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omax__less__iff__conj_2) ).
fof(f21849,plain,
spl0_2338,
inference(avatar_split_clause,[],[f2237,f21847]) ).
fof(f21847,plain,
( spl0_2338
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2338])]) ).
fof(f2237,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Omeet(X18,X27,X1),X1) = c_LOrder_Ojoin(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__meet__eq__join_0) ).
fof(f21845,plain,
spl0_2337,
inference(avatar_split_clause,[],[f2228,f21843]) ).
fof(f21843,plain,
( spl0_2337
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2337])]) ).
fof(f2228,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_uminus(c_LOrder_Ojoin(X18,X27,X1),X1) = c_LOrder_Omeet(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__join__eq__meet_0) ).
fof(f21841,plain,
spl0_2336,
inference(avatar_split_clause,[],[f2214,f21839]) ).
fof(f21839,plain,
( spl0_2336
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2336])]) ).
fof(f2214,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_plus(X18,X27,X1),X1) = c_plus(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ominus__add__distrib_0) ).
fof(f21837,plain,
spl0_2335,
inference(avatar_split_clause,[],[f2142,f21835]) ).
fof(f21835,plain,
( spl0_2335
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2335])]) ).
fof(f2142,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__1_1) ).
fof(f21833,plain,
spl0_2334,
inference(avatar_split_clause,[],[f2141,f21831]) ).
fof(f21831,plain,
( spl0_2334
<=> ! [X0,X1,X3] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2334])]) ).
fof(f2141,axiom,
! [X3,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(X3,X1) != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__1_0) ).
fof(f21826,plain,
spl0_2333,
inference(avatar_split_clause,[],[f2120,f21824]) ).
fof(f21824,plain,
( spl0_2333
<=> ! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1) = c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2333])]) ).
fof(f2120,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(X11)),X1) = c_minus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__5_0) ).
fof(f21822,plain,
spl0_2332,
inference(avatar_split_clause,[],[f1843,f21820]) ).
fof(f21820,plain,
( spl0_2332
<=> ! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2332])]) ).
fof(f1843,axiom,
! [X83,X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_6) ).
fof(f21818,plain,
spl0_2331,
inference(avatar_split_clause,[],[f1836,f21816]) ).
fof(f21816,plain,
( spl0_2331
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2331])]) ).
fof(f1836,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_nat) = c_Numeral_Onumber__of(X83,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__nat__number__of_10) ).
fof(f21814,plain,
spl0_2330,
inference(avatar_split_clause,[],[f1824,f21812]) ).
fof(f21812,plain,
( spl0_2330
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2330])]) ).
fof(f1824,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X83,tc_nat) = c_plus(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oadd__nat__number__of_0) ).
fof(f21810,plain,
spl0_2329,
inference(avatar_split_clause,[],[f1821,f21808]) ).
fof(f21808,plain,
( spl0_2329
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2329])]) ).
fof(f1821,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_times(X15,X21,tc_nat),X1) = c_times(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__mult_0) ).
fof(f21806,plain,
spl0_2328,
inference(avatar_split_clause,[],[f1809,f21804]) ).
fof(f21804,plain,
( spl0_2328
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2328])]) ).
fof(f1809,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_NatArith_Oof__nat(c_plus(X15,X21,tc_nat),X1) = c_plus(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__add_0) ).
fof(f21802,plain,
spl0_2327,
inference(avatar_split_clause,[],[f1781,f21800]) ).
fof(f21800,plain,
( spl0_2327
<=> ! [X21,X1,X0] :
( c_0 = X21
| c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2327])]) ).
fof(f1781,axiom,
! [X21,X0,X1] :
( c_0 = X21
| c_List_Otl(c_List_Oreplicate(X21,X0,X1),X1) = c_List_Oreplicate(c_minus(X21,c_1,tc_nat),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otl__replicate_0) ).
fof(f21798,plain,
spl0_2326,
inference(avatar_split_clause,[],[f1699,f21796]) ).
fof(f21796,plain,
( spl0_2326
<=> ! [X43,X23,X3,X1] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2326])]) ).
fof(f1699,axiom,
! [X3,X1,X23,X43] :
( ~ c_less(X43,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Onth(c_List_Olist__update(X23,X43,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__list__update__eq_0) ).
fof(f21794,plain,
spl0_2325,
inference(avatar_split_clause,[],[f1633,f21792]) ).
fof(f21792,plain,
( spl0_2325
<=> ! [X1,X43,X3] :
( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2325])]) ).
fof(f1633,axiom,
! [X3,X1,X43] :
( ~ c_less(X43,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat)
| c_List_Olist__update(X3,X43,c_List_Onth(X3,X43,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__update__id_0) ).
fof(f21790,plain,
spl0_2324,
inference(avatar_split_clause,[],[f1592,f21788]) ).
fof(f21788,plain,
( spl0_2324
<=> ! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2324])]) ).
fof(f1592,axiom,
! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_List_Olast(X23,X1) = c_List_Olast(c_List_Odrop(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast__drop_0) ).
fof(f21786,plain,
( spl0_2323
| ~ spl0_1
| ~ spl0_2300 ),
inference(avatar_split_clause,[],[f21543,f21353,f3013,f21783]) ).
fof(f21783,plain,
( spl0_2323
<=> c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2323])]) ).
fof(f21353,plain,
( spl0_2300
<=> ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2300])]) ).
fof(f21543,plain,
( c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1
| ~ spl0_2300 ),
inference(resolution,[],[f21354,f3015]) ).
fof(f21354,plain,
( ! [X0] :
( ~ c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg) )
| ~ spl0_2300 ),
inference(avatar_component_clause,[],[f21353]) ).
fof(f21781,plain,
spl0_2322,
inference(avatar_split_clause,[],[f1525,f21779]) ).
fof(f21779,plain,
( spl0_2322
<=> ! [X12,X1,X23,X25] :
( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2322])]) ).
fof(f1525,axiom,
! [X1,X25,X12,X23] :
( c_in(X25,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__in__lists__conv_1) ).
fof(f21777,plain,
spl0_2321,
inference(avatar_split_clause,[],[f1524,f21775]) ).
fof(f21775,plain,
( spl0_2321
<=> ! [X23,X12,X25,X1] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2321])]) ).
fof(f1524,axiom,
! [X1,X12,X23,X25] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_append(X23,X25,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__in__lists__conv_0) ).
fof(f21773,plain,
spl0_2320,
inference(avatar_split_clause,[],[f1417,f21771]) ).
fof(f21771,plain,
( spl0_2320
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2320])]) ).
fof(f1417,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_times(X11,X48,tc_IntDef_Oint),X1) = c_times(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__mult_0) ).
fof(f21769,plain,
spl0_2319,
inference(avatar_split_clause,[],[f1403,f21767]) ).
fof(f21767,plain,
( spl0_2319
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2319])]) ).
fof(f1403,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_minus(X11,X48,tc_IntDef_Oint),X1) = c_minus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__diff_0) ).
fof(f21765,plain,
spl0_2318,
inference(avatar_split_clause,[],[f1402,f21763]) ).
fof(f21763,plain,
( spl0_2318
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2318])]) ).
fof(f1402,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_plus(X11,X48,tc_IntDef_Oint),X1) = c_plus(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__add_0) ).
fof(f21761,plain,
spl0_2317,
inference(avatar_split_clause,[],[f1366,f21759]) ).
fof(f21759,plain,
( spl0_2317
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2317])]) ).
fof(f1366,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_ONats__mult_0) ).
fof(f21757,plain,
spl0_2316,
inference(avatar_split_clause,[],[f1365,f21755]) ).
fof(f21755,plain,
( spl0_2316
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2316])]) ).
fof(f1365,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_in(X18,c_IntDef_ONats,X1)
| ~ c_in(X27,c_IntDef_ONats,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_ONats__add_0) ).
fof(f21753,plain,
spl0_2315,
inference(avatar_split_clause,[],[f1362,f21751]) ).
fof(f21751,plain,
( spl0_2315
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2315])]) ).
fof(f1362,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_times(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInts__mult_0) ).
fof(f21749,plain,
spl0_2314,
inference(avatar_split_clause,[],[f1360,f21747]) ).
fof(f21747,plain,
( spl0_2314
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2314])]) ).
fof(f1360,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_minus(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInts__diff_0) ).
fof(f21745,plain,
spl0_2313,
inference(avatar_split_clause,[],[f1359,f21743]) ).
fof(f21743,plain,
( spl0_2313
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2313])]) ).
fof(f1359,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| ~ c_in(X27,c_IntDef_OInts,X1)
| c_in(c_plus(X18,X27,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInts__add_0) ).
fof(f21739,plain,
spl0_2312,
inference(avatar_split_clause,[],[f1306,f21737]) ).
fof(f21737,plain,
( spl0_2312
<=> ! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
| c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2312])]) ).
fof(f1306,axiom,
! [X21,X16,X15] :
( ~ c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,X15,tc_nat)
| c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__greatest__iff_2) ).
fof(f21735,plain,
spl0_2311,
inference(avatar_split_clause,[],[f1290,f21733]) ).
fof(f21733,plain,
( spl0_2311
<=> ! [X2,X5,X1] :
( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2311])]) ).
fof(f1290,axiom,
! [X2,X1,X5] :
( ~ c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__converse_1) ).
fof(f21731,plain,
spl0_2310,
inference(avatar_split_clause,[],[f1289,f21729]) ).
fof(f21729,plain,
( spl0_2310
<=> ! [X2,X5,X1] :
( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2310])]) ).
fof(f1289,axiom,
! [X2,X1,X5] :
( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(X2,X1)))
| ~ c_in(c_Relation_Oconverse(X5,X2,X1),c_Finite__Set_OFinites,tc_set(tc_prod(X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__converse_0) ).
fof(f21727,plain,
spl0_2309,
inference(avatar_split_clause,[],[f114,f21725]) ).
fof(f21725,plain,
( spl0_2309
<=> ! [X13,X12,X27,X2,X1] :
( ~ c_in(X27,X13,X1)
| c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2309])]) ).
fof(f114,axiom,
! [X2,X1,X27,X12,X13] :
( ~ c_in(X27,X13,X1)
| c_in(c_Sum__Type_OInr(X27,X1,X2),c_Sum__Type_OPlus(X12,X13,X2,X1),tc_sum(X2,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OInrI_0) ).
fof(f21723,plain,
spl0_2308,
inference(avatar_split_clause,[],[f113,f21721]) ).
fof(f21721,plain,
( spl0_2308
<=> ! [X18,X13,X12,X2,X1] :
( ~ c_in(X18,X12,X1)
| c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2308])]) ).
fof(f113,axiom,
! [X2,X18,X1,X12,X13] :
( ~ c_in(X18,X12,X1)
| c_in(c_Sum__Type_OInl(X18,X1,X2),c_Sum__Type_OPlus(X12,X13,X1,X2),tc_sum(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OInlI_0) ).
fof(f21719,plain,
spl0_2307,
inference(avatar_split_clause,[],[f76,f21717]) ).
fof(f76,axiom,
! [X2,X1,X18,X27,X5] :
( c_in(X27,c_Relation_ORange(X5,X1,X2),X2)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ORangeI_0) ).
fof(f21715,plain,
spl0_2306,
inference(avatar_split_clause,[],[f72,f21713]) ).
fof(f21713,plain,
( spl0_2306
<=> ! [X12,X5,X27,X2,X1] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2306])]) ).
fof(f72,axiom,
! [X2,X1,X27,X5,X12] :
( ~ c_in(X27,c_Relation_OImage(X5,X12,X2,X1),X1)
| c_in(c_Main_OImageE__1(X12,X27,X5,X2,X1),X12,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImageE_0) ).
fof(f21711,plain,
spl0_2305,
inference(avatar_split_clause,[],[f71,f21709]) ).
fof(f21709,plain,
( spl0_2305
<=> ! [X1,X28] :
( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2305])]) ).
fof(f71,axiom,
! [X28,X1] :
( ~ c_in(X28,c_Relation_OId,tc_prod(X1,X1))
| c_Pair(c_Main_OIdE__1(X28,X1),c_Main_OIdE__1(X28,X1),X1,X1) = X28 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OIdE_0) ).
fof(f21707,plain,
spl0_2304,
inference(avatar_split_clause,[],[f70,f21705]) ).
fof(f70,axiom,
! [X2,X18,X1,X27,X5] :
( c_in(X18,c_Relation_ODomain(X5,X1,X2),X1)
| ~ c_in(c_Pair(X18,X27,X1,X2),X5,tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ODomainI_0) ).
fof(f21703,plain,
spl0_2303,
inference(avatar_split_clause,[],[f58,f21701]) ).
fof(f21701,plain,
( spl0_2303
<=> ! [X12,X0,X1,X26] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2303])]) ).
fof(f58,axiom,
! [X0,X1,X26,X12] :
( c_in(X26,c_List_Olists(X12,X1),tc_List_Olist(X1))
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OlistsE_0) ).
fof(f21699,plain,
( spl0_2302
| ~ spl0_1874
| ~ spl0_2300 ),
inference(avatar_split_clause,[],[f21544,f21353,f14164,f21696]) ).
fof(f21544,plain,
( c_in(v_X,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1874
| ~ spl0_2300 ),
inference(resolution,[],[f21354,f14166]) ).
fof(f21694,plain,
spl0_2301,
inference(avatar_split_clause,[],[f46,f21692]) ).
fof(f21692,plain,
( spl0_2301
<=> ! [X24,X23,X12,X1] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2301])]) ).
fof(f46,axiom,
! [X1,X24,X12,X23] :
( c_in(X24,X12,X1)
| ~ c_in(X24,c_List_Oset(X23,X1),X1)
| ~ c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oin__listsD__dest_0) ).
fof(f21355,plain,
( spl0_2300
| ~ spl0_1881
| ~ spl0_2163 ),
inference(avatar_split_clause,[],[f18468,f18422,f14202,f21353]) ).
fof(f18422,plain,
( spl0_2163
<=> c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2163])]) ).
fof(f18468,plain,
( ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) )
| ~ spl0_1881
| ~ spl0_2163 ),
inference(resolution,[],[f18424,f14203]) ).
fof(f18424,plain,
( c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_2163 ),
inference(avatar_component_clause,[],[f18422]) ).
fof(f20698,plain,
( spl0_2299
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2230 ),
inference(avatar_split_clause,[],[f20024,f20021,f14323,f9129,f7368,f20696]) ).
fof(f20696,plain,
( spl0_2299
<=> ! [X12,X0,X1] :
( c_List_Oreplicate(c_1,X0,X1) = c_List_Osublist(c_List_Oreplicate(c_1,X0,X1),X12,X1)
| ~ c_in(c_0,X12,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2299])]) ).
fof(f20021,plain,
( spl0_2230
<=> ! [X0,X12,X1] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2230])]) ).
fof(f20024,plain,
( ! [X0,X1,X12] :
( c_List_Oreplicate(c_1,X0,X1) = c_List_Osublist(c_List_Oreplicate(c_1,X0,X1),X12,X1)
| ~ c_in(c_0,X12,tc_nat) )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2230 ),
inference(forward_demodulation,[],[f20022,f15117]) ).
fof(f20022,plain,
( ! [X0,X1,X12] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) )
| ~ spl0_2230 ),
inference(avatar_component_clause,[],[f20021]) ).
fof(f20694,plain,
( spl0_2298
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2229 ),
inference(avatar_split_clause,[],[f20019,f20016,f14323,f9129,f7368,f20692]) ).
fof(f20692,plain,
( spl0_2298
<=> ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Oreplicate(c_1,X0,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2298])]) ).
fof(f20016,plain,
( spl0_2229
<=> ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2229])]) ).
fof(f20019,plain,
( ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Oreplicate(c_1,X0,X41),X41)
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2229 ),
inference(forward_demodulation,[],[f20017,f15117]) ).
fof(f20017,plain,
( ! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41)
| ~ spl0_2229 ),
inference(avatar_component_clause,[],[f20016]) ).
fof(f20600,plain,
( spl0_2297
| ~ spl0_1513
| ~ spl0_2236 ),
inference(avatar_split_clause,[],[f20179,f20046,f10664,f20598]) ).
fof(f10664,plain,
( spl0_1513
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1513])]) ).
fof(f20179,plain,
( ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,v_H,tc_Message_Omsg) )
| ~ spl0_1513
| ~ spl0_2236 ),
inference(resolution,[],[f20047,f10665]) ).
fof(f10665,plain,
( ! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,X88,tc_Message_Omsg) )
| ~ spl0_1513 ),
inference(avatar_component_clause,[],[f10664]) ).
fof(f20515,plain,
( spl0_2296
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2218 ),
inference(avatar_split_clause,[],[f19958,f19955,f14323,f9129,f7368,f20513]) ).
fof(f20513,plain,
( spl0_2296
<=> ! [X1,X3] :
( c_append(c_List_Obutlast(X3,X1),c_List_Oreplicate(c_1,c_List_Olast(X3,X1),X1),X1) = X3
| c_List_Olist_ONil = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2296])]) ).
fof(f19955,plain,
( spl0_2218
<=> ! [X1,X3] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2218])]) ).
fof(f19958,plain,
( ! [X3,X1] :
( c_append(c_List_Obutlast(X3,X1),c_List_Oreplicate(c_1,c_List_Olast(X3,X1),X1),X1) = X3
| c_List_Olist_ONil = X3 )
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2218 ),
inference(forward_demodulation,[],[f19956,f15117]) ).
fof(f19956,plain,
( ! [X3,X1] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 )
| ~ spl0_2218 ),
inference(avatar_component_clause,[],[f19955]) ).
fof(f20322,plain,
( spl0_2293
| spl0_2295 ),
inference(avatar_split_clause,[],[f3006,f20320,f20299]) ).
fof(f20299,plain,
( spl0_2293
<=> ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2293])]) ).
fof(f20320,plain,
( spl0_2295
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2295])]) ).
fof(f3006,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_0,X1),X1) ),
inference(inner_rewriting,[],[f2334]) ).
fof(f2334,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__eq__number__of_3) ).
fof(f20308,plain,
( ~ spl0_1124
| ~ spl0_2293 ),
inference(avatar_contradiction_clause,[],[f20307]) ).
fof(f20307,plain,
( $false
| ~ spl0_1124
| ~ spl0_2293 ),
inference(trivial_inequality_removal,[],[f20305]) ).
fof(f20305,plain,
( c_0 != c_0
| ~ spl0_1124
| ~ spl0_2293 ),
inference(superposition,[],[f20300,f8846]) ).
fof(f8846,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat)
| ~ spl0_1124 ),
inference(avatar_component_clause,[],[f8844]) ).
fof(f8844,plain,
( spl0_1124
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1124])]) ).
fof(f20300,plain,
( ! [X11] : c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ spl0_2293 ),
inference(avatar_component_clause,[],[f20299]) ).
fof(f20304,plain,
( spl0_2293
| spl0_2294 ),
inference(avatar_split_clause,[],[f3005,f20302,f20299]) ).
fof(f20302,plain,
( spl0_2294
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1)
| ~ class_Ring__and__Field_Oordered__idom(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2294])]) ).
fof(f3005,plain,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_0,X1),c_0,X1) ),
inference(inner_rewriting,[],[f2317]) ).
fof(f2317,axiom,
! [X0,X11,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 != c_Numeral_Onumber__of(X11,tc_nat)
| ~ c_lessequals(c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__le__zero__eq__number__of_0) ).
fof(f20297,plain,
spl0_2292,
inference(avatar_split_clause,[],[f3001,f20295]) ).
fof(f20295,plain,
( spl0_2292
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2292])]) ).
fof(f3001,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1313,f2114]) ).
fof(f2114,axiom,
! [X3] : c_Numeral_Obin__add(c_Numeral_OPls,X3) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__Pls_0) ).
fof(f1313,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__10_1) ).
fof(f20293,plain,
spl0_2291,
inference(avatar_split_clause,[],[f2999,f20291]) ).
fof(f20291,plain,
( spl0_2291
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2291])]) ).
fof(f2999,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f1325,f2114]) ).
fof(f1325,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__16_1) ).
fof(f20289,plain,
spl0_2290,
inference(avatar_split_clause,[],[f2991,f20287]) ).
fof(f20287,plain,
( spl0_2290
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2290])]) ).
fof(f2991,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1312,f2114]) ).
fof(f1312,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__10_0) ).
fof(f20285,plain,
spl0_2289,
inference(avatar_split_clause,[],[f2989,f20283]) ).
fof(f20283,plain,
( spl0_2289
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2289])]) ).
fof(f2989,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f1324,f2114]) ).
fof(f1324,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X0)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__16_0) ).
fof(f20281,plain,
spl0_2288,
inference(avatar_split_clause,[],[f2957,f20279]) ).
fof(f20279,plain,
( spl0_2288
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2288])]) ).
fof(f2957,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f1336,f2156]) ).
fof(f1336,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__7_1) ).
fof(f20277,plain,
( spl0_2287
| ~ spl0_1243
| ~ spl0_2236 ),
inference(avatar_split_clause,[],[f20184,f20046,f9347,f20275]) ).
fof(f20275,plain,
( spl0_2287
<=> ! [X4] : c_in(c_Message_Omsg_ONumber(X4),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2287])]) ).
fof(f20184,plain,
( ! [X4] : c_in(c_Message_Omsg_ONumber(X4),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1243
| ~ spl0_2236 ),
inference(resolution,[],[f20047,f9348]) ).
fof(f20270,plain,
( spl0_2286
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2285 ),
inference(avatar_split_clause,[],[f20266,f20262,f11543,f9209,f20268]) ).
fof(f20268,plain,
( spl0_2286
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2286])]) ).
fof(f20262,plain,
( spl0_2285
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2285])]) ).
fof(f20266,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2285 ),
inference(forward_demodulation,[],[f20265,f9210]) ).
fof(f20265,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1619
| ~ spl0_2285 ),
inference(forward_demodulation,[],[f20263,f11545]) ).
fof(f20263,plain,
( ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_2285 ),
inference(avatar_component_clause,[],[f20262]) ).
fof(f20264,plain,
spl0_2285,
inference(avatar_split_clause,[],[f2956,f20262]) ).
fof(f2956,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f1340,f2156]) ).
fof(f1340,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__9_1) ).
fof(f20260,plain,
spl0_2284,
inference(avatar_split_clause,[],[f2951,f20258]) ).
fof(f20258,plain,
( spl0_2284
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2284])]) ).
fof(f2951,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X3)),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f1335,f2156]) ).
fof(f1335,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__7_0) ).
fof(f20249,plain,
( spl0_2283
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2282 ),
inference(avatar_split_clause,[],[f20245,f20241,f11543,f9209,f20247]) ).
fof(f20247,plain,
( spl0_2283
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2283])]) ).
fof(f20241,plain,
( spl0_2282
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2282])]) ).
fof(f20245,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__pred(X0),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2282 ),
inference(forward_demodulation,[],[f20244,f9210]) ).
fof(f20244,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OMin),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_1619
| ~ spl0_2282 ),
inference(forward_demodulation,[],[f20242,f11545]) ).
fof(f20242,plain,
( ! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) )
| ~ spl0_2282 ),
inference(avatar_component_clause,[],[f20241]) ).
fof(f20243,plain,
spl0_2282,
inference(avatar_split_clause,[],[f2950,f20241]) ).
fof(f2950,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f1339,f2156]) ).
fof(f1339,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__9_0) ).
fof(f20238,plain,
( spl0_2281
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2280 ),
inference(avatar_split_clause,[],[f20234,f20230,f11543,f9209,f20236]) ).
fof(f20236,plain,
( spl0_2281
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__pred(X47),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2281])]) ).
fof(f20230,plain,
( spl0_2280
<=> ! [X1,X47] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2280])]) ).
fof(f20234,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__pred(X47),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1209
| ~ spl0_1619
| ~ spl0_2280 ),
inference(forward_demodulation,[],[f20233,f9210]) ).
fof(f20233,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OMin),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1619
| ~ spl0_2280 ),
inference(forward_demodulation,[],[f20231,f11545]) ).
fof(f20231,plain,
( ! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_2280 ),
inference(avatar_component_clause,[],[f20230]) ).
fof(f20232,plain,
spl0_2280,
inference(avatar_split_clause,[],[f2890,f20230]) ).
fof(f2890,plain,
! [X47,X1] :
( c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1332,f2156]) ).
fof(f1332,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__5_0) ).
fof(f20228,plain,
( spl0_2279
| ~ spl0_1242
| ~ spl0_2236 ),
inference(avatar_split_clause,[],[f20182,f20046,f9343,f20226]) ).
fof(f20226,plain,
( spl0_2279
<=> ! [X2] : c_in(c_Message_Omsg_OAgent(X2),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2279])]) ).
fof(f20182,plain,
( ! [X2] : c_in(c_Message_Omsg_OAgent(X2),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1242
| ~ spl0_2236 ),
inference(resolution,[],[f20047,f9344]) ).
fof(f20224,plain,
spl0_2278,
inference(avatar_split_clause,[],[f2889,f20222]) ).
fof(f20222,plain,
( spl0_2278
<=> ! [X11,X1] :
( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2278])]) ).
fof(f2889,plain,
! [X11,X1] :
( c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obin__minus(X11)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1331,f2156]) ).
fof(f1331,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_minus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obin__minus(X11)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__4_0) ).
fof(f20220,plain,
spl0_2277,
inference(avatar_split_clause,[],[f2776,f20218]) ).
fof(f20218,plain,
( spl0_2277
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2277])]) ).
fof(f2776,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OHash__synth_0) ).
fof(f20216,plain,
spl0_2276,
inference(avatar_split_clause,[],[f2675,f20214]) ).
fof(f20214,plain,
( spl0_2276
<=> ! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2276])]) ).
fof(f2675,axiom,
! [X18,X1,X12] : c_insert(X18,X12,X1) = c_insert(X18,c_minus(X12,c_insert(X18,c_emptyset,X1),tc_set(X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__Diff__single_0) ).
fof(f20212,plain,
spl0_2275,
inference(avatar_split_clause,[],[f2650,f20210]) ).
fof(f20210,plain,
( spl0_2275
<=> ! [X13,X12,X1] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2275])]) ).
fof(f2650,axiom,
! [X1,X12,X13] : c_Union(c_union(X12,X13,tc_set(X1)),X1) = c_union(c_Union(X12,X1),c_Union(X13,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__Un__distrib_0) ).
fof(f20208,plain,
spl0_2274,
inference(avatar_split_clause,[],[f2624,f20206]) ).
fof(f20206,plain,
( spl0_2274
<=> ! [X13,X12,X1] : c_Pow(c_inter(X12,X13,X1),X1) = c_inter(c_Pow(X12,X1),c_Pow(X13,X1),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2274])]) ).
fof(f2624,axiom,
! [X1,X12,X13] : c_Pow(c_inter(X12,X13,X1),X1) = c_inter(c_Pow(X12,X1),c_Pow(X13,X1),tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OPow__Int__eq_0) ).
fof(f20204,plain,
spl0_2273,
inference(avatar_split_clause,[],[f2596,f20202]) ).
fof(f20202,plain,
( spl0_2273
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2273])]) ).
fof(f2596,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__iff_2) ).
fof(f20200,plain,
spl0_2272,
inference(avatar_split_clause,[],[f2585,f20198]) ).
fof(f20198,plain,
( spl0_2272
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2272])]) ).
fof(f2585,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__subset__Compl__iff_1) ).
fof(f20196,plain,
spl0_2271,
inference(avatar_split_clause,[],[f2584,f20194]) ).
fof(f20194,plain,
( spl0_2271
<=> ! [X13,X12,X1] :
( c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2271])]) ).
fof(f2584,axiom,
! [X1,X12,X13] :
( c_lessequals(X13,X12,tc_set(X1))
| ~ c_lessequals(c_uminus(X12,tc_set(X1)),c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__subset__Compl__iff_0) ).
fof(f20192,plain,
spl0_2270,
inference(avatar_split_clause,[],[f2574,f20190]) ).
fof(f2574,axiom,
! [X1,X12,X13] : c_uminus(c_minus(X12,X13,tc_set(X1)),tc_set(X1)) = c_union(c_uminus(X12,tc_set(X1)),X13,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__Diff__eq_0) ).
fof(f20188,plain,
spl0_2269,
inference(avatar_split_clause,[],[f2506,f20186]) ).
fof(f20186,plain,
( spl0_2269
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_times(X18,c_divide(X27,X18,X1),X1) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2269])]) ).
fof(f2506,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_times(X18,c_divide(X27,X18,X1),X1) = X27 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Otimes__divide__self__right_1) ).
fof(f20178,plain,
spl0_2268,
inference(avatar_split_clause,[],[f2504,f20176]) ).
fof(f20176,plain,
( spl0_2268
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_times(c_divide(X27,X18,X1),X18,X1) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2268])]) ).
fof(f2504,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_times(c_divide(X27,X18,X1),X18,X1) = X27 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Otimes__divide__self__left_1) ).
fof(f20174,plain,
spl0_2267,
inference(avatar_split_clause,[],[f2486,f20172]) ).
fof(f20172,plain,
( spl0_2267
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(c_times(X18,c_0,X1),c_times(X27,c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2267])]) ).
fof(f2486,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(c_times(X18,c_0,X1),c_times(X27,c_0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__right__if_0) ).
fof(f20170,plain,
spl0_2266,
inference(avatar_split_clause,[],[f2485,f20168]) ).
fof(f20168,plain,
( spl0_2266
<=> ! [X4,X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_times(X18,X4,X1),X4,X1) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2266])]) ).
fof(f2485,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_times(X18,X4,X1),X4,X1) = X18 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__right__if2_1) ).
fof(f20166,plain,
spl0_2265,
inference(avatar_split_clause,[],[f2480,f20164]) ).
fof(f20164,plain,
( spl0_2265
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(c_times(c_0,X18,X1),c_times(c_0,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2265])]) ).
fof(f2480,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(c_times(c_0,X18,X1),c_times(c_0,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__left__if_0) ).
fof(f20162,plain,
spl0_2264,
inference(avatar_split_clause,[],[f2479,f20160]) ).
fof(f20160,plain,
( spl0_2264
<=> ! [X4,X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_times(X4,X18,X1),X4,X1) = X18 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2264])]) ).
fof(f2479,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X4
| c_divide(c_times(X4,X18,X1),X4,X1) = X18 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__divide__cancel__left__if2_1) ).
fof(f20158,plain,
spl0_2263,
inference(avatar_split_clause,[],[f2403,f20156]) ).
fof(f20156,plain,
( spl0_2263
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_divide(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2263])]) ).
fof(f2403,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_divide(X18,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__eq__0__iff_0) ).
fof(f20154,plain,
spl0_2262,
inference(avatar_split_clause,[],[f2360,f20152]) ).
fof(f20152,plain,
( spl0_2262
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2262])]) ).
fof(f2360,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Ozero__less__power__abs__iff_1) ).
fof(f20150,plain,
spl0_2261,
inference(avatar_split_clause,[],[f2359,f20148]) ).
fof(f20148,plain,
( spl0_2261
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2261])]) ).
fof(f2359,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Ozero__less__power__abs__iff_0) ).
fof(f20146,plain,
spl0_2260,
inference(avatar_split_clause,[],[f2194,f20144]) ).
fof(f20144,plain,
( spl0_2260
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2260])]) ).
fof(f2194,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__less__cancel__right_1) ).
fof(f20142,plain,
spl0_2259,
inference(avatar_split_clause,[],[f2193,f20140]) ).
fof(f20140,plain,
( spl0_2259
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2259])]) ).
fof(f2193,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__less__cancel__right_0) ).
fof(f20138,plain,
( spl0_2258
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2215 ),
inference(avatar_split_clause,[],[f20002,f19942,f14629,f9315,f20135]) ).
fof(f20135,plain,
( spl0_2258
<=> c_Message_Oparts(c_UNIV) = c_union(c_Message_Oparts(c_UNIV),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2258])]) ).
fof(f20002,plain,
( c_Message_Oparts(c_UNIV) = c_union(c_Message_Oparts(c_UNIV),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2215 ),
inference(forward_demodulation,[],[f19992,f9316]) ).
fof(f19992,plain,
( c_union(c_Message_Oparts(c_UNIV),c_emptyset,tc_Message_Omsg) = c_union(c_Message_Oparts(c_UNIV),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ spl0_1976
| ~ spl0_2215 ),
inference(superposition,[],[f14630,f19944]) ).
fof(f20133,plain,
spl0_2257,
inference(avatar_split_clause,[],[f2192,f20131]) ).
fof(f20131,plain,
( spl0_2257
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2257])]) ).
fof(f2192,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__less__cancel__left_1) ).
fof(f20129,plain,
spl0_2256,
inference(avatar_split_clause,[],[f2191,f20127]) ).
fof(f20127,plain,
( spl0_2256
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2256])]) ).
fof(f2191,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__less__cancel__left_0) ).
fof(f20125,plain,
spl0_2255,
inference(avatar_split_clause,[],[f2189,f20123]) ).
fof(f20123,plain,
( spl0_2255
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2255])]) ).
fof(f2189,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__le__cancel__right_1) ).
fof(f20121,plain,
spl0_2254,
inference(avatar_split_clause,[],[f2188,f20119]) ).
fof(f20119,plain,
( spl0_2254
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2254])]) ).
fof(f2188,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X18,X4,X1),c_plus(X27,X4,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__le__cancel__right_0) ).
fof(f20117,plain,
spl0_2253,
inference(avatar_split_clause,[],[f2187,f20115]) ).
fof(f20115,plain,
( spl0_2253
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2253])]) ).
fof(f2187,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__le__cancel__left_1) ).
fof(f20113,plain,
spl0_2252,
inference(avatar_split_clause,[],[f2186,f20111]) ).
fof(f20111,plain,
( spl0_2252
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2252])]) ).
fof(f2186,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_plus(X4,X18,X1),c_plus(X4,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__le__cancel__left_0) ).
fof(f20109,plain,
spl0_2251,
inference(avatar_split_clause,[],[f2146,f20107]) ).
fof(f20107,plain,
( spl0_2251
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2251])]) ).
fof(f2146,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__4_1) ).
fof(f20105,plain,
spl0_2250,
inference(avatar_split_clause,[],[f2145,f20103]) ).
fof(f20103,plain,
( spl0_2250
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2250])]) ).
fof(f2145,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB0),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__4_0) ).
fof(f20101,plain,
spl0_2249,
inference(avatar_split_clause,[],[f2138,f20099]) ).
fof(f20099,plain,
( spl0_2249
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2249])]) ).
fof(f2138,axiom,
! [X0,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__12_1) ).
fof(f20097,plain,
spl0_2248,
inference(avatar_split_clause,[],[f2137,f20095]) ).
fof(f20095,plain,
( spl0_2248
<=> ! [X11,X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2248])]) ).
fof(f2137,axiom,
! [X0,X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X11,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OBit(X11,X0),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__12_0) ).
fof(f20093,plain,
( spl0_2247
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2215 ),
inference(avatar_split_clause,[],[f20001,f19942,f14625,f9311,f20090]) ).
fof(f20090,plain,
( spl0_2247
<=> c_Message_Oparts(c_UNIV) = c_union(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2247])]) ).
fof(f20001,plain,
( c_Message_Oparts(c_UNIV) = c_union(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2215 ),
inference(forward_demodulation,[],[f19991,f9312]) ).
fof(f19991,plain,
( c_union(c_emptyset,c_Message_Oparts(c_UNIV),tc_Message_Omsg) = c_union(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1975
| ~ spl0_2215 ),
inference(superposition,[],[f14626,f19944]) ).
fof(f20088,plain,
spl0_2246,
inference(avatar_split_clause,[],[f2119,f20086]) ).
fof(f2119,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__mult(X47,X11),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__4_0) ).
fof(f20084,plain,
spl0_2245,
inference(avatar_split_clause,[],[f2116,f20082]) ).
fof(f2116,axiom,
! [X11,X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,X11),X1) = c_plus(c_Numeral_Onumber__of(X47,X1),c_Numeral_Onumber__of(X11,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__1_0) ).
fof(f20080,plain,
spl0_2244,
inference(avatar_split_clause,[],[f1971,f20078]) ).
fof(f20078,plain,
( spl0_2244
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(c_1,X2),X18,X2)
| c_less(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2244])]) ).
fof(f1971,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(c_1,X2),X18,X2)
| c_less(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__less__iff__1_1) ).
fof(f20076,plain,
spl0_2243,
inference(avatar_split_clause,[],[f1970,f20074]) ).
fof(f20074,plain,
( spl0_2243
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(X18,X2),c_1,X2)
| c_less(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2243])]) ).
fof(f1970,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_uminus(X18,X2),c_1,X2)
| c_less(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__less__iff__1_0) ).
fof(f20072,plain,
spl0_2242,
inference(avatar_split_clause,[],[f1967,f20070]) ).
fof(f20070,plain,
( spl0_2242
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2242])]) ).
fof(f1967,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(c_1,X2),X18,X2)
| c_lessequals(c_uminus(X18,X2),c_1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__le__iff__1_1) ).
fof(f20068,plain,
spl0_2241,
inference(avatar_split_clause,[],[f1966,f20066]) ).
fof(f20066,plain,
( spl0_2241
<=> ! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2241])]) ).
fof(f1966,axiom,
! [X2,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_uminus(X18,X2),c_1,X2)
| c_lessequals(c_uminus(c_1,X2),X18,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ominus__le__iff__1_0) ).
fof(f20064,plain,
spl0_2240,
inference(avatar_split_clause,[],[f1960,f20062]) ).
fof(f20062,plain,
( spl0_2240
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2240])]) ).
fof(f1960,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(X27,c_uminus(c_1,X2),X2)
| c_less(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__minus__iff__1_1) ).
fof(f20060,plain,
spl0_2239,
inference(avatar_split_clause,[],[f1959,f20058]) ).
fof(f20058,plain,
( spl0_2239
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2239])]) ).
fof(f1959,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_less(c_1,c_uminus(X27,X2),X2)
| c_less(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oless__minus__iff__1_0) ).
fof(f20056,plain,
spl0_2238,
inference(avatar_split_clause,[],[f1944,f20054]) ).
fof(f20054,plain,
( spl0_2238
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2238])]) ).
fof(f1944,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(X27,c_uminus(c_1,X2),X2)
| c_lessequals(c_1,c_uminus(X27,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__minus__iff__1_1) ).
fof(f20052,plain,
spl0_2237,
inference(avatar_split_clause,[],[f1943,f20050]) ).
fof(f20050,plain,
( spl0_2237
<=> ! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2237])]) ).
fof(f1943,axiom,
! [X2,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X2)
| ~ class_HOL_Oone(X2)
| ~ c_lessequals(c_1,c_uminus(X27,X2),X2)
| c_lessequals(X27,c_uminus(c_1,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Ole__minus__iff__1_0) ).
fof(f20048,plain,
( spl0_2236
| ~ spl0_1881
| ~ spl0_2184 ),
inference(avatar_split_clause,[],[f18572,f18514,f14202,f20046]) ).
fof(f18572,plain,
( ! [X0] :
( c_in(X0,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ c_in(X0,c_Message_Osynth(v_H),tc_Message_Omsg) )
| ~ spl0_1881
| ~ spl0_2184 ),
inference(resolution,[],[f18516,f14203]) ).
fof(f20044,plain,
spl0_2235,
inference(avatar_split_clause,[],[f1932,f20042]) ).
fof(f20042,plain,
( spl0_2235
<=> ! [X2,X11] :
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Numeral_Onumber(X2)
| c_HOL_Oinverse(c_Numeral_Onumber__of(X11,X2),X2) = c_divide(c_1,c_Numeral_Onumber__of(X11,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2235])]) ).
fof(f1932,axiom,
! [X2,X11] :
( ~ class_Ring__and__Field_Ofield(X2)
| ~ class_Numeral_Onumber(X2)
| c_HOL_Oinverse(c_Numeral_Onumber__of(X11,X2),X2) = c_divide(c_1,c_Numeral_Onumber__of(X11,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oinverse__eq__divide__number__of_0) ).
fof(f20040,plain,
spl0_2234,
inference(avatar_split_clause,[],[f1922,f20038]) ).
fof(f20038,plain,
( spl0_2234
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_divide(X0,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_uminus(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2234])]) ).
fof(f1922,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_divide(X0,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) = c_uminus(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Odivide__minus1_0) ).
fof(f20036,plain,
spl0_2233,
inference(avatar_split_clause,[],[f1869,f20034]) ).
fof(f20034,plain,
( spl0_2233
<=> ! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2233])]) ).
fof(f1869,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,X1) = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oof__nat__number__of__eq_1) ).
fof(f20032,plain,
spl0_2232,
inference(avatar_split_clause,[],[f1780,f20030]) ).
fof(f20030,plain,
( spl0_2232
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2232])]) ).
fof(f1780,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Otl(c_append(X23,X25,X1),X1) = c_append(c_List_Otl(X23,X1),X25,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otl__append2_0) ).
fof(f20028,plain,
spl0_2231,
inference(avatar_split_clause,[],[f1769,f20026]) ).
fof(f20026,plain,
( spl0_2231
<=> ! [X0,X23,X21,X1] : c_List_Otake(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(X21,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2231])]) ).
fof(f1769,axiom,
! [X21,X0,X1,X23] : c_List_Otake(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olist_OCons(X0,c_List_Otake(X21,X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__Suc__Cons_0) ).
fof(f20023,plain,
spl0_2230,
inference(avatar_split_clause,[],[f1764,f20021]) ).
fof(f1764,axiom,
! [X0,X1,X12] :
( ~ c_in(c_0,X12,tc_nat)
| c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osublist__singleton_0) ).
fof(f20018,plain,
spl0_2229,
inference(avatar_split_clause,[],[f1724,f20016]) ).
fof(f1724,axiom,
! [X41,X0,X23] : c_List_Orev(c_List_Olist_OCons(X0,X23,X41),X41) = c_append(c_List_Orev(X23,X41),c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev_Osimps__2_0) ).
fof(f20014,plain,
spl0_2228,
inference(avatar_split_clause,[],[f1713,f20012]) ).
fof(f20012,plain,
( spl0_2228
<=> ! [X41,X0,X23] :
( ~ c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2228])]) ).
fof(f1713,axiom,
! [X41,X0,X23] :
( ~ c_in(X0,c_List_Oset(X23,X41),X41)
| c_List_Oremdups(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Oremdups(X23,X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremdups_Osimps__2_0) ).
fof(f20010,plain,
spl0_2227,
inference(avatar_split_clause,[],[f1703,f20008]) ).
fof(f20008,plain,
( spl0_2227
<=> ! [X43,X23,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Otake(X21,X23,X1),X43,X1) = c_List_Onth(X23,X43,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2227])]) ).
fof(f1703,axiom,
! [X21,X1,X23,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Otake(X21,X23,X1),X43,X1) = c_List_Onth(X23,X43,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__take_0) ).
fof(f20006,plain,
spl0_2226,
inference(avatar_split_clause,[],[f1701,f20004]) ).
fof(f20004,plain,
( spl0_2226
<=> ! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2226])]) ).
fof(f1701,axiom,
! [X21,X1,X23] :
( ~ c_less(X21,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat)
| c_in(c_List_Onth(X23,X21,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__mem_0) ).
fof(f19986,plain,
spl0_2225,
inference(avatar_split_clause,[],[f1700,f19984]) ).
fof(f19984,plain,
( spl0_2225
<=> ! [X59,X0,X23,X43,X1] :
( X43 = X59
| c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2225])]) ).
fof(f1700,axiom,
! [X59,X0,X1,X23,X43] :
( X43 = X59
| c_List_Onth(c_List_Olist__update(X23,X43,X0,X1),X59,X1) = c_List_Onth(X23,X59,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__list__update__neq_0) ).
fof(f19982,plain,
spl0_2224,
inference(avatar_split_clause,[],[f1637,f19980]) ).
fof(f19980,plain,
( spl0_2224
<=> ! [X13,X12,X1] : c_List_Olists(c_inter(X12,X13,X1),X1) = c_inter(c_List_Olists(X12,X1),c_List_Olists(X13,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2224])]) ).
fof(f1637,axiom,
! [X1,X12,X13] : c_List_Olists(c_inter(X12,X13,X1),X1) = c_inter(c_List_Olists(X12,X1),c_List_Olists(X13,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olists__Int__eq_0) ).
fof(f19978,plain,
spl0_2223,
inference(avatar_split_clause,[],[f1618,f19976]) ).
fof(f19976,plain,
( spl0_2223
<=> ! [X5,X1,X0] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2223])]) ).
fof(f1618,axiom,
! [X0,X1,X5] : ~ c_in(c_Pair(X0,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olexord(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexord__Nil__right_0) ).
fof(f19974,plain,
spl0_2222,
inference(avatar_split_clause,[],[f1605,f19972]) ).
fof(f19972,plain,
( spl0_2222
<=> ! [X1,X23] :
( c_List_Oremdups(X23,X1) = X23
| c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2222])]) ).
fof(f1605,axiom,
! [X1,X23] :
( c_List_Oremdups(X23,X1) = X23
| c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)) != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__remdups__eq_0) ).
fof(f19970,plain,
spl0_2221,
inference(avatar_split_clause,[],[f1557,f19968]) ).
fof(f19968,plain,
( spl0_2221
<=> ! [X25,X1,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2221])]) ).
fof(f1557,axiom,
! [X1,X25,X23] :
( ~ c_List_Odistinct(c_append(X23,X25,X1),X1)
| c_emptyset = c_inter(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__append_2) ).
fof(f19966,plain,
spl0_2220,
inference(avatar_split_clause,[],[f1545,f19964]) ).
fof(f19964,plain,
( spl0_2220
<=> ! [X25,X1,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2220])]) ).
fof(f1545,axiom,
! [X1,X25,X23] : c_List_Oconcat(c_append(X23,X25,tc_List_Olist(X1)),X1) = c_append(c_List_Oconcat(X23,X1),c_List_Oconcat(X25,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oconcat__append_0) ).
fof(f19962,plain,
spl0_2219,
inference(avatar_split_clause,[],[f1538,f19960]) ).
fof(f19960,plain,
( spl0_2219
<=> ! [X41,X0,X23] :
( c_List_Olist_ONil = X23
| c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2219])]) ).
fof(f1538,axiom,
! [X41,X0,X23] :
( c_List_Olist_ONil = X23
| c_List_Obutlast(c_List_Olist_OCons(X0,X23,X41),X41) = c_List_Olist_OCons(X0,c_List_Obutlast(X23,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Obutlast_Osimps__2_1) ).
fof(f19957,plain,
spl0_2218,
inference(avatar_split_clause,[],[f1519,f19955]) ).
fof(f1519,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_append(c_List_Obutlast(X3,X1),c_List_Olist_OCons(c_List_Olast(X3,X1),c_List_Olist_ONil,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__butlast__last__id_0) ).
fof(f19953,plain,
spl0_2217,
inference(avatar_split_clause,[],[f1515,f19951]) ).
fof(f19951,plain,
( spl0_2217
<=> ! [X25,X5,X1] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2217])]) ).
fof(f1515,axiom,
! [X1,X5,X25] : ~ c_in(c_Pair(c_List_Olist_ONil,X25,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__notin__lex_0) ).
fof(f19949,plain,
spl0_2216,
inference(avatar_split_clause,[],[f1507,f19947]) ).
fof(f19947,plain,
( spl0_2216
<=> ! [X50,X1,X24] :
( c_List_Olist_ONil = X24
| c_List_Olist_ONil != c_List_Oconcat(X50,X1)
| ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2216])]) ).
fof(f1507,axiom,
! [X50,X1,X24] :
( c_List_Olist_ONil = X24
| c_List_Olist_ONil != c_List_Oconcat(X50,X1)
| ~ c_in(X24,c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__eq__concat__conv_0) ).
fof(f19945,plain,
( spl0_2215
| ~ spl0_1838
| ~ spl0_2163 ),
inference(avatar_split_clause,[],[f18470,f18422,f12970,f19942]) ).
fof(f18470,plain,
( c_emptyset = c_minus(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_1838
| ~ spl0_2163 ),
inference(resolution,[],[f18424,f12971]) ).
fof(f19940,plain,
spl0_2214,
inference(avatar_split_clause,[],[f1506,f19938]) ).
fof(f19938,plain,
( spl0_2214
<=> ! [X5,X1,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2214])]) ).
fof(f1506,axiom,
! [X1,X5,X23] : ~ c_in(c_Pair(X23,c_List_Olist_ONil,tc_List_Olist(X1),tc_List_Olist(X1)),c_List_Olex(X5,X1),tc_prod(tc_List_Olist(X1),tc_List_Olist(X1))),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil2__notin__lex_0) ).
fof(f19936,plain,
spl0_2213,
inference(avatar_split_clause,[],[f1311,f19934]) ).
fof(f19934,plain,
( spl0_2213
<=> ! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2213])]) ).
fof(f1311,axiom,
! [X21,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oabs__power__minus__one_0) ).
fof(f19932,plain,
spl0_2212,
inference(avatar_split_clause,[],[f1303,f19930]) ).
fof(f19930,plain,
( spl0_2212
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2212])]) ).
fof(f1303,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X21,X15,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__add2_H_0) ).
fof(f19928,plain,
spl0_2211,
inference(avatar_split_clause,[],[f1302,f19926]) ).
fof(f19926,plain,
( spl0_2211
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2211])]) ).
fof(f1302,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(X15,c_plus(X15,X21,tc_nat),tc_nat,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__add2_0) ).
fof(f19924,plain,
spl0_2210,
inference(avatar_split_clause,[],[f1301,f19922]) ).
fof(f19922,plain,
( spl0_2210
<=> ! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2210])]) ).
fof(f1301,axiom,
! [X21,X15] : c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)) = c_GCD_Ogcd(c_Pair(c_plus(X15,X21,tc_nat),X21,tc_nat,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__add1_0) ).
fof(f19920,plain,
spl0_2209,
inference(avatar_split_clause,[],[f1272,f19918]) ).
fof(f19918,plain,
( spl0_2209
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2209])]) ).
fof(f1272,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMin(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__in_0) ).
fof(f19916,plain,
spl0_2208,
inference(avatar_split_clause,[],[f1257,f19914]) ).
fof(f19914,plain,
( spl0_2208
<=> ! [X12,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2208])]) ).
fof(f1257,axiom,
! [X1,X12] :
( ~ class_Orderings_Olinorder(X1)
| c_emptyset = X12
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Finite__Set_OMax(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__in_0) ).
fof(f19912,plain,
spl0_2207,
inference(avatar_split_clause,[],[f81,f19910]) ).
fof(f19910,plain,
( spl0_2207
<=> ! [X12,X1,X18] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2207])]) ).
fof(f81,axiom,
! [X18,X1,X12] :
( ~ c_in(X18,X12,X1)
| c_in(c_Pair(X18,X18,X1,X1),c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OdiagI_0) ).
fof(f19908,plain,
spl0_2206,
inference(avatar_split_clause,[],[f47,f19906]) ).
fof(f19906,plain,
( spl0_2206
<=> ! [X12,X1,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2206])]) ).
fof(f47,axiom,
! [X1,X12,X23] :
( c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1))
| c_in(c_Main_Oin__listsI__1(X12,X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oin__listsI_0) ).
fof(f19446,plain,
( spl0_2204
| ~ spl0_2205
| ~ spl0_1497
| ~ spl0_2202 ),
inference(avatar_split_clause,[],[f19392,f19126,f10599,f19443,f19439]) ).
fof(f19443,plain,
( spl0_2205
<=> c_emptyset = c_Message_Oparts(c_UNIV) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2205])]) ).
fof(f19392,plain,
( c_emptyset != c_Message_Oparts(c_UNIV)
| c_emptyset = c_Message_Osynth(v_H)
| ~ spl0_1497
| ~ spl0_2202 ),
inference(superposition,[],[f10600,f19128]) ).
fof(f19287,plain,
( spl0_2203
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2201 ),
inference(avatar_split_clause,[],[f18863,f18609,f14629,f9315,f19284]) ).
fof(f19284,plain,
( spl0_2203
<=> c_Message_Oparts(c_UNIV) = c_union(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2203])]) ).
fof(f18863,plain,
( c_Message_Oparts(c_UNIV) = c_union(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_Message_Omsg)
| ~ spl0_1235
| ~ spl0_1976
| ~ spl0_2201 ),
inference(forward_demodulation,[],[f18854,f9316]) ).
fof(f18854,plain,
( c_union(c_Message_Oparts(c_UNIV),c_Message_Osynth(v_H),tc_Message_Omsg) = c_union(c_Message_Oparts(c_UNIV),c_emptyset,tc_Message_Omsg)
| ~ spl0_1976
| ~ spl0_2201 ),
inference(superposition,[],[f14630,f18611]) ).
fof(f19129,plain,
( spl0_2202
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2201 ),
inference(avatar_split_clause,[],[f18862,f18609,f14625,f9311,f19126]) ).
fof(f18862,plain,
( c_Message_Oparts(c_UNIV) = c_union(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1234
| ~ spl0_1975
| ~ spl0_2201 ),
inference(forward_demodulation,[],[f18853,f9312]) ).
fof(f18853,plain,
( c_union(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_Message_Omsg) = c_union(c_emptyset,c_Message_Oparts(c_UNIV),tc_Message_Omsg)
| ~ spl0_1975
| ~ spl0_2201 ),
inference(superposition,[],[f14626,f18611]) ).
fof(f18612,plain,
( spl0_2201
| ~ spl0_1838
| ~ spl0_2184 ),
inference(avatar_split_clause,[],[f18574,f18514,f12970,f18609]) ).
fof(f18574,plain,
( c_emptyset = c_minus(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_1838
| ~ spl0_2184 ),
inference(resolution,[],[f18516,f12971]) ).
fof(f18604,plain,
spl0_2200,
inference(avatar_split_clause,[],[f3004,f18602]) ).
fof(f18602,plain,
( spl0_2200
<=> ! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2200])]) ).
fof(f3004,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f3003,f2115]) ).
fof(f2115,axiom,
! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__Pls__right_0) ).
fof(f3003,plain,
! [X0,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f1317,f2126]) ).
fof(f2126,axiom,
c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__minus__Pls_0) ).
fof(f1317,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__12_1) ).
fof(f18600,plain,
spl0_2199,
inference(avatar_split_clause,[],[f2997,f18598]) ).
fof(f18598,plain,
( spl0_2199
<=> ! [X1,X3] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2199])]) ).
fof(f2997,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f2996,f2115]) ).
fof(f2996,plain,
! [X3,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1321,f2126]) ).
fof(f1321,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__14_1) ).
fof(f18596,plain,
spl0_2198,
inference(avatar_split_clause,[],[f2994,f18594]) ).
fof(f18594,plain,
( spl0_2198
<=> ! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2198])]) ).
fof(f2994,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f2993,f2115]) ).
fof(f2993,plain,
! [X0,X1] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1) ),
inference(forward_demodulation,[],[f1316,f2126]) ).
fof(f1316,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_Numeral_Onumber__of(X0,X1),c_0,X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__12_0) ).
fof(f18592,plain,
spl0_2197,
inference(avatar_split_clause,[],[f2987,f18590]) ).
fof(f18590,plain,
( spl0_2197
<=> ! [X1,X3] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2197])]) ).
fof(f2987,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X3,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f2986,f2115]) ).
fof(f2986,plain,
! [X3,X1] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1) ),
inference(forward_demodulation,[],[f1320,f2126]) ).
fof(f1320,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,c_Numeral_Onumber__of(X3,X1),X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__add(X3,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__14_0) ).
fof(f18588,plain,
spl0_2196,
inference(avatar_split_clause,[],[f2968,f18586]) ).
fof(f18586,plain,
( spl0_2196
<=> ! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2196])]) ).
fof(f2968,plain,
! [X21,X15] :
( c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f2097,f2016]) ).
fof(f2097,axiom,
! [X21,X15] :
( ~ c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_1,X15,tc_nat)
| c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oone__le__mult__iff_2) ).
fof(f18584,plain,
spl0_2195,
inference(avatar_split_clause,[],[f2888,f18582]) ).
fof(f18582,plain,
( spl0_2195
<=> ! [X1,X47] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2195])]) ).
fof(f2888,plain,
! [X47,X1] :
( c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1330,f2156]) ).
fof(f1330,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_Numeral_Onumber__of(X47,X1),c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(X47,c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__3_0) ).
fof(f18580,plain,
spl0_2194,
inference(avatar_split_clause,[],[f2887,f18578]) ).
fof(f18578,plain,
( spl0_2194
<=> ! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2194])]) ).
fof(f2887,plain,
! [X11,X1] :
( c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_Obin__succ(c_Numeral_OPls),X11),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1329,f2156]) ).
fof(f1329,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X11),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__2_0) ).
fof(f18570,plain,
spl0_2193,
inference(avatar_split_clause,[],[f2872,f18568]) ).
fof(f18568,plain,
( spl0_2193
<=> ! [X5,X1] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2193])]) ).
fof(f2872,plain,
! [X1,X5] : c_List_Olistset(c_List_Olist_ONil,X1) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_List_Olistset(c_List_Olist_ONil,X1),tc_List_Olist(X1),tc_List_Olist(X1)),
inference(forward_demodulation,[],[f1636,f1639]) ).
fof(f1639,axiom,
! [X41] : c_List_Olistset(c_List_Olist_ONil,X41) = c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X41)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistset_Osimps__1_0) ).
fof(f1636,axiom,
! [X1,X5] : c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)) = c_Relation_OImage(c_List_Olistrel(X5,X1),c_insert(c_List_Olist_ONil,c_emptyset,tc_List_Olist(X1)),tc_List_Olist(X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistrel__Nil_0) ).
fof(f18550,plain,
( spl0_2192
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1660
| ~ spl0_2191 ),
inference(avatar_split_clause,[],[f18546,f18543,f11770,f9161,f7368,f18548]) ).
fof(f18548,plain,
( spl0_2192
<=> ! [X18,X64,X1] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_Suc(c_Nat_Osize(X64,tc_List_Olist(X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2192])]) ).
fof(f18543,plain,
( spl0_2191
<=> ! [X18,X64,X1] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2191])]) ).
fof(f18546,plain,
( ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_Suc(c_Nat_Osize(X64,tc_List_Olist(X1)))
| ~ spl0_1057
| ~ spl0_1197
| ~ spl0_1660
| ~ spl0_2191 ),
inference(forward_demodulation,[],[f18544,f12162]) ).
fof(f18544,plain,
( ! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat)
| ~ spl0_2191 ),
inference(avatar_component_clause,[],[f18543]) ).
fof(f18545,plain,
spl0_2191,
inference(avatar_split_clause,[],[f2869,f18543]) ).
fof(f2869,plain,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_1,tc_nat),
inference(forward_demodulation,[],[f1627,f2016]) ).
fof(f1627,axiom,
! [X18,X1,X64] : c_Nat_Osize(c_List_Olist_OCons(X18,X64,X1),tc_List_Olist(X1)) = c_plus(c_Nat_Osize(X64,tc_List_Olist(X1)),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist_Osize__2_0) ).
fof(f18541,plain,
spl0_2190,
inference(avatar_split_clause,[],[f2864,f18539]) ).
fof(f18539,plain,
( spl0_2190
<=> ! [X18,X13,X32,X1] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2190])]) ).
fof(f2864,plain,
! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_union(X13,c_insert(X18,X32,X1),X1),
inference(forward_demodulation,[],[f2643,f2644]) ).
fof(f2644,axiom,
! [X18,X1,X12,X13] : c_union(X12,c_insert(X18,X13,X1),X1) = c_insert(X18,c_union(X12,X13,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__insert__right_0) ).
fof(f2643,axiom,
! [X18,X1,X32,X13] : c_union(c_insert(X18,X13,X1),X32,X1) = c_insert(X18,c_union(X13,X32,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__insert__left_0) ).
fof(f18537,plain,
spl0_2189,
inference(avatar_split_clause,[],[f2722,f18535]) ).
fof(f18535,plain,
( spl0_2189
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2189])]) ).
fof(f2722,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_Wellfounded__Recursion_Owf(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Owf__insert_0) ).
fof(f18533,plain,
spl0_2188,
inference(avatar_split_clause,[],[f2719,f18531]) ).
fof(f18531,plain,
( spl0_2188
<=> ! [X5,X1,X0,X3] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2188])]) ).
fof(f2719,axiom,
! [X3,X0,X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_insert(c_Pair(X3,X0,X1,X1),X5,tc_prod(X1,X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Oacyclic__insert_0) ).
fof(f18529,plain,
spl0_2187,
inference(avatar_split_clause,[],[f2678,f18527]) ).
fof(f18527,plain,
( spl0_2187
<=> ! [X13,X12,X1,X18] :
( c_emptyset = c_inter(X12,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2187])]) ).
fof(f2678,axiom,
! [X1,X18,X12,X13] :
( c_emptyset = c_inter(X12,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__disjoint__1_1) ).
fof(f18525,plain,
spl0_2186,
inference(avatar_split_clause,[],[f2665,f18523]) ).
fof(f18523,plain,
( spl0_2186
<=> ! [X13,X12,X27,X1] :
( c_emptyset = c_inter(X12,X13,X1)
| c_emptyset != c_inter(X12,c_insert(X27,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2186])]) ).
fof(f2665,axiom,
! [X1,X27,X12,X13] :
( c_emptyset = c_inter(X12,X13,X1)
| c_emptyset != c_inter(X12,c_insert(X27,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Odisjoint__insert__2_1) ).
fof(f18521,plain,
spl0_2185,
inference(avatar_split_clause,[],[f2657,f18519]) ).
fof(f2657,axiom,
! [X1,X24,X12,X32] :
( ~ c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| c_in(X12,c_Union(X32,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__iff_2) ).
fof(f18517,plain,
( spl0_2184
| ~ spl0_1997
| ~ spl0_2163 ),
inference(avatar_split_clause,[],[f18466,f18422,f14722,f18514]) ).
fof(f18466,plain,
( c_lessequals(c_Message_Osynth(v_H),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_1997
| ~ spl0_2163 ),
inference(resolution,[],[f18424,f14723]) ).
fof(f18512,plain,
spl0_2183,
inference(avatar_split_clause,[],[f2644,f18510]) ).
fof(f18508,plain,
spl0_2182,
inference(avatar_split_clause,[],[f2640,f18506]) ).
fof(f2640,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__iff_0) ).
fof(f18504,plain,
spl0_2181,
inference(avatar_split_clause,[],[f2620,f18502]) ).
fof(f18502,plain,
( spl0_2181
<=> ! [X24,X12,X32,X1] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2181])]) ).
fof(f2620,axiom,
! [X1,X24,X12,X32] :
( c_in(X12,X24,X1)
| ~ c_in(X24,X32,tc_set(X1))
| ~ c_in(X12,c_Inter(X32,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__iff_0) ).
fof(f18500,plain,
spl0_2180,
inference(avatar_split_clause,[],[f2608,f18498]) ).
fof(f18498,plain,
( spl0_2180
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_inter(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2180])]) ).
fof(f2608,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,X12,X1)
| c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__iff_2) ).
fof(f18496,plain,
spl0_2179,
inference(avatar_split_clause,[],[f2593,f18494]) ).
fof(f18494,plain,
( spl0_2179
<=> ! [X13,X12,X1] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2179])]) ).
fof(f2593,axiom,
! [X1,X12,X13] : c_minus(X12,X13,tc_set(X1)) = c_minus(c_minus(X12,X13,tc_set(X1)),X13,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__idemp_0) ).
fof(f18492,plain,
spl0_2178,
inference(avatar_split_clause,[],[f2572,f18490]) ).
fof(f18490,plain,
( spl0_2178
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2178])]) ).
fof(f2572,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OlessThan__subset__iff_1) ).
fof(f18488,plain,
spl0_2177,
inference(avatar_split_clause,[],[f2571,f18486]) ).
fof(f18486,plain,
( spl0_2177
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2177])]) ).
fof(f2571,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OlessThan(X0,X1),c_SetInterval_OlessThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OlessThan__subset__iff_0) ).
fof(f18484,plain,
spl0_2176,
inference(avatar_split_clause,[],[f2561,f18482]) ).
fof(f18482,plain,
( spl0_2176
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2176])]) ).
fof(f2561,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThan__subset__iff_1) ).
fof(f18480,plain,
spl0_2175,
inference(avatar_split_clause,[],[f2560,f18478]) ).
fof(f2560,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OgreaterThan(X0,X1),c_SetInterval_OgreaterThan(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThan__subset__iff_0) ).
fof(f18476,plain,
spl0_2174,
inference(avatar_split_clause,[],[f2548,f18474]) ).
fof(f18474,plain,
( spl0_2174
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2174])]) ).
fof(f2548,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,c_plus(X26,c_1,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__greaterThanLessThan__int_0) ).
fof(f18465,plain,
spl0_2173,
inference(avatar_split_clause,[],[f2541,f18463]) ).
fof(f18463,plain,
( spl0_2173
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2173])]) ).
fof(f2541,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_plus(c_minus(X14,X26,tc_IntDef_Oint),c_1,tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__atLeastAtMost__int_0) ).
fof(f18461,plain,
spl0_2172,
inference(avatar_split_clause,[],[f2539,f18459]) ).
fof(f18459,plain,
( spl0_2172
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2172])]) ).
fof(f2539,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X0,X3,X1)
| c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatMost__subset__iff_1) ).
fof(f18457,plain,
spl0_2171,
inference(avatar_split_clause,[],[f2538,f18455]) ).
fof(f18455,plain,
( spl0_2171
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2171])]) ).
fof(f2538,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X3,X1)
| ~ c_lessequals(c_SetInterval_OatMost(X0,X1),c_SetInterval_OatMost(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatMost__subset__iff_0) ).
fof(f18453,plain,
spl0_2170,
inference(avatar_split_clause,[],[f2533,f18451]) ).
fof(f18451,plain,
( spl0_2170
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2170])]) ).
fof(f2533,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X3,X0,X1)
| c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeast__subset__iff_1) ).
fof(f18449,plain,
spl0_2169,
inference(avatar_split_clause,[],[f2532,f18447]) ).
fof(f18447,plain,
( spl0_2169
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2169])]) ).
fof(f2532,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X3,X0,X1)
| ~ c_lessequals(c_SetInterval_OatLeast(X0,X1),c_SetInterval_OatLeast(X3,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeast__subset__iff_0) ).
fof(f18445,plain,
spl0_2168,
inference(avatar_split_clause,[],[f2513,f18443]) ).
fof(f18443,plain,
( spl0_2168
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| c_less(c_0,c_divide(c_1,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2168])]) ).
fof(f2513,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X27,X1)
| c_less(c_0,c_divide(c_1,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ozero__less__divide__1__iff_1) ).
fof(f18441,plain,
spl0_2167,
inference(avatar_split_clause,[],[f2512,f18439]) ).
fof(f18439,plain,
( spl0_2167
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(c_0,X27,X1)
| ~ c_less(c_0,c_divide(c_1,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2167])]) ).
fof(f2512,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(c_0,X27,X1)
| ~ c_less(c_0,c_divide(c_1,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ozero__less__divide__1__iff_0) ).
fof(f18437,plain,
spl0_2166,
inference(avatar_split_clause,[],[f2510,f18435]) ).
fof(f18435,plain,
( spl0_2166
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_0,X27,X1)
| c_lessequals(c_0,c_divide(c_1,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2166])]) ).
fof(f2510,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_0,X27,X1)
| c_lessequals(c_0,c_divide(c_1,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ozero__le__divide__1__iff_1) ).
fof(f18433,plain,
spl0_2165,
inference(avatar_split_clause,[],[f2509,f18431]) ).
fof(f18431,plain,
( spl0_2165
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(c_0,X27,X1)
| ~ c_lessequals(c_0,c_divide(c_1,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2165])]) ).
fof(f2509,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(c_0,X27,X1)
| ~ c_lessequals(c_0,c_divide(c_1,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ozero__le__divide__1__iff_0) ).
fof(f18429,plain,
spl0_2164,
inference(avatar_split_clause,[],[f2490,f18427]) ).
fof(f18427,plain,
( spl0_2164
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2164])]) ).
fof(f2490,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_uminus(c_times(X18,X27,X1),X1) = c_times(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__minus__right_0) ).
fof(f18425,plain,
( spl0_2163
| ~ spl0_1144
| ~ spl0_2132 ),
inference(avatar_split_clause,[],[f18377,f18286,f8931,f18422]) ).
fof(f8931,plain,
( spl0_1144
<=> ! [X12,X1] : c_lessequals(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1144])]) ).
fof(f18286,plain,
( spl0_2132
<=> ! [X10] :
( c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(X10),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),X10,tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2132])]) ).
fof(f18377,plain,
( c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(c_UNIV),tc_set(tc_Message_Omsg))
| ~ spl0_1144
| ~ spl0_2132 ),
inference(resolution,[],[f18287,f8932]) ).
fof(f8932,plain,
( ! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1))
| ~ spl0_1144 ),
inference(avatar_component_clause,[],[f8931]) ).
fof(f18287,plain,
( ! [X10] :
( ~ c_lessequals(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),X10,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(X10),tc_set(tc_Message_Omsg)) )
| ~ spl0_2132 ),
inference(avatar_component_clause,[],[f18286]) ).
fof(f18420,plain,
spl0_2162,
inference(avatar_split_clause,[],[f2489,f18418]) ).
fof(f18418,plain,
( spl0_2162
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2162])]) ).
fof(f2489,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(c_uminus(X18,X1),X27,X1) = c_uminus(c_times(X18,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__minus__left_0) ).
fof(f18416,plain,
spl0_2161,
inference(avatar_split_clause,[],[f2467,f18414]) ).
fof(f18414,plain,
( spl0_2161
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2161])]) ).
fof(f2467,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oring(X1)
| c_times(X18,X27,X1) = c_times(c_uminus(X18,X1),c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ominus__mult__minus_0) ).
fof(f18412,plain,
spl0_2160,
inference(avatar_split_clause,[],[f2446,f18410]) ).
fof(f18410,plain,
( spl0_2160
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse(c_uminus(X18,X1),X1) = c_uminus(c_HOL_Oinverse(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2160])]) ).
fof(f2446,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse(c_uminus(X18,X1),X1) = c_uminus(c_HOL_Oinverse(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__minus__eq_0) ).
fof(f18408,plain,
spl0_2159,
inference(avatar_split_clause,[],[f2433,f18406]) ).
fof(f18406,plain,
( spl0_2159
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X27,X18,X1) = c_HOL_Oinverse(c_divide(X18,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2159])]) ).
fof(f2433,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X27,X18,X1) = c_HOL_Oinverse(c_divide(X18,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__divide_0) ).
fof(f18404,plain,
spl0_2158,
inference(avatar_split_clause,[],[f2422,f18402]) ).
fof(f18402,plain,
( spl0_2158
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_divide(c_uminus(X18,X1),X27,X1) = c_uminus(c_divide(X18,X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2158])]) ).
fof(f2422,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_divide(c_uminus(X18,X1),X27,X1) = c_uminus(c_divide(X18,X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__minus__left_0) ).
fof(f18400,plain,
spl0_2157,
inference(avatar_split_clause,[],[f2417,f18398]) ).
fof(f18398,plain,
( spl0_2157
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| c_less(c_divide(c_1,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2157])]) ).
fof(f2417,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X27,c_0,X1)
| c_less(c_divide(c_1,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__less__0__1__iff_1) ).
fof(f18396,plain,
spl0_2156,
inference(avatar_split_clause,[],[f2416,f18394]) ).
fof(f18394,plain,
( spl0_2156
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(X27,c_0,X1)
| ~ c_less(c_divide(c_1,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2156])]) ).
fof(f2416,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(X27,c_0,X1)
| ~ c_less(c_divide(c_1,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__less__0__1__iff_0) ).
fof(f18392,plain,
spl0_2155,
inference(avatar_split_clause,[],[f2411,f18390]) ).
fof(f18390,plain,
( spl0_2155
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X27,c_0,X1)
| c_lessequals(c_divide(c_1,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2155])]) ).
fof(f2411,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X27,c_0,X1)
| c_lessequals(c_divide(c_1,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__le__0__1__iff_1) ).
fof(f18388,plain,
spl0_2154,
inference(avatar_split_clause,[],[f2410,f18386]) ).
fof(f18386,plain,
( spl0_2154
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(X27,c_0,X1)
| ~ c_lessequals(c_divide(c_1,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2154])]) ).
fof(f2410,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(X27,c_0,X1)
| ~ c_lessequals(c_divide(c_1,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__le__0__1__iff_0) ).
fof(f18384,plain,
spl0_2153,
inference(avatar_split_clause,[],[f2393,f18382]) ).
fof(f18382,plain,
( spl0_2153
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oabs(c_HOL_Oinverse(X18,X1),X1) = c_HOL_Oinverse(c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2153])]) ).
fof(f2393,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_HOL_Oabs(c_HOL_Oinverse(X18,X1),X1) = c_HOL_Oinverse(c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oabs__inverse_0) ).
fof(f18374,plain,
spl0_2152,
inference(avatar_split_clause,[],[f2312,f18372]) ).
fof(f18372,plain,
( spl0_2152
<=> ! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2152])]) ).
fof(f2312,axiom,
! [X11,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Numeral_Onumber__of(X11,tc_nat)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(X11,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Opower__0__left__number__of_1) ).
fof(f18370,plain,
spl0_2151,
inference(avatar_split_clause,[],[f2306,f18368]) ).
fof(f18368,plain,
( spl0_2151
<=> ! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2151])]) ).
fof(f2306,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Power_Orecpower(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oneg__one__even__power_0) ).
fof(f18366,plain,
spl0_2150,
inference(avatar_split_clause,[],[f2304,f18364]) ).
fof(f18364,plain,
( spl0_2150
<=> ! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2150])]) ).
fof(f2304,axiom,
! [X0,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_1 = c_Nat_Opower(c_uminus(c_1,X1),X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ominus__one__even__power_0) ).
fof(f18362,plain,
spl0_2149,
inference(avatar_split_clause,[],[f2209,f18360]) ).
fof(f18360,plain,
( spl0_2149
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2149])]) ).
fof(f2209,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_1) ).
fof(f18358,plain,
spl0_2148,
inference(avatar_split_clause,[],[f2208,f18356]) ).
fof(f18356,plain,
( spl0_2148
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2148])]) ).
fof(f2208,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ class_Orderings_Olinorder(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odouble__add__less__zero__iff__single__less__zero_0) ).
fof(f18354,plain,
spl0_2147,
inference(avatar_split_clause,[],[f2080,f18352]) ).
fof(f18352,plain,
( spl0_2147
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2147])]) ).
fof(f2080,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__0__less__mult__iff_2) ).
fof(f18350,plain,
spl0_2146,
inference(avatar_split_clause,[],[f2060,f18348]) ).
fof(f18348,plain,
( spl0_2146
<=> ! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2146])]) ).
fof(f2060,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X15,X16,tc_nat) != c_times(X21,X16,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__cancel2_0) ).
fof(f18346,plain,
spl0_2145,
inference(avatar_split_clause,[],[f2058,f18344]) ).
fof(f18344,plain,
( spl0_2145
<=> ! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2145])]) ).
fof(f2058,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_0 = X16
| c_times(X16,X15,tc_nat) != c_times(X16,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__cancel1_0) ).
fof(f18342,plain,
spl0_2144,
inference(avatar_split_clause,[],[f2037,f18340]) ).
fof(f18340,plain,
( spl0_2144
<=> ! [X16,X59,X43] : c_minus(c_minus(X43,X59,tc_nat),X16,tc_nat) = c_minus(X43,c_plus(X59,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2144])]) ).
fof(f18338,plain,
spl0_2143,
inference(avatar_split_clause,[],[f2028,f18336]) ).
fof(f18336,plain,
( spl0_2143
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2143])]) ).
fof(f2028,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__gr__0_0) ).
fof(f18328,plain,
spl0_2142,
inference(avatar_split_clause,[],[f1863,f18326]) ).
fof(f18326,plain,
( spl0_2142
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2142])]) ).
fof(f1863,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_times(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Omult__nat__number__of_0) ).
fof(f18324,plain,
spl0_2141,
inference(avatar_split_clause,[],[f1860,f18322]) ).
fof(f18322,plain,
( spl0_2141
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2141])]) ).
fof(f1860,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Divides_Oop_Amod(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Omod__nat__number__of_0) ).
fof(f18320,plain,
spl0_2140,
inference(avatar_split_clause,[],[f1847,f18318]) ).
fof(f18318,plain,
( spl0_2140
<=> ! [X47] :
( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2140])]) ).
fof(f1847,axiom,
! [X47] :
( c_0 != c_Numeral_Onumber__of(X47,tc_nat)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__number__of__0_0) ).
fof(f18316,plain,
spl0_2139,
inference(avatar_split_clause,[],[f1827,f18314]) ).
fof(f18314,plain,
( spl0_2139
<=> ! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2139])]) ).
fof(f1827,axiom,
! [X83,X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_div(c_Numeral_Onumber__of(X47,tc_nat),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Odiv__nat__number__of_0) ).
fof(f18312,plain,
spl0_2138,
inference(avatar_split_clause,[],[f1801,f18310]) ).
fof(f18310,plain,
( spl0_2138
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2138])]) ).
fof(f1801,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Odiff__less_0) ).
fof(f18308,plain,
spl0_2137,
inference(avatar_split_clause,[],[f1776,f18306]) ).
fof(f18306,plain,
( spl0_2137
<=> ! [X15,X23,X21,X1] : c_List_Otake(X21,c_List_Otake(X15,X23,X1),X1) = c_List_Otake(c_Orderings_Omin(X21,X15,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2137])]) ).
fof(f1776,axiom,
! [X21,X1,X15,X23] : c_List_Otake(X21,c_List_Otake(X15,X23,X1),X1) = c_List_Otake(c_Orderings_Omin(X21,X15,tc_nat),X23,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__take_0) ).
fof(f18304,plain,
spl0_2136,
inference(avatar_split_clause,[],[f1775,f18302]) ).
fof(f18302,plain,
( spl0_2136
<=> ! [X43,X0,X16,X1] : c_List_Otake(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2136])]) ).
fof(f1775,axiom,
! [X0,X1,X16,X43] : c_List_Otake(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_Orderings_Omin(X43,X16,tc_nat),X0,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__replicate_0) ).
fof(f18300,plain,
spl0_2135,
inference(avatar_split_clause,[],[f1749,f18298]) ).
fof(f18298,plain,
( spl0_2135
<=> ! [X25,X1,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2135])]) ).
fof(f1749,axiom,
! [X1,X25,X23] : c_List_Oset(c_append(X23,X25,X1),X1) = c_union(c_List_Oset(X23,X1),c_List_Oset(X25,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__append_0) ).
fof(f18296,plain,
spl0_2134,
inference(avatar_split_clause,[],[f1739,f18294]) ).
fof(f1739,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| c_0 != c_Divides_Oop_Amod(X21,c_Nat_Osize(X3,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate__id_0) ).
fof(f18292,plain,
spl0_2133,
inference(avatar_split_clause,[],[f1708,f18290]) ).
fof(f18290,plain,
( spl0_2133
<=> ! [X41,X0,X23,X25] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2133])]) ).
fof(f1708,axiom,
! [X41,X0,X25,X23] : c_append(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Olist_OCons(X0,c_append(X23,X25,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oop_A_64_Oappend__Cons_0) ).
fof(f18288,plain,
( spl0_2132
| ~ spl0_1863
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f16416,f16338,f13072,f18286]) ).
fof(f16338,plain,
( spl0_2014
<=> c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2014])]) ).
fof(f16416,plain,
( ! [X10] :
( c_lessequals(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(X10),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),X10,tc_set(tc_Message_Omsg)) )
| ~ spl0_1863
| ~ spl0_2014 ),
inference(superposition,[],[f13073,f16340]) ).
fof(f16340,plain,
( c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_2014 ),
inference(avatar_component_clause,[],[f16338]) ).
fof(f18284,plain,
spl0_2131,
inference(avatar_split_clause,[],[f1696,f18282]) ).
fof(f18282,plain,
( spl0_2131
<=> ! [X3,X23,X25,X1] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2131])]) ).
fof(f1696,axiom,
! [X3,X1,X25,X23] : c_List_Onth(c_append(X23,c_List_Olist_OCons(X3,X25,X1),X1),c_Nat_Osize(X23,tc_List_Olist(X1)),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__append__length_0) ).
fof(f18280,plain,
spl0_2130,
inference(avatar_split_clause,[],[f1691,f18278]) ).
fof(f18278,plain,
( spl0_2130
<=> ! [X58,X0,X23,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2130])]) ).
fof(f1691,axiom,
! [X58,X0,X1,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Osublist(X23,X58,X1),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onotin__set__sublistI_0) ).
fof(f18276,plain,
spl0_2129,
inference(avatar_split_clause,[],[f1690,f18274]) ).
fof(f18274,plain,
( spl0_2129
<=> ! [X3,X0,X23,X1] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2129])]) ).
fof(f1690,axiom,
! [X3,X0,X1,X23] :
( c_in(X0,c_List_Oset(X23,X1),X1)
| ~ c_in(X0,c_List_Oset(c_List_Oremove1(X3,X23,X1),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onotin__set__remove1_0) ).
fof(f18272,plain,
spl0_2128,
inference(avatar_split_clause,[],[f1611,f18270]) ).
fof(f18270,plain,
( spl0_2128
<=> ! [X21,X1,X23] : c_Nat_Osize(c_List_Otake(X21,X23,X1),tc_List_Olist(X1)) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2128])]) ).
fof(f1611,axiom,
! [X21,X1,X23] : c_Nat_Osize(c_List_Otake(X21,X23,X1),tc_List_Olist(X1)) = c_Orderings_Omin(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__take_0) ).
fof(f18268,plain,
spl0_2127,
inference(avatar_split_clause,[],[f1601,f18266]) ).
fof(f18266,plain,
( spl0_2127
<=> ! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2127])]) ).
fof(f1601,axiom,
! [X21,X1,X23] : c_Nat_Osize(c_List_Odrop(X21,X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__drop_0) ).
fof(f18264,plain,
spl0_2126,
inference(avatar_split_clause,[],[f1587,f18262]) ).
fof(f18262,plain,
( spl0_2126
<=> ! [X41,X0,X23,X25] : c_List_Oitrev(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Oitrev(X23,c_List_Olist_OCons(X0,X25,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2126])]) ).
fof(f1587,axiom,
! [X41,X0,X25,X23] : c_List_Oitrev(c_List_Olist_OCons(X0,X23,X41),X25,X41) = c_List_Oitrev(X23,c_List_Olist_OCons(X0,X25,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oitrev_Osimps__2_0) ).
fof(f18260,plain,
spl0_2125,
inference(avatar_split_clause,[],[f1577,f18258]) ).
fof(f18258,plain,
( spl0_2125
<=> ! [X43,X0,X16,X1] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2125])]) ).
fof(f1577,axiom,
! [X0,X1,X16,X43] : c_List_Odrop(X43,c_List_Oreplicate(X16,X0,X1),X1) = c_List_Oreplicate(c_minus(X16,X43,tc_nat),X0,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__replicate_0) ).
fof(f18256,plain,
spl0_2124,
inference(avatar_split_clause,[],[f1574,f18254]) ).
fof(f18254,plain,
( spl0_2124
<=> ! [X15,X23,X21,X1] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2124])]) ).
fof(f1574,axiom,
! [X21,X1,X15,X23] : c_List_Odrop(X21,c_List_Odrop(X15,X23,X1),X1) = c_List_Odrop(c_plus(X21,X15,tc_nat),X23,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__drop_0) ).
fof(f18252,plain,
spl0_2123,
inference(avatar_split_clause,[],[f1554,f18250]) ).
fof(f18250,plain,
( spl0_2123
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(X23,X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2123])]) ).
fof(f1554,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(X23,X41)
| c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct_Osimps__2_2) ).
fof(f18248,plain,
spl0_2122,
inference(avatar_split_clause,[],[f1547,f18246]) ).
fof(f18246,plain,
( spl0_2122
<=> ! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2122])]) ).
fof(f1547,axiom,
! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_Oconcat__eq__Nil__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oconcat__eq__Nil__conv_1) ).
fof(f18244,plain,
( spl0_2121
| ~ spl0_1863
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f16415,f16338,f13072,f18242]) ).
fof(f18242,plain,
( spl0_2121
<=> ! [X9] :
( c_lessequals(c_Message_Oparts(X9),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X9,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2121])]) ).
fof(f16415,plain,
( ! [X9] :
( c_lessequals(c_Message_Oparts(X9),c_Message_Oparts(c_Message_Osynth(v_H)),tc_set(tc_Message_Omsg))
| ~ c_lessequals(X9,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_set(tc_Message_Omsg)) )
| ~ spl0_1863
| ~ spl0_2014 ),
inference(superposition,[],[f13073,f16340]) ).
fof(f18240,plain,
spl0_2120,
inference(avatar_split_clause,[],[f1518,f18238]) ).
fof(f18238,plain,
( spl0_2120
<=> ! [X51,X23,X25,X1] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2120])]) ).
fof(f1518,axiom,
! [X51,X1,X25,X23] : c_append(c_append(X23,X25,X1),X51,X1) = c_append(X23,c_append(X25,X51,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__assoc_0) ).
fof(f18236,plain,
spl0_2119,
inference(avatar_split_clause,[],[f1508,f18234]) ).
fof(f18234,plain,
( spl0_2119
<=> ! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2119])]) ).
fof(f1508,axiom,
! [X50,X1] :
( c_List_Olist_ONil = c_List_Oconcat(X50,X1)
| c_in(c_Main_ONil__eq__concat__conv__1(X50,X1),c_List_Oset(X50,tc_List_Olist(X1)),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__eq__concat__conv_1) ).
fof(f18232,plain,
spl0_2118,
inference(avatar_split_clause,[],[f1495,f18230]) ).
fof(f18230,plain,
( spl0_2118
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2118])]) ).
fof(f1495,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__zminus__zminus_0) ).
fof(f18228,plain,
spl0_2117,
inference(avatar_split_clause,[],[f1239,f18226]) ).
fof(f18226,plain,
( spl0_2117
<=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2117])]) ).
fof(f1239,axiom,
! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X21,X16,tc_nat),tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__mult__self2_0) ).
fof(f18224,plain,
spl0_2116,
inference(avatar_split_clause,[],[f1237,f18222]) ).
fof(f18222,plain,
( spl0_2116
<=> ! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2116])]) ).
fof(f1237,axiom,
! [X21,X16,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,c_times(X16,X21,tc_nat),tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__mult__self1_0) ).
fof(f18220,plain,
spl0_2115,
inference(avatar_split_clause,[],[f1217,f18218]) ).
fof(f18218,plain,
( spl0_2115
<=> ! [X21,X15] :
( ~ c_less(c_1,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2115])]) ).
fof(f1217,axiom,
! [X21,X15] :
( ~ c_less(c_1,X21,tc_nat)
| ~ c_less(c_0,X15,tc_nat)
| c_less(c_div(X15,X21,tc_nat),X15,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__less__dividend_0) ).
fof(f18216,plain,
spl0_2114,
inference(avatar_split_clause,[],[f1162,f18214]) ).
fof(f1162,axiom,
! [X21,X16] : c_Binomial_Obinomial(c_Suc(X21),c_Suc(X16)) = c_plus(c_Binomial_Obinomial(X21,X16),c_Binomial_Obinomial(X21,c_Suc(X16)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Binomial_Obinomial__Suc__Suc_0) ).
fof(f18212,plain,
spl0_2113,
inference(avatar_split_clause,[],[f127,f18210]) ).
fof(f18210,plain,
( spl0_2113
<=> ! [X35,X36,X2,X1] :
( ~ c_Wellfounded__Recursion_Owf(X35,X2)
| ~ c_Wellfounded__Recursion_Owf(X36,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2113])]) ).
fof(f127,axiom,
! [X2,X36,X1,X35] :
( ~ c_Wellfounded__Recursion_Owf(X35,X2)
| ~ c_Wellfounded__Recursion_Owf(X36,X1)
| c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Olex__prod(X36,X35,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Relations_Owf__lex__prod_0) ).
fof(f18208,plain,
spl0_2112,
inference(avatar_split_clause,[],[f125,f18206]) ).
fof(f18206,plain,
( spl0_2112
<=> ! [X34,X33,X2,X1] :
( ~ c_Relation_Otrans(X33,X2)
| ~ c_Relation_Otrans(X34,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2112])]) ).
fof(f125,axiom,
! [X2,X1,X34,X33] :
( ~ c_Relation_Otrans(X33,X2)
| ~ c_Relation_Otrans(X34,X1)
| c_Relation_Otrans(c_Wellfounded__Relations_Olex__prod(X34,X33,X1,X2),tc_prod(X1,X2)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Relations_Otrans__lex__prod_0) ).
fof(f18204,plain,
spl0_2111,
inference(avatar_split_clause,[],[f80,f18202]) ).
fof(f18202,plain,
( spl0_2111
<=> ! [X12,X1,X4] :
( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
| ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2111])]) ).
fof(f80,axiom,
! [X1,X4,X12] :
( c_in(c_Main_OdiagE__1(X12,X4,X1),X12,X1)
| ~ c_in(X4,c_Relation_Odiag(X12,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OdiagE_1) ).
fof(f18142,plain,
( spl0_2110
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2104 ),
inference(avatar_split_clause,[],[f16816,f16813,f14323,f9129,f7368,f18140]) ).
fof(f18140,plain,
( spl0_2110
<=> ! [X25,X1,X3] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_List_Oitrev(X25,c_List_Oreplicate(c_1,X3,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2110])]) ).
fof(f16813,plain,
( spl0_2104
<=> ! [X25,X1,X3] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_List_Oitrev(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2104])]) ).
fof(f16816,plain,
( ! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_List_Oitrev(X25,c_List_Oreplicate(c_1,X3,X1),X1),X1)
| ~ spl0_1057
| ~ spl0_1189
| ~ spl0_1907
| ~ spl0_2104 ),
inference(forward_demodulation,[],[f16814,f15117]) ).
fof(f16814,plain,
( ! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_List_Oitrev(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1)
| ~ spl0_2104 ),
inference(avatar_component_clause,[],[f16813]) ).
fof(f17871,plain,
( spl0_2109
| ~ spl0_1233
| ~ spl0_2014
| ~ spl0_2107 ),
inference(avatar_split_clause,[],[f17786,f17353,f16338,f9307,f17868]) ).
fof(f17868,plain,
( spl0_2109
<=> c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_union(c_Message_Osynth(v_H),c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2109])]) ).
fof(f9307,plain,
( spl0_1233
<=> ! [X1,X3] : c_union(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1233])]) ).
fof(f17353,plain,
( spl0_2107
<=> ! [X5] : c_Message_Oparts(c_union(X5,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_union(X5,c_Message_Osynth(v_H),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2107])]) ).
fof(f17786,plain,
( c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_union(c_Message_Osynth(v_H),c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg))
| ~ spl0_1233
| ~ spl0_2014
| ~ spl0_2107 ),
inference(forward_demodulation,[],[f17785,f16340]) ).
fof(f17785,plain,
( c_Message_Oparts(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)) = c_Message_Oparts(c_union(c_Message_Osynth(v_H),c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg))
| ~ spl0_1233
| ~ spl0_2107 ),
inference(forward_demodulation,[],[f17762,f2864]) ).
fof(f17762,plain,
( c_Message_Oparts(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)) = c_Message_Oparts(c_union(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_1233
| ~ spl0_2107 ),
inference(superposition,[],[f17354,f9308]) ).
fof(f9308,plain,
( ! [X3,X1] : c_union(X3,X3,X1) = X3
| ~ spl0_1233 ),
inference(avatar_component_clause,[],[f9307]) ).
fof(f17354,plain,
( ! [X5] : c_Message_Oparts(c_union(X5,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_union(X5,c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_2107 ),
inference(avatar_component_clause,[],[f17353]) ).
fof(f17552,plain,
( spl0_2108
| ~ spl0_1858
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f16429,f16338,f13052,f17550]) ).
fof(f17550,plain,
( spl0_2108
<=> ! [X6] : c_Message_Oparts(c_union(c_Message_Osynth(v_H),X6,tc_Message_Omsg)) = c_Message_Oparts(c_union(c_Message_Osynth(v_H),c_insert(v_X,X6,tc_Message_Omsg),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2108])]) ).
fof(f13052,plain,
( spl0_1858
<=> ! [X20,X88] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1858])]) ).
fof(f16429,plain,
( ! [X6] : c_Message_Oparts(c_union(c_Message_Osynth(v_H),X6,tc_Message_Omsg)) = c_Message_Oparts(c_union(c_Message_Osynth(v_H),c_insert(v_X,X6,tc_Message_Omsg),tc_Message_Omsg))
| ~ spl0_1858
| ~ spl0_2014 ),
inference(forward_demodulation,[],[f16428,f2864]) ).
fof(f16428,plain,
( ! [X6] : c_Message_Oparts(c_union(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),X6,tc_Message_Omsg)) = c_Message_Oparts(c_union(c_Message_Osynth(v_H),X6,tc_Message_Omsg))
| ~ spl0_1858
| ~ spl0_2014 ),
inference(forward_demodulation,[],[f16413,f13053]) ).
fof(f13053,plain,
( ! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg)
| ~ spl0_1858 ),
inference(avatar_component_clause,[],[f13052]) ).
fof(f16413,plain,
( ! [X6] : c_Message_Oparts(c_union(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),X6,tc_Message_Omsg)) = c_union(c_Message_Oparts(c_Message_Osynth(v_H)),c_Message_Oparts(X6),tc_Message_Omsg)
| ~ spl0_1858
| ~ spl0_2014 ),
inference(superposition,[],[f13053,f16340]) ).
fof(f17355,plain,
( spl0_2107
| ~ spl0_1858
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f16427,f16338,f13052,f17353]) ).
fof(f16427,plain,
( ! [X5] : c_Message_Oparts(c_union(X5,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)) = c_Message_Oparts(c_union(X5,c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_1858
| ~ spl0_2014 ),
inference(forward_demodulation,[],[f16412,f13053]) ).
fof(f16412,plain,
( ! [X5] : c_Message_Oparts(c_union(X5,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg)) = c_union(c_Message_Oparts(X5),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ spl0_1858
| ~ spl0_2014 ),
inference(superposition,[],[f13053,f16340]) ).
fof(f16991,plain,
( ~ spl0_2105
| spl0_2106
| ~ spl0_1874
| ~ spl0_2016 ),
inference(avatar_split_clause,[],[f16890,f16400,f14164,f16989,f16985]) ).
fof(f16989,plain,
( spl0_2106
<=> ! [X181] :
( v_X = X181
| ~ c_in(X181,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2106])]) ).
fof(f16890,plain,
( ! [X181] :
( v_X = X181
| ~ c_in(X181,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ c_Infinite__Set_Oatmost__one(c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg) )
| ~ spl0_1874
| ~ spl0_2016 ),
inference(resolution,[],[f16401,f14166]) ).
fof(f16815,plain,
spl0_2104,
inference(avatar_split_clause,[],[f2868,f16813]) ).
fof(f2868,plain,
! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_List_Oitrev(X25,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1),
inference(forward_demodulation,[],[f1727,f1585]) ).
fof(f1585,axiom,
! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oitrev_0) ).
fof(f1727,axiom,
! [X3,X1,X25] : c_List_Olist_OCons(X3,X25,X1) = c_List_Orev(c_append(c_List_Orev(X25,X1),c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__eq__Cons__iff_1) ).
fof(f16811,plain,
spl0_2103,
inference(avatar_split_clause,[],[f2863,f16809]) ).
fof(f16809,plain,
( spl0_2103
<=> ! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2103])]) ).
fof(f2863,plain,
! [X83] : c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)) = c_div(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat),
inference(forward_demodulation,[],[f1870,f2016]) ).
fof(f1870,axiom,
! [X83] : c_div(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) = c_IntDef_Onat(c_div(c_1,c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oone__div__nat__number__of_0) ).
fof(f16807,plain,
spl0_2102,
inference(avatar_split_clause,[],[f2745,f16805]) ).
fof(f16805,plain,
( spl0_2102
<=> ! [X86,X91,X88] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2102])]) ).
fof(f2745,axiom,
! [X91,X88,X86] : c_Message_OkeysFor(c_insert(c_Message_Omsg_OCrypt(X91,X86),X88,tc_Message_Omsg)) = c_insert(c_Message_OinvKey(X91),c_Message_OkeysFor(X88),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__Crypt_0) ).
fof(f16803,plain,
( spl0_2101
| ~ spl0_1511
| ~ spl0_2028 ),
inference(avatar_split_clause,[],[f16522,f16476,f10656,f16801]) ).
fof(f16801,plain,
( spl0_2101
<=> ! [X0] :
( c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ c_in(X0,c_insert(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2101])]) ).
fof(f16476,plain,
( spl0_2028
<=> c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2028])]) ).
fof(f16522,plain,
( ! [X0] :
( c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ c_in(X0,c_insert(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) )
| ~ spl0_1511
| ~ spl0_2028 ),
inference(superposition,[],[f10657,f16478]) ).
fof(f16478,plain,
( c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_2028 ),
inference(avatar_component_clause,[],[f16476]) ).
fof(f16799,plain,
spl0_2100,
inference(avatar_split_clause,[],[f2727,f16797]) ).
fof(f16797,plain,
( spl0_2100
<=> ! [X0,X3] :
( ~ c_less(X0,X3,tc_nat)
| c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2100])]) ).
fof(f2727,axiom,
! [X3,X0] :
( ~ c_less(X0,X3,tc_nat)
| c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Relations_Oless__than__iff_1) ).
fof(f16795,plain,
spl0_2099,
inference(avatar_split_clause,[],[f2726,f16793]) ).
fof(f16793,plain,
( spl0_2099
<=> ! [X0,X3] :
( c_less(X0,X3,tc_nat)
| ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2099])]) ).
fof(f2726,axiom,
! [X3,X0] :
( c_less(X0,X3,tc_nat)
| ~ c_in(c_Pair(X0,X3,tc_nat,tc_nat),c_Wellfounded__Relations_Oless__than,tc_prod(tc_nat,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Relations_Oless__than__iff_0) ).
fof(f16791,plain,
spl0_2098,
inference(avatar_split_clause,[],[f2711,f16789]) ).
fof(f16789,plain,
( spl0_2098
<=> ! [X85,X1] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X85,X1),c_Transitive__Closure_Ortrancl(X85,X1),X1,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2098])]) ).
fof(f2711,axiom,
! [X1,X85] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Relation_Orel__comp(c_Transitive__Closure_Ortrancl(X85,X1),c_Transitive__Closure_Ortrancl(X85,X1),X1,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Ortrancl__idemp__self__comp_0) ).
fof(f16787,plain,
spl0_2097,
inference(avatar_split_clause,[],[f2683,f16785]) ).
fof(f16785,plain,
( spl0_2097
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_in(X18,X12,X1)
| ~ c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2097])]) ).
fof(f2683,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_in(X18,X12,X1)
| ~ c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__iff_0) ).
fof(f16783,plain,
spl0_2096,
inference(avatar_split_clause,[],[f2658,f16781]) ).
fof(f16781,plain,
( spl0_2096
<=> ! [X13,X18,X1] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2096])]) ).
fof(f2658,axiom,
! [X18,X1,X13] : c_Union(c_insert(X18,X13,tc_set(X1)),X1) = c_union(X18,c_Union(X13,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__insert_0) ).
fof(f16779,plain,
spl0_2095,
inference(avatar_split_clause,[],[f2655,f16777]) ).
fof(f16777,plain,
( spl0_2095
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2095])]) ).
fof(f2655,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnion__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__iff_0) ).
fof(f16775,plain,
spl0_2094,
inference(avatar_split_clause,[],[f2623,f16773]) ).
fof(f2623,axiom,
! [X18,X1,X13] : c_Inter(c_insert(X18,X13,tc_set(X1)),X1) = c_inter(X18,c_Inter(X13,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__insert_0) ).
fof(f16771,plain,
spl0_2093,
inference(avatar_split_clause,[],[f2621,f16769]) ).
fof(f16769,plain,
( spl0_2093
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2093])]) ).
fof(f2621,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInter__iff__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__iff_1) ).
fof(f16767,plain,
spl0_2092,
inference(avatar_split_clause,[],[f2488,f16765]) ).
fof(f16765,plain,
( spl0_2092
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_times(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2092])]) ).
fof(f2488,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X1)
| c_0 = X18
| c_0 = X27
| c_0 != c_times(X18,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__eq__0__iff_0) ).
fof(f16763,plain,
spl0_2091,
inference(avatar_split_clause,[],[f2472,f16761]) ).
fof(f16761,plain,
( spl0_2091
<=> ! [X4,X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X27
| c_0 = X4
| c_times(X27,X4,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2091])]) ).
fof(f2472,axiom,
! [X1,X27,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X27
| c_0 = X4
| c_times(X27,X4,X1) != X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__cancel__right1_0) ).
fof(f16755,plain,
spl0_2090,
inference(avatar_split_clause,[],[f2471,f16753]) ).
fof(f16753,plain,
( spl0_2090
<=> ! [X18,X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X4,X18,X1) != X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2090])]) ).
fof(f2471,axiom,
! [X1,X18,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = X18
| c_0 = X4
| c_times(X4,X18,X1) != X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__cancel__left2_0) ).
fof(f16751,plain,
spl0_2089,
inference(avatar_split_clause,[],[f2457,f16749]) ).
fof(f16749,plain,
( spl0_2089
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_0,c_HOL_Oinverse(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2089])]) ).
fof(f2457,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_0,c_HOL_Oinverse(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__positive__iff__positive_1) ).
fof(f16747,plain,
spl0_2088,
inference(avatar_split_clause,[],[f2456,f16745]) ).
fof(f16745,plain,
( spl0_2088
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_0,c_HOL_Oinverse(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2088])]) ).
fof(f2456,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_0,c_HOL_Oinverse(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__positive__iff__positive_0) ).
fof(f16743,plain,
spl0_2087,
inference(avatar_split_clause,[],[f2453,f16741]) ).
fof(f16741,plain,
( spl0_2087
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_HOL_Oinverse(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2087])]) ).
fof(f2453,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_HOL_Oinverse(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_1) ).
fof(f16739,plain,
spl0_2086,
inference(avatar_split_clause,[],[f2452,f16737]) ).
fof(f16737,plain,
( spl0_2086
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_HOL_Oinverse(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2086])]) ).
fof(f2452,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_HOL_Oinverse(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__nonpositive__iff__nonpositive_0) ).
fof(f16735,plain,
spl0_2085,
inference(avatar_split_clause,[],[f2451,f16733]) ).
fof(f16733,plain,
( spl0_2085
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_HOL_Oinverse(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2085])]) ).
fof(f2451,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_HOL_Oinverse(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_1) ).
fof(f16731,plain,
spl0_2084,
inference(avatar_split_clause,[],[f2450,f16729]) ).
fof(f16729,plain,
( spl0_2084
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_HOL_Oinverse(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2084])]) ).
fof(f2450,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_HOL_Oinverse(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__nonnegative__iff__nonnegative_0) ).
fof(f16727,plain,
spl0_2083,
inference(avatar_split_clause,[],[f2449,f16725]) ).
fof(f16725,plain,
( spl0_2083
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_HOL_Oinverse(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2083])]) ).
fof(f2449,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_HOL_Oinverse(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__negative__iff__negative_1) ).
fof(f16723,plain,
spl0_2082,
inference(avatar_split_clause,[],[f2448,f16721]) ).
fof(f16721,plain,
( spl0_2082
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_HOL_Oinverse(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2082])]) ).
fof(f2448,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_HOL_Oinverse(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__negative__iff__negative_0) ).
fof(f16719,plain,
spl0_2081,
inference(avatar_split_clause,[],[f2436,f16717]) ).
fof(f16717,plain,
( spl0_2081
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_HOL_Oinverse(X18,X1) != c_HOL_Oinverse(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2081])]) ).
fof(f2436,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_HOL_Oinverse(X18,X1) != c_HOL_Oinverse(X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__eq__iff__eq_0) ).
fof(f16715,plain,
( spl0_2080
| ~ spl0_1511
| ~ spl0_2014 ),
inference(avatar_split_clause,[],[f16409,f16338,f10656,f16713]) ).
fof(f16713,plain,
( spl0_2080
<=> ! [X0] :
( c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ c_in(X0,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2080])]) ).
fof(f16409,plain,
( ! [X0] :
( c_in(X0,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ c_in(X0,c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg) )
| ~ spl0_1511
| ~ spl0_2014 ),
inference(superposition,[],[f10657,f16340]) ).
fof(f16711,plain,
spl0_2079,
inference(avatar_split_clause,[],[f2363,f16709]) ).
fof(f16709,plain,
( spl0_2079
<=> ! [X2,X42,X18,X84,X27,X1] :
( X27 = X84
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2079])]) ).
fof(f2363,axiom,
! [X2,X18,X1,X27,X84,X42] :
( X27 = X84
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Product__Type_OPair__eq_1) ).
fof(f16707,plain,
spl0_2078,
inference(avatar_split_clause,[],[f2362,f16705]) ).
fof(f16705,plain,
( spl0_2078
<=> ! [X18,X42,X84,X27,X2,X1] :
( X18 = X42
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2078])]) ).
fof(f2362,axiom,
! [X2,X18,X1,X27,X84,X42] :
( X18 = X42
| c_Pair(X18,X27,X1,X2) != c_Pair(X42,X84,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Product__Type_OPair__eq_0) ).
fof(f16703,plain,
spl0_2077,
inference(avatar_split_clause,[],[f2349,f16701]) ).
fof(f16701,plain,
( spl0_2077
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_0 = c_Nat_Opower(c_0,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2077])]) ).
fof(f2349,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_0 = c_Nat_Opower(c_0,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__eq__0__iff_2) ).
fof(f16699,plain,
spl0_2076,
inference(avatar_split_clause,[],[f2348,f16697]) ).
fof(f16697,plain,
( spl0_2076
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X21,tc_nat)
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2076])]) ).
fof(f2348,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X21,tc_nat)
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__eq__0__iff_1) ).
fof(f16695,plain,
spl0_2075,
inference(avatar_split_clause,[],[f2268,f16693]) ).
fof(f16693,plain,
( spl0_2075
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2075])]) ).
fof(f2268,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X0,X3,X2) = c_Orderings_Omax(X0,c_Orderings_Omax(X0,X3,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__sup_Osup__left__idem_0) ).
fof(f16691,plain,
spl0_2074,
inference(avatar_split_clause,[],[f2263,f16689]) ).
fof(f16689,plain,
( spl0_2074
<=> ! [X2,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2074])]) ).
fof(f2263,axiom,
! [X2,X3,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X0,X3,X2) = c_Orderings_Omin(X0,c_Orderings_Omin(X0,X3,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__inf_Oinf__left__idem_0) ).
fof(f16687,plain,
spl0_2073,
inference(avatar_split_clause,[],[f2246,f16685]) ).
fof(f16685,plain,
( spl0_2073
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2073])]) ).
fof(f2246,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Opprt(X18,X1),c_OrderedGroup_Opprt(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Opprt__mono_0) ).
fof(f16683,plain,
spl0_2072,
inference(avatar_split_clause,[],[f2242,f16681]) ).
fof(f16681,plain,
( spl0_2072
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2072])]) ).
fof(f2242,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_OrderedGroup_Onprt(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Onprt__mono_0) ).
fof(f16679,plain,
spl0_2071,
inference(avatar_split_clause,[],[f2236,f16677]) ).
fof(f16677,plain,
( spl0_2071
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2071])]) ).
fof(f2236,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__less__iff__less_1) ).
fof(f16675,plain,
spl0_2070,
inference(avatar_split_clause,[],[f2235,f16673]) ).
fof(f16673,plain,
( spl0_2070
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2070])]) ).
fof(f2235,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__less__iff__less_0) ).
fof(f16671,plain,
spl0_2069,
inference(avatar_split_clause,[],[f2232,f16669]) ).
fof(f16669,plain,
( spl0_2069
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2069])]) ).
fof(f2232,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__le__iff__le_1) ).
fof(f16667,plain,
spl0_2068,
inference(avatar_split_clause,[],[f2231,f16665]) ).
fof(f16665,plain,
( spl0_2068
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2068])]) ).
fof(f2231,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_uminus(X27,X1),c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__le__iff__le_0) ).
fof(f16663,plain,
spl0_2067,
inference(avatar_split_clause,[],[f2195,f16661]) ).
fof(f16661,plain,
( spl0_2067
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2067])]) ).
fof(f2195,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X4,X18,X1) != c_plus(X27,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__right__cancel_0) ).
fof(f16659,plain,
spl0_2066,
inference(avatar_split_clause,[],[f2190,f16657]) ).
fof(f16657,plain,
( spl0_2066
<=> ! [X18,X4,X27,X1] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2066])]) ).
fof(f2190,axiom,
! [X1,X18,X27,X4] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X1)
| X4 = X27
| c_plus(X18,X27,X1) != c_plus(X18,X4,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__left__cancel_0) ).
fof(f16655,plain,
spl0_2065,
inference(avatar_split_clause,[],[f2111,f16653]) ).
fof(f16653,plain,
( spl0_2065
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2065])]) ).
fof(f2111,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,c_Numeral_Obin__succ(X11)),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__BIT__11_0) ).
fof(f16651,plain,
spl0_2064,
inference(avatar_split_clause,[],[f2085,f16649]) ).
fof(f16649,plain,
( spl0_2064
<=> ! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2064])]) ).
fof(f2085,axiom,
! [X21,X16,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__add__left__cancel__less_1) ).
fof(f16647,plain,
spl0_2063,
inference(avatar_split_clause,[],[f2084,f16645]) ).
fof(f16645,plain,
( spl0_2063
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2063])]) ).
fof(f2084,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__add__left__cancel__less_0) ).
fof(f16643,plain,
spl0_2062,
inference(avatar_split_clause,[],[f2083,f16641]) ).
fof(f16641,plain,
( spl0_2062
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2062])]) ).
fof(f2083,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__add__left__cancel__le_1) ).
fof(f16639,plain,
spl0_2061,
inference(avatar_split_clause,[],[f2082,f16637]) ).
fof(f16637,plain,
( spl0_2061
<=> ! [X21,X16,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2061])]) ).
fof(f2082,axiom,
! [X21,X16,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_plus(X16,X15,tc_nat),c_plus(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__add__left__cancel__le_0) ).
fof(f16635,plain,
spl0_2060,
inference(avatar_split_clause,[],[f2076,f16633]) ).
fof(f16633,plain,
( spl0_2060
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2060])]) ).
fof(f2076,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__less__cancel2_1) ).
fof(f16631,plain,
spl0_2059,
inference(avatar_split_clause,[],[f2075,f16629]) ).
fof(f16629,plain,
( spl0_2059
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2059])]) ).
fof(f2075,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__less__cancel2_0) ).
fof(f16627,plain,
spl0_2058,
inference(avatar_split_clause,[],[f2073,f16625]) ).
fof(f16625,plain,
( spl0_2058
<=> ! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2058])]) ).
fof(f2073,axiom,
! [X21,X16,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__less__cancel1_1) ).
fof(f16623,plain,
spl0_2057,
inference(avatar_split_clause,[],[f2072,f16621]) ).
fof(f16621,plain,
( spl0_2057
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2057])]) ).
fof(f2072,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| ~ c_less(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__less__cancel1_0) ).
fof(f16619,plain,
spl0_2056,
inference(avatar_split_clause,[],[f2071,f16617]) ).
fof(f16617,plain,
( spl0_2056
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2056])]) ).
fof(f2071,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__le__cancel2_2) ).
fof(f16615,plain,
spl0_2055,
inference(avatar_split_clause,[],[f2070,f16613]) ).
fof(f16613,plain,
( spl0_2055
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2055])]) ).
fof(f2070,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X15,X16,tc_nat),c_times(X21,X16,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__le__cancel2_1) ).
fof(f16611,plain,
spl0_2054,
inference(avatar_split_clause,[],[f2068,f16609]) ).
fof(f16609,plain,
( spl0_2054
<=> ! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2054])]) ).
fof(f2068,axiom,
! [X21,X16,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__le__cancel1_2) ).
fof(f16607,plain,
spl0_2053,
inference(avatar_split_clause,[],[f2067,f16605]) ).
fof(f16605,plain,
( spl0_2053
<=> ! [X16,X21,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2053])]) ).
fof(f2067,axiom,
! [X21,X16,X15] :
( c_less(c_0,X16,tc_nat)
| c_lessequals(c_times(X16,X15,tc_nat),c_times(X16,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__le__cancel1_1) ).
fof(f16603,plain,
spl0_2052,
inference(avatar_split_clause,[],[f1927,f16601]) ).
fof(f16601,plain,
( spl0_2052
<=> ! [X2,X27] :
( ~ class_HOL_Oone(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_1 != c_uminus(X27,X2)
| c_uminus(c_1,X2) = X27 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2052])]) ).
fof(f1927,axiom,
! [X2,X27] :
( ~ class_HOL_Oone(X2)
| ~ class_OrderedGroup_Oab__group__add(X2)
| c_1 != c_uminus(X27,X2)
| c_uminus(c_1,X2) = X27 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oequation__minus__iff__1_0) ).
fof(f16599,plain,
spl0_2051,
inference(avatar_split_clause,[],[f1868,f16597]) ).
fof(f16597,plain,
( spl0_2051
<=> ! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2051])]) ).
fof(f1868,axiom,
! [X1,X47] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_NatArith_Oof__nat(c_Numeral_Onumber__of(X47,tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oof__nat__number__of__eq_0) ).
fof(f16595,plain,
spl0_2050,
inference(avatar_split_clause,[],[f1823,f16593]) ).
fof(f16593,plain,
( spl0_2050
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2050])]) ).
fof(f1823,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(X47),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_OSuc__nat__number__of_1) ).
fof(f16591,plain,
( spl0_2049
| ~ spl0_141
| ~ spl0_1984 ),
inference(avatar_split_clause,[],[f16118,f14665,f3701,f16589]) ).
fof(f16589,plain,
( spl0_2049
<=> ! [X19] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X19) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2049])]) ).
fof(f16118,plain,
( ! [X19] : ~ c_Wellfounded__Recursion_Owf(c_UNIV,X19)
| ~ spl0_141
| ~ spl0_1984 ),
inference(resolution,[],[f14666,f3702]) ).
fof(f16587,plain,
spl0_2048,
inference(avatar_split_clause,[],[f1820,f16585]) ).
fof(f16585,plain,
( spl0_2048
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X15,X21,tc_nat)
| c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2048])]) ).
fof(f1820,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(X15,X21,tc_nat)
| c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__less__iff_1) ).
fof(f16583,plain,
spl0_2047,
inference(avatar_split_clause,[],[f1819,f16581]) ).
fof(f16581,plain,
( spl0_2047
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(X15,X21,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2047])]) ).
fof(f1819,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(X15,X21,tc_nat)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__less__iff_0) ).
fof(f16579,plain,
spl0_2046,
inference(avatar_split_clause,[],[f1817,f16577]) ).
fof(f16577,plain,
( spl0_2046
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2046])]) ).
fof(f1817,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__le__iff_1) ).
fof(f16575,plain,
spl0_2045,
inference(avatar_split_clause,[],[f1816,f16573]) ).
fof(f16573,plain,
( spl0_2045
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2045])]) ).
fof(f1816,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__le__iff_0) ).
fof(f16571,plain,
spl0_2044,
inference(avatar_split_clause,[],[f1760,f16569]) ).
fof(f16569,plain,
( spl0_2044
<=> ! [X0,X1,X23] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
| c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2044])]) ).
fof(f1760,axiom,
! [X0,X1,X23] :
( c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = X23
| c_List_Orev(X23,X1) != c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osingleton__rev__conv_0) ).
fof(f16567,plain,
spl0_2043,
inference(avatar_split_clause,[],[f1756,f16565]) ).
fof(f16565,plain,
( spl0_2043
<=> ! [X21,X1,X0] :
( c_0 = X21
| c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2043])]) ).
fof(f1756,axiom,
! [X21,X0,X1] :
( c_0 = X21
| c_insert(X0,c_emptyset,X1) = c_List_Oset(c_List_Oreplicate(X21,X0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__replicate_0) ).
fof(f16563,plain,
spl0_2042,
inference(avatar_split_clause,[],[f1710,f16561]) ).
fof(f16561,plain,
( spl0_2042
<=> ! [X41,X0,X3,X25] :
( X0 = X3
| c_List_Oop_Amem(X0,X25,X41)
| ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2042])]) ).
fof(f1710,axiom,
! [X3,X41,X0,X25] :
( X0 = X3
| c_List_Oop_Amem(X0,X25,X41)
| ~ c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oop_Amem_Osimps__2_0) ).
fof(f16559,plain,
spl0_2041,
inference(avatar_split_clause,[],[f1640,f16557]) ).
fof(f16557,plain,
( spl0_2041
<=> ! [X41,X12,X66] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2041])]) ).
fof(f1640,axiom,
! [X41,X66,X12] : c_List_Olistset(c_List_Olist_OCons(X12,X66,tc_set(X41)),X41) = c_List_Oset__Cons(X12,c_List_Olistset(X66,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olistset_Osimps__2_0) ).
fof(f16555,plain,
spl0_2040,
inference(avatar_split_clause,[],[f1632,f16553]) ).
fof(f16553,plain,
( spl0_2040
<=> ! [X0,X3,X43,X1] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
| c_List_Olist__update(X3,X43,X0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2040])]) ).
fof(f1632,axiom,
! [X3,X0,X1,X43] :
( ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X43,tc_nat)
| c_List_Olist__update(X3,X43,X0,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__update__beyond_0) ).
fof(f16551,plain,
spl0_2039,
inference(avatar_split_clause,[],[f1612,f16549]) ).
fof(f16549,plain,
( spl0_2039
<=> ! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2039])]) ).
fof(f1612,axiom,
! [X1,X23] : c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) = c_Nat_Osize(c_List_Otl(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__tl_0) ).
fof(f16519,plain,
spl0_2038,
inference(avatar_split_clause,[],[f1600,f16517]) ).
fof(f16517,plain,
( spl0_2038
<=> ! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2038])]) ).
fof(f1600,axiom,
! [X1,X23] : c_Nat_Osize(c_List_Obutlast(X23,X1),tc_List_Olist(X1)) = c_minus(c_Nat_Osize(X23,tc_List_Olist(X1)),c_1,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__butlast_0) ).
fof(f16515,plain,
spl0_2037,
inference(avatar_split_clause,[],[f1596,f16513]) ).
fof(f1596,axiom,
! [X59,X43] :
( ~ c_less(X43,X59,tc_nat)
| c_List_Olast(c_List_Oupt(X43,X59),tc_nat) = c_minus(X59,c_1,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast__upt_0) ).
fof(f16511,plain,
spl0_2036,
inference(avatar_split_clause,[],[f1544,f16509]) ).
fof(f16509,plain,
( spl0_2036
<=> ! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2036])]) ).
fof(f1544,axiom,
! [X41,X0,X23] : c_List_Oconcat(c_List_Olist_OCons(X0,X23,tc_List_Olist(X41)),X41) = c_append(X0,c_List_Oconcat(X23,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oconcat_Osimps__2_0) ).
fof(f16507,plain,
spl0_2035,
inference(avatar_split_clause,[],[f1456,f16505]) ).
fof(f16505,plain,
( spl0_2035
<=> ! [X5,X49] : c_IntDiv_OnegateSnd(c_Pair(X49,X5,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(X49,c_uminus(X5,tc_IntDef_Oint),tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2035])]) ).
fof(f16503,plain,
spl0_2034,
inference(avatar_split_clause,[],[f1431,f16501]) ).
fof(f16501,plain,
( spl0_2034
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2034])]) ).
fof(f1431,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozless__nat__conj_2) ).
fof(f16499,plain,
spl0_2033,
inference(avatar_split_clause,[],[f1415,f16497]) ).
fof(f16497,plain,
( spl0_2033
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2033])]) ).
fof(f1415,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,X48,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__less__iff_1) ).
fof(f16495,plain,
spl0_2032,
inference(avatar_split_clause,[],[f1414,f16493]) ).
fof(f16493,plain,
( spl0_2032
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2032])]) ).
fof(f1414,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__less__iff_0) ).
fof(f16491,plain,
spl0_2031,
inference(avatar_split_clause,[],[f1411,f16489]) ).
fof(f16489,plain,
( spl0_2031
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2031])]) ).
fof(f1411,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__le__iff_1) ).
fof(f16487,plain,
spl0_2030,
inference(avatar_split_clause,[],[f1410,f16485]) ).
fof(f1410,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__le__iff_0) ).
fof(f16483,plain,
spl0_2029,
inference(avatar_split_clause,[],[f1281,f16481]) ).
fof(f16481,plain,
( spl0_2029
<=> ! [X13,X1,X46] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2029])]) ).
fof(f1281,axiom,
! [X46,X1,X13] :
( ~ c_in(X13,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_minus(X13,X46,tc_set(X1)),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Diff_0) ).
fof(f16479,plain,
( spl0_2028
| ~ spl0_1
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f16221,f14693,f3013,f16476]) ).
fof(f14693,plain,
( spl0_1991
<=> ! [X86,X88] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1991])]) ).
fof(f16221,plain,
( c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_insert(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_1
| ~ spl0_1991 ),
inference(resolution,[],[f14694,f3015]) ).
fof(f14694,plain,
( ! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) )
| ~ spl0_1991 ),
inference(avatar_component_clause,[],[f14693]) ).
fof(f16474,plain,
spl0_2027,
inference(avatar_split_clause,[],[f1207,f16472]) ).
fof(f16472,plain,
( spl0_2027
<=> ! [X43,X16,X2,X1] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2027])]) ).
fof(f1207,axiom,
! [X2,X1,X16,X43] : c_Datatype__Universe_ONumb(X43,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_ONumb(X43,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__Numb_0) ).
fof(f16470,plain,
spl0_2026,
inference(avatar_split_clause,[],[f1206,f16468]) ).
fof(f16468,plain,
( spl0_2026
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2026])]) ).
fof(f1206,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OLeaf(X18,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__Leaf_0) ).
fof(f16466,plain,
spl0_2025,
inference(avatar_split_clause,[],[f1203,f16464]) ).
fof(f16464,plain,
( spl0_2025
<=> ! [X18,X16,X2,X1] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2025])]) ).
fof(f1203,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OAtom(X18,X1,X2) = c_Datatype__Universe_Ontrunc(c_Suc(X16),c_Datatype__Universe_OAtom(X18,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__Atom_0) ).
fof(f16462,plain,
spl0_2024,
inference(avatar_split_clause,[],[f1198,f16460]) ).
fof(f16460,plain,
( spl0_2024
<=> ! [X9,X7,X8,X10,X2,X1] :
( X7 = X8
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2024])]) ).
fof(f1198,axiom,
! [X2,X10,X1,X8,X9,X7] :
( X7 = X8
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OScons__Scons__eq_1) ).
fof(f16458,plain,
spl0_2023,
inference(avatar_split_clause,[],[f1197,f16456]) ).
fof(f16456,plain,
( spl0_2023
<=> ! [X7,X10,X8,X9,X2,X1] :
( X9 = X10
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2023])]) ).
fof(f1197,axiom,
! [X2,X10,X1,X8,X9,X7] :
( X9 = X10
| c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OScons(X10,X8,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OScons__Scons__eq_0) ).
fof(f16454,plain,
spl0_2022,
inference(avatar_split_clause,[],[f119,f16452]) ).
fof(f16452,plain,
( spl0_2022
<=> ! [X5,X1,X28] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2022])]) ).
fof(f119,axiom,
! [X28,X1,X5] :
( ~ c_in(X28,X5,tc_prod(X1,X1))
| c_in(X28,c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Or__into__rtrancl_0) ).
fof(f16450,plain,
spl0_2021,
inference(avatar_split_clause,[],[f99,f16448]) ).
fof(f16448,plain,
( spl0_2021
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2021])]) ).
fof(f99,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(c_Main_OUnionE__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnionE_0) ).
fof(f16446,plain,
spl0_2020,
inference(avatar_split_clause,[],[f96,f16444]) ).
fof(f16444,plain,
( spl0_2020
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2020])]) ).
fof(f96,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| c_in(c_Main_OInterI__1(X12,X32,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInterI_0) ).
fof(f16442,plain,
spl0_2019,
inference(avatar_split_clause,[],[f59,f16440]) ).
fof(f16440,plain,
( spl0_2019
<=> ! [X0,X12,X1,X26] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2019])]) ).
fof(f59,axiom,
! [X0,X1,X26,X12] :
( c_in(X0,X12,X1)
| ~ c_in(c_List_Olist_OCons(X0,X26,X1),c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_OlistsE_1) ).
fof(f16438,plain,
spl0_2018,
inference(avatar_split_clause,[],[f48,f16436]) ).
fof(f16436,plain,
( spl0_2018
<=> ! [X12,X1,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2018])]) ).
fof(f48,axiom,
! [X1,X12,X23] :
( ~ c_in(c_Main_Oin__listsI__1(X12,X23,X1),X12,X1)
| c_in(X23,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oin__listsI_1) ).
fof(f16406,plain,
spl0_2017,
inference(avatar_split_clause,[],[f43,f16404]) ).
fof(f16404,plain,
( spl0_2017
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2017])]) ).
fof(f43,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_IntDef_Oint)
| c_times(X17,c_Main_Ozmod__eq__0D__dest__1(X17,X15),tc_IntDef_Oint) = X15 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__eq__0D__dest_0) ).
fof(f16402,plain,
spl0_2016,
inference(avatar_split_clause,[],[f36,f16400]) ).
fof(f36,axiom,
! [X3,X0,X1,X22] :
( ~ c_Infinite__Set_Oatmost__one(X22,X1)
| X0 = X3
| ~ c_in(X0,X22,X1)
| ~ c_in(X3,X22,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Infinite__Set_Oatmost__one__unique_0) ).
fof(f16398,plain,
spl0_2015,
inference(avatar_split_clause,[],[f27,f16396]) ).
fof(f16396,plain,
( spl0_2015
<=> ! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2015])]) ).
fof(f27,axiom,
! [X17,X15] :
( c_0 != c_Divides_Oop_Amod(X15,X17,tc_nat)
| c_times(X17,c_Main_Omod__eq__0D__dest__1(X17,X15),tc_nat) = X15 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__eq__0D__dest_0) ).
fof(f16341,plain,
( spl0_2014
| ~ spl0_1874
| ~ spl0_1991 ),
inference(avatar_split_clause,[],[f16222,f14693,f14164,f16338]) ).
fof(f16222,plain,
( c_Message_Oparts(c_Message_Osynth(v_H)) = c_Message_Oparts(c_insert(v_X,c_Message_Osynth(v_H),tc_Message_Omsg))
| ~ spl0_1874
| ~ spl0_1991 ),
inference(resolution,[],[f14694,f14166]) ).
fof(f16196,plain,
( spl0_2013
| ~ spl0_1593
| ~ spl0_1984 ),
inference(avatar_split_clause,[],[f16111,f14665,f11246,f16194]) ).
fof(f16194,plain,
( spl0_2013
<=> ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2013])]) ).
fof(f11246,plain,
( spl0_1593
<=> ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1593])]) ).
fof(f16111,plain,
( ! [X0] : ~ c_Wellfounded__Recursion_Owf(c_Relation_OId,X0)
| ~ spl0_1593
| ~ spl0_1984 ),
inference(resolution,[],[f14666,f11247]) ).
fof(f11247,plain,
( ! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1))
| ~ spl0_1593 ),
inference(avatar_component_clause,[],[f11246]) ).
fof(f16072,plain,
( spl0_2012
| ~ spl0_1288
| ~ spl0_1864 ),
inference(avatar_split_clause,[],[f14103,f13076,f9543,f16070]) ).
fof(f16070,plain,
( spl0_2012
<=> ! [X0] : ~ c_less(c_Suc(c_Suc(X0)),X0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2012])]) ).
fof(f9543,plain,
( spl0_1288
<=> ! [X43,X59] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1288])]) ).
fof(f14103,plain,
( ! [X0] : ~ c_less(c_Suc(c_Suc(X0)),X0,tc_nat)
| ~ spl0_1288
| ~ spl0_1864 ),
inference(superposition,[],[f9544,f13077]) ).
fof(f9544,plain,
( ! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat)
| ~ spl0_1288 ),
inference(avatar_component_clause,[],[f9543]) ).
fof(f15866,plain,
( ~ spl0_2010
| spl0_2011
| ~ spl0_139
| ~ spl0_1785 ),
inference(avatar_split_clause,[],[f13485,f12740,f3693,f15864,f15860]) ).
fof(f15860,plain,
( spl0_2010
<=> class_OrderedGroup_Opordered__ab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2010])]) ).
fof(f15864,plain,
( spl0_2011
<=> ! [X0] : c_lessequals(X0,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2011])]) ).
fof(f12740,plain,
( spl0_1785
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1785])]) ).
fof(f13485,plain,
( ! [X0] :
( c_lessequals(X0,c_0,tc_nat)
| ~ class_OrderedGroup_Opordered__ab__group__add(tc_nat) )
| ~ spl0_139
| ~ spl0_1785 ),
inference(resolution,[],[f12741,f3694]) ).
fof(f12741,plain,
( ! [X18,X1] :
( ~ c_lessequals(c_0,c_uminus(X18,X1),X1)
| c_lessequals(X18,c_0,X1)
| ~ class_OrderedGroup_Opordered__ab__group__add(X1) )
| ~ spl0_1785 ),
inference(avatar_component_clause,[],[f12740]) ).
fof(f15134,plain,
( ~ spl0_2008
| spl0_2009
| ~ spl0_139
| ~ spl0_1738 ),
inference(avatar_split_clause,[],[f13188,f12547,f3693,f15132,f15128]) ).
fof(f15128,plain,
( spl0_2008
<=> class_Ring__and__Field_Oordered__idom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2008])]) ).
fof(f15132,plain,
( spl0_2009
<=> ! [X0] : c_lessequals(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2009])]) ).
fof(f12547,plain,
( spl0_1738
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1738])]) ).
fof(f13188,plain,
( ! [X0] :
( c_lessequals(c_0,X0,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(tc_nat) )
| ~ spl0_139
| ~ spl0_1738 ),
inference(resolution,[],[f12548,f3694]) ).
fof(f12548,plain,
( ! [X48,X1] :
( ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ class_Ring__and__Field_Oordered__idom(X1) )
| ~ spl0_1738 ),
inference(avatar_component_clause,[],[f12547]) ).
fof(f14781,plain,
spl0_2007,
inference(avatar_split_clause,[],[f2960,f14779]) ).
fof(f14779,plain,
( spl0_2007
<=> ! [X1,X3] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2007])]) ).
fof(f2960,plain,
! [X3,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f1334,f2114]) ).
fof(f1334,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X3,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__6_1) ).
fof(f14777,plain,
spl0_2006,
inference(avatar_split_clause,[],[f2955,f14775]) ).
fof(f14775,plain,
( spl0_2006
<=> ! [X1,X3] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2006])]) ).
fof(f2955,plain,
! [X3,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X3),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1) ),
inference(forward_demodulation,[],[f1333,f2114]) ).
fof(f1333,axiom,
! [X3,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X3,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(c_Numeral_OPls,c_Numeral_Obin__minus(X3)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__6_0) ).
fof(f14773,plain,
spl0_2005,
inference(avatar_split_clause,[],[f2912,f14771]) ).
fof(f14771,plain,
( spl0_2005
<=> ! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2005])]) ).
fof(f2912,plain,
! [X83] :
( c_1 = c_Divides_Oop_Amod(c_1,c_Numeral_Onumber__of(X83,tc_nat),tc_nat)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1871,f2016]) ).
fof(f1871,axiom,
! [X83] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X83,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Suc(c_0) = c_Divides_Oop_Amod(c_Suc(c_0),c_Numeral_Onumber__of(X83,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oone__mod__nat__number__of_0) ).
fof(f14758,plain,
( spl0_2004
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2003 ),
inference(avatar_split_clause,[],[f14754,f14751,f13076,f9197,f7368,f14756]) ).
fof(f14751,plain,
( spl0_2003
<=> ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2003])]) ).
fof(f14754,plain,
( ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Suc(c_1),tc_nat) = X3
| ~ spl0_1057
| ~ spl0_1206
| ~ spl0_1864
| ~ spl0_2003 ),
inference(forward_demodulation,[],[f14752,f14121]) ).
fof(f14752,plain,
( ! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3
| ~ spl0_2003 ),
inference(avatar_component_clause,[],[f14751]) ).
fof(f14753,plain,
spl0_2003,
inference(avatar_split_clause,[],[f2867,f14751]) ).
fof(f2867,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f2866,f2156]) ).
fof(f2866,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f2865,f2154]) ).
fof(f2865,plain,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
inference(forward_demodulation,[],[f1883,f2156]) ).
fof(f1883,axiom,
! [X3] : c_div(c_plus(X3,X3,tc_nat),c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oadd__self__div__2_0) ).
fof(f14744,plain,
spl0_2002,
inference(avatar_split_clause,[],[f2862,f14742]) ).
fof(f14742,plain,
( spl0_2002
<=> ! [X25,X1,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_List_Oitrev(X25,c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2002])]) ).
fof(f2862,plain,
! [X1,X25,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_List_Oitrev(X25,c_List_Orev(X23,X1),X1),
inference(forward_demodulation,[],[f1725,f1585]) ).
fof(f1725,axiom,
! [X1,X25,X23] : c_List_Orev(c_append(X23,X25,X1),X1) = c_append(c_List_Orev(X25,X1),c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__append_0) ).
fof(f14740,plain,
spl0_2001,
inference(avatar_split_clause,[],[f2853,f14738]) ).
fof(f2853,plain,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11),X11),
inference(forward_demodulation,[],[f2128,f2127]) ).
fof(f2127,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__mult__0_0) ).
fof(f2128,axiom,
! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),X11) = c_Numeral_Obin__add(c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0),X11),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__mult__1_0) ).
fof(f14736,plain,
spl0_2000,
inference(avatar_split_clause,[],[f2821,f14734]) ).
fof(f14734,plain,
( spl0_2000
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2000])]) ).
fof(f2821,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth__subset__iff_1) ).
fof(f14732,plain,
spl0_1999,
inference(avatar_split_clause,[],[f2820,f14730]) ).
fof(f2820,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Osynth(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Osynth(X20),c_Message_Osynth(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth__subset__iff_0) ).
fof(f14728,plain,
spl0_1998,
inference(avatar_split_clause,[],[f2815,f14726]) ).
fof(f14726,plain,
( spl0_1998
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1998])]) ).
fof(f2815,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__subset__iff_1) ).
fof(f14724,plain,
spl0_1997,
inference(avatar_split_clause,[],[f2814,f14722]) ).
fof(f2814,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oparts(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__subset__iff_0) ).
fof(f14720,plain,
spl0_1996,
inference(avatar_split_clause,[],[f2812,f14718]) ).
fof(f14718,plain,
( spl0_1996
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1996])]) ).
fof(f2812,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__Number_0) ).
fof(f14716,plain,
spl0_1995,
inference(avatar_split_clause,[],[f2811,f14714]) ).
fof(f14714,plain,
( spl0_1995
<=> ! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1995])]) ).
fof(f2811,axiom,
! [X88,X7] : c_Message_Oparts(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__Nonce_0) ).
fof(f14712,plain,
spl0_1994,
inference(avatar_split_clause,[],[f2809,f14710]) ).
fof(f14710,plain,
( spl0_1994
<=> ! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1994])]) ).
fof(f2809,axiom,
! [X91,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OKey(X91),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__Key_0) ).
fof(f14708,plain,
spl0_1993,
inference(avatar_split_clause,[],[f2808,f14706]) ).
fof(f14706,plain,
( spl0_1993
<=> ! [X86,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1993])]) ).
fof(f2808,axiom,
! [X88,X86] : c_Message_Oparts(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__Hash_0) ).
fof(f14699,plain,
spl0_1992,
inference(avatar_split_clause,[],[f2806,f14697]) ).
fof(f14697,plain,
( spl0_1992
<=> ! [X102,X88] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1992])]) ).
fof(f2806,axiom,
! [X88,X102] : c_Message_Oparts(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__insert__Agent_0) ).
fof(f14695,plain,
spl0_1991,
inference(avatar_split_clause,[],[f2804,f14693]) ).
fof(f2804,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| c_Message_Oparts(X88) = c_Message_Oparts(c_insert(X86,X88,tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__cut__eq_0) ).
fof(f14691,plain,
spl0_1990,
inference(avatar_split_clause,[],[f2801,f14689]) ).
fof(f14689,plain,
( spl0_1990
<=> ! [X20,X88] :
( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1990])]) ).
fof(f2801,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__subset__iff_1) ).
fof(f14687,plain,
spl0_1989,
inference(avatar_split_clause,[],[f2800,f14685]) ).
fof(f2800,axiom,
! [X88,X20] :
( c_lessequals(X20,c_Message_Oanalz(X88),tc_set(tc_Message_Omsg))
| ~ c_lessequals(c_Message_Oanalz(X20),c_Message_Oanalz(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__subset__iff_0) ).
fof(f14683,plain,
spl0_1988,
inference(avatar_split_clause,[],[f2798,f14681]) ).
fof(f14681,plain,
( spl0_1988
<=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1988])]) ).
fof(f2798,axiom,
! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONumber(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__insert__Number_0) ).
fof(f14679,plain,
spl0_1987,
inference(avatar_split_clause,[],[f2797,f14677]) ).
fof(f14677,plain,
( spl0_1987
<=> ! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1987])]) ).
fof(f2797,axiom,
! [X88,X7] : c_Message_Oanalz(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_ONonce(X7),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__insert__Nonce_0) ).
fof(f14675,plain,
spl0_1986,
inference(avatar_split_clause,[],[f2794,f14673]) ).
fof(f14673,plain,
( spl0_1986
<=> ! [X86,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1986])]) ).
fof(f2794,axiom,
! [X88,X86] : c_Message_Oanalz(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OHash(X86),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__insert__Hash_0) ).
fof(f14671,plain,
spl0_1985,
inference(avatar_split_clause,[],[f2793,f14669]) ).
fof(f14669,plain,
( spl0_1985
<=> ! [X102,X88] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1985])]) ).
fof(f2793,axiom,
! [X88,X102] : c_Message_Oanalz(c_insert(c_Message_Omsg_OAgent(X102),X88,tc_Message_Omsg)) = c_insert(c_Message_Omsg_OAgent(X102),c_Message_Oanalz(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__insert__Agent_0) ).
fof(f14667,plain,
spl0_1984,
inference(avatar_split_clause,[],[f2725,f14665]) ).
fof(f2725,axiom,
! [X1,X18,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| ~ c_in(c_Pair(X18,X18,X1,X1),X5,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Owf__not__refl_0) ).
fof(f14663,plain,
spl0_1983,
inference(avatar_split_clause,[],[f2689,f14661]) ).
fof(f14661,plain,
( spl0_1983
<=> ! [X13,X12,X0,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1983])]) ).
fof(f2689,axiom,
! [X0,X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__subset_1) ).
fof(f14655,plain,
spl0_1982,
inference(avatar_split_clause,[],[f2680,f14653]) ).
fof(f14653,plain,
( spl0_1982
<=> ! [X18,X13,X12,X1] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1982])]) ).
fof(f2680,axiom,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_inter(c_insert(X18,X12,X1),X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__disjoint__2_0) ).
fof(f14651,plain,
spl0_1981,
inference(avatar_split_clause,[],[f2669,f14649]) ).
fof(f14649,plain,
( spl0_1981
<=> ! [X12,X1,X24] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1981])]) ).
fof(f2669,axiom,
! [X1,X24,X12] :
( c_emptyset = X24
| c_emptyset != c_Union(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oempty__Union__conv_0) ).
fof(f14647,plain,
spl0_1980,
inference(avatar_split_clause,[],[f2661,f14645]) ).
fof(f14645,plain,
( spl0_1980
<=> ! [X18,X13,X12,X1] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_inter(X13,c_insert(X18,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1980])]) ).
fof(f2661,axiom,
! [X18,X1,X12,X13] :
( ~ c_in(X18,X13,X1)
| c_emptyset != c_inter(X13,c_insert(X18,X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Odisjoint__insert__1_0) ).
fof(f14643,plain,
spl0_1979,
inference(avatar_split_clause,[],[f2656,f14641]) ).
fof(f14641,plain,
( spl0_1979
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1979])]) ).
fof(f2656,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnion__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__iff_1) ).
fof(f14639,plain,
spl0_1978,
inference(avatar_split_clause,[],[f2646,f14637]) ).
fof(f14637,plain,
( spl0_1978
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1978])]) ).
fof(f2646,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X13,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__subset__iff_1) ).
fof(f14635,plain,
spl0_1977,
inference(avatar_split_clause,[],[f2645,f14633]) ).
fof(f2645,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X12,X32,tc_set(X1))
| ~ c_lessequals(c_union(X12,X13,X1),X32,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__subset__iff_0) ).
fof(f14631,plain,
spl0_1976,
inference(avatar_split_clause,[],[f2631,f14629]) ).
fof(f2631,axiom,
! [X1,X12,X13] : c_union(X12,X13,X1) = c_union(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__Diff__cancel_0) ).
fof(f14627,plain,
spl0_1975,
inference(avatar_split_clause,[],[f2630,f14625]) ).
fof(f2630,axiom,
! [X1,X12,X13] : c_union(c_minus(X13,X12,tc_set(X1)),X12,X1) = c_union(X13,X12,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__Diff__cancel2_0) ).
fof(f14623,plain,
spl0_1974,
inference(avatar_split_clause,[],[f2622,f14621]) ).
fof(f14621,plain,
( spl0_1974
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1974])]) ).
fof(f2622,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInter__iff__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__iff_2) ).
fof(f14619,plain,
spl0_1973,
inference(avatar_split_clause,[],[f2616,f14617]) ).
fof(f14617,plain,
( spl0_1973
<=> ! [X12,X1,X24] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1973])]) ).
fof(f2616,axiom,
! [X1,X24,X12] :
( c_UNIV = X24
| c_UNIV != c_Inter(X12,X1)
| ~ c_in(X24,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__UNIV__conv__2_0) ).
fof(f14613,plain,
spl0_1972,
inference(avatar_split_clause,[],[f2610,f14611]) ).
fof(f14611,plain,
( spl0_1972
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1972])]) ).
fof(f2610,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X13,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__subset__iff_1) ).
fof(f14609,plain,
spl0_1971,
inference(avatar_split_clause,[],[f2609,f14607]) ).
fof(f14607,plain,
( spl0_1971
<=> ! [X13,X12,X32,X1] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1971])]) ).
fof(f2609,axiom,
! [X1,X12,X32,X13] :
( c_lessequals(X32,X12,tc_set(X1))
| ~ c_lessequals(X32,c_inter(X12,X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__subset__iff_0) ).
fof(f14605,plain,
spl0_1970,
inference(avatar_split_clause,[],[f2586,f14603]) ).
fof(f14603,plain,
( spl0_1970
<=> ! [X13,X12,X1] : c_inter(X12,X13,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1970])]) ).
fof(f2586,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_minus(X12,c_uminus(X13,tc_set(X1)),tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__Compl_0) ).
fof(f14601,plain,
spl0_1969,
inference(avatar_split_clause,[],[f2555,f14599]) ).
fof(f14599,plain,
( spl0_1969
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1969])]) ).
fof(f2555,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanLessThan__iff_1) ).
fof(f14597,plain,
spl0_1968,
inference(avatar_split_clause,[],[f2554,f14595]) ).
fof(f14595,plain,
( spl0_1968
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1968])]) ).
fof(f2554,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanLessThan__iff_0) ).
fof(f14593,plain,
spl0_1967,
inference(avatar_split_clause,[],[f2552,f14591]) ).
fof(f14591,plain,
( spl0_1967
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1967])]) ).
fof(f2552,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanAtMost__iff_1) ).
fof(f14589,plain,
spl0_1966,
inference(avatar_split_clause,[],[f2551,f14587]) ).
fof(f14587,plain,
( spl0_1966
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1966])]) ).
fof(f2551,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThanAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanAtMost__iff_0) ).
fof(f14585,plain,
spl0_1965,
inference(avatar_split_clause,[],[f2525,f14583]) ).
fof(f14583,plain,
( spl0_1965
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1965])]) ).
fof(f2525,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastLessThan__iff_1) ).
fof(f14581,plain,
spl0_1964,
inference(avatar_split_clause,[],[f2524,f14579]) ).
fof(f14579,plain,
( spl0_1964
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1964])]) ).
fof(f2524,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastLessThan(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastLessThan__iff_0) ).
fof(f14577,plain,
spl0_1963,
inference(avatar_split_clause,[],[f2520,f14575]) ).
fof(f14575,plain,
( spl0_1963
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1963])]) ).
fof(f2520,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X14,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastAtMost__iff_1) ).
fof(f14571,plain,
spl0_1962,
inference(avatar_split_clause,[],[f2519,f14569]) ).
fof(f14569,plain,
( spl0_1962
<=> ! [X43,X14,X1,X26] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1962])]) ).
fof(f2519,axiom,
! [X1,X26,X14,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X26,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeastAtMost(X26,X14,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastAtMost__iff_0) ).
fof(f14567,plain,
spl0_1961,
inference(avatar_split_clause,[],[f2505,f14565]) ).
fof(f14565,plain,
( spl0_1961
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_times(c_0,c_divide(X27,c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1961])]) ).
fof(f2505,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_times(c_0,c_divide(X27,c_0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Otimes__divide__self__right_0) ).
fof(f14563,plain,
spl0_1960,
inference(avatar_split_clause,[],[f2503,f14561]) ).
fof(f14561,plain,
( spl0_1960
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_times(c_divide(X27,c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1960])]) ).
fof(f2503,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_times(c_divide(X27,c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Otimes__divide__self__left_0) ).
fof(f14559,plain,
spl0_1959,
inference(avatar_split_clause,[],[f2500,f14557]) ).
fof(f14557,plain,
( spl0_1959
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_1 = c_times(X18,c_HOL_Oinverse(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1959])]) ).
fof(f2500,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_1 = c_times(X18,c_HOL_Oinverse(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oright__inverse_0) ).
fof(f14555,plain,
spl0_1958,
inference(avatar_split_clause,[],[f2497,f14553]) ).
fof(f14553,plain,
( spl0_1958
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_1 != c_divide(X18,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1958])]) ).
fof(f2497,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| X18 = X27
| c_1 != c_divide(X18,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oone__eq__divide__iff_1) ).
fof(f14551,plain,
spl0_1957,
inference(avatar_split_clause,[],[f2495,f14549]) ).
fof(f14549,plain,
( spl0_1957
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_0 = X18
| c_0 != c_divide(c_1,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1957])]) ).
fof(f2495,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_0 = X18
| c_0 != c_divide(c_1,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oone__divide__eq__0__iff_0) ).
fof(f14547,plain,
spl0_1956,
inference(avatar_split_clause,[],[f2428,f14545]) ).
fof(f14545,plain,
( spl0_1956
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_1 = c_times(c_HOL_Oinverse(X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1956])]) ).
fof(f2428,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_1 = c_times(c_HOL_Oinverse(X18,X1),X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ofield__class_Oaxioms__1_0) ).
fof(f14543,plain,
spl0_1955,
inference(avatar_split_clause,[],[f2409,f14541]) ).
fof(f14541,plain,
( spl0_1955
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_0 = X0
| c_1 = c_divide(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1955])]) ).
fof(f2409,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_0 = X0
| c_1 = c_divide(X0,X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__eq__eq__1_2) ).
fof(f14539,plain,
spl0_1954,
inference(avatar_split_clause,[],[f2408,f14537]) ).
fof(f14537,plain,
( spl0_1954
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| X18 = X27
| c_1 != c_divide(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1954])]) ).
fof(f2408,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| X18 = X27
| c_1 != c_divide(X27,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__eq__eq__1_1) ).
fof(f14535,plain,
spl0_1953,
inference(avatar_split_clause,[],[f2400,f14533]) ).
fof(f14533,plain,
( spl0_1953
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X18,c_0,X1) = c_divide(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1953])]) ).
fof(f2400,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X18,c_0,X1) = c_divide(X27,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__cancel__right_1) ).
fof(f14531,plain,
spl0_1952,
inference(avatar_split_clause,[],[f2398,f14529]) ).
fof(f14529,plain,
( spl0_1952
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(c_0,X18,X1) = c_divide(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1952])]) ).
fof(f2398,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_divide(c_0,X18,X1) = c_divide(c_0,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__cancel__left_1) ).
fof(f14527,plain,
spl0_1951,
inference(avatar_split_clause,[],[f2387,f14525]) ).
fof(f14525,plain,
( spl0_1951
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1951])]) ).
fof(f2387,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(c_Pair(X18,X27,X1,X1),c_Relation_OId,tc_prod(X1,X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Opair__in__Id__conv_0) ).
fof(f14523,plain,
spl0_1950,
inference(avatar_split_clause,[],[f2367,f14521]) ).
fof(f2367,axiom,
! [X2,X48,X1] : c_Pair(c_Main_Osurj__pair__1(X48,X1,X2),c_Main_Osurj__pair__2(X48,X1,X2),X1,X2) = X48,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Product__Type_Osurj__pair_0) ).
fof(f14519,plain,
spl0_1949,
inference(avatar_split_clause,[],[f2365,f14517]) ).
fof(f2365,axiom,
! [X2,X3,X1] : c_Pair(c_fst(X3,X1,X2),c_snd(X3,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Product__Type_Opair__collapse_0) ).
fof(f14515,plain,
spl0_1948,
inference(avatar_split_clause,[],[f2361,f14513]) ).
fof(f14513,plain,
( spl0_1948
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1948])]) ).
fof(f2361,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),c_0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Ozero__less__power__abs__iff_2) ).
fof(f14511,plain,
spl0_1947,
inference(avatar_split_clause,[],[f2358,f14509]) ).
fof(f14509,plain,
( spl0_1947
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1947])]) ).
fof(f2358,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X18,X1),X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Ozero__le__power__abs_0) ).
fof(f14507,plain,
spl0_1946,
inference(avatar_split_clause,[],[f2347,f14505]) ).
fof(f14505,plain,
( spl0_1946
<=> ! [X18,X21,X1] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1946])]) ).
fof(f2347,axiom,
! [X21,X1,X18] :
( ~ class_Power_Orecpower(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X18
| c_0 != c_Nat_Opower(X18,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__eq__0__iff_0) ).
fof(f14503,plain,
spl0_1945,
inference(avatar_split_clause,[],[f2345,f14501]) ).
fof(f14501,plain,
( spl0_1945
<=> ! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_nat) = c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1945])]) ).
fof(f2345,axiom,
! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_nat) = c_times(X28,c_Nat_Opower(X28,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower_Osimps__2_0) ).
fof(f14499,plain,
spl0_1944,
inference(avatar_split_clause,[],[f2339,f14497]) ).
fof(f14497,plain,
( spl0_1944
<=> ! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1944])]) ).
fof(f2339,axiom,
! [X0,X11] :
( ~ c_less(c_0,X0,tc_nat)
| c_less(c_0,c_Nat_Opower(X0,c_Numeral_Onumber__of(X11,tc_nat),tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Ozero__less__power__nat__eq__number__of_2) ).
fof(f14495,plain,
spl0_1943,
inference(avatar_split_clause,[],[f2295,f14493]) ).
fof(f14493,plain,
( spl0_1943
<=> ! [X0,X21] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1943])]) ).
fof(f2295,axiom,
! [X21,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_less(c_0,X21,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__power_2) ).
fof(f14489,plain,
spl0_1942,
inference(avatar_split_clause,[],[f2282,f14487]) ).
fof(f14487,plain,
( spl0_1942
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1942])]) ).
fof(f2282,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_less(c_0,X3,tc_nat)
| c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__power_2) ).
fof(f14485,plain,
spl0_1941,
inference(avatar_split_clause,[],[f2265,f14483]) ).
fof(f14483,plain,
( spl0_1941
<=> ! [X2,X48,X0,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1941])]) ).
fof(f2265,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X3,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_1) ).
fof(f14481,plain,
spl0_1940,
inference(avatar_split_clause,[],[f2264,f14479]) ).
fof(f14479,plain,
( spl0_1940
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1940])]) ).
fof(f2264,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(c_Orderings_Omax(X0,X3,X2),X48,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__sup_Oabove__sup__conv_0) ).
fof(f14477,plain,
spl0_1939,
inference(avatar_split_clause,[],[f2260,f14475]) ).
fof(f14475,plain,
( spl0_1939
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1939])]) ).
fof(f2260,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X48,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_1) ).
fof(f14473,plain,
spl0_1938,
inference(avatar_split_clause,[],[f2259,f14471]) ).
fof(f14471,plain,
( spl0_1938
<=> ! [X48,X0,X3,X2] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1938])]) ).
fof(f2259,axiom,
! [X2,X3,X48,X0] :
( ~ class_Orderings_Olinorder(X2)
| c_lessequals(X0,X3,X2)
| ~ c_lessequals(X0,c_Orderings_Omin(X3,X48,X2),X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__inf_Obelow__inf__conv_0) ).
fof(f14469,plain,
spl0_1937,
inference(avatar_split_clause,[],[f2257,f14467]) ).
fof(f14467,plain,
( spl0_1937
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1937])]) ).
fof(f2257,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X3,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__less__iff__conj_1) ).
fof(f14465,plain,
spl0_1936,
inference(avatar_split_clause,[],[f2256,f14463]) ).
fof(f14463,plain,
( spl0_1936
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1936])]) ).
fof(f2256,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X48,X0,X1)
| ~ c_less(X48,c_Orderings_Omin(X0,X3,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__less__iff__conj_0) ).
fof(f14461,plain,
spl0_1935,
inference(avatar_split_clause,[],[f2254,f14459]) ).
fof(f14459,plain,
( spl0_1935
<=> ! [X48,X1,X0,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1935])]) ).
fof(f2254,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X3,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omax__less__iff__conj_1) ).
fof(f14457,plain,
spl0_1934,
inference(avatar_split_clause,[],[f2253,f14455]) ).
fof(f14455,plain,
( spl0_1934
<=> ! [X48,X0,X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1934])]) ).
fof(f2253,axiom,
! [X3,X48,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_less(X0,X48,X1)
| ~ c_less(c_Orderings_Omax(X0,X3,X1),X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omax__less__iff__conj_0) ).
fof(f14453,plain,
spl0_1933,
inference(avatar_split_clause,[],[f2249,f14451]) ).
fof(f14451,plain,
( spl0_1933
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1933])]) ).
fof(f2249,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_1) ).
fof(f14449,plain,
spl0_1932,
inference(avatar_split_clause,[],[f2248,f14447]) ).
fof(f14447,plain,
( spl0_1932
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1932])]) ).
fof(f2248,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_0,c_plus(X18,X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ozero__le__double__add__iff__zero__le__single__add_0) ).
fof(f14445,plain,
spl0_1931,
inference(avatar_split_clause,[],[f2215,f14443]) ).
fof(f14443,plain,
( spl0_1931
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1931])]) ).
fof(f2215,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_minus(X18,X27,X1),X1) = c_minus(X27,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ominus__diff__eq_0) ).
fof(f14441,plain,
spl0_1930,
inference(avatar_split_clause,[],[f2212,f14439]) ).
fof(f14439,plain,
( spl0_1930
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1930])]) ).
fof(f2212,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Omeet(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Omeet__0__eq__0_0) ).
fof(f14437,plain,
spl0_1929,
inference(avatar_split_clause,[],[f2210,f14435]) ).
fof(f14435,plain,
( spl0_1929
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1929])]) ).
fof(f2210,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = X18
| c_0 != c_LOrder_Ojoin(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ojoin__0__eq__0_0) ).
fof(f14433,plain,
spl0_1928,
inference(avatar_split_clause,[],[f2207,f14431]) ).
fof(f14431,plain,
( spl0_1928
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1928])]) ).
fof(f2207,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_1) ).
fof(f14429,plain,
spl0_1927,
inference(avatar_split_clause,[],[f2206,f14427]) ).
fof(f14427,plain,
( spl0_1927
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1927])]) ).
fof(f2206,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_plus(X18,X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odouble__add__le__zero__iff__single__add__le__zero_0) ).
fof(f14425,plain,
spl0_1926,
inference(avatar_split_clause,[],[f2204,f14423]) ).
fof(f14423,plain,
( spl0_1926
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1926])]) ).
fof(f2204,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_plus(X18,X27,X1) = c_minus(X18,c_uminus(X27,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__minus__eq__add_0) ).
fof(f14421,plain,
spl0_1925,
inference(avatar_split_clause,[],[f2203,f14419]) ).
fof(f14419,plain,
( spl0_1925
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1925])]) ).
fof(f2203,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,X27,X1)
| c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__less__0__iff__less_1) ).
fof(f14417,plain,
spl0_1924,
inference(avatar_split_clause,[],[f2202,f14415]) ).
fof(f14415,plain,
( spl0_1924
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1924])]) ).
fof(f2202,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,X27,X1)
| ~ c_less(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__less__0__iff__less_0) ).
fof(f14413,plain,
spl0_1923,
inference(avatar_split_clause,[],[f2201,f14411]) ).
fof(f14411,plain,
( spl0_1923
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1923])]) ).
fof(f2201,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,X27,X1)
| c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__le__0__iff__le_1) ).
fof(f14394,plain,
spl0_1922,
inference(avatar_split_clause,[],[f2200,f14392]) ).
fof(f14392,plain,
( spl0_1922
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1922])]) ).
fof(f2200,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,X27,X1)
| ~ c_lessequals(c_minus(X18,X27,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__le__0__iff__le_0) ).
fof(f14390,plain,
spl0_1921,
inference(avatar_split_clause,[],[f2184,f14388]) ).
fof(f14388,plain,
( spl0_1921
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1921])]) ).
fof(f2184,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_uminus(X18,X1) = c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__of__nonpos_0) ).
fof(f14386,plain,
spl0_1920,
inference(avatar_split_clause,[],[f2110,f14384]) ).
fof(f14384,plain,
( spl0_1920
<=> ! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1920])]) ).
fof(f2110,axiom,
! [X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB1),c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__BIT__10_0) ).
fof(f14382,plain,
spl0_1919,
inference(avatar_split_clause,[],[f2109,f14380]) ).
fof(f14380,plain,
( spl0_1919
<=> ! [X11,X3,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1919])]) ).
fof(f2109,axiom,
! [X3,X11,X47] : c_Numeral_Obin__add(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),c_Numeral_OBit(X11,X3)) = c_Numeral_OBit(c_Numeral_Obin__add(X47,X11),X3),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__BIT__0_0) ).
fof(f14378,plain,
spl0_1918,
inference(avatar_split_clause,[],[f2099,f14376]) ).
fof(f14376,plain,
( spl0_1918
<=> ! [X21,X15] : c_times(c_Suc(X15),X21,tc_nat) = c_plus(X21,c_times(X15,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1918])]) ).
fof(f2099,axiom,
! [X21,X15] : c_times(c_Suc(X15),X21,tc_nat) = c_plus(X21,c_times(X15,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oop_A_K_Omult__Suc_0) ).
fof(f14374,plain,
spl0_1917,
inference(avatar_split_clause,[],[f2057,f14372]) ).
fof(f14372,plain,
( spl0_1917
<=> ! [X21,X15] : c_times(X15,c_Suc(X21),tc_nat) = c_plus(X15,c_times(X15,X21,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1917])]) ).
fof(f2057,axiom,
! [X21,X15] : c_times(X15,c_Suc(X21),tc_nat) = c_plus(X15,c_times(X15,X21,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__Suc__right_0) ).
fof(f14370,plain,
spl0_1916,
inference(avatar_split_clause,[],[f2045,f14368]) ).
fof(f14368,plain,
( spl0_1916
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1916])]) ).
fof(f2045,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(X21,c_minus(X3,X21,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ole__add__diff__inverse_0) ).
fof(f14366,plain,
spl0_1915,
inference(avatar_split_clause,[],[f2044,f14364]) ).
fof(f14364,plain,
( spl0_1915
<=> ! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1915])]) ).
fof(f2044,axiom,
! [X21,X3] :
( ~ c_lessequals(X21,X3,tc_nat)
| c_plus(c_minus(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ole__add__diff__inverse2_0) ).
fof(f14362,plain,
spl0_1914,
inference(avatar_split_clause,[],[f1852,f14360]) ).
fof(f14360,plain,
( spl0_1914
<=> ! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1914])]) ).
fof(f1852,axiom,
! [X47] :
( c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Numeral_Onumber__of(X47,tc_IntDef_Oint) = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oint__nat__number__of_1) ).
fof(f14358,plain,
spl0_1913,
inference(avatar_split_clause,[],[f1802,f14356]) ).
fof(f14356,plain,
( spl0_1913
<=> ! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_NatArith_Oof__nat(c_Suc(X15),X41) = c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1913])]) ).
fof(f1802,axiom,
! [X41,X15] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X41)
| c_NatArith_Oof__nat(c_Suc(X15),X41) = c_plus(c_NatArith_Oof__nat(X15,X41),c_1,X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat_Oof__nat__Suc_0) ).
fof(f14345,plain,
spl0_1912,
inference(avatar_split_clause,[],[f1799,f14343]) ).
fof(f14343,plain,
( spl0_1912
<=> ! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1912])]) ).
fof(f1799,axiom,
! [X21,X3] :
( ~ c_lessequals(X3,X21,tc_nat)
| c_minus(X21,c_minus(X21,X3,tc_nat),tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Odiff__diff__cancel_0) ).
fof(f14341,plain,
spl0_1911,
inference(avatar_split_clause,[],[f1770,f14339]) ).
fof(f14339,plain,
( spl0_1911
<=> ! [X21,X1,X3] :
( c_List_Otake(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1911])]) ).
fof(f1770,axiom,
! [X21,X3,X1] :
( c_List_Otake(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__all_0) ).
fof(f14337,plain,
spl0_1910,
inference(avatar_split_clause,[],[f1765,f14335]) ).
fof(f14335,plain,
( spl0_1910
<=> ! [X0,X12,X1] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1910])]) ).
fof(f1765,axiom,
! [X0,X1,X12] :
( c_in(c_0,X12,tc_nat)
| c_List_Olist_ONil = c_List_Osublist(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osublist__singleton_1) ).
fof(f14333,plain,
spl0_1909,
inference(avatar_split_clause,[],[f1748,f14331]) ).
fof(f14331,plain,
( spl0_1909
<=> ! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1909])]) ).
fof(f1748,axiom,
! [X41,X0,X23] : c_List_Oset(c_List_Olist_OCons(X0,X23,X41),X41) = c_insert(X0,c_List_Oset(X23,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset_Osimps__2_0) ).
fof(f14329,plain,
spl0_1908,
inference(avatar_split_clause,[],[f1742,f14327]) ).
fof(f14327,plain,
( spl0_1908
<=> ! [X21,X1,X3] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1908])]) ).
fof(f1742,axiom,
! [X21,X3,X1] :
( c_List_Orotate(X21,X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate__length01_0) ).
fof(f14325,plain,
spl0_1907,
inference(avatar_split_clause,[],[f1723,f14323]) ).
fof(f1723,axiom,
! [X21,X41,X0] : c_List_Oreplicate(c_Suc(X21),X0,X41) = c_List_Olist_OCons(X0,c_List_Oreplicate(X21,X0,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oreplicate_Oreplicate__Suc_0) ).
fof(f14321,plain,
spl0_1906,
inference(avatar_split_clause,[],[f1702,f14319]) ).
fof(f14319,plain,
( spl0_1906
<=> ! [X43,X3,X21,X1] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1906])]) ).
fof(f1702,axiom,
! [X21,X3,X1,X43] :
( ~ c_less(X43,X21,tc_nat)
| c_List_Onth(c_List_Oreplicate(X21,X3,X1),X43,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__replicate_0) ).
fof(f14317,plain,
spl0_1905,
inference(avatar_split_clause,[],[f1693,f14315]) ).
fof(f14315,plain,
( spl0_1905
<=> ! [X21,X1,X23,X0] : c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Suc(X21),X1) = c_List_Onth(X23,X21,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1905])]) ).
fof(f1693,axiom,
! [X21,X0,X1,X23] : c_List_Onth(c_List_Olist_OCons(X0,X23,X1),c_Suc(X21),X1) = c_List_Onth(X23,X21,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__Cons__Suc_0) ).
fof(f14313,plain,
spl0_1904,
inference(avatar_split_clause,[],[f1604,f14311]) ).
fof(f14311,plain,
( spl0_1904
<=> ! [X43,X0,X23,X1] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1904])]) ).
fof(f1604,axiom,
! [X0,X1,X23,X43] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Olist__update(X23,X43,X0,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__list__update_0) ).
fof(f14309,plain,
spl0_1903,
inference(avatar_split_clause,[],[f1591,f14307]) ).
fof(f14307,plain,
( spl0_1903
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1903])]) ).
fof(f1591,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olast(c_append(X23,X25,X1),X1) = c_List_Olast(X25,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast__appendR_0) ).
fof(f14290,plain,
spl0_1902,
inference(avatar_split_clause,[],[f1589,f14288]) ).
fof(f14288,plain,
( spl0_1902
<=> ! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1902])]) ).
fof(f1589,axiom,
! [X0,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olast(c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Olast(X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast_Osimps_1) ).
fof(f14286,plain,
spl0_1901,
inference(avatar_split_clause,[],[f1581,f14284]) ).
fof(f14284,plain,
( spl0_1901
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1901])]) ).
fof(f1581,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Ohd(c_append(X23,X25,X1),X1) = c_List_Ohd(X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ohd__append2_0) ).
fof(f14282,plain,
spl0_1900,
inference(avatar_split_clause,[],[f1580,f14280]) ).
fof(f1580,axiom,
! [X3,X1] :
( c_List_Olist_ONil = X3
| c_List_Olist_OCons(c_List_Ohd(X3,X1),c_List_Otl(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ohd__Cons__tl_0) ).
fof(f14278,plain,
spl0_1899,
inference(avatar_split_clause,[],[f1578,f14276]) ).
fof(f14276,plain,
( spl0_1899
<=> ! [X59,X43,X15] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1899])]) ).
fof(f1578,axiom,
! [X59,X15,X43] : c_List_Odrop(X15,c_List_Oupt(X43,X59),tc_nat) = c_List_Oupt(c_plus(X43,X15,tc_nat),X59),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__upt_0) ).
fof(f14274,plain,
spl0_1898,
inference(avatar_split_clause,[],[f1576,f14272]) ).
fof(f14272,plain,
( spl0_1898
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1898])]) ).
fof(f1576,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = c_List_Odrop(X21,X23,X1)
| ~ c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__eq__Nil_1) ).
fof(f14270,plain,
spl0_1897,
inference(avatar_split_clause,[],[f1575,f14268]) ).
fof(f14268,plain,
( spl0_1897
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1897])]) ).
fof(f1575,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil != c_List_Odrop(X21,X23,X1)
| c_lessequals(c_Nat_Osize(X23,tc_List_Olist(X1)),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__eq__Nil_0) ).
fof(f14266,plain,
spl0_1896,
inference(avatar_split_clause,[],[f1572,f14264]) ).
fof(f14264,plain,
( spl0_1896
<=> ! [X0,X23,X21,X1] : c_List_Odrop(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(X21,X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1896])]) ).
fof(f1572,axiom,
! [X21,X0,X1,X23] : c_List_Odrop(c_Suc(X21),c_List_Olist_OCons(X0,X23,X1),X1) = c_List_Odrop(X21,X23,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__Suc__Cons_0) ).
fof(f14262,plain,
spl0_1895,
inference(avatar_split_clause,[],[f1475,f14260]) ).
fof(f14260,plain,
( spl0_1895
<=> ! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1895])]) ).
fof(f1475,axiom,
! [X18,X27] : c_div(c_uminus(X18,tc_IntDef_Oint),c_uminus(X27,tc_IntDef_Oint),tc_IntDef_Oint) = c_div(X18,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__zminus__zminus_0) ).
fof(f14258,plain,
spl0_1894,
inference(avatar_split_clause,[],[f1465,f14256]) ).
fof(f14256,plain,
( spl0_1894
<=> ! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_IntDef_Oint) = c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1894])]) ).
fof(f1465,axiom,
! [X21,X28] : c_Nat_Opower(X28,c_Suc(X21),tc_IntDef_Oint) = c_times(X28,c_Nat_Opower(X28,X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Opower_Osimps__2_0) ).
fof(f14254,plain,
spl0_1893,
inference(avatar_split_clause,[],[f1416,f14252]) ).
fof(f14252,plain,
( spl0_1893
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1893])]) ).
fof(f1416,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_uminus(X48,tc_IntDef_Oint),X1) = c_uminus(c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__minus_0) ).
fof(f14248,plain,
spl0_1892,
inference(avatar_split_clause,[],[f1305,f14246]) ).
fof(f14246,plain,
( spl0_1892
<=> ! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1892])]) ).
fof(f1305,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X21,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__greatest__iff_1) ).
fof(f14244,plain,
spl0_1891,
inference(avatar_split_clause,[],[f1304,f14242]) ).
fof(f14242,plain,
( spl0_1891
<=> ! [X16,X21,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1891])]) ).
fof(f1304,axiom,
! [X21,X16,X15] :
( c_Divides_Oop_Advd(X16,X15,tc_nat)
| ~ c_Divides_Oop_Advd(X16,c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__greatest__iff_0) ).
fof(f14240,plain,
spl0_1890,
inference(avatar_split_clause,[],[f1291,f14238]) ).
fof(f14238,plain,
( spl0_1890
<=> ! [X12,X1,X18] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1890])]) ).
fof(f1291,axiom,
! [X1,X18,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__insert_0) ).
fof(f14236,plain,
spl0_1889,
inference(avatar_split_clause,[],[f1287,f14234]) ).
fof(f14234,plain,
( spl0_1889
<=> ! [X20,X1,X19] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1889])]) ).
fof(f1287,axiom,
! [X1,X19,X20] :
( c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Un_1) ).
fof(f14232,plain,
spl0_1888,
inference(avatar_split_clause,[],[f1286,f14230]) ).
fof(f1286,axiom,
! [X1,X19,X20] :
( c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_union(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Un_0) ).
fof(f14228,plain,
spl0_1887,
inference(avatar_split_clause,[],[f1285,f14226]) ).
fof(f14226,plain,
( spl0_1887
<=> ! [X12,X1] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1887])]) ).
fof(f1285,axiom,
! [X1,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Pow__iff_1) ).
fof(f14224,plain,
spl0_1886,
inference(avatar_split_clause,[],[f1284,f14222]) ).
fof(f14222,plain,
( spl0_1886
<=> ! [X12,X1] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1886])]) ).
fof(f1284,axiom,
! [X1,X12] :
( c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| ~ c_in(c_Pow(X12,X1),c_Finite__Set_OFinites,tc_set(tc_set(X1))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Pow__iff_0) ).
fof(f14220,plain,
spl0_1885,
inference(avatar_split_clause,[],[f1276,f14218]) ).
fof(f14218,plain,
( spl0_1885
<=> ! [X12,X1] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1885])]) ).
fof(f1276,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_0 != c_Finite__Set_Ocard(X12,X1)
| ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ocard__0__eq_0) ).
fof(f14216,plain,
spl0_1884,
inference(avatar_split_clause,[],[f1223,f14214]) ).
fof(f14214,plain,
( spl0_1884
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1884])]) ).
fof(f1223,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X3,X21,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__mult__self__is__m_0) ).
fof(f14212,plain,
spl0_1883,
inference(avatar_split_clause,[],[f1221,f14210]) ).
fof(f14210,plain,
( spl0_1883
<=> ! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1883])]) ).
fof(f1221,axiom,
! [X21,X3] :
( ~ c_less(c_0,X21,tc_nat)
| c_div(c_times(X21,X3,tc_nat),X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__mult__self1__is__m_0) ).
fof(f14208,plain,
spl0_1882,
inference(avatar_split_clause,[],[f111,f14206]) ).
fof(f111,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| ~ c_lessequals(X13,X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osubset__antisym_0) ).
fof(f14204,plain,
spl0_1881,
inference(avatar_split_clause,[],[f108,f14202]) ).
fof(f108,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,X13,X1)
| ~ c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OsubsetD_0) ).
fof(f14200,plain,
spl0_1880,
inference(avatar_split_clause,[],[f104,f14198]) ).
fof(f104,axiom,
! [X1,X12,X13] :
( X12 = X13
| ~ c_lessequals(X12,X13,tc_set(X1))
| c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OpsubsetI_0) ).
fof(f14196,plain,
spl0_1879,
inference(avatar_split_clause,[],[f100,f14194]) ).
fof(f14194,plain,
( spl0_1879
<=> ! [X12,X32,X1] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1879])]) ).
fof(f100,axiom,
! [X1,X12,X32] :
( ~ c_in(X12,c_Union(X32,X1),X1)
| c_in(X12,c_Main_OUnionE__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnionE_1) ).
fof(f14192,plain,
spl0_1878,
inference(avatar_split_clause,[],[f97,f14190]) ).
fof(f14190,plain,
( spl0_1878
<=> ! [X12,X32,X1] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1878])]) ).
fof(f97,axiom,
! [X1,X12,X32] :
( c_in(X12,c_Inter(X32,X1),X1)
| ~ c_in(X12,c_Main_OInterI__1(X12,X32,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInterI_1) ).
fof(f14188,plain,
spl0_1877,
inference(avatar_split_clause,[],[f31,f14186]) ).
fof(f14186,plain,
( spl0_1877
<=> ! [X20,X1,X19] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1877])]) ).
fof(f31,axiom,
! [X1,X19,X20] :
( ~ c_in(X20,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Int_1) ).
fof(f14184,plain,
spl0_1876,
inference(avatar_split_clause,[],[f30,f14182]) ).
fof(f14182,plain,
( spl0_1876
<=> ! [X20,X1,X19] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1876])]) ).
fof(f30,axiom,
! [X1,X19,X20] :
( ~ c_in(X19,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_inter(X19,X20,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ofinite__Int_0) ).
fof(f14180,plain,
spl0_1875,
inference(avatar_split_clause,[],[f29,f14178]) ).
fof(f14178,plain,
( spl0_1875
<=> ! [X12,X1,X18] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1875])]) ).
fof(f29,axiom,
! [X1,X18,X12] :
( ~ c_in(X12,c_Finite__Set_OFinites,tc_set(X1))
| c_in(c_insert(X18,X12,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OFinites_OinsertI_0) ).
fof(f14167,plain,
( spl0_1874
| ~ spl0_1
| ~ spl0_1862 ),
inference(avatar_split_clause,[],[f14087,f13068,f3013,f14164]) ).
fof(f14087,plain,
( c_in(v_X,c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg)
| ~ spl0_1
| ~ spl0_1862 ),
inference(resolution,[],[f13069,f3015]) ).
fof(f14005,plain,
( spl0_1873
| ~ spl0_1233
| ~ spl0_1524
| ~ spl0_1854 ),
inference(avatar_split_clause,[],[f13989,f13036,f10951,f9307,f14003]) ).
fof(f14003,plain,
( spl0_1873
<=> ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1873])]) ).
fof(f10951,plain,
( spl0_1524
<=> ! [X0] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_Relation_OId,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1524])]) ).
fof(f13989,plain,
( ! [X3] : c_Relation_OId = c_Transitive__Closure_Otrancl(c_Relation_OId,X3)
| ~ spl0_1233
| ~ spl0_1524
| ~ spl0_1854 ),
inference(forward_demodulation,[],[f13983,f10952]) ).
fof(f10952,plain,
( ! [X0] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_Relation_OId,X0)
| ~ spl0_1524 ),
inference(avatar_component_clause,[],[f10951]) ).
fof(f13983,plain,
( ! [X3] : c_Transitive__Closure_Ortrancl(c_Relation_OId,X3) = c_Transitive__Closure_Otrancl(c_Relation_OId,X3)
| ~ spl0_1233
| ~ spl0_1854 ),
inference(superposition,[],[f13037,f9308]) ).
fof(f13570,plain,
( spl0_1872
| ~ spl0_1135
| ~ spl0_1592 ),
inference(avatar_split_clause,[],[f11578,f11242,f8893,f13568]) ).
fof(f13568,plain,
( spl0_1872
<=> ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1872])]) ).
fof(f11242,plain,
( spl0_1592
<=> ! [X12,X1] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1592])]) ).
fof(f11578,plain,
( ! [X0] : c_emptyset = c_Relation_Oconverse(c_emptyset,X0,X0)
| ~ spl0_1135
| ~ spl0_1592 ),
inference(superposition,[],[f11243,f8894]) ).
fof(f11243,plain,
( ! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1)
| ~ spl0_1592 ),
inference(avatar_component_clause,[],[f11242]) ).
fof(f13429,plain,
( spl0_1871
| ~ spl0_1055
| ~ spl0_1557 ),
inference(avatar_split_clause,[],[f11446,f11101,f7360,f13427]) ).
fof(f13427,plain,
( spl0_1871
<=> ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1871])]) ).
fof(f7360,plain,
( spl0_1055
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1055])]) ).
fof(f11101,plain,
( spl0_1557
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1557])]) ).
fof(f11446,plain,
( ! [X0] : c_Divides_Oop_Advd(X0,c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1055
| ~ spl0_1557 ),
inference(resolution,[],[f11102,f7361]) ).
fof(f7361,plain,
( ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint)
| ~ spl0_1055 ),
inference(avatar_component_clause,[],[f7360]) ).
fof(f11102,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1557 ),
inference(avatar_component_clause,[],[f11101]) ).
fof(f13350,plain,
( spl0_1870
| ~ spl0_1055
| ~ spl0_1554 ),
inference(avatar_split_clause,[],[f11436,f11088,f7360,f13348]) ).
fof(f13348,plain,
( spl0_1870
<=> ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1870])]) ).
fof(f11088,plain,
( spl0_1554
<=> ! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1554])]) ).
fof(f11436,plain,
( ! [X0] : c_Divides_Oop_Advd(c_uminus(X0,tc_IntDef_Oint),X0,tc_IntDef_Oint)
| ~ spl0_1055
| ~ spl0_1554 ),
inference(resolution,[],[f11089,f7361]) ).
fof(f11089,plain,
( ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint) )
| ~ spl0_1554 ),
inference(avatar_component_clause,[],[f11088]) ).
fof(f13134,plain,
( spl0_1869
| ~ spl0_1584
| ~ spl0_1726 ),
inference(avatar_split_clause,[],[f13121,f12498,f11210,f13132]) ).
fof(f13132,plain,
( spl0_1869
<=> ! [X21] : c_lessequals(X21,c_IntDef_ONats,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1869])]) ).
fof(f11210,plain,
( spl0_1584
<=> ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1584])]) ).
fof(f12498,plain,
( spl0_1726
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1726])]) ).
fof(f13121,plain,
( ! [X21] : c_lessequals(X21,c_IntDef_ONats,tc_set(tc_nat))
| ~ spl0_1584
| ~ spl0_1726 ),
inference(resolution,[],[f12499,f11211]) ).
fof(f11211,plain,
( ! [X0] : c_in(X0,c_IntDef_ONats,tc_nat)
| ~ spl0_1584 ),
inference(avatar_component_clause,[],[f11210]) ).
fof(f12499,plain,
( ! [X1,X12,X13] :
( ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1)
| c_lessequals(X12,X13,tc_set(X1)) )
| ~ spl0_1726 ),
inference(avatar_component_clause,[],[f12498]) ).
fof(f13094,plain,
spl0_1868,
inference(avatar_split_clause,[],[f2959,f13092]) ).
fof(f13092,plain,
( spl0_1868
<=> ! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1868])]) ).
fof(f2959,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2958,f2115]) ).
fof(f2958,plain,
! [X0,X1] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f1338,f2126]) ).
fof(f1338,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(X0,X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__8_1) ).
fof(f13090,plain,
spl0_1867,
inference(avatar_split_clause,[],[f2893,f13088]) ).
fof(f13088,plain,
( spl0_1867
<=> ! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1867])]) ).
fof(f2893,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f2892,f2156]) ).
fof(f2892,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f2891,f2154]) ).
fof(f2891,plain,
! [X1] :
( c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X1)
| ~ class_Power_Orecpower(X1) ),
inference(forward_demodulation,[],[f1878,f2156]) ).
fof(f1878,axiom,
! [X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Ozero__power2_0) ).
fof(f13086,plain,
spl0_1866,
inference(avatar_split_clause,[],[f2886,f13084]) ).
fof(f2886,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2885,f2156]) ).
fof(f2885,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2884,f2154]) ).
fof(f2884,plain,
! [X1] :
( c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f1328,f2156]) ).
fof(f1328,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_plus(c_1,c_1,X1) = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__1_0) ).
fof(f13082,plain,
spl0_1865,
inference(avatar_split_clause,[],[f2861,f13080]) ).
fof(f13080,plain,
( spl0_1865
<=> ! [X21] : c_Suc(c_Suc(X21)) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1865])]) ).
fof(f2861,plain,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f2860,f2156]) ).
fof(f2860,plain,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f2859,f2154]) ).
fof(f2859,plain,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat),
inference(forward_demodulation,[],[f1881,f2156]) ).
fof(f1881,axiom,
! [X21] : c_plus(c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),X21,tc_nat) = c_Suc(c_Suc(X21)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oadd__2__eq__Suc_0) ).
fof(f13078,plain,
spl0_1864,
inference(avatar_split_clause,[],[f2858,f13076]) ).
fof(f2858,plain,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_Obin__succ(c_Numeral_OPls)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2857,f2156]) ).
fof(f2857,plain,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)),tc_nat),tc_nat),
inference(forward_demodulation,[],[f2856,f2154]) ).
fof(f2856,plain,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_Obin__succ(c_Numeral_OPls),c_Numeral_Obit_OB0),tc_nat),tc_nat),
inference(forward_demodulation,[],[f1882,f2156]) ).
fof(f1882,axiom,
! [X21] : c_Suc(c_Suc(X21)) = c_plus(X21,c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),c_Numeral_Obit_OB0),tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatSimprocs_Oadd__2__eq__Suc_H_0) ).
fof(f13074,plain,
spl0_1863,
inference(avatar_split_clause,[],[f2824,f13072]) ).
fof(f2824,axiom,
! [X88,X20] :
( ~ c_lessequals(X20,X88,tc_set(tc_Message_Omsg))
| c_lessequals(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_set(tc_Message_Omsg)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__mono_0) ).
fof(f13070,plain,
spl0_1862,
inference(avatar_split_clause,[],[f2823,f13068]) ).
fof(f2823,axiom,
! [X91,X88,X86] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OCrypt(X91,X86),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts_OBody_0) ).
fof(f13066,plain,
spl0_1861,
inference(avatar_split_clause,[],[f2780,f13064]) ).
fof(f13064,plain,
( spl0_1861
<=> ! [X86,X87,X88] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1861])]) ).
fof(f2780,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OMPair__analz_1) ).
fof(f13062,plain,
spl0_1860,
inference(avatar_split_clause,[],[f2779,f13060]) ).
fof(f13060,plain,
( spl0_1860
<=> ! [X87,X86,X88] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1860])]) ).
fof(f2779,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oanalz(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OMPair__analz_0) ).
fof(f13058,plain,
spl0_1859,
inference(avatar_split_clause,[],[f2771,f13056]) ).
fof(f13056,plain,
( spl0_1859
<=> ! [X13,X12,X1] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1859])]) ).
fof(f2771,axiom,
! [X1,X12,X13] : c_union(X13,X12,X1) = c_union(X12,c_union(X13,X12,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Ostrange__Un__eq_0) ).
fof(f13054,plain,
spl0_1858,
inference(avatar_split_clause,[],[f2768,f13052]) ).
fof(f2768,axiom,
! [X88,X20] : c_Message_Oparts(c_union(X20,X88,tc_Message_Omsg)) = c_union(c_Message_Oparts(X20),c_Message_Oparts(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__Un_0) ).
fof(f13050,plain,
spl0_1857,
inference(avatar_split_clause,[],[f2742,f13048]) ).
fof(f13048,plain,
( spl0_1857
<=> ! [X93,X88] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1857])]) ).
fof(f2742,axiom,
! [X88,X93] : c_Message_OkeysFor(c_union(X88,X93,tc_Message_Omsg)) = c_union(c_Message_OkeysFor(X88),c_Message_OkeysFor(X93),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__Un_0) ).
fof(f13046,plain,
spl0_1856,
inference(avatar_split_clause,[],[f2729,f13044]) ).
fof(f2729,axiom,
! [X88,X86,X87] :
( c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OMPair__parts_1) ).
fof(f13042,plain,
spl0_1855,
inference(avatar_split_clause,[],[f2728,f13040]) ).
fof(f2728,axiom,
! [X88,X86,X87] :
( c_in(X87,c_Message_Oparts(X88),tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OMPair(X86,X87),c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OMPair__parts_0) ).
fof(f13038,plain,
spl0_1854,
inference(avatar_split_clause,[],[f2716,f13036]) ).
fof(f2716,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Otrancl(c_union(X5,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Otrancl__reflcl_0) ).
fof(f13034,plain,
spl0_1853,
inference(avatar_split_clause,[],[f2712,f13032]) ).
fof(f13032,plain,
( spl0_1853
<=> ! [X85,X1] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Transitive__Closure_Ortrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1853])]) ).
fof(f2712,axiom,
! [X1,X85] : c_Transitive__Closure_Ortrancl(X85,X1) = c_Transitive__Closure_Ortrancl(c_union(X85,c_Relation_OId,tc_prod(X1,X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Ortrancl__reflcl_0) ).
fof(f13030,plain,
spl0_1852,
inference(avatar_split_clause,[],[f2708,f13028]) ).
fof(f13028,plain,
( spl0_1852
<=> ! [X5,X1] : c_Transitive__Closure_Ortrancl(X5,X1) = c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1852])]) ).
fof(f2708,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_union(c_Transitive__Closure_Otrancl(X5,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Oreflcl__trancl_0) ).
fof(f13026,plain,
spl0_1851,
inference(avatar_split_clause,[],[f2703,f13024]) ).
fof(f13024,plain,
( spl0_1851
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1851])]) ).
fof(f2703,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInr(X0,X2,X1) != c_Sum__Type_OInr(X3,X2,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OInr__eq_0) ).
fof(f13022,plain,
spl0_1850,
inference(avatar_split_clause,[],[f2701,f13020]) ).
fof(f13020,plain,
( spl0_1850
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1850])]) ).
fof(f2701,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Sum__Type_OInl(X0,X1,X2) != c_Sum__Type_OInl(X3,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OInl__eq_0) ).
fof(f13018,plain,
spl0_1849,
inference(avatar_split_clause,[],[f2695,f13016]) ).
fof(f13016,plain,
( spl0_1849
<=> ! [X18,X12,X27,X1] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1849])]) ).
fof(f2695,axiom,
! [X18,X1,X27,X12] :
( X18 = X27
| c_insert(X18,X12,X1) != c_insert(X27,c_emptyset,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osingleton__insert__inj__eq_H_0) ).
fof(f13014,plain,
spl0_1848,
inference(avatar_split_clause,[],[f2688,f13012]) ).
fof(f13012,plain,
( spl0_1848
<=> ! [X13,X0,X12,X1] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1848])]) ).
fof(f2688,axiom,
! [X0,X1,X12,X13] :
( c_in(X0,X13,X1)
| ~ c_lessequals(c_insert(X0,X12,X1),X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__subset_0) ).
fof(f13010,plain,
spl0_1847,
inference(avatar_split_clause,[],[f2676,f13008]) ).
fof(f13008,plain,
( spl0_1847
<=> ! [X12,X0,X1] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1847])]) ).
fof(f2676,axiom,
! [X0,X1,X12] : c_insert(X0,X12,X1) = c_insert(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__absorb2_0) ).
fof(f13004,plain,
spl0_1846,
inference(avatar_split_clause,[],[f2670,f13002]) ).
fof(f13002,plain,
( spl0_1846
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1846])]) ).
fof(f2670,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_Oempty__Union__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oempty__Union__conv_1) ).
fof(f13000,plain,
spl0_1845,
inference(avatar_split_clause,[],[f2653,f12998]) ).
fof(f12998,plain,
( spl0_1845
<=> ! [X12,X1] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1845])]) ).
fof(f2653,axiom,
! [X1,X12] :
( c_emptyset = c_Union(X12,X1)
| c_in(c_Main_OUnion__empty__conv__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__empty__conv_1) ).
fof(f12996,plain,
spl0_1844,
inference(avatar_split_clause,[],[f2628,f12994]) ).
fof(f12994,plain,
( spl0_1844
<=> ! [X13,X12,X1] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1844])]) ).
fof(f2628,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OPow__iff_1) ).
fof(f12992,plain,
spl0_1843,
inference(avatar_split_clause,[],[f2627,f12990]) ).
fof(f12990,plain,
( spl0_1843
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1843])]) ).
fof(f2627,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(X12,c_Pow(X13,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OPow__iff_0) ).
fof(f12988,plain,
spl0_1842,
inference(avatar_split_clause,[],[f2617,f12986]) ).
fof(f12986,plain,
( spl0_1842
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1842])]) ).
fof(f2617,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__2__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__UNIV__conv__2_1) ).
fof(f12984,plain,
spl0_1841,
inference(avatar_split_clause,[],[f2614,f12982]) ).
fof(f12982,plain,
( spl0_1841
<=> ! [X12,X1] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1841])]) ).
fof(f2614,axiom,
! [X1,X12] :
( c_UNIV = c_Inter(X12,X1)
| c_in(c_Main_OInter__UNIV__conv__1__1(X12,X1),X12,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__UNIV__conv__1_1) ).
fof(f12980,plain,
spl0_1840,
inference(avatar_split_clause,[],[f2595,f12978]) ).
fof(f12978,plain,
( spl0_1840
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1840])]) ).
fof(f2595,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__iff_1) ).
fof(f12976,plain,
spl0_1839,
inference(avatar_split_clause,[],[f2594,f12974]) ).
fof(f12974,plain,
( spl0_1839
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1839])]) ).
fof(f2594,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_minus(X12,X13,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__iff_0) ).
fof(f12972,plain,
spl0_1838,
inference(avatar_split_clause,[],[f2592,f12970]) ).
fof(f2592,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X12,X13,tc_set(X1))
| c_emptyset = c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__eq__empty__iff_1) ).
fof(f12968,plain,
spl0_1837,
inference(avatar_split_clause,[],[f2591,f12966]) ).
fof(f12966,plain,
( spl0_1837
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1837])]) ).
fof(f2591,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_emptyset != c_minus(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__eq__empty__iff_0) ).
fof(f12958,plain,
spl0_1836,
inference(avatar_split_clause,[],[f2581,f12956]) ).
fof(f12956,plain,
( spl0_1836
<=> ! [X13,X12,X1] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1836])]) ).
fof(f2581,axiom,
! [X1,X12,X13] :
( X12 = X13
| c_uminus(X12,tc_set(X1)) != c_uminus(X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__eq__Compl__iff_0) ).
fof(f12954,plain,
spl0_1835,
inference(avatar_split_clause,[],[f2570,f12952]) ).
fof(f12952,plain,
( spl0_1835
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1835])]) ).
fof(f2570,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X43,X16,X1)
| c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OlessThan__iff_1) ).
fof(f12950,plain,
spl0_1834,
inference(avatar_split_clause,[],[f2569,f12948]) ).
fof(f12948,plain,
( spl0_1834
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1834])]) ).
fof(f2569,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OlessThan(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OlessThan__iff_0) ).
fof(f12946,plain,
spl0_1833,
inference(avatar_split_clause,[],[f2568,f12944]) ).
fof(f12944,plain,
( spl0_1833
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1833])]) ).
fof(f2568,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OlessThan(X0,X1) != c_SetInterval_OlessThan(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OlessThan__eq__iff_0) ).
fof(f12942,plain,
spl0_1832,
inference(avatar_split_clause,[],[f2559,f12940]) ).
fof(f12940,plain,
( spl0_1832
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1832])]) ).
fof(f2559,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_less(X16,X43,X1)
| c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThan__iff_1) ).
fof(f12938,plain,
spl0_1831,
inference(avatar_split_clause,[],[f2558,f12936]) ).
fof(f12936,plain,
( spl0_1831
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1831])]) ).
fof(f2558,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_less(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OgreaterThan(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThan__iff_0) ).
fof(f12934,plain,
spl0_1830,
inference(avatar_split_clause,[],[f2557,f12932]) ).
fof(f12932,plain,
( spl0_1830
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1830])]) ).
fof(f2557,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OgreaterThan(X0,X1) != c_SetInterval_OgreaterThan(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThan__eq__iff_0) ).
fof(f12930,plain,
spl0_1829,
inference(avatar_split_clause,[],[f2550,f12928]) ).
fof(f2550,axiom,
! [X1,X26,X16] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X26,X16,X1)
| c_emptyset = c_SetInterval_OgreaterThanAtMost(X16,X26,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OgreaterThanAtMost__empty_0) ).
fof(f12926,plain,
spl0_1828,
inference(avatar_split_clause,[],[f2547,f12924]) ).
fof(f12924,plain,
( spl0_1828
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1828])]) ).
fof(f2547,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,c_Suc(X26),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__greaterThanLessThan_0) ).
fof(f12922,plain,
spl0_1827,
inference(avatar_split_clause,[],[f2546,f12920]) ).
fof(f12920,plain,
( spl0_1827
<=> ! [X14,X26] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1827])]) ).
fof(f2546,axiom,
! [X26,X14] : c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__greaterThanAtMost__int_0) ).
fof(f12912,plain,
spl0_1826,
inference(avatar_split_clause,[],[f2543,f12910]) ).
fof(f12910,plain,
( spl0_1826
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1826])]) ).
fof(f2543,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),tc_IntDef_Oint) = c_IntDef_Onat(c_minus(X14,X26,tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__atLeastLessThan__int_0) ).
fof(f12908,plain,
spl0_1825,
inference(avatar_split_clause,[],[f2540,f12906]) ).
fof(f12906,plain,
( spl0_1825
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Suc(X14),X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1825])]) ).
fof(f2540,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),tc_nat) = c_minus(c_Suc(X14),X26,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__atLeastAtMost_0) ).
fof(f12904,plain,
spl0_1824,
inference(avatar_split_clause,[],[f2537,f12902]) ).
fof(f12902,plain,
( spl0_1824
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1824])]) ).
fof(f2537,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X43,X16,X1)
| c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatMost__iff_1) ).
fof(f12900,plain,
spl0_1823,
inference(avatar_split_clause,[],[f2536,f12898]) ).
fof(f12898,plain,
( spl0_1823
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1823])]) ).
fof(f2536,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X43,X16,X1)
| ~ c_in(X43,c_SetInterval_OatMost(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatMost__iff_0) ).
fof(f12896,plain,
spl0_1822,
inference(avatar_split_clause,[],[f2535,f12894]) ).
fof(f12894,plain,
( spl0_1822
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1822])]) ).
fof(f2535,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatMost(X0,X1) != c_SetInterval_OatMost(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatMost__eq__iff_0) ).
fof(f12892,plain,
spl0_1821,
inference(avatar_split_clause,[],[f2531,f12890]) ).
fof(f12890,plain,
( spl0_1821
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1821])]) ).
fof(f2531,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| ~ c_lessequals(X16,X43,X1)
| c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeast__iff_1) ).
fof(f12888,plain,
spl0_1820,
inference(avatar_split_clause,[],[f2530,f12886]) ).
fof(f12886,plain,
( spl0_1820
<=> ! [X16,X1,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1820])]) ).
fof(f2530,axiom,
! [X1,X16,X43] :
( ~ class_Orderings_Oord(X1)
| c_lessequals(X16,X43,X1)
| ~ c_in(X43,c_SetInterval_OatLeast(X16,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeast__iff_0) ).
fof(f12884,plain,
spl0_1819,
inference(avatar_split_clause,[],[f2529,f12882]) ).
fof(f12882,plain,
( spl0_1819
<=> ! [X0,X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1819])]) ).
fof(f2529,axiom,
! [X3,X0,X1] :
( ~ class_Orderings_Olinorder(X1)
| X0 = X3
| c_SetInterval_OatLeast(X0,X1) != c_SetInterval_OatLeast(X3,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeast__eq__iff_0) ).
fof(f12880,plain,
spl0_1818,
inference(avatar_split_clause,[],[f2523,f12878]) ).
fof(f2523,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_lessequals(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastLessThan(X15,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f12876,plain,
spl0_1817,
inference(avatar_split_clause,[],[f2518,f12874]) ).
fof(f2518,axiom,
! [X21,X1,X15] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X21,X15,X1)
| c_emptyset = c_SetInterval_OatLeastAtMost(X15,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastAtMost__empty_0) ).
fof(f12872,plain,
( spl0_1816
| ~ spl0_1172
| ~ spl0_1440 ),
inference(avatar_split_clause,[],[f10764,f10368,f9061,f12870]) ).
fof(f12870,plain,
( spl0_1816
<=> ! [X1] : c_0 = c_div(X1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1816])]) ).
fof(f9061,plain,
( spl0_1172
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1172])]) ).
fof(f10368,plain,
( spl0_1440
<=> ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1440])]) ).
fof(f10764,plain,
( ! [X1] : c_0 = c_div(X1,c_0,tc_IntDef_Oint)
| ~ spl0_1172
| ~ spl0_1440 ),
inference(superposition,[],[f10369,f9062]) ).
fof(f9062,plain,
( ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3
| ~ spl0_1172 ),
inference(avatar_component_clause,[],[f9061]) ).
fof(f10369,plain,
( ! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint)
| ~ spl0_1440 ),
inference(avatar_component_clause,[],[f10368]) ).
fof(f12868,plain,
spl0_1815,
inference(avatar_split_clause,[],[f2517,f12866]) ).
fof(f12866,plain,
( spl0_1815
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1815])]) ).
fof(f2517,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatLeast(X16,X1) = c_uminus(c_SetInterval_OlessThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OCompl__lessThan_0) ).
fof(f12864,plain,
spl0_1814,
inference(avatar_split_clause,[],[f2516,f12862]) ).
fof(f12862,plain,
( spl0_1814
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1814])]) ).
fof(f2516,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_SetInterval_OatMost(X16,X1) = c_uminus(c_SetInterval_OgreaterThan(X16,X1),tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OCompl__greaterThan_0) ).
fof(f12860,plain,
spl0_1813,
inference(avatar_split_clause,[],[f2515,f12858]) ).
fof(f12858,plain,
( spl0_1813
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1813])]) ).
fof(f2515,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatMost(X16,X1),tc_set(X1)) = c_SetInterval_OgreaterThan(X16,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OCompl__atMost_0) ).
fof(f12856,plain,
spl0_1812,
inference(avatar_split_clause,[],[f2514,f12854]) ).
fof(f12854,plain,
( spl0_1812
<=> ! [X16,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1812])]) ).
fof(f2514,axiom,
! [X1,X16] :
( ~ class_Orderings_Olinorder(X1)
| c_uminus(c_SetInterval_OatLeast(X16,X1),tc_set(X1)) = c_SetInterval_OlessThan(X16,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OCompl__atLeast_0) ).
fof(f12852,plain,
spl0_1811,
inference(avatar_split_clause,[],[f2454,f12850]) ).
fof(f12850,plain,
( spl0_1811
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_0 != c_HOL_Oinverse(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1811])]) ).
fof(f2454,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = X18
| c_0 != c_HOL_Oinverse(X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_0) ).
fof(f12848,plain,
spl0_1810,
inference(avatar_split_clause,[],[f2434,f12846]) ).
fof(f12846,plain,
( spl0_1810
<=> ! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_1 = X0
| c_1 != c_HOL_Oinverse(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1810])]) ).
fof(f2434,axiom,
! [X0,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_1 = X0
| c_1 != c_HOL_Oinverse(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__eq__1__iff_0) ).
fof(f12844,plain,
spl0_1809,
inference(avatar_split_clause,[],[f2373,f12842]) ).
fof(f2373,axiom,
! [X1,X12,X13] : c_inter(X12,X13,X1) = c_Relation_OImage(c_Relation_Odiag(X12,X1),X13,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImage__diag_0) ).
fof(f12840,plain,
spl0_1808,
inference(avatar_split_clause,[],[f2302,f12838]) ).
fof(f12838,plain,
( spl0_1808
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1808])]) ).
fof(f2302,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__sum_3) ).
fof(f12836,plain,
spl0_1807,
inference(avatar_split_clause,[],[f2301,f12834]) ).
fof(f12834,plain,
( spl0_1807
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1807])]) ).
fof(f2301,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__sum_2) ).
fof(f12832,plain,
spl0_1806,
inference(avatar_split_clause,[],[f2300,f12830]) ).
fof(f12830,plain,
( spl0_1806
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1806])]) ).
fof(f2300,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__sum_1) ).
fof(f12823,plain,
spl0_1805,
inference(avatar_split_clause,[],[f2299,f12821]) ).
fof(f12821,plain,
( spl0_1805
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1805])]) ).
fof(f2299,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__sum_0) ).
fof(f12819,plain,
spl0_1804,
inference(avatar_split_clause,[],[f2296,f12817]) ).
fof(f12817,plain,
( spl0_1804
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1804])]) ).
fof(f2296,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__product_0) ).
fof(f12815,plain,
spl0_1803,
inference(avatar_split_clause,[],[f2289,f12813]) ).
fof(f12813,plain,
( spl0_1803
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1803])]) ).
fof(f2289,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__sum_3) ).
fof(f12811,plain,
spl0_1802,
inference(avatar_split_clause,[],[f2288,f12809]) ).
fof(f12809,plain,
( spl0_1802
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1802])]) ).
fof(f2288,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__sum_2) ).
fof(f12807,plain,
spl0_1801,
inference(avatar_split_clause,[],[f2287,f12805]) ).
fof(f12805,plain,
( spl0_1801
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1801])]) ).
fof(f2287,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__sum_1) ).
fof(f12803,plain,
spl0_1800,
inference(avatar_split_clause,[],[f2286,f12801]) ).
fof(f12801,plain,
( spl0_1800
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1800])]) ).
fof(f2286,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_plus(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__sum_0) ).
fof(f12799,plain,
spl0_1799,
inference(avatar_split_clause,[],[f2283,f12797]) ).
fof(f12797,plain,
( spl0_1799
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1799])]) ).
fof(f2283,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(X3,tc_nat)
| ~ c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__product_0) ).
fof(f12795,plain,
spl0_1798,
inference(avatar_split_clause,[],[f2277,f12793]) ).
fof(f12793,plain,
( spl0_1798
<=> ! [X0,X3] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1798])]) ).
fof(f2277,axiom,
! [X3,X0] :
( c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__difference_3) ).
fof(f12791,plain,
spl0_1797,
inference(avatar_split_clause,[],[f2276,f12789]) ).
fof(f12789,plain,
( spl0_1797
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1797])]) ).
fof(f2276,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__difference_2) ).
fof(f12787,plain,
spl0_1796,
inference(avatar_split_clause,[],[f2275,f12785]) ).
fof(f12785,plain,
( spl0_1796
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1796])]) ).
fof(f2275,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(X3,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__difference_1) ).
fof(f12783,plain,
( spl0_1795
| ~ spl0_59
| ~ spl0_1418 ),
inference(avatar_split_clause,[],[f10288,f10145,f3303,f12780]) ).
fof(f12780,plain,
( spl0_1795
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1795])]) ).
fof(f10145,plain,
( spl0_1418
<=> ! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1418])]) ).
fof(f10288,plain,
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1418 ),
inference(resolution,[],[f10146,f3305]) ).
fof(f10146,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1) )
| ~ spl0_1418 ),
inference(avatar_component_clause,[],[f10145]) ).
fof(f12778,plain,
spl0_1794,
inference(avatar_split_clause,[],[f2274,f12776]) ).
fof(f12776,plain,
( spl0_1794
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1794])]) ).
fof(f2274,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_minus(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__difference_0) ).
fof(f12774,plain,
spl0_1793,
inference(avatar_split_clause,[],[f2234,f12772]) ).
fof(f12772,plain,
( spl0_1793
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1793])]) ).
fof(f2234,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(c_0,X18,X1)
| c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__less__0__iff__less_1) ).
fof(f12770,plain,
spl0_1792,
inference(avatar_split_clause,[],[f2233,f12768]) ).
fof(f12768,plain,
( spl0_1792
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1792])]) ).
fof(f2233,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(c_0,X18,X1)
| ~ c_less(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__less__0__iff__less_0) ).
fof(f12766,plain,
spl0_1791,
inference(avatar_split_clause,[],[f2230,f12764]) ).
fof(f12764,plain,
( spl0_1791
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1791])]) ).
fof(f2230,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(c_0,X18,X1)
| c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__le__0__iff__le_1) ).
fof(f12762,plain,
spl0_1790,
inference(avatar_split_clause,[],[f2229,f12760]) ).
fof(f12760,plain,
( spl0_1790
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1790])]) ).
fof(f2229,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(c_0,X18,X1)
| ~ c_lessequals(c_uminus(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__le__0__iff__le_0) ).
fof(f12758,plain,
spl0_1789,
inference(avatar_split_clause,[],[f2227,f12756]) ).
fof(f12756,plain,
( spl0_1789
<=> ! [X18,X27,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1789])]) ).
fof(f2227,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_uminus(X18,X1) != c_uminus(X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__equal__iff__equal_0) ).
fof(f12754,plain,
spl0_1788,
inference(avatar_split_clause,[],[f2224,f12752]) ).
fof(f12752,plain,
( spl0_1788
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1788])]) ).
fof(f2224,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_less(X18,c_0,X1)
| c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__0__less__iff__less_1) ).
fof(f12750,plain,
spl0_1787,
inference(avatar_split_clause,[],[f2223,f12748]) ).
fof(f12748,plain,
( spl0_1787
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1787])]) ).
fof(f2223,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_less(X18,c_0,X1)
| ~ c_less(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__0__less__iff__less_0) ).
fof(f12746,plain,
spl0_1786,
inference(avatar_split_clause,[],[f2222,f12744]) ).
fof(f12744,plain,
( spl0_1786
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1786])]) ).
fof(f2222,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| ~ c_lessequals(X18,c_0,X1)
| c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__0__le__iff__le_1) ).
fof(f12742,plain,
spl0_1785,
inference(avatar_split_clause,[],[f2221,f12740]) ).
fof(f2221,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X1)
| c_lessequals(X18,c_0,X1)
| ~ c_lessequals(c_0,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__0__le__iff__le_0) ).
fof(f12738,plain,
( spl0_1784
| ~ spl0_1313
| ~ spl0_1402 ),
inference(avatar_split_clause,[],[f10268,f10079,f9643,f12735]) ).
fof(f12735,plain,
( spl0_1784
<=> c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1784])]) ).
fof(f10268,plain,
( c_in(c_0,c_SetInterval_OatMost(c_0,tc_nat),tc_nat)
| ~ spl0_1313
| ~ spl0_1402 ),
inference(superposition,[],[f9644,f10081]) ).
fof(f12733,plain,
spl0_1783,
inference(avatar_split_clause,[],[f2167,f12731]) ).
fof(f12731,plain,
( spl0_1783
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1783])]) ).
fof(f2167,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(X48,X1) = c_times(X48,c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Omult__minus1__right_0) ).
fof(f12729,plain,
spl0_1782,
inference(avatar_split_clause,[],[f2166,f12727]) ).
fof(f12727,plain,
( spl0_1782
<=> ! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1782])]) ).
fof(f2166,axiom,
! [X48,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_times(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X48,X1) = c_uminus(X48,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Omult__minus1_0) ).
fof(f12725,plain,
spl0_1781,
inference(avatar_split_clause,[],[f2117,f12723]) ).
fof(f2117,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_uminus(c_Numeral_Onumber__of(X11,X1),X1) = c_Numeral_Onumber__of(c_Numeral_Obin__minus(X11),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__2_0) ).
fof(f12721,plain,
spl0_1780,
inference(avatar_split_clause,[],[f2086,f12719]) ).
fof(f12719,plain,
( spl0_1780
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1780])]) ).
fof(f2086,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X15,X16,tc_nat) != c_plus(X21,X16,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__add__right__cancel_0) ).
fof(f12717,plain,
spl0_1779,
inference(avatar_split_clause,[],[f2081,f12715]) ).
fof(f12715,plain,
( spl0_1779
<=> ! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1779])]) ).
fof(f2081,axiom,
! [X21,X16,X15] :
( X15 = X21
| c_plus(X16,X15,tc_nat) != c_plus(X16,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__add__left__cancel_0) ).
fof(f12713,plain,
spl0_1778,
inference(avatar_split_clause,[],[f2065,f12711]) ).
fof(f12711,plain,
( spl0_1778
<=> ! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1778])]) ).
fof(f2065,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 = X21
| c_0 != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__is__0_0) ).
fof(f12709,plain,
spl0_1777,
inference(avatar_split_clause,[],[f2055,f12707]) ).
fof(f2055,axiom,
! [X21,X15] : c_Orderings_Omin(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omin(X15,X21,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omin__Suc__Suc_0) ).
fof(f12705,plain,
spl0_1776,
inference(avatar_split_clause,[],[f2052,f12703]) ).
fof(f12703,plain,
( spl0_1776
<=> ! [X21,X15] : c_Orderings_Omax(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omax(X15,X21,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1776])]) ).
fof(f2052,axiom,
! [X21,X15] : c_Orderings_Omax(c_Suc(X15),c_Suc(X21),tc_nat) = c_Suc(c_Orderings_Omax(X15,X21,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omax__Suc__Suc_0) ).
fof(f12701,plain,
spl0_1775,
inference(avatar_split_clause,[],[f2036,f12699]) ).
fof(f12699,plain,
( spl0_1775
<=> ! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1775])]) ).
fof(f2036,axiom,
! [X21,X43] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_minus(X21,c_Suc(X43),tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__Suc__less_0) ).
fof(f12697,plain,
spl0_1774,
inference(avatar_split_clause,[],[f1854,f12695]) ).
fof(f12695,plain,
( spl0_1774
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1774])]) ).
fof(f1854,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint)
| c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__0__number__of_1) ).
fof(f12693,plain,
( spl0_1773
| ~ spl0_109
| ~ spl0_1389 ),
inference(avatar_split_clause,[],[f10248,f10027,f3553,f12691]) ).
fof(f12691,plain,
( spl0_1773
<=> ! [X1] : c_Nat_Opower(X1,c_1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1773])]) ).
fof(f10027,plain,
( spl0_1389
<=> ! [X1,X3] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1389])]) ).
fof(f10248,plain,
( ! [X1] : c_Nat_Opower(X1,c_1,tc_nat) = X1
| ~ spl0_109
| ~ spl0_1389 ),
inference(resolution,[],[f10028,f3555]) ).
fof(f10028,plain,
( ! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 )
| ~ spl0_1389 ),
inference(avatar_component_clause,[],[f10027]) ).
fof(f12689,plain,
spl0_1772,
inference(avatar_split_clause,[],[f1853,f12687]) ).
fof(f12687,plain,
( spl0_1772
<=> ! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1772])]) ).
fof(f1853,axiom,
! [X47] :
( ~ c_less(c_0,c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_Obin__minus(X47),tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oless__0__number__of_0) ).
fof(f12685,plain,
spl0_1771,
inference(avatar_split_clause,[],[f1850,f12683]) ).
fof(f12683,plain,
( spl0_1771
<=> ! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1771])]) ).
fof(f1850,axiom,
! [X21,X15] : c_IntDef_Oint(c_plus(X15,X21,tc_nat)) = c_plus(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oint_A_Im2_A_L_An2_J_A_61_61_Aint_Am2_A_L_Aint_An2_0) ).
fof(f12681,plain,
spl0_1770,
inference(avatar_split_clause,[],[f1813,f12679]) ).
fof(f12679,plain,
( spl0_1770
<=> ! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1770])]) ).
fof(f1813,axiom,
! [X21,X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| X15 = X21
| c_NatArith_Oof__nat(X21,X1) != c_NatArith_Oof__nat(X15,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__eq__iff_0) ).
fof(f12677,plain,
spl0_1769,
inference(avatar_split_clause,[],[f1807,f12675]) ).
fof(f12675,plain,
( spl0_1769
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1769])]) ).
fof(f1807,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__0__less__iff_1) ).
fof(f12673,plain,
spl0_1768,
inference(avatar_split_clause,[],[f1806,f12671]) ).
fof(f12671,plain,
( spl0_1768
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1768])]) ).
fof(f1806,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__0__less__iff_0) ).
fof(f12669,plain,
spl0_1767,
inference(avatar_split_clause,[],[f1784,f12667]) ).
fof(f12667,plain,
( spl0_1767
<=> ! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1767])]) ).
fof(f1784,axiom,
! [X59,X43] :
( c_0 = X59
| c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil != c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oupt__eq__Nil__conv_0) ).
fof(f12665,plain,
spl0_1766,
inference(avatar_split_clause,[],[f1772,f12663]) ).
fof(f12663,plain,
( spl0_1766
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Otake(X21,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1766])]) ).
fof(f1772,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_0 = X21
| c_List_Olist_ONil != c_List_Otake(X21,X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__eq__Nil_0) ).
fof(f12661,plain,
spl0_1765,
inference(avatar_split_clause,[],[f1743,f12659]) ).
fof(f12659,plain,
( spl0_1765
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1765])]) ).
fof(f1743,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X23,X25,X1) != c_append(X23,X51,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osame__append__eq_0) ).
fof(f12657,plain,
spl0_1764,
inference(avatar_split_clause,[],[f1738,f12655]) ).
fof(f12655,plain,
( spl0_1764
<=> ! [X21,X1,X23] : c_List_Orotate(c_Suc(X21),X23,X1) = c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1764])]) ).
fof(f1738,axiom,
! [X21,X1,X23] : c_List_Orotate(c_Suc(X21),X23,X1) = c_List_Orotate1(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate__Suc_0) ).
fof(f12653,plain,
spl0_1763,
inference(avatar_split_clause,[],[f1737,f12651]) ).
fof(f12651,plain,
( spl0_1763
<=> ! [X1,X3] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1763])]) ).
fof(f1737,axiom,
! [X3,X1] :
( c_List_Orotate1(X3,X1) = X3
| ~ c_lessequals(c_Nat_Osize(X3,tc_List_Olist(X1)),c_1,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate1__length01_0) ).
fof(f12648,plain,
spl0_1762,
inference(avatar_split_clause,[],[f1626,f12646]) ).
fof(f12646,plain,
( spl0_1762
<=> ! [X18,X42,X64,X63,X1] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1762])]) ).
fof(f1626,axiom,
! [X1,X18,X63,X42,X64] :
( X63 = X64
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist_Oinject_1) ).
fof(f12644,plain,
spl0_1761,
inference(avatar_split_clause,[],[f1625,f12642]) ).
fof(f12642,plain,
( spl0_1761
<=> ! [X18,X42,X64,X63,X1] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1761])]) ).
fof(f1625,axiom,
! [X18,X1,X63,X42,X64] :
( X18 = X42
| c_List_Olist_OCons(X42,X63,X1) != c_List_Olist_OCons(X18,X64,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist_Oinject_0) ).
fof(f12640,plain,
spl0_1760,
inference(avatar_split_clause,[],[f1610,f12638]) ).
fof(f12638,plain,
( spl0_1760
<=> ! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1760])]) ).
fof(f1610,axiom,
! [X21,X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate(X21,X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__rotate_0) ).
fof(f12636,plain,
spl0_1759,
inference(avatar_split_clause,[],[f1552,f12634]) ).
fof(f12634,plain,
( spl0_1759
<=> ! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1759])]) ).
fof(f1552,axiom,
! [X41,X0,X23] :
( ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41)
| ~ c_in(X0,c_List_Oset(X23,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct_Osimps__2_0) ).
fof(f12632,plain,
spl0_1758,
inference(avatar_split_clause,[],[f1535,f12630]) ).
fof(f12630,plain,
( spl0_1758
<=> ! [X21,X1,X3] : c_append(c_List_Otake(X21,X3,X1),c_List_Odrop(X21,X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1758])]) ).
fof(f1535,axiom,
! [X21,X3,X1] : c_append(c_List_Otake(X21,X3,X1),c_List_Odrop(X21,X3,X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__take__drop__id_0) ).
fof(f12628,plain,
spl0_1757,
inference(avatar_split_clause,[],[f1530,f12626]) ).
fof(f12626,plain,
( spl0_1757
<=> ! [X51,X23,X25,X1] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1757])]) ).
fof(f1530,axiom,
! [X51,X1,X25,X23] :
( X25 = X51
| c_append(X25,X23,X1) != c_append(X51,X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__same__eq_0) ).
fof(f12624,plain,
spl0_1756,
inference(avatar_split_clause,[],[f1493,f12622]) ).
fof(f12622,plain,
( spl0_1756
<=> ! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1756])]) ).
fof(f1493,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_plus(X27,X18,tc_IntDef_Oint),X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__zadd__self2_0) ).
fof(f12620,plain,
spl0_1755,
inference(avatar_split_clause,[],[f1492,f12618]) ).
fof(f12618,plain,
( spl0_1755
<=> ! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1755])]) ).
fof(f1492,axiom,
! [X18,X27] : c_Divides_Oop_Amod(c_plus(X18,X27,tc_IntDef_Oint),X18,tc_IntDef_Oint) = c_Divides_Oop_Amod(X27,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__zadd__self1_0) ).
fof(f12616,plain,
spl0_1754,
inference(avatar_split_clause,[],[f1485,f12614]) ).
fof(f12614,plain,
( spl0_1754
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1754])]) ).
fof(f1485,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozero__less__zpower__abs__iff_1) ).
fof(f12611,plain,
( spl0_1753
| ~ spl0_1318
| ~ spl0_1752 ),
inference(avatar_split_clause,[],[f12607,f12604,f9727,f12609]) ).
fof(f12609,plain,
( spl0_1753
<=> ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1753])]) ).
fof(f9727,plain,
( spl0_1318
<=> c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1318])]) ).
fof(f12604,plain,
( spl0_1752
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1752])]) ).
fof(f12607,plain,
( ! [X21] :
( ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = X21 )
| ~ spl0_1318
| ~ spl0_1752 ),
inference(forward_demodulation,[],[f12605,f9729]) ).
fof(f9729,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_1318 ),
inference(avatar_component_clause,[],[f9727]) ).
fof(f12605,plain,
( ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) )
| ~ spl0_1752 ),
inference(avatar_component_clause,[],[f12604]) ).
fof(f12606,plain,
spl0_1752,
inference(avatar_split_clause,[],[f1484,f12604]) ).
fof(f1484,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_HOL_Oabs(c_0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozero__less__zpower__abs__iff_0) ).
fof(f12602,plain,
spl0_1751,
inference(avatar_split_clause,[],[f1477,f12600]) ).
fof(f12600,plain,
( spl0_1751
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1751])]) ).
fof(f1477,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X27,X3,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__zmult__self2_0) ).
fof(f12598,plain,
spl0_1750,
inference(avatar_split_clause,[],[f1476,f12596]) ).
fof(f12596,plain,
( spl0_1750
<=> ! [X27,X3] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1750])]) ).
fof(f1476,axiom,
! [X3,X27] :
( c_0 = X27
| c_div(c_times(X3,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__zmult__self1_0) ).
fof(f12594,plain,
spl0_1749,
inference(avatar_split_clause,[],[f1457,f12592]) ).
fof(f12592,plain,
( spl0_1749
<=> ! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1749])]) ).
fof(f1457,axiom,
! [X27] : c_IntDiv_OposDivAlg(c_Pair(c_0,X27,tc_IntDef_Oint,tc_IntDef_Oint)) = c_Pair(c_0,c_0,tc_IntDef_Oint,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_OposDivAlg__0_0) ).
fof(f12590,plain,
spl0_1748,
inference(avatar_split_clause,[],[f1442,f12588]) ).
fof(f12588,plain,
( spl0_1748
<=> ! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1748])]) ).
fof(f1442,axiom,
! [X18,X27] : c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__mod__trivial_0) ).
fof(f12586,plain,
spl0_1747,
inference(avatar_split_clause,[],[f1413,f12584]) ).
fof(f12584,plain,
( spl0_1747
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1747])]) ).
fof(f1413,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(X11,c_0,tc_IntDef_Oint)
| c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__less__0__iff_1) ).
fof(f12582,plain,
spl0_1746,
inference(avatar_split_clause,[],[f1412,f12580]) ).
fof(f12580,plain,
( spl0_1746
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1746])]) ).
fof(f1412,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(X11,c_0,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__less__0__iff_0) ).
fof(f12578,plain,
spl0_1745,
inference(avatar_split_clause,[],[f1409,f12576]) ).
fof(f12576,plain,
( spl0_1745
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1745])]) ).
fof(f1409,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(X11,c_0,tc_IntDef_Oint)
| c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__le__0__iff_1) ).
fof(f12574,plain,
spl0_1744,
inference(avatar_split_clause,[],[f1408,f12572]) ).
fof(f12572,plain,
( spl0_1744
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1744])]) ).
fof(f1408,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(X11,c_0,tc_IntDef_Oint)
| ~ c_lessequals(c_IntDef_Oof__int(X11,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__le__0__iff_0) ).
fof(f12570,plain,
( ~ spl0_1743
| ~ spl0_1511
| spl0_1720 ),
inference(avatar_split_clause,[],[f12525,f12419,f10656,f12567]) ).
fof(f12567,plain,
( spl0_1743
<=> c_in(v_X,v_H,tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1743])]) ).
fof(f12525,plain,
( ~ c_in(v_X,v_H,tc_Message_Omsg)
| ~ spl0_1511
| spl0_1720 ),
inference(resolution,[],[f12421,f10657]) ).
fof(f12421,plain,
( ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| spl0_1720 ),
inference(avatar_component_clause,[],[f12419]) ).
fof(f12565,plain,
spl0_1742,
inference(avatar_split_clause,[],[f1406,f12563]) ).
fof(f12563,plain,
( spl0_1742
<=> ! [X11,X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1742])]) ).
fof(f1406,axiom,
! [X48,X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| X11 = X48
| c_IntDef_Oof__int(X48,X1) != c_IntDef_Oof__int(X11,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__eq__iff_0) ).
fof(f12561,plain,
spl0_1741,
inference(avatar_split_clause,[],[f1400,f12559]) ).
fof(f12559,plain,
( spl0_1741
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1741])]) ).
fof(f1400,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__0__less__iff_1) ).
fof(f12557,plain,
spl0_1740,
inference(avatar_split_clause,[],[f1399,f12555]) ).
fof(f12555,plain,
( spl0_1740
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1740])]) ).
fof(f1399,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__0__less__iff_0) ).
fof(f12553,plain,
spl0_1739,
inference(avatar_split_clause,[],[f1398,f12551]) ).
fof(f12551,plain,
( spl0_1739
<=> ! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1739])]) ).
fof(f1398,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__0__le__iff_1) ).
fof(f12549,plain,
spl0_1738,
inference(avatar_split_clause,[],[f1397,f12547]) ).
fof(f1397,axiom,
! [X48,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_lessequals(c_0,X48,tc_IntDef_Oint)
| ~ c_lessequals(c_0,c_IntDef_Oof__int(X48,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__0__le__iff_0) ).
fof(f12545,plain,
spl0_1737,
inference(avatar_split_clause,[],[f1361,f12543]) ).
fof(f12543,plain,
( spl0_1737
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1737])]) ).
fof(f1361,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| ~ c_in(X18,c_IntDef_OInts,X1)
| c_in(c_uminus(X18,X1),c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInts__minus_0) ).
fof(f12541,plain,
spl0_1736,
inference(avatar_split_clause,[],[f1356,f12539]) ).
fof(f12539,plain,
( spl0_1736
<=> ! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1736])]) ).
fof(f1356,axiom,
! [X3] :
( c_IntDef_ORep__Integ(c_IntDef_OAbs__Integ(X3)) = X3
| ~ c_in(X3,c_IntDef_OInteg,tc_set(tc_prod(tc_nat,tc_nat))) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInteg_OAbs__Integ__inverse_0) ).
fof(f12537,plain,
spl0_1735,
inference(avatar_split_clause,[],[f1342,f12535]) ).
fof(f12535,plain,
( spl0_1735
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1735])]) ).
fof(f1342,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_lessequals(c_0,c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oint__eq__iff__number__of_1) ).
fof(f12533,plain,
spl0_1734,
inference(avatar_split_clause,[],[f1341,f12531]) ).
fof(f12531,plain,
( spl0_1734
<=> ! [X15,X47] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1734])]) ).
fof(f1341,axiom,
! [X47,X15] :
( c_IntDef_Oint(X15) != c_Numeral_Onumber__of(X47,tc_IntDef_Oint)
| c_IntDef_Onat(c_Numeral_Onumber__of(X47,tc_IntDef_Oint)) = X15 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oint__eq__iff__number__of_0) ).
fof(f12529,plain,
spl0_1733,
inference(avatar_split_clause,[],[f1243,f12527]) ).
fof(f12527,plain,
( spl0_1733
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1733])]) ).
fof(f1243,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Onat__mod__mod__trivial_0) ).
fof(f12524,plain,
spl0_1732,
inference(avatar_split_clause,[],[f1233,f12522]) ).
fof(f12522,plain,
( spl0_1732
<=> ! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1732])]) ).
fof(f1233,axiom,
! [X21,X15] : c_Divides_Oop_Amod(X15,X21,tc_nat) = c_Divides_Oop_Amod(c_plus(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__add__self2_0) ).
fof(f12520,plain,
spl0_1731,
inference(avatar_split_clause,[],[f1232,f12518]) ).
fof(f12518,plain,
( spl0_1731
<=> ! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1731])]) ).
fof(f1232,axiom,
! [X21,X15] : c_Divides_Oop_Amod(c_plus(X21,X15,tc_nat),X21,tc_nat) = c_Divides_Oop_Amod(X15,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__add__self1_0) ).
fof(f12516,plain,
spl0_1730,
inference(avatar_split_clause,[],[f1191,f12514]) ).
fof(f12514,plain,
( spl0_1730
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1730])]) ).
fof(f1191,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn1(X7,X1,X2) != c_Datatype__Universe_OIn1(X9,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OIn1__eq_0) ).
fof(f12512,plain,
spl0_1729,
inference(avatar_split_clause,[],[f1189,f12510]) ).
fof(f12510,plain,
( spl0_1729
<=> ! [X7,X9,X2,X1] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1729])]) ).
fof(f1189,axiom,
! [X2,X1,X9,X7] :
( X7 = X9
| c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn0(X7,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OIn0__eq_0) ).
fof(f12508,plain,
spl0_1728,
inference(avatar_split_clause,[],[f1185,f12506]) ).
fof(f12506,plain,
( spl0_1728
<=> ! [X2,X18,X27,X1] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1728])]) ).
fof(f1185,axiom,
! [X2,X18,X1,X27] :
( X18 = X27
| c_Datatype__Universe_OAtom(X18,X1,X2) != c_Datatype__Universe_OAtom(X27,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OAtom__Atom__eq_0) ).
fof(f12504,plain,
spl0_1727,
inference(avatar_split_clause,[],[f120,f12502]) ).
fof(f120,axiom,
! [X18,X1,X5] : c_in(c_Pair(X18,X18,X1,X1),c_Transitive__Closure_Ortrancl(X5,X1),tc_prod(X1,X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Ortrancl_Ortrancl__refl_0) ).
fof(f12500,plain,
spl0_1726,
inference(avatar_split_clause,[],[f110,f12498]) ).
fof(f110,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| ~ c_in(c_Main_OsubsetI__1(X12,X13,X1),X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OsubsetI_1) ).
fof(f12496,plain,
spl0_1725,
inference(avatar_split_clause,[],[f109,f12494]) ).
fof(f12494,plain,
( spl0_1725
<=> ! [X13,X12,X1] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1725])]) ).
fof(f109,axiom,
! [X1,X12,X13] :
( c_lessequals(X12,X13,tc_set(X1))
| c_in(c_Main_OsubsetI__1(X12,X13,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OsubsetI_0) ).
fof(f12492,plain,
spl0_1724,
inference(avatar_split_clause,[],[f49,f12490]) ).
fof(f12490,plain,
( spl0_1724
<=> ! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1724])]) ).
fof(f49,axiom,
! [X1,X23] : c_lessequals(c_Nat_Osize(c_List_Oremdups(X23,X1),tc_List_Olist(X1)),c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__remdups__leq_0) ).
fof(f12488,plain,
spl0_1723,
inference(avatar_split_clause,[],[f2,f12486]) ).
fof(f12486,plain,
( spl0_1723
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1723])]) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_ONumb(X0,X1,X2) != c_Datatype__Universe_ONumb(X3,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_ONumb__inject__dest_0) ).
fof(f12484,plain,
( ~ spl0_1722
| spl0_117
| ~ spl0_1698 ),
inference(avatar_split_clause,[],[f12407,f11922,f3593,f12481]) ).
fof(f11922,plain,
( spl0_1698
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1698])]) ).
fof(f12407,plain,
( ~ c_in(v_X,c_Message_Osynth(v_H),tc_Message_Omsg)
| spl0_117
| ~ spl0_1698 ),
inference(resolution,[],[f11923,f3595]) ).
fof(f11923,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_union(X12,X13,X1),X1)
| ~ c_in(X4,X13,X1) )
| ~ spl0_1698 ),
inference(avatar_component_clause,[],[f11922]) ).
fof(f12479,plain,
spl0_1721,
inference(avatar_split_clause,[],[f1,f12477]) ).
fof(f12477,plain,
( spl0_1721
<=> ! [X0,X3,X2,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1721])]) ).
fof(f1,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_Datatype__Universe_OLeaf(X0,X1,X2) != c_Datatype__Universe_OLeaf(X3,X1,X2) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OLeaf__inject__dest_0) ).
fof(f12422,plain,
( ~ spl0_1720
| spl0_117
| ~ spl0_1697 ),
inference(avatar_split_clause,[],[f12401,f11918,f3593,f12419]) ).
fof(f11918,plain,
( spl0_1697
<=> ! [X4,X13,X12,X1] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1697])]) ).
fof(f12401,plain,
( ~ c_in(v_X,c_Message_Oparts(v_H),tc_Message_Omsg)
| spl0_117
| ~ spl0_1697 ),
inference(resolution,[],[f11919,f3595]) ).
fof(f11919,plain,
( ! [X1,X4,X12,X13] :
( c_in(X4,c_union(X12,X13,X1),X1)
| ~ c_in(X4,X12,X1) )
| ~ spl0_1697 ),
inference(avatar_component_clause,[],[f11918]) ).
fof(f12333,plain,
( ~ spl0_1718
| spl0_1719
| ~ spl0_1198
| ~ spl0_1677 ),
inference(avatar_split_clause,[],[f12268,f11838,f9165,f12331,f12327]) ).
fof(f12327,plain,
( spl0_1718
<=> class_OrderedGroup_Oab__group__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1718])]) ).
fof(f12331,plain,
( spl0_1719
<=> ! [X0] : c_0 = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1719])]) ).
fof(f12268,plain,
( ! [X0] :
( c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_1198
| ~ spl0_1677 ),
inference(trivial_inequality_removal,[],[f12260]) ).
fof(f12260,plain,
( ! [X0] :
( c_0 != c_0
| c_0 = X0
| ~ class_OrderedGroup_Oab__group__add(tc_nat) )
| ~ spl0_1198
| ~ spl0_1677 ),
inference(superposition,[],[f11839,f9166]) ).
fof(f12222,plain,
( spl0_1717
| ~ spl0_62
| ~ spl0_1389 ),
inference(avatar_split_clause,[],[f10247,f10027,f3318,f12220]) ).
fof(f12220,plain,
( spl0_1717
<=> ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1717])]) ).
fof(f10247,plain,
( ! [X0] : c_Nat_Opower(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_62
| ~ spl0_1389 ),
inference(resolution,[],[f10028,f3320]) ).
fof(f12152,plain,
( spl0_1716
| ~ spl0_109
| ~ spl0_1388 ),
inference(avatar_split_clause,[],[f10246,f10023,f3553,f12150]) ).
fof(f12150,plain,
( spl0_1716
<=> ! [X1] : c_1 = c_Nat_Opower(c_1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1716])]) ).
fof(f10023,plain,
( spl0_1388
<=> ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1388])]) ).
fof(f10246,plain,
( ! [X1] : c_1 = c_Nat_Opower(c_1,X1,tc_nat)
| ~ spl0_109
| ~ spl0_1388 ),
inference(resolution,[],[f10024,f3555]) ).
fof(f10024,plain,
( ! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) )
| ~ spl0_1388 ),
inference(avatar_component_clause,[],[f10023]) ).
fof(f12102,plain,
( spl0_1715
| ~ spl0_62
| ~ spl0_1388 ),
inference(avatar_split_clause,[],[f10245,f10023,f3318,f12100]) ).
fof(f12100,plain,
( spl0_1715
<=> ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1715])]) ).
fof(f10245,plain,
( ! [X0] : c_1 = c_Nat_Opower(c_1,X0,tc_IntDef_Oint)
| ~ spl0_62
| ~ spl0_1388 ),
inference(resolution,[],[f10024,f3320]) ).
fof(f12034,plain,
( spl0_1714
| ~ spl0_114
| ~ spl0_1385 ),
inference(avatar_split_clause,[],[f10241,f10011,f3578,f12032]) ).
fof(f12032,plain,
( spl0_1714
<=> ! [X1] : c_Orderings_Omax(X1,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1714])]) ).
fof(f3578,plain,
( spl0_114
<=> class_Orderings_Olinorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_114])]) ).
fof(f10011,plain,
( spl0_1385
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1385])]) ).
fof(f10241,plain,
( ! [X1] : c_Orderings_Omax(X1,X1,tc_nat) = X1
| ~ spl0_114
| ~ spl0_1385 ),
inference(resolution,[],[f10012,f3580]) ).
fof(f3580,plain,
( class_Orderings_Olinorder(tc_nat)
| ~ spl0_114 ),
inference(avatar_component_clause,[],[f3578]) ).
fof(f10012,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 )
| ~ spl0_1385 ),
inference(avatar_component_clause,[],[f10011]) ).
fof(f12014,plain,
( spl0_1713
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_1629 ),
inference(avatar_split_clause,[],[f11648,f11645,f10503,f3303,f12012]) ).
fof(f12012,plain,
( spl0_1713
<=> ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1713])]) ).
fof(f11645,plain,
( spl0_1629
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1629])]) ).
fof(f11648,plain,
( ! [X1] :
( c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_uminus(c_1,tc_IntDef_Oint),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_1629 ),
inference(forward_demodulation,[],[f11646,f10850]) ).
fof(f11646,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) )
| ~ spl0_1629 ),
inference(avatar_component_clause,[],[f11645]) ).
fof(f12002,plain,
( spl0_1712
| ~ spl0_31
| ~ spl0_1385 ),
inference(avatar_split_clause,[],[f10240,f10011,f3163,f12000]) ).
fof(f12000,plain,
( spl0_1712
<=> ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1712])]) ).
fof(f3163,plain,
( spl0_31
<=> class_Orderings_Olinorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f10240,plain,
( ! [X0] : c_Orderings_Omax(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_1385 ),
inference(resolution,[],[f10012,f3165]) ).
fof(f3165,plain,
( class_Orderings_Olinorder(tc_IntDef_Oint)
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f3163]) ).
fof(f11976,plain,
spl0_1711,
inference(avatar_split_clause,[],[f2906,f11974]) ).
fof(f11974,plain,
( spl0_1711
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1711])]) ).
fof(f2906,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X21,tc_nat) ),
inference(forward_demodulation,[],[f2096,f2016]) ).
fof(f2096,axiom,
! [X21,X15] :
( c_lessequals(c_1,X21,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oone__le__mult__iff_1) ).
fof(f11972,plain,
spl0_1710,
inference(avatar_split_clause,[],[f2905,f11970]) ).
fof(f11970,plain,
( spl0_1710
<=> ! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1710])]) ).
fof(f2905,plain,
! [X21,X15] :
( ~ c_lessequals(c_1,c_times(X15,X21,tc_nat),tc_nat)
| c_lessequals(c_1,X15,tc_nat) ),
inference(forward_demodulation,[],[f2095,f2016]) ).
fof(f2095,axiom,
! [X21,X15] :
( c_lessequals(c_1,X15,tc_nat)
| ~ c_lessequals(c_Suc(c_0),c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oone__le__mult__iff_0) ).
fof(f11968,plain,
spl0_1709,
inference(avatar_split_clause,[],[f2901,f11966]) ).
fof(f11966,plain,
( spl0_1709
<=> ! [X3] :
( c_Suc(c_minus(X3,c_1,tc_nat)) = X3
| ~ c_less(c_0,X3,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1709])]) ).
fof(f2901,plain,
! [X3] :
( c_Suc(c_minus(X3,c_1,tc_nat)) = X3
| ~ c_less(c_0,X3,tc_nat) ),
inference(forward_demodulation,[],[f2024,f2016]) ).
fof(f2024,axiom,
! [X3] :
( ~ c_less(c_0,X3,tc_nat)
| c_Suc(c_minus(X3,c_Suc(c_0),tc_nat)) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__pred_0) ).
fof(f11964,plain,
spl0_1708,
inference(avatar_split_clause,[],[f2899,f11962]) ).
fof(f11962,plain,
( spl0_1708
<=> ! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1708])]) ).
fof(f2899,plain,
! [X21,X43] :
( c_lessequals(c_1,c_Nat_Opower(X43,X21,tc_nat),tc_nat)
| ~ c_lessequals(c_1,X43,tc_nat) ),
inference(forward_demodulation,[],[f2340,f2016]) ).
fof(f2340,axiom,
! [X21,X43] :
( ~ c_lessequals(c_1,X43,tc_nat)
| c_lessequals(c_Suc(c_0),c_Nat_Opower(X43,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Onat__one__le__power_0) ).
fof(f11960,plain,
spl0_1707,
inference(avatar_split_clause,[],[f2852,f11958]) ).
fof(f2852,plain,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2764,f2016]) ).
fof(f2764,axiom,
! [X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__5_0) ).
fof(f11956,plain,
spl0_1706,
inference(avatar_split_clause,[],[f2822,f11954]) ).
fof(f11954,plain,
( spl0_1706
<=> ! [X86,X88] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1706])]) ).
fof(f2822,axiom,
! [X88,X86] :
( c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| ~ c_in(X86,c_Message_Osynth(c_Message_Osynth(X88)),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth__synthD__dest_0) ).
fof(f11952,plain,
( spl0_1705
| ~ spl0_114
| ~ spl0_1384 ),
inference(avatar_split_clause,[],[f10239,f10007,f3578,f11950]) ).
fof(f11950,plain,
( spl0_1705
<=> ! [X1] : c_Orderings_Omin(X1,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1705])]) ).
fof(f10007,plain,
( spl0_1384
<=> ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1384])]) ).
fof(f10239,plain,
( ! [X1] : c_Orderings_Omin(X1,X1,tc_nat) = X1
| ~ spl0_114
| ~ spl0_1384 ),
inference(resolution,[],[f10008,f3580]) ).
fof(f10008,plain,
( ! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 )
| ~ spl0_1384 ),
inference(avatar_component_clause,[],[f10007]) ).
fof(f11948,plain,
spl0_1704,
inference(avatar_split_clause,[],[f2817,f11946]) ).
fof(f2817,axiom,
! [X88,X86] :
( ~ c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg)
| c_in(c_Message_Omsg_OHash(X86),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth_OHash_0) ).
fof(f11944,plain,
spl0_1703,
inference(avatar_split_clause,[],[f2783,f11942]) ).
fof(f11942,plain,
( spl0_1703
<=> ! [X88,X7] :
( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1703])]) ).
fof(f2783,axiom,
! [X88,X7] :
( c_in(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_ONonce(X7),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_ONonce__synth__eq_0) ).
fof(f11940,plain,
spl0_1702,
inference(avatar_split_clause,[],[f2777,f11938]) ).
fof(f11938,plain,
( spl0_1702
<=> ! [X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1702])]) ).
fof(f2777,axiom,
! [X91,X88] :
( c_in(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)
| ~ c_in(c_Message_Omsg_OKey(X91),c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OKey__synth__eq_0) ).
fof(f11936,plain,
spl0_1701,
inference(avatar_split_clause,[],[f2715,f11934]) ).
fof(f11934,plain,
( spl0_1701
<=> ! [X5,X1] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1701])]) ).
fof(f2715,axiom,
! [X1,X5] : c_Relation_ORange(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ORange(X5,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Otrancl__range_0) ).
fof(f11932,plain,
spl0_1700,
inference(avatar_split_clause,[],[f2713,f11930]) ).
fof(f11930,plain,
( spl0_1700
<=> ! [X5,X1] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1700])]) ).
fof(f2713,axiom,
! [X1,X5] : c_Relation_ODomain(c_Transitive__Closure_Otrancl(X5,X1),X1,X1) = c_Relation_ODomain(X5,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Otrancl__domain_0) ).
fof(f11928,plain,
spl0_1699,
inference(avatar_split_clause,[],[f2685,f11926]) ).
fof(f11926,plain,
( spl0_1699
<=> ! [X18,X12,X27,X1] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1699])]) ).
fof(f2685,axiom,
! [X18,X1,X27,X12] :
( ~ c_in(X18,X12,X1)
| c_in(X18,c_insert(X27,X12,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__iff_2) ).
fof(f11924,plain,
spl0_1698,
inference(avatar_split_clause,[],[f2642,f11922]) ).
fof(f2642,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X13,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__iff_2) ).
fof(f11920,plain,
spl0_1697,
inference(avatar_split_clause,[],[f2641,f11918]) ).
fof(f2641,axiom,
! [X1,X4,X12,X13] :
( ~ c_in(X4,X12,X1)
| c_in(X4,c_union(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__iff_1) ).
fof(f11916,plain,
spl0_1696,
inference(avatar_split_clause,[],[f2607,f11914]) ).
fof(f11914,plain,
( spl0_1696
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1696])]) ).
fof(f2607,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X13,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__iff_1) ).
fof(f11912,plain,
spl0_1695,
inference(avatar_split_clause,[],[f2606,f11910]) ).
fof(f11910,plain,
( spl0_1695
<=> ! [X4,X13,X12,X1] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1695])]) ).
fof(f2606,axiom,
! [X1,X4,X12,X13] :
( c_in(X4,X12,X1)
| ~ c_in(X4,c_inter(X12,X13,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__iff_0) ).
fof(f11908,plain,
( spl0_1694
| ~ spl0_31
| ~ spl0_1384 ),
inference(avatar_split_clause,[],[f10238,f10007,f3163,f11906]) ).
fof(f11906,plain,
( spl0_1694
<=> ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1694])]) ).
fof(f10238,plain,
( ! [X0] : c_Orderings_Omin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_31
| ~ spl0_1384 ),
inference(resolution,[],[f10008,f3165]) ).
fof(f11904,plain,
spl0_1693,
inference(avatar_split_clause,[],[f2583,f11902]) ).
fof(f11902,plain,
( spl0_1693
<=> ! [X12,X1,X4] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1693])]) ).
fof(f2583,axiom,
! [X1,X4,X12] :
( c_in(X4,X12,X1)
| c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__iff_1) ).
fof(f11900,plain,
spl0_1692,
inference(avatar_split_clause,[],[f2582,f11898]) ).
fof(f11898,plain,
( spl0_1692
<=> ! [X12,X1,X4] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1692])]) ).
fof(f2582,axiom,
! [X1,X4,X12] :
( ~ c_in(X4,X12,X1)
| ~ c_in(X4,c_uminus(X12,tc_set(X1)),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__iff_0) ).
fof(f11896,plain,
spl0_1691,
inference(avatar_split_clause,[],[f2545,f11894]) ).
fof(f11894,plain,
( spl0_1691
<=> ! [X14,X26] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1691])]) ).
fof(f2545,axiom,
! [X26,X14] : c_minus(X14,X26,tc_nat) = c_Finite__Set_Ocard(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__greaterThanAtMost_0) ).
fof(f11892,plain,
spl0_1690,
inference(avatar_split_clause,[],[f2542,f11890]) ).
fof(f11890,plain,
( spl0_1690
<=> ! [X14,X26] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1690])]) ).
fof(f2542,axiom,
! [X26,X14] : c_Finite__Set_Ocard(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),tc_nat) = c_minus(X14,X26,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__atLeastLessThan_0) ).
fof(f11888,plain,
spl0_1689,
inference(avatar_split_clause,[],[f2522,f11886]) ).
fof(f11886,plain,
( spl0_1689
<=> ! [X18,X1] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1689])]) ).
fof(f2522,axiom,
! [X1,X18] :
( ~ class_Orderings_Oorder(X1)
| c_insert(X18,c_emptyset,X1) = c_SetInterval_OatLeastAtMost(X18,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastAtMost__singleton_0) ).
fof(f11884,plain,
spl0_1688,
inference(avatar_split_clause,[],[f2437,f11882]) ).
fof(f11882,plain,
( spl0_1688
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse(c_HOL_Oinverse(X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1688])]) ).
fof(f2437,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_HOL_Oinverse(c_HOL_Oinverse(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__inverse__eq_0) ).
fof(f11880,plain,
spl0_1687,
inference(avatar_split_clause,[],[f2432,f11878]) ).
fof(f11878,plain,
( spl0_1687
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X18,c_0,X1) = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1687])]) ).
fof(f2432,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(X18,c_0,X1) = c_times(X27,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ofield__mult__cancel__right_1) ).
fof(f11876,plain,
spl0_1686,
inference(avatar_split_clause,[],[f2430,f11874]) ).
fof(f11874,plain,
( spl0_1686
<=> ! [X18,X27,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_0,X18,X1) = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1686])]) ).
fof(f2430,axiom,
! [X1,X18,X27] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_times(c_0,X18,X1) = c_times(c_0,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ofield__mult__cancel__left_1) ).
fof(f11872,plain,
spl0_1685,
inference(avatar_split_clause,[],[f2271,f11870]) ).
fof(f11870,plain,
( spl0_1685
<=> ! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1685])]) ).
fof(f2271,axiom,
! [X47] :
( c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| ~ c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_1) ).
fof(f11868,plain,
spl0_1684,
inference(avatar_split_clause,[],[f2270,f11866]) ).
fof(f11866,plain,
( spl0_1684
<=> ! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1684])]) ).
fof(f2270,axiom,
! [X47] :
( ~ c_Parity_Oeven(c_Numeral_Onumber__of(X47,tc_nat),tc_nat)
| c_Parity_Oeven(c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven_A_Inumber__of_Av_J_A_61_61_Aeven_A_Iint_A_Inumber__of_Av_J_J_0) ).
fof(f11864,plain,
( spl0_1683
| ~ spl0_85
| ~ spl0_1380 ),
inference(avatar_split_clause,[],[f10233,f9991,f3433,f11862]) ).
fof(f11862,plain,
( spl0_1683
<=> ! [X1] : c_times(X1,c_1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1683])]) ).
fof(f3433,plain,
( spl0_85
<=> class_OrderedGroup_Omonoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_85])]) ).
fof(f9991,plain,
( spl0_1380
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1380])]) ).
fof(f10233,plain,
( ! [X1] : c_times(X1,c_1,tc_nat) = X1
| ~ spl0_85
| ~ spl0_1380 ),
inference(resolution,[],[f9992,f3435]) ).
fof(f3435,plain,
( class_OrderedGroup_Omonoid__mult(tc_nat)
| ~ spl0_85 ),
inference(avatar_component_clause,[],[f3433]) ).
fof(f9992,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 )
| ~ spl0_1380 ),
inference(avatar_component_clause,[],[f9991]) ).
fof(f11860,plain,
spl0_1682,
inference(avatar_split_clause,[],[f2252,f11858]) ).
fof(f11858,plain,
( spl0_1682
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1682])]) ).
fof(f2252,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_less(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ozero__less__abs__iff_1) ).
fof(f11856,plain,
spl0_1681,
inference(avatar_split_clause,[],[f2245,f11854]) ).
fof(f11854,plain,
( spl0_1681
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1681])]) ).
fof(f2245,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_OrderedGroup_Opprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Opprt__eq__id_0) ).
fof(f11852,plain,
spl0_1680,
inference(avatar_split_clause,[],[f2244,f11850]) ).
fof(f11850,plain,
( spl0_1680
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1680])]) ).
fof(f2244,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X0,c_0,X1)
| c_0 = c_OrderedGroup_Opprt(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Opprt__eq__0_0) ).
fof(f11848,plain,
spl0_1679,
inference(avatar_split_clause,[],[f2240,f11846]) ).
fof(f11846,plain,
( spl0_1679
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1679])]) ).
fof(f2240,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(X3,c_0,X1)
| c_OrderedGroup_Onprt(X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Onprt__eq__id_0) ).
fof(f11844,plain,
spl0_1678,
inference(avatar_split_clause,[],[f2239,f11842]) ).
fof(f11842,plain,
( spl0_1678
<=> ! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1678])]) ).
fof(f2239,axiom,
! [X0,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| ~ c_lessequals(c_0,X0,X1)
| c_0 = c_OrderedGroup_Onprt(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Onprt__eq__0_0) ).
fof(f11840,plain,
spl0_1677,
inference(avatar_split_clause,[],[f2199,f11838]) ).
fof(f2199,axiom,
! [X1,X18,X27] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| X18 = X27
| c_0 != c_minus(X18,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__eq__0__iff__eq_0) ).
fof(f11836,plain,
spl0_1676,
inference(avatar_split_clause,[],[f2183,f11834]) ).
fof(f2183,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_lessequals(c_0,X3,X1)
| c_HOL_Oabs(X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__of__nonneg_0) ).
fof(f11832,plain,
spl0_1675,
inference(avatar_split_clause,[],[f2181,f11830]) ).
fof(f11830,plain,
( spl0_1675
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1675])]) ).
fof(f2181,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__minus__cancel_0) ).
fof(f11828,plain,
spl0_1674,
inference(avatar_split_clause,[],[f2179,f11826]) ).
fof(f11826,plain,
( spl0_1674
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1674])]) ).
fof(f2179,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| ~ c_lessequals(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__le__zero__iff_0) ).
fof(f11824,plain,
spl0_1673,
inference(avatar_split_clause,[],[f2178,f11822]) ).
fof(f11822,plain,
( spl0_1673
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1673])]) ).
fof(f2178,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_HOL_Oabs(X18,X1) = c_HOL_Oabs(c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__idempotent_0) ).
fof(f11820,plain,
( spl0_1672
| ~ spl0_18
| ~ spl0_1380 ),
inference(avatar_split_clause,[],[f10232,f9991,f3098,f11818]) ).
fof(f11818,plain,
( spl0_1672
<=> ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1672])]) ).
fof(f3098,plain,
( spl0_18
<=> class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f10232,plain,
( ! [X0] : c_times(X0,c_1,tc_IntDef_Oint) = X0
| ~ spl0_18
| ~ spl0_1380 ),
inference(resolution,[],[f9992,f3100]) ).
fof(f3100,plain,
( class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint)
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f3098]) ).
fof(f11816,plain,
spl0_1671,
inference(avatar_split_clause,[],[f2147,f11814]) ).
fof(f11814,plain,
( spl0_1671
<=> ! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1671])]) ).
fof(f2147,axiom,
! [X11,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OBit(X11,c_Numeral_Obit_OB1),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__5_0) ).
fof(f11812,plain,
spl0_1670,
inference(avatar_split_clause,[],[f2127,f11810]) ).
fof(f11810,plain,
( spl0_1670
<=> ! [X11,X47] : c_Numeral_Obin__mult(c_Numeral_OBit(X47,c_Numeral_Obit_OB0),X11) = c_Numeral_OBit(c_Numeral_Obin__mult(X47,X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1670])]) ).
fof(f11808,plain,
spl0_1669,
inference(avatar_split_clause,[],[f2104,f11806]) ).
fof(f11806,plain,
( spl0_1669
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1669])]) ).
fof(f2104,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ozero__less__diff_1) ).
fof(f11804,plain,
spl0_1668,
inference(avatar_split_clause,[],[f2103,f11802]) ).
fof(f11802,plain,
( spl0_1668
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1668])]) ).
fof(f2103,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_0,c_minus(X21,X15,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ozero__less__diff_0) ).
fof(f11800,plain,
spl0_1667,
inference(avatar_split_clause,[],[f2101,f11798]) ).
fof(f2101,axiom,
! [X21,X15] : c_Suc(c_plus(X15,X21,tc_nat)) = c_plus(c_Suc(X15),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oop_A_L_Oadd__Suc_0) ).
fof(f11796,plain,
spl0_1666,
inference(avatar_split_clause,[],[f2079,f11794]) ).
fof(f11794,plain,
( spl0_1666
<=> ! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1666])]) ).
fof(f2079,axiom,
! [X21,X15] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__0__less__mult__iff_1) ).
fof(f11792,plain,
spl0_1665,
inference(avatar_split_clause,[],[f2078,f11790]) ).
fof(f11790,plain,
( spl0_1665
<=> ! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1665])]) ).
fof(f2078,axiom,
! [X21,X15] :
( c_less(c_0,X15,tc_nat)
| ~ c_less(c_0,c_times(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onat__0__less__mult__iff_0) ).
fof(f11788,plain,
spl0_1664,
inference(avatar_split_clause,[],[f2035,f11786]) ).
fof(f2035,axiom,
! [X21,X15] : c_minus(X15,X21,tc_nat) = c_minus(c_Suc(X15),c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__Suc__Suc_0) ).
fof(f11784,plain,
spl0_1663,
inference(avatar_split_clause,[],[f2030,f11782]) ).
fof(f11782,plain,
( spl0_1663
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1663])]) ).
fof(f2030,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__gr__0_2) ).
fof(f11780,plain,
spl0_1662,
inference(avatar_split_clause,[],[f2029,f11778]) ).
fof(f11778,plain,
( spl0_1662
<=> ! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1662])]) ).
fof(f2029,axiom,
! [X21,X15] :
( ~ c_less(c_0,X15,tc_nat)
| c_less(c_0,c_plus(X15,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__gr__0_1) ).
fof(f11776,plain,
( spl0_1661
| ~ spl0_85
| ~ spl0_1379 ),
inference(avatar_split_clause,[],[f10231,f9987,f3433,f11774]) ).
fof(f11774,plain,
( spl0_1661
<=> ! [X1] : c_times(c_1,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1661])]) ).
fof(f9987,plain,
( spl0_1379
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1379])]) ).
fof(f10231,plain,
( ! [X1] : c_times(c_1,X1,tc_nat) = X1
| ~ spl0_85
| ~ spl0_1379 ),
inference(resolution,[],[f9988,f3435]) ).
fof(f9988,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 )
| ~ spl0_1379 ),
inference(avatar_component_clause,[],[f9987]) ).
fof(f11772,plain,
spl0_1660,
inference(avatar_split_clause,[],[f2027,f11770]) ).
fof(f2027,axiom,
! [X21,X15] : c_plus(X15,c_Suc(X21),tc_nat) = c_Suc(c_plus(X15,X21,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__Suc__right_0) ).
fof(f11768,plain,
spl0_1659,
inference(avatar_split_clause,[],[f1851,f11766]) ).
fof(f11766,plain,
( spl0_1659
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1659])]) ).
fof(f1851,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oint__nat__number__of_0) ).
fof(f11764,plain,
spl0_1658,
inference(avatar_split_clause,[],[f1822,f11762]) ).
fof(f11762,plain,
( spl0_1658
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1658])]) ).
fof(f1822,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_1 = c_Suc(c_Numeral_Onumber__of(X47,tc_nat)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_OSuc__nat__number__of_0) ).
fof(f11760,plain,
spl0_1657,
inference(avatar_split_clause,[],[f1814,f11758]) ).
fof(f11758,plain,
( spl0_1657
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1657])]) ).
fof(f1814,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| ~ c_lessequals(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__le__0__iff_0) ).
fof(f11756,plain,
spl0_1656,
inference(avatar_split_clause,[],[f1766,f11754]) ).
fof(f11754,plain,
( spl0_1656
<=> ! [X21,X1,X26] : c_List_Osublist(X26,c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Otake(X21,X26,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1656])]) ).
fof(f1766,axiom,
! [X21,X1,X26] : c_List_Osublist(X26,c_SetInterval_OlessThan(X21,tc_nat),X1) = c_List_Otake(X21,X26,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osublist__upt__eq__take_0) ).
fof(f11752,plain,
spl0_1655,
inference(avatar_split_clause,[],[f1761,f11750]) ).
fof(f11750,plain,
( spl0_1655
<=> ! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1655])]) ).
fof(f1761,axiom,
! [X0,X1] : c_List_Olist_OCons(X0,c_List_Olist_ONil,X1) = c_List_Orev(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osingleton__rev__conv_1) ).
fof(f11748,plain,
spl0_1654,
inference(avatar_split_clause,[],[f1731,f11746]) ).
fof(f11746,plain,
( spl0_1654
<=> ! [X0,X1,X21] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1654])]) ).
fof(f1731,axiom,
! [X21,X0,X1] : c_List_Oreplicate(X21,X0,X1) = c_List_Orev(c_List_Oreplicate(X21,X0,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__replicate_0) ).
fof(f11744,plain,
spl0_1653,
inference(avatar_split_clause,[],[f1712,f11742]) ).
fof(f11742,plain,
( spl0_1653
<=> ! [X41,X0,X3,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1653])]) ).
fof(f1712,axiom,
! [X41,X3,X0,X25] :
( ~ c_List_Oop_Amem(X0,X25,X41)
| c_List_Oop_Amem(X0,c_List_Olist_OCons(X3,X25,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oop_Amem_Osimps__2_2) ).
fof(f11740,plain,
spl0_1652,
inference(avatar_split_clause,[],[f1613,f11738]) ).
fof(f11738,plain,
( spl0_1652
<=> ! [X43,X59] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1652])]) ).
fof(f1613,axiom,
! [X59,X43] : c_Nat_Osize(c_List_Oupt(X43,X59),tc_List_Olist(tc_nat)) = c_minus(X59,X43,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__upt_0) ).
fof(f11736,plain,
spl0_1651,
inference(avatar_split_clause,[],[f1609,f11734]) ).
fof(f11734,plain,
( spl0_1651
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1651])]) ).
fof(f1609,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orotate1(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__rotate1_0) ).
fof(f11732,plain,
( spl0_1650
| ~ spl0_18
| ~ spl0_1379 ),
inference(avatar_split_clause,[],[f10230,f9987,f3098,f11730]) ).
fof(f11730,plain,
( spl0_1650
<=> ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1650])]) ).
fof(f10230,plain,
( ! [X0] : c_times(c_1,X0,tc_IntDef_Oint) = X0
| ~ spl0_18
| ~ spl0_1379 ),
inference(resolution,[],[f9988,f3100]) ).
fof(f11728,plain,
spl0_1649,
inference(avatar_split_clause,[],[f1608,f11726]) ).
fof(f11726,plain,
( spl0_1649
<=> ! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1649])]) ).
fof(f1608,axiom,
! [X1,X23] : c_Nat_Osize(X23,tc_List_Olist(X1)) = c_Nat_Osize(c_List_Orev(X23,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__rev_0) ).
fof(f11724,plain,
spl0_1648,
inference(avatar_split_clause,[],[f1595,f11722]) ).
fof(f11722,plain,
( spl0_1648
<=> ! [X1,X23,X3] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1648])]) ).
fof(f1595,axiom,
! [X3,X1,X23] : c_List_Olast(c_append(X23,c_List_Olist_OCons(X3,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast__snoc_0) ).
fof(f11720,plain,
spl0_1647,
inference(avatar_split_clause,[],[f1594,f11718]) ).
fof(f11718,plain,
( spl0_1647
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1647])]) ).
fof(f1594,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Olast(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast__replicate_0) ).
fof(f11716,plain,
spl0_1646,
inference(avatar_split_clause,[],[f1593,f11714]) ).
fof(f11714,plain,
( spl0_1646
<=> ! [X60,X1] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1646])]) ).
fof(f1593,axiom,
! [X1,X60] :
( c_List_Olist_ONil = X60
| c_in(c_List_Olast(X60,X1),c_List_Oset(X60,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast__in__set_0) ).
fof(f11712,plain,
spl0_1645,
inference(avatar_split_clause,[],[f1585,f11710]) ).
fof(f11710,plain,
( spl0_1645
<=> ! [X0,X1,X23] : c_List_Oitrev(X23,X0,X1) = c_append(c_List_Orev(X23,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1645])]) ).
fof(f11708,plain,
spl0_1644,
inference(avatar_split_clause,[],[f1584,f11706]) ).
fof(f1584,axiom,
! [X3,X59] :
( ~ c_less(X3,X59,tc_nat)
| c_List_Ohd(c_List_Oupt(X3,X59),tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ohd__upt_0) ).
fof(f11704,plain,
spl0_1643,
inference(avatar_split_clause,[],[f1583,f11702]) ).
fof(f11702,plain,
( spl0_1643
<=> ! [X21,X1,X3] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1643])]) ).
fof(f1583,axiom,
! [X21,X3,X1] :
( c_0 = X21
| c_List_Ohd(c_List_Oreplicate(X21,X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ohd__replicate_0) ).
fof(f11700,plain,
spl0_1642,
inference(avatar_split_clause,[],[f1582,f11698]) ).
fof(f11698,plain,
( spl0_1642
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1642])]) ).
fof(f1582,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_in(c_List_Ohd(X23,X1),c_List_Oset(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ohd__in__set_0) ).
fof(f11696,plain,
spl0_1641,
inference(avatar_split_clause,[],[f1539,f11694]) ).
fof(f11694,plain,
( spl0_1641
<=> ! [X0,X1,X3] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1641])]) ).
fof(f1539,axiom,
! [X3,X0,X1] : c_List_Obutlast(c_append(X3,c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Obutlast__snoc_0) ).
fof(f11692,plain,
spl0_1640,
inference(avatar_split_clause,[],[f1463,f11690]) ).
fof(f11690,plain,
( spl0_1640
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1640])]) ).
fof(f1463,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_lessequals(c_0,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Opos__mod__sign_0) ).
fof(f11688,plain,
( spl0_1639
| ~ spl0_11
| ~ spl0_1378 ),
inference(avatar_split_clause,[],[f10229,f9983,f3063,f11686]) ).
fof(f11686,plain,
( spl0_1639
<=> ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1639])]) ).
fof(f9983,plain,
( spl0_1378
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1378])]) ).
fof(f10229,plain,
( ! [X0] : c_0 = c_minus(X0,X0,tc_IntDef_Oint)
| ~ spl0_11
| ~ spl0_1378 ),
inference(resolution,[],[f9984,f3065]) ).
fof(f9984,plain,
( ! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) )
| ~ spl0_1378 ),
inference(avatar_component_clause,[],[f9983]) ).
fof(f11684,plain,
spl0_1638,
inference(avatar_split_clause,[],[f1462,f11682]) ).
fof(f11682,plain,
( spl0_1638
<=> ! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1638])]) ).
fof(f1462,axiom,
! [X18,X27] :
( ~ c_less(c_0,X27,tc_IntDef_Oint)
| c_less(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Opos__mod__bound_0) ).
fof(f11680,plain,
spl0_1637,
inference(avatar_split_clause,[],[f1455,f11678]) ).
fof(f11678,plain,
( spl0_1637
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1637])]) ).
fof(f1455,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_lessequals(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Oneg__mod__sign_0) ).
fof(f11676,plain,
spl0_1636,
inference(avatar_split_clause,[],[f1454,f11674]) ).
fof(f11674,plain,
( spl0_1636
<=> ! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1636])]) ).
fof(f1454,axiom,
! [X18,X27] :
( ~ c_less(X27,c_0,tc_IntDef_Oint)
| c_less(X27,c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Oneg__mod__bound_0) ).
fof(f11672,plain,
spl0_1635,
inference(avatar_split_clause,[],[f1418,f11670]) ).
fof(f11670,plain,
( spl0_1635
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1635])]) ).
fof(f1418,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_NatArith_Oof__nat(X21,X1) = c_IntDef_Oof__int(c_NatArith_Oof__nat(X21,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__of__nat__eq_0) ).
fof(f11668,plain,
spl0_1634,
inference(avatar_split_clause,[],[f1354,f11666]) ).
fof(f11666,plain,
( spl0_1634
<=> ! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1634])]) ).
fof(f1354,axiom,
! [X48,X11] :
( ~ c_less(X11,X48,tc_IntDef_Oint)
| c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Ozle__diff1__eq_1) ).
fof(f11664,plain,
spl0_1633,
inference(avatar_split_clause,[],[f1353,f11662]) ).
fof(f11662,plain,
( spl0_1633
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1633])]) ).
fof(f1353,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_lessequals(X11,c_minus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Ozle__diff1__eq_0) ).
fof(f11660,plain,
spl0_1632,
inference(avatar_split_clause,[],[f1352,f11658]) ).
fof(f11658,plain,
( spl0_1632
<=> ! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1632])]) ).
fof(f1352,axiom,
! [X48,X11] :
( ~ c_lessequals(X11,X48,tc_IntDef_Oint)
| c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Ozle__add1__eq__le_1) ).
fof(f11656,plain,
spl0_1631,
inference(avatar_split_clause,[],[f1351,f11654]) ).
fof(f11654,plain,
( spl0_1631
<=> ! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1631])]) ).
fof(f1351,axiom,
! [X48,X11] :
( c_lessequals(X11,X48,tc_IntDef_Oint)
| ~ c_less(X11,c_plus(X48,c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Ozle__add1__eq__le_0) ).
fof(f11652,plain,
spl0_1630,
inference(avatar_split_clause,[],[f1348,f11650]) ).
fof(f11650,plain,
( spl0_1630
<=> ! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1630])]) ).
fof(f1348,axiom,
! [X48,X11] : c_plus(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) = c_minus(X48,X11,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oz1_A_L_A_N_Aw1_A_61_61_Az1_A_N_Aw1_0) ).
fof(f11647,plain,
spl0_1629,
inference(avatar_split_clause,[],[f1345,f11645]) ).
fof(f1345,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_IntDef_Oof__int(c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oof__int__m1_0) ).
fof(f11643,plain,
( spl0_1628
| ~ spl0_11
| ~ spl0_1377 ),
inference(avatar_split_clause,[],[f10228,f9979,f3063,f11641]) ).
fof(f11641,plain,
( spl0_1628
<=> ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1628])]) ).
fof(f9979,plain,
( spl0_1377
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1377])]) ).
fof(f10228,plain,
( ! [X0] : c_minus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_11
| ~ spl0_1377 ),
inference(resolution,[],[f9980,f3065]) ).
fof(f9980,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 )
| ~ spl0_1377 ),
inference(avatar_component_clause,[],[f9979]) ).
fof(f11639,plain,
spl0_1627,
inference(avatar_split_clause,[],[f1310,f11637]) ).
fof(f11637,plain,
( spl0_1627
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1627])]) ).
fof(f1310,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oabs__minus__one_0) ).
fof(f11635,plain,
spl0_1626,
inference(avatar_split_clause,[],[f1307,f11633]) ).
fof(f11633,plain,
( spl0_1626
<=> ! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1626])]) ).
fof(f1307,axiom,
! [X21,X3] : c_GCD_Ogcd(c_Pair(X3,c_times(X3,X21,tc_nat),tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__mult_0) ).
fof(f11631,plain,
spl0_1625,
inference(avatar_split_clause,[],[f1236,f11629]) ).
fof(f11629,plain,
( spl0_1625
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1625])]) ).
fof(f1236,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__less__divisor_0) ).
fof(f11627,plain,
spl0_1624,
inference(avatar_split_clause,[],[f1234,f11625]) ).
fof(f11625,plain,
( spl0_1624
<=> ! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1624])]) ).
fof(f1234,axiom,
! [X21,X15] :
( ~ c_less(c_0,X21,tc_nat)
| c_lessequals(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__le__divisor_0) ).
fof(f11623,plain,
spl0_1623,
inference(avatar_split_clause,[],[f1178,f11621]) ).
fof(f1178,axiom,
! [X2,X18,X1,X27] : c_0 = c_Nat_Osize(c_Pair(X18,X27,X1,X2),tc_prod(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Oprod_Osize_0) ).
fof(f11619,plain,
spl0_1622,
inference(avatar_split_clause,[],[f1166,f11617]) ).
fof(f11617,plain,
( spl0_1622
<=> ! [X0,X1,X40] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1622])]) ).
fof(f1166,axiom,
! [X40,X0,X1] :
( c_Datatype_Ooption_OSome(X0,X1) = X40
| ~ c_in(X0,c_Datatype_Oo2s(X40,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Oelem__o2s_0) ).
fof(f11604,plain,
( spl0_1621
| ~ spl0_6
| ~ spl0_1376 ),
inference(avatar_split_clause,[],[f10226,f9975,f3038,f11602]) ).
fof(f11602,plain,
( spl0_1621
<=> ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1621])]) ).
fof(f3038,plain,
( spl0_6
<=> class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f9975,plain,
( spl0_1376
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1376])]) ).
fof(f10226,plain,
( ! [X0] : c_plus(c_0,X0,tc_IntDef_Oint) = X0
| ~ spl0_6
| ~ spl0_1376 ),
inference(resolution,[],[f9976,f3040]) ).
fof(f3040,plain,
( class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint)
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f3038]) ).
fof(f9976,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 )
| ~ spl0_1376 ),
inference(avatar_component_clause,[],[f9975]) ).
fof(f11596,plain,
( spl0_1620
| ~ spl0_6
| ~ spl0_1375 ),
inference(avatar_split_clause,[],[f10224,f9971,f3038,f11594]) ).
fof(f11594,plain,
( spl0_1620
<=> ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1620])]) ).
fof(f9971,plain,
( spl0_1375
<=> ! [X1,X3] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1375])]) ).
fof(f10224,plain,
( ! [X0] : c_plus(X0,c_0,tc_IntDef_Oint) = X0
| ~ spl0_6
| ~ spl0_1375 ),
inference(resolution,[],[f9972,f3040]) ).
fof(f9972,plain,
( ! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 )
| ~ spl0_1375 ),
inference(avatar_component_clause,[],[f9971]) ).
fof(f11546,plain,
( spl0_1619
| ~ spl0_1061
| ~ spl0_1062
| ~ spl0_1126
| ~ spl0_1212
| ~ spl0_1475
| ~ spl0_1577 ),
inference(avatar_split_clause,[],[f11535,f11182,f10511,f9222,f8854,f7391,f7386,f11543]) ).
fof(f7386,plain,
( spl0_1061
<=> c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1061])]) ).
fof(f7391,plain,
( spl0_1062
<=> c_Numeral_OMin = c_Numeral_Obin__pred(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1062])]) ).
fof(f10511,plain,
( spl0_1475
<=> ! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1475])]) ).
fof(f11182,plain,
( spl0_1577
<=> ! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1577])]) ).
fof(f11535,plain,
( c_Numeral_OMin = c_Numeral_Obin__minus(c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1061
| ~ spl0_1062
| ~ spl0_1126
| ~ spl0_1212
| ~ spl0_1475
| ~ spl0_1577 ),
inference(forward_demodulation,[],[f11534,f9224]) ).
fof(f11534,plain,
( c_Numeral_OMin = c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1))
| ~ spl0_1061
| ~ spl0_1062
| ~ spl0_1126
| ~ spl0_1475
| ~ spl0_1577 ),
inference(forward_demodulation,[],[f11533,f7393]) ).
fof(f7393,plain,
( c_Numeral_OMin = c_Numeral_Obin__pred(c_Numeral_OPls)
| ~ spl0_1062 ),
inference(avatar_component_clause,[],[f7391]) ).
fof(f11533,plain,
( c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_Obin__pred(c_Numeral_OPls)
| ~ spl0_1061
| ~ spl0_1126
| ~ spl0_1475
| ~ spl0_1577 ),
inference(forward_demodulation,[],[f11532,f8856]) ).
fof(f11532,plain,
( c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_Obin__pred(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0))
| ~ spl0_1061
| ~ spl0_1475
| ~ spl0_1577 ),
inference(forward_demodulation,[],[f11527,f10512]) ).
fof(f10512,plain,
( ! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1)
| ~ spl0_1475 ),
inference(avatar_component_clause,[],[f10511]) ).
fof(f11527,plain,
( c_Numeral_Obin__minus(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_OPls),c_Numeral_Obit_OB1)
| ~ spl0_1061
| ~ spl0_1577 ),
inference(superposition,[],[f11183,f7388]) ).
fof(f7388,plain,
( c_Numeral_OPls = c_Numeral_Obin__minus(c_Numeral_OPls)
| ~ spl0_1061 ),
inference(avatar_component_clause,[],[f7386]) ).
fof(f11183,plain,
( ! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1)
| ~ spl0_1577 ),
inference(avatar_component_clause,[],[f11182]) ).
fof(f11480,plain,
( spl0_1618
| ~ spl0_103
| ~ spl0_1349 ),
inference(avatar_split_clause,[],[f10185,f9865,f3523,f11478]) ).
fof(f11478,plain,
( spl0_1618
<=> ! [X1] : c_LOrder_Omeet(X1,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1618])]) ).
fof(f3523,plain,
( spl0_103
<=> class_LOrder_Omeet__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_103])]) ).
fof(f9865,plain,
( spl0_1349
<=> ! [X1,X3] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1349])]) ).
fof(f10185,plain,
( ! [X1] : c_LOrder_Omeet(X1,X1,tc_nat) = X1
| ~ spl0_103
| ~ spl0_1349 ),
inference(resolution,[],[f9866,f3525]) ).
fof(f3525,plain,
( class_LOrder_Omeet__semilorder(tc_nat)
| ~ spl0_103 ),
inference(avatar_component_clause,[],[f3523]) ).
fof(f9866,plain,
( ! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 )
| ~ spl0_1349 ),
inference(avatar_component_clause,[],[f9865]) ).
fof(f11445,plain,
( spl0_1617
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_1556 ),
inference(avatar_split_clause,[],[f11099,f11096,f10503,f3303,f11443]) ).
fof(f11443,plain,
( spl0_1617
<=> ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1617])]) ).
fof(f11096,plain,
( spl0_1556
<=> ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1556])]) ).
fof(f11099,plain,
( ! [X18] : c_uminus(X18,tc_IntDef_Oint) = c_div(X18,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1473
| ~ spl0_1556 ),
inference(forward_demodulation,[],[f11097,f10850]) ).
fof(f11097,plain,
( ! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint)
| ~ spl0_1556 ),
inference(avatar_component_clause,[],[f11096]) ).
fof(f11395,plain,
( spl0_1616
| spl0_1094
| ~ spl0_1542 ),
inference(avatar_split_clause,[],[f11382,f11039,f8707,f11392]) ).
fof(f11392,plain,
( spl0_1616
<=> c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1616])]) ).
fof(f8707,plain,
( spl0_1094
<=> c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1094])]) ).
fof(f11382,plain,
( c_0 = c_Finite__Set_Ocard(c_UNIV,tc_nat)
| spl0_1094
| ~ spl0_1542 ),
inference(resolution,[],[f11040,f8709]) ).
fof(f8709,plain,
( ~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat))
| spl0_1094 ),
inference(avatar_component_clause,[],[f8707]) ).
fof(f11357,plain,
( spl0_1615
| ~ spl0_28
| ~ spl0_1349 ),
inference(avatar_split_clause,[],[f10184,f9865,f3148,f11355]) ).
fof(f11355,plain,
( spl0_1615
<=> ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1615])]) ).
fof(f3148,plain,
( spl0_28
<=> class_LOrder_Omeet__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f10184,plain,
( ! [X0] : c_LOrder_Omeet(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_28
| ~ spl0_1349 ),
inference(resolution,[],[f9866,f3150]) ).
fof(f3150,plain,
( class_LOrder_Omeet__semilorder(tc_IntDef_Oint)
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f3148]) ).
fof(f11334,plain,
( spl0_1614
| ~ spl0_112
| ~ spl0_1347 ),
inference(avatar_split_clause,[],[f10183,f9856,f3568,f11332]) ).
fof(f11332,plain,
( spl0_1614
<=> ! [X1] : c_LOrder_Ojoin(X1,X1,tc_nat) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1614])]) ).
fof(f3568,plain,
( spl0_112
<=> class_LOrder_Ojoin__semilorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_112])]) ).
fof(f9856,plain,
( spl0_1347
<=> ! [X1,X3] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1347])]) ).
fof(f10183,plain,
( ! [X1] : c_LOrder_Ojoin(X1,X1,tc_nat) = X1
| ~ spl0_112
| ~ spl0_1347 ),
inference(resolution,[],[f9857,f3570]) ).
fof(f3570,plain,
( class_LOrder_Ojoin__semilorder(tc_nat)
| ~ spl0_112 ),
inference(avatar_component_clause,[],[f3568]) ).
fof(f9857,plain,
( ! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 )
| ~ spl0_1347 ),
inference(avatar_component_clause,[],[f9856]) ).
fof(f11328,plain,
spl0_1613,
inference(avatar_split_clause,[],[f2954,f11326]) ).
fof(f11326,plain,
( spl0_1613
<=> ! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1613])]) ).
fof(f2954,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_0,X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(inner_rewriting,[],[f2953]) ).
fof(f2953,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(X0,X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f2952,f2115]) ).
fof(f2952,plain,
! [X0,X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_OPls),X1),X1)
| ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1) ),
inference(forward_demodulation,[],[f1337,f2126]) ).
fof(f1337,axiom,
! [X0,X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 != c_Numeral_Onumber__of(X0,X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_Obin__add(X0,c_Numeral_Obin__minus(c_Numeral_OPls)),X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oarith__special__8_0) ).
fof(f11324,plain,
spl0_1612,
inference(avatar_split_clause,[],[f2855,f11322]) ).
fof(f11322,plain,
( spl0_1612
<=> ! [X96,X90] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1612])]) ).
fof(f2855,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OHash(X96),tc_Message_Omsg) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
inference(forward_demodulation,[],[f2854,f2852]) ).
fof(f2854,plain,
! [X90,X96] : c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg) = c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_1,tc_nat),
inference(forward_demodulation,[],[f2766,f2016]) ).
fof(f2766,axiom,
! [X90,X96] : c_plus(c_Nat_Osize(X96,tc_Message_Omsg),c_Suc(c_0),tc_nat) = c_Nat_Osize(c_Message_Omsg_OCrypt(X90,X96),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__7_0) ).
fof(f11320,plain,
spl0_1611,
inference(avatar_split_clause,[],[f2851,f11318]) ).
fof(f11318,plain,
( spl0_1611
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1611])]) ).
fof(f2851,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f1209,f2016]) ).
fof(f1209,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn0(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__one__In0_0) ).
fof(f11316,plain,
spl0_1610,
inference(avatar_split_clause,[],[f2850,f11314]) ).
fof(f11314,plain,
( spl0_1610
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1610])]) ).
fof(f2850,plain,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_1,c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
inference(forward_demodulation,[],[f1210,f2016]) ).
fof(f1210,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_Suc(c_0),c_Datatype__Universe_OIn1(X9,X1,X2),X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__one__In1_0) ).
fof(f11312,plain,
spl0_1609,
inference(avatar_split_clause,[],[f2759,f11310]) ).
fof(f11310,plain,
( spl0_1609
<=> ! [X89,X96,X97,X90] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1609])]) ).
fof(f2759,axiom,
! [X90,X89,X96,X97] :
( X96 = X97
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__7_1) ).
fof(f11308,plain,
spl0_1608,
inference(avatar_split_clause,[],[f2758,f11306]) ).
fof(f11306,plain,
( spl0_1608
<=> ! [X96,X97,X90,X89] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1608])]) ).
fof(f2758,axiom,
! [X90,X89,X96,X97] :
( X89 = X90
| c_Message_Omsg_OCrypt(X90,X96) != c_Message_Omsg_OCrypt(X89,X97) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__7_0) ).
fof(f11304,plain,
spl0_1607,
inference(avatar_split_clause,[],[f2757,f11302]) ).
fof(f11302,plain,
( spl0_1607
<=> ! [X100,X101,X98,X99] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1607])]) ).
fof(f2757,axiom,
! [X101,X98,X99,X100] :
( X99 = X101
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__6_1) ).
fof(f11300,plain,
spl0_1606,
inference(avatar_split_clause,[],[f2756,f11298]) ).
fof(f11298,plain,
( spl0_1606
<=> ! [X101,X98,X100,X99] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1606])]) ).
fof(f2756,axiom,
! [X101,X98,X99,X100] :
( X98 = X100
| c_Message_Omsg_OMPair(X98,X99) != c_Message_Omsg_OMPair(X100,X101) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__6_0) ).
fof(f11296,plain,
( spl0_1605
| ~ spl0_29
| ~ spl0_1347 ),
inference(avatar_split_clause,[],[f10182,f9856,f3153,f11294]) ).
fof(f11294,plain,
( spl0_1605
<=> ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1605])]) ).
fof(f3153,plain,
( spl0_29
<=> class_LOrder_Ojoin__semilorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f10182,plain,
( ! [X0] : c_LOrder_Ojoin(X0,X0,tc_IntDef_Oint) = X0
| ~ spl0_29
| ~ spl0_1347 ),
inference(resolution,[],[f9857,f3155]) ).
fof(f3155,plain,
( class_LOrder_Ojoin__semilorder(tc_IntDef_Oint)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f3153]) ).
fof(f11292,plain,
spl0_1604,
inference(avatar_split_clause,[],[f2748,f11290]) ).
fof(f11290,plain,
( spl0_1604
<=> ! [X87,X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1604])]) ).
fof(f2748,axiom,
! [X88,X86,X87] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OMPair(X86,X87),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__MPair_0) ).
fof(f11288,plain,
spl0_1603,
inference(avatar_split_clause,[],[f2671,f11286]) ).
fof(f11286,plain,
( spl0_1603
<=> ! [X12,X1] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1603])]) ).
fof(f2671,axiom,
! [X1,X12] :
( c_emptyset != c_Main_Oempty__Union__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oempty__Union__conv_2) ).
fof(f11284,plain,
spl0_1602,
inference(avatar_split_clause,[],[f2654,f11282]) ).
fof(f11282,plain,
( spl0_1602
<=> ! [X12,X1] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1602])]) ).
fof(f2654,axiom,
! [X1,X12] :
( c_emptyset != c_Main_OUnion__empty__conv__1(X12,X1)
| c_emptyset = c_Union(X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__empty__conv_2) ).
fof(f11280,plain,
spl0_1601,
inference(avatar_split_clause,[],[f2618,f11278]) ).
fof(f11278,plain,
( spl0_1601
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1601])]) ).
fof(f2618,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__2__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__UNIV__conv__2_2) ).
fof(f11276,plain,
spl0_1600,
inference(avatar_split_clause,[],[f2615,f11274]) ).
fof(f11274,plain,
( spl0_1600
<=> ! [X12,X1] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1600])]) ).
fof(f2615,axiom,
! [X1,X12] :
( c_UNIV != c_Main_OInter__UNIV__conv__1__1(X12,X1)
| c_UNIV = c_Inter(X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__UNIV__conv__1_2) ).
fof(f11272,plain,
spl0_1599,
inference(avatar_split_clause,[],[f2589,f11270]) ).
fof(f11270,plain,
( spl0_1599
<=> ! [X13,X12,X1] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1599])]) ).
fof(f2589,axiom,
! [X1,X12,X13] : c_emptyset = c_inter(X12,c_minus(X13,X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__disjoint_0) ).
fof(f11268,plain,
spl0_1598,
inference(avatar_split_clause,[],[f2527,f11266]) ).
fof(f11266,plain,
( spl0_1598
<=> ! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1598])]) ).
fof(f2527,axiom,
! [X15] : c_SetInterval_OatLeastLessThan(X15,c_Suc(X15),tc_nat) = c_insert(X15,c_emptyset,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f11264,plain,
spl0_1597,
inference(avatar_split_clause,[],[f2508,f11262]) ).
fof(f11262,plain,
( spl0_1597
<=> ! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_0 = c_divide(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1597])]) ).
fof(f2508,axiom,
! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_0 = c_divide(c_1,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ozero__eq__1__divide__iff_1) ).
fof(f11260,plain,
spl0_1596,
inference(avatar_split_clause,[],[f2425,f11258]) ).
fof(f11258,plain,
( spl0_1596
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_1 != c_divide(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1596])]) ).
fof(f2425,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Oordered__field(X1)
| c_1 != c_divide(X27,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oeq__divide__eq__1_0) ).
fof(f11256,plain,
spl0_1595,
inference(avatar_split_clause,[],[f2405,f11254]) ).
fof(f11254,plain,
( spl0_1595
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1595])]) ).
fof(f2405,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(X18,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__eq__0__iff_2) ).
fof(f11252,plain,
spl0_1594,
inference(avatar_split_clause,[],[f2404,f11250]) ).
fof(f11250,plain,
( spl0_1594
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1594])]) ).
fof(f2404,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_divide(c_0,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__eq__0__iff_1) ).
fof(f11248,plain,
spl0_1593,
inference(avatar_split_clause,[],[f2388,f11246]) ).
fof(f2388,axiom,
! [X0,X1] : c_in(c_Pair(X0,X0,X1,X1),c_Relation_OId,tc_prod(X1,X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Opair__in__Id__conv_1) ).
fof(f11244,plain,
spl0_1592,
inference(avatar_split_clause,[],[f2383,f11242]) ).
fof(f2383,axiom,
! [X1,X12] : c_Relation_Odiag(X12,X1) = c_Relation_Oconverse(c_Relation_Odiag(X12,X1),X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Oconverse__diag_0) ).
fof(f11240,plain,
spl0_1591,
inference(avatar_split_clause,[],[f2366,f11238]) ).
fof(f2366,axiom,
! [X2,X3,X18,X1] : c_snd(c_Pair(X18,X3,X2,X1),X2,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Product__Type_Osnd__conv_0) ).
fof(f11236,plain,
spl0_1590,
inference(avatar_split_clause,[],[f2364,f11234]) ).
fof(f2364,axiom,
! [X2,X3,X1,X27] : c_fst(c_Pair(X3,X27,X1,X2),X1,X2) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Product__Type_Ofst__conv_0) ).
fof(f11232,plain,
spl0_1589,
inference(avatar_split_clause,[],[f2342,f11230]) ).
fof(f11230,plain,
( spl0_1589
<=> ! [X0,X21] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1589])]) ).
fof(f2342,axiom,
! [X21,X0] :
( c_0 = X0
| c_less(c_0,c_Nat_Opower(X0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Onat__zero__less__power__iff_1) ).
fof(f11228,plain,
spl0_1588,
inference(avatar_split_clause,[],[f2341,f11226]) ).
fof(f11226,plain,
( spl0_1588
<=> ! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1588])]) ).
fof(f2341,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(c_0,c_Nat_Opower(c_0,X21,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Onat__zero__less__power__iff_0) ).
fof(f11224,plain,
spl0_1587,
inference(avatar_split_clause,[],[f2294,f11222]) ).
fof(f11222,plain,
( spl0_1587
<=> ! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1587])]) ).
fof(f2294,axiom,
! [X21,X0] :
( c_less(c_0,X21,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__power_1) ).
fof(f11220,plain,
spl0_1586,
inference(avatar_split_clause,[],[f2281,f11218]) ).
fof(f11218,plain,
( spl0_1586
<=> ! [X0,X3] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1586])]) ).
fof(f2281,axiom,
! [X3,X0] :
( c_less(c_0,X3,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__power_1) ).
fof(f11216,plain,
spl0_1585,
inference(avatar_split_clause,[],[f2247,f11214]) ).
fof(f11214,plain,
( spl0_1585
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1585])]) ).
fof(f2247,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(X18,c_uminus(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oright__minus_0) ).
fof(f11212,plain,
( ~ spl0_95
| spl0_1584
| ~ spl0_1092
| ~ spl0_1345 ),
inference(avatar_split_clause,[],[f10180,f9848,f8699,f11210,f3483]) ).
fof(f3483,plain,
( spl0_95
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_95])]) ).
fof(f8699,plain,
( spl0_1092
<=> ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1092])]) ).
fof(f9848,plain,
( spl0_1345
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1345])]) ).
fof(f10180,plain,
( ! [X0] :
( c_in(X0,c_IntDef_ONats,tc_nat)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat) )
| ~ spl0_1092
| ~ spl0_1345 ),
inference(superposition,[],[f9849,f8700]) ).
fof(f8700,plain,
( ! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3
| ~ spl0_1092 ),
inference(avatar_component_clause,[],[f8699]) ).
fof(f9849,plain,
( ! [X21,X1] :
( c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1)
| ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1) )
| ~ spl0_1345 ),
inference(avatar_component_clause,[],[f9848]) ).
fof(f11208,plain,
spl0_1583,
inference(avatar_split_clause,[],[f2225,f11206]) ).
fof(f11206,plain,
( spl0_1583
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1583])]) ).
fof(f2225,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = X18
| c_0 != c_uminus(X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__equal__0__iff__equal_0) ).
fof(f11204,plain,
spl0_1582,
inference(avatar_split_clause,[],[f2213,f11202]) ).
fof(f11202,plain,
( spl0_1582
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1582])]) ).
fof(f2213,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Omeet(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Omeet__0__eq__0_1) ).
fof(f11200,plain,
spl0_1581,
inference(avatar_split_clause,[],[f2211,f11198]) ).
fof(f11198,plain,
( spl0_1581
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1581])]) ).
fof(f2211,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_LOrder_Ojoin(c_0,c_uminus(c_0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ojoin__0__eq__0_1) ).
fof(f11196,plain,
spl0_1580,
inference(avatar_split_clause,[],[f2197,f11194]) ).
fof(f11194,plain,
( spl0_1580
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1580])]) ).
fof(f2197,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(X18,X1) = c_minus(c_0,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__0_0) ).
fof(f11192,plain,
spl0_1579,
inference(avatar_split_clause,[],[f2175,f11190]) ).
fof(f11190,plain,
( spl0_1579
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1579])]) ).
fof(f2175,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = X18
| c_0 != c_HOL_Oabs(X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__eq__0_0) ).
fof(f11188,plain,
spl0_1578,
inference(avatar_split_clause,[],[f2171,f11186]) ).
fof(f11186,plain,
( spl0_1578
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1578])]) ).
fof(f2171,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_plus(c_uminus(X18,X1),X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oab__group__add__class_Oaxioms__1_0) ).
fof(f11184,plain,
spl0_1577,
inference(avatar_split_clause,[],[f2124,f11182]) ).
fof(f2124,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__pred(c_Numeral_Obin__minus(X11)),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__minus__1_0) ).
fof(f11180,plain,
spl0_1576,
inference(avatar_split_clause,[],[f2039,f11178]) ).
fof(f11178,plain,
( spl0_1576
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1576])]) ).
fof(f2039,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_0 = c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__is__0__eq_H_0) ).
fof(f11176,plain,
spl0_1575,
inference(avatar_split_clause,[],[f2038,f11174]) ).
fof(f2038,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| c_0 != c_minus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__is__0__eq_0) ).
fof(f11172,plain,
spl0_1574,
inference(avatar_split_clause,[],[f2022,f11170]) ).
fof(f11170,plain,
( spl0_1574
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Suc(X15),c_Suc(X21),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1574])]) ).
fof(f2022,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__less__eq_1) ).
fof(f11168,plain,
( ~ spl0_1573
| ~ spl0_1051
| ~ spl0_1057
| ~ spl0_1344 ),
inference(avatar_split_clause,[],[f10179,f9844,f7368,f7341,f11165]) ).
fof(f11165,plain,
( spl0_1573
<=> c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1573])]) ).
fof(f9844,plain,
( spl0_1344
<=> ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1344])]) ).
fof(f10179,plain,
( ~ c_lessequals(c_0,c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1057
| ~ spl0_1344 ),
inference(forward_demodulation,[],[f10178,f7343]) ).
fof(f10178,plain,
( ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_1),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1057
| ~ spl0_1344 ),
inference(superposition,[],[f9845,f7370]) ).
fof(f9845,plain,
( ! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1344 ),
inference(avatar_component_clause,[],[f9844]) ).
fof(f11163,plain,
spl0_1572,
inference(avatar_split_clause,[],[f2021,f11161]) ).
fof(f11161,plain,
( spl0_1572
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1572])]) ).
fof(f2021,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_Suc(X15),c_Suc(X21),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__less__eq_0) ).
fof(f11159,plain,
spl0_1571,
inference(avatar_split_clause,[],[f2020,f11157]) ).
fof(f11157,plain,
( spl0_1571
<=> ! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1571])]) ).
fof(f2020,axiom,
! [X21,X15] :
( ~ c_lessequals(X21,X15,tc_nat)
| c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__le__mono_1) ).
fof(f11155,plain,
spl0_1570,
inference(avatar_split_clause,[],[f2019,f11153]) ).
fof(f11153,plain,
( spl0_1570
<=> ! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1570])]) ).
fof(f2019,axiom,
! [X21,X15] :
( c_lessequals(X21,X15,tc_nat)
| ~ c_lessequals(c_Suc(X21),c_Suc(X15),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__le__mono_0) ).
fof(f11151,plain,
spl0_1569,
inference(avatar_split_clause,[],[f1849,f11149]) ).
fof(f11149,plain,
( spl0_1569
<=> ! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1569])]) ).
fof(f1849,axiom,
! [X47] :
( ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__number__of__0_2) ).
fof(f11147,plain,
spl0_1568,
inference(avatar_split_clause,[],[f1848,f11145]) ).
fof(f11145,plain,
( spl0_1568
<=> ! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1568])]) ).
fof(f1848,axiom,
! [X47] :
( ~ c_IntDef_Oneg(c_Numeral_Onumber__of(X47,tc_IntDef_Oint),tc_IntDef_Oint)
| c_0 = c_Numeral_Onumber__of(X47,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Oeq__number__of__0_1) ).
fof(f11143,plain,
spl0_1567,
inference(avatar_split_clause,[],[f1811,f11141]) ).
fof(f11141,plain,
( spl0_1567
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| c_0 != c_NatArith_Oof__nat(X15,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1567])]) ).
fof(f1811,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = X15
| c_0 != c_NatArith_Oof__nat(X15,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__eq__0__iff_0) ).
fof(f11139,plain,
spl0_1566,
inference(avatar_split_clause,[],[f1783,f11137]) ).
fof(f11137,plain,
( spl0_1566
<=> ! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1566])]) ).
fof(f1783,axiom,
! [X59,X43] :
( c_lessequals(X43,X59,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,c_Suc(X59)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oupt_Oupt__Suc_1) ).
fof(f11135,plain,
spl0_1565,
inference(avatar_split_clause,[],[f1759,f11133]) ).
fof(f11133,plain,
( spl0_1565
<=> ! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1565])]) ).
fof(f1759,axiom,
! [X21,X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate(X21,X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__rotate_0) ).
fof(f11131,plain,
spl0_1564,
inference(avatar_split_clause,[],[f1730,f11129]) ).
fof(f11129,plain,
( spl0_1564
<=> ! [X25,X1,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1564])]) ).
fof(f1730,axiom,
! [X1,X25,X23] :
( X23 = X25
| c_List_Orev(X23,X1) != c_List_Orev(X25,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__is__rev__conv_0) ).
fof(f11127,plain,
spl0_1563,
inference(avatar_split_clause,[],[f1603,f11125]) ).
fof(f11125,plain,
( spl0_1563
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1563])]) ).
fof(f1603,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_less(c_0,c_Nat_Osize(X23,tc_List_Olist(X1)),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__greater__0__conv_1) ).
fof(f11123,plain,
spl0_1562,
inference(avatar_split_clause,[],[f1548,f11121]) ).
fof(f11121,plain,
( spl0_1562
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1562])]) ).
fof(f1548,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_Oconcat__eq__Nil__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oconcat__eq__Nil__conv_2) ).
fof(f11119,plain,
spl0_1561,
inference(avatar_split_clause,[],[f1541,f11117]) ).
fof(f11117,plain,
( spl0_1561
<=> ! [X54,X57,X55,X56] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1561])]) ).
fof(f1541,axiom,
! [X56,X54,X57,X55] :
( X55 = X57
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ochar_Oinject_1) ).
fof(f11115,plain,
spl0_1560,
inference(avatar_split_clause,[],[f1540,f11113]) ).
fof(f11113,plain,
( spl0_1560
<=> ! [X55,X54,X56,X57] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1560])]) ).
fof(f1540,axiom,
! [X56,X54,X57,X55] :
( X54 = X56
| c_List_Ochar_OChar(X54,X55) != c_List_Ochar_OChar(X56,X57) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ochar_Oinject_0) ).
fof(f11111,plain,
spl0_1559,
inference(avatar_split_clause,[],[f1509,f11109]) ).
fof(f11109,plain,
( spl0_1559
<=> ! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1559])]) ).
fof(f1509,axiom,
! [X50,X1] :
( c_List_Olist_ONil != c_Main_ONil__eq__concat__conv__1(X50,X1)
| c_List_Olist_ONil = c_List_Oconcat(X50,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__eq__concat__conv_2) ).
fof(f11107,plain,
spl0_1558,
inference(avatar_split_clause,[],[f1488,f11105]) ).
fof(f11105,plain,
( spl0_1558
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1558])]) ).
fof(f1488,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozminus__dvd__iff_1) ).
fof(f11103,plain,
spl0_1557,
inference(avatar_split_clause,[],[f1487,f11101]) ).
fof(f1487,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(c_uminus(X48,tc_IntDef_Oint),X11,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozminus__dvd__iff_0) ).
fof(f11098,plain,
spl0_1556,
inference(avatar_split_clause,[],[f1467,f11096]) ).
fof(f1467,axiom,
! [X18] : c_div(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) = c_uminus(X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__minus1__right_0) ).
fof(f11094,plain,
spl0_1555,
inference(avatar_split_clause,[],[f1440,f11092]) ).
fof(f11092,plain,
( spl0_1555
<=> ! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1555])]) ).
fof(f1440,axiom,
! [X48,X11] :
( ~ c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odvd__zminus__iff_1) ).
fof(f11090,plain,
spl0_1554,
inference(avatar_split_clause,[],[f1439,f11088]) ).
fof(f1439,axiom,
! [X48,X11] :
( c_Divides_Oop_Advd(X48,X11,tc_IntDef_Oint)
| ~ c_Divides_Oop_Advd(X48,c_uminus(X11,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Odvd__zminus__iff_0) ).
fof(f11086,plain,
spl0_1553,
inference(avatar_split_clause,[],[f1430,f11084]) ).
fof(f11084,plain,
( spl0_1553
<=> ! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1553])]) ).
fof(f1430,axiom,
! [X48,X11] :
( c_less(X11,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozless__nat__conj_1) ).
fof(f11082,plain,
( ~ spl0_131
| ~ spl0_1552
| ~ spl0_1057
| ~ spl0_1302 ),
inference(avatar_split_clause,[],[f9731,f9599,f7368,f11079,f3656]) ).
fof(f3656,plain,
( spl0_131
<=> c_Parity_Oeven(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_131])]) ).
fof(f11079,plain,
( spl0_1552
<=> c_Parity_Oeven(c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1552])]) ).
fof(f9599,plain,
( spl0_1302
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1302])]) ).
fof(f9731,plain,
( ~ c_Parity_Oeven(c_1,tc_nat)
| ~ c_Parity_Oeven(c_0,tc_nat)
| ~ spl0_1057
| ~ spl0_1302 ),
inference(superposition,[],[f9600,f7370]) ).
fof(f9600,plain,
( ! [X0] :
( ~ c_Parity_Oeven(c_Suc(X0),tc_nat)
| ~ c_Parity_Oeven(X0,tc_nat) )
| ~ spl0_1302 ),
inference(avatar_component_clause,[],[f9599]) ).
fof(f11077,plain,
spl0_1551,
inference(avatar_split_clause,[],[f1429,f11075]) ).
fof(f11075,plain,
( spl0_1551
<=> ! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1551])]) ).
fof(f1429,axiom,
! [X48,X11] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_IntDef_Onat(X11),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozless__nat__conj_0) ).
fof(f11073,plain,
spl0_1550,
inference(avatar_split_clause,[],[f1428,f11071]) ).
fof(f11071,plain,
( spl0_1550
<=> ! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1550])]) ).
fof(f1428,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozless__int_1) ).
fof(f11069,plain,
spl0_1549,
inference(avatar_split_clause,[],[f1427,f11067]) ).
fof(f11067,plain,
( spl0_1549
<=> ! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1549])]) ).
fof(f1427,axiom,
! [X21,X15] :
( c_less(X15,X21,tc_nat)
| ~ c_less(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozless__int_0) ).
fof(f11065,plain,
spl0_1548,
inference(avatar_split_clause,[],[f1426,f11063]) ).
fof(f11063,plain,
( spl0_1548
<=> ! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1548])]) ).
fof(f1426,axiom,
! [X21,X15] :
( ~ c_lessequals(X15,X21,tc_nat)
| c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozle__int_1) ).
fof(f11061,plain,
spl0_1547,
inference(avatar_split_clause,[],[f1425,f11059]) ).
fof(f11059,plain,
( spl0_1547
<=> ! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1547])]) ).
fof(f1425,axiom,
! [X21,X15] :
( c_lessequals(X15,X21,tc_nat)
| ~ c_lessequals(c_IntDef_Oint(X15),c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozle__int_0) ).
fof(f11057,plain,
spl0_1546,
inference(avatar_split_clause,[],[f1407,f11055]) ).
fof(f11055,plain,
( spl0_1546
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1546])]) ).
fof(f1407,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_IntDef_Oof__int(c_IntDef_Oint(X21),X1) = c_NatArith_Oof__nat(X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__int__eq_0) ).
fof(f11053,plain,
spl0_1545,
inference(avatar_split_clause,[],[f1404,f11051]) ).
fof(f11051,plain,
( spl0_1545
<=> ! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X11
| c_0 != c_IntDef_Oof__int(X11,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1545])]) ).
fof(f1404,axiom,
! [X11,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = X11
| c_0 != c_IntDef_Oof__int(X11,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__eq__0__iff_0) ).
fof(f11049,plain,
spl0_1544,
inference(avatar_split_clause,[],[f1390,f11047]) ).
fof(f11047,plain,
( spl0_1544
<=> ! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1544])]) ).
fof(f1390,axiom,
! [X21,X15] :
( c_0 = X15
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onegative__eq__positive_1) ).
fof(f11045,plain,
spl0_1543,
inference(avatar_split_clause,[],[f1389,f11043]) ).
fof(f11043,plain,
( spl0_1543
<=> ! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1543])]) ).
fof(f1389,axiom,
! [X21,X15] :
( c_0 = X21
| c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onegative__eq__positive_0) ).
fof(f11041,plain,
spl0_1542,
inference(avatar_split_clause,[],[f1279,f11039]) ).
fof(f1279,axiom,
! [X1,X12] :
( c_0 = c_Finite__Set_Ocard(X12,X1)
| c_in(X12,c_Finite__Set_OFinites,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ocard__infinite_0) ).
fof(f11034,plain,
spl0_1541,
inference(avatar_split_clause,[],[f1275,f11032]) ).
fof(f11032,plain,
( spl0_1541
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1541])]) ).
fof(f1275,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMin(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMin__singleton_0) ).
fof(f11030,plain,
spl0_1540,
inference(avatar_split_clause,[],[f1265,f11028]) ).
fof(f11028,plain,
( spl0_1540
<=> ! [X1,X3] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1540])]) ).
fof(f1265,axiom,
! [X3,X1] :
( ~ class_Orderings_Olinorder(X1)
| c_Finite__Set_OMax(c_insert(X3,c_emptyset,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OMax__singleton_0) ).
fof(f11026,plain,
spl0_1539,
inference(avatar_split_clause,[],[f1235,f11024]) ).
fof(f1235,axiom,
! [X21,X3] :
( ~ c_less(X3,X21,tc_nat)
| c_Divides_Oop_Amod(X3,X21,tc_nat) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__less_0) ).
fof(f11022,plain,
spl0_1538,
inference(avatar_split_clause,[],[f1224,f11020]) ).
fof(f11020,plain,
( spl0_1538
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1538])]) ).
fof(f1224,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_1 = c_div(X21,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__self_0) ).
fof(f11018,plain,
spl0_1537,
inference(avatar_split_clause,[],[f1216,f11016]) ).
fof(f1216,axiom,
! [X21,X15] :
( ~ c_less(X15,X21,tc_nat)
| c_0 = c_div(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__less_0) ).
fof(f11014,plain,
spl0_1536,
inference(avatar_split_clause,[],[f1196,f11012]) ).
fof(f11012,plain,
( spl0_1536
<=> ! [X9,X7,X16,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1536])]) ).
fof(f1196,axiom,
! [X2,X1,X9,X7,X16] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_ONumb__not__Scons_0) ).
fof(f11010,plain,
spl0_1535,
inference(avatar_split_clause,[],[f1194,f11008]) ).
fof(f11008,plain,
( spl0_1535
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1535])]) ).
fof(f1194,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OLeaf(X18,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OLeaf__not__Scons_0) ).
fof(f11006,plain,
spl0_1534,
inference(avatar_split_clause,[],[f1186,f11004]) ).
fof(f11004,plain,
( spl0_1534
<=> ! [X18,X7,X9,X2,X1] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1534])]) ).
fof(f1186,axiom,
! [X2,X1,X18,X9,X7] : c_Datatype__Universe_OScons(X9,X7,X1,X2) != c_Datatype__Universe_OAtom(X18,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OAtom__not__Scons_0) ).
fof(f11002,plain,
spl0_1533,
inference(avatar_split_clause,[],[f1180,f11000]) ).
fof(f11000,plain,
( spl0_1533
<=> ! [X2,X27,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1533])]) ).
fof(f1180,axiom,
! [X2,X1,X27] : c_0 = c_Nat_Osize(c_Sum__Type_OInr(X27,X2,X1),tc_sum(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Osum_Osize__2_0) ).
fof(f10998,plain,
spl0_1532,
inference(avatar_split_clause,[],[f1179,f10996]) ).
fof(f10996,plain,
( spl0_1532
<=> ! [X2,X1,X18] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1532])]) ).
fof(f1179,axiom,
! [X2,X18,X1] : c_0 = c_Nat_Osize(c_Sum__Type_OInl(X18,X1,X2),tc_sum(X1,X2)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Osum_Osize__1_0) ).
fof(f10994,plain,
spl0_1531,
inference(avatar_split_clause,[],[f1175,f10992]) ).
fof(f10992,plain,
( spl0_1531
<=> ! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1531])]) ).
fof(f1175,axiom,
! [X18,X1,X42] :
( X18 = X42
| c_Datatype_Ooption_OSome(X42,X1) != c_Datatype_Ooption_OSome(X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ooption_Oinject_0) ).
fof(f10990,plain,
spl0_1530,
inference(avatar_split_clause,[],[f1170,f10988]) ).
fof(f10988,plain,
( spl0_1530
<=> ! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1530])]) ).
fof(f1170,axiom,
! [X41,X0] : c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X41),X41) = c_insert(X0,c_emptyset,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Oo2s_Osimps__2_0) ).
fof(f10986,plain,
spl0_1529,
inference(avatar_split_clause,[],[f1169,f10984]) ).
fof(f10984,plain,
( spl0_1529
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1529])]) ).
fof(f1169,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__Some__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Onot__Some__eq_0) ).
fof(f10982,plain,
spl0_1528,
inference(avatar_split_clause,[],[f1168,f10980]) ).
fof(f10980,plain,
( spl0_1528
<=> ! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1528])]) ).
fof(f1168,axiom,
! [X0,X1] :
( c_Datatype_Ooption_ONone = X0
| c_Datatype_Ooption_OSome(c_Main_Onot__None__eq__1(X0,X1),X1) = X0 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Onot__None__eq_0) ).
fof(f10978,plain,
spl0_1527,
inference(avatar_split_clause,[],[f105,f10976]) ).
fof(f10976,plain,
( spl0_1527
<=> ! [X18,X27,X1] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1527])]) ).
fof(f105,axiom,
! [X18,X1,X27] :
( X18 = X27
| ~ c_in(X27,c_insert(X18,c_emptyset,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OsingletonD__dest_0) ).
fof(f10974,plain,
spl0_1526,
inference(avatar_split_clause,[],[f103,f10972]) ).
fof(f10972,plain,
( spl0_1526
<=> ! [X13,X12,X1] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1526])]) ).
fof(f103,axiom,
! [X1,X12,X13] :
( ~ c_less(X12,X13,tc_set(X1))
| c_lessequals(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OpsubsetE_1) ).
fof(f10970,plain,
spl0_1525,
inference(avatar_split_clause,[],[f102,f10968]) ).
fof(f102,axiom,
! [X1,X12,X13] :
( ~ c_lessequals(X13,X12,tc_set(X1))
| ~ c_less(X12,X13,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OpsubsetE_0) ).
fof(f10953,plain,
( spl0_1524
| ~ spl0_1145
| ~ spl0_1502 ),
inference(avatar_split_clause,[],[f10929,f10619,f8935,f10951]) ).
fof(f8935,plain,
( spl0_1145
<=> ! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1145])]) ).
fof(f10619,plain,
( spl0_1502
<=> ! [X5,X1] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1502])]) ).
fof(f10929,plain,
( ! [X0] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_Relation_OId,X0)
| ~ spl0_1145
| ~ spl0_1502 ),
inference(superposition,[],[f10620,f8936]) ).
fof(f8936,plain,
( ! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1)
| ~ spl0_1145 ),
inference(avatar_component_clause,[],[f8935]) ).
fof(f10620,plain,
( ! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X1),X1)
| ~ spl0_1502 ),
inference(avatar_component_clause,[],[f10619]) ).
fof(f10938,plain,
( spl0_1523
| ~ spl0_1236
| ~ spl0_1496 ),
inference(avatar_split_clause,[],[f10913,f10595,f9319,f10936]) ).
fof(f10936,plain,
( spl0_1523
<=> ! [X2] : c_emptyset != c_Pow(c_emptyset,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1523])]) ).
fof(f9319,plain,
( spl0_1236
<=> ! [X12,X1,X18] : c_emptyset != c_insert(X18,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1236])]) ).
fof(f10913,plain,
( ! [X2] : c_emptyset != c_Pow(c_emptyset,X2)
| ~ spl0_1236
| ~ spl0_1496 ),
inference(superposition,[],[f9320,f10596]) ).
fof(f9320,plain,
( ! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1)
| ~ spl0_1236 ),
inference(avatar_component_clause,[],[f9319]) ).
fof(f10884,plain,
( spl0_1522
| ~ spl0_1316
| ~ spl0_1470 ),
inference(avatar_split_clause,[],[f10833,f10491,f9678,f10882]) ).
fof(f10882,plain,
( spl0_1522
<=> ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1522])]) ).
fof(f9678,plain,
( spl0_1316
<=> ! [X1] : c_lessequals(X1,X1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1316])]) ).
fof(f10491,plain,
( spl0_1470
<=> ! [X43,X59] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1470])]) ).
fof(f10833,plain,
( ! [X0] : c_List_Olist_ONil = c_List_Oupt(X0,X0)
| ~ spl0_1316
| ~ spl0_1470 ),
inference(resolution,[],[f10492,f9679]) ).
fof(f9679,plain,
( ! [X1] : c_lessequals(X1,X1,tc_nat)
| ~ spl0_1316 ),
inference(avatar_component_clause,[],[f9678]) ).
fof(f10492,plain,
( ! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) )
| ~ spl0_1470 ),
inference(avatar_component_clause,[],[f10491]) ).
fof(f10823,plain,
( spl0_1521
| ~ spl0_1236
| ~ spl0_1462 ),
inference(avatar_split_clause,[],[f10819,f10458,f9319,f10821]) ).
fof(f10821,plain,
( spl0_1521
<=> ! [X2] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1521])]) ).
fof(f10819,plain,
( ! [X2] : c_emptyset != c_List_Olistset(c_List_Olist_ONil,X2)
| ~ spl0_1236
| ~ spl0_1462 ),
inference(superposition,[],[f9320,f10459]) ).
fof(f10801,plain,
( spl0_1520
| ~ spl0_1256
| ~ spl0_1276 ),
inference(avatar_split_clause,[],[f9691,f9495,f9415,f10799]) ).
fof(f10799,plain,
( spl0_1520
<=> ! [X1] : c_0 = c_times(X1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1520])]) ).
fof(f9415,plain,
( spl0_1256
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1256])]) ).
fof(f9495,plain,
( spl0_1276
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1276])]) ).
fof(f9691,plain,
( ! [X1] : c_0 = c_times(X1,c_0,tc_IntDef_Oint)
| ~ spl0_1256
| ~ spl0_1276 ),
inference(resolution,[],[f9496,f9416]) ).
fof(f9416,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1256 ),
inference(avatar_component_clause,[],[f9415]) ).
fof(f9496,plain,
( ! [X15] :
( ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint)
| c_0 = X15 )
| ~ spl0_1276 ),
inference(avatar_component_clause,[],[f9495]) ).
fof(f10773,plain,
( spl0_1519
| ~ spl0_1255
| ~ spl0_1276 ),
inference(avatar_split_clause,[],[f9690,f9495,f9411,f10771]) ).
fof(f10771,plain,
( spl0_1519
<=> ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1519])]) ).
fof(f9411,plain,
( spl0_1255
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1255])]) ).
fof(f9690,plain,
( ! [X0] : c_0 = c_times(c_0,X0,tc_IntDef_Oint)
| ~ spl0_1255
| ~ spl0_1276 ),
inference(resolution,[],[f9496,f9412]) ).
fof(f9412,plain,
( ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1255 ),
inference(avatar_component_clause,[],[f9411]) ).
fof(f10720,plain,
( spl0_1518
| ~ spl0_1051
| ~ spl0_1272 ),
inference(avatar_split_clause,[],[f9681,f9479,f7341,f10717]) ).
fof(f10717,plain,
( spl0_1518
<=> c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1518])]) ).
fof(f9479,plain,
( spl0_1272
<=> ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1272])]) ).
fof(f9681,plain,
( c_0 = c_IntDef_Onat(c_uminus(c_1,tc_IntDef_Oint))
| ~ spl0_1051
| ~ spl0_1272 ),
inference(superposition,[],[f9480,f7343]) ).
fof(f9480,plain,
( ! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint))
| ~ spl0_1272 ),
inference(avatar_component_clause,[],[f9479]) ).
fof(f10682,plain,
spl0_1517,
inference(avatar_split_clause,[],[f2904,f10680]) ).
fof(f10680,plain,
( spl0_1517
<=> ! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1517])]) ).
fof(f2904,plain,
! [X48] :
( ~ c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1346,f2016]) ).
fof(f1346,axiom,
! [X48] :
( c_less(c_1,X48,tc_IntDef_Oint)
| ~ c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oone__less__nat__eq_0) ).
fof(f10678,plain,
spl0_1516,
inference(avatar_split_clause,[],[f2900,f10676]) ).
fof(f10676,plain,
( spl0_1516
<=> ! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1516])]) ).
fof(f2900,plain,
! [X48] :
( c_less(c_1,c_IntDef_Onat(X48),tc_nat)
| ~ c_less(c_1,X48,tc_IntDef_Oint) ),
inference(forward_demodulation,[],[f1347,f2016]) ).
fof(f1347,axiom,
! [X48] :
( ~ c_less(c_1,X48,tc_IntDef_Oint)
| c_less(c_Suc(c_0),c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Oone__less__nat__eq_1) ).
fof(f10674,plain,
spl0_1515,
inference(avatar_split_clause,[],[f2895,f10672]) ).
fof(f10672,plain,
( spl0_1515
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1515])]) ).
fof(f2895,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X21 ),
inference(forward_demodulation,[],[f2063,f2016]) ).
fof(f2063,axiom,
! [X21,X15] :
( c_1 = X21
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__eq__1__iff_1) ).
fof(f10670,plain,
spl0_1514,
inference(avatar_split_clause,[],[f2894,f10668]) ).
fof(f10668,plain,
( spl0_1514
<=> ! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1514])]) ).
fof(f2894,plain,
! [X21,X15] :
( c_1 != c_times(X15,X21,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f2092,f2016]) ).
fof(f2092,axiom,
! [X21,X15] :
( c_1 = X15
| c_Suc(c_0) != c_times(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oone__eq__mult__iff_0) ).
fof(f10666,plain,
spl0_1513,
inference(avatar_split_clause,[],[f2818,f10664]) ).
fof(f2818,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Osynth(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth_OInj_0) ).
fof(f10662,plain,
spl0_1512,
inference(avatar_split_clause,[],[f2787,f10660]) ).
fof(f10660,plain,
( spl0_1512
<=> ! [X86,X88] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1512])]) ).
fof(f2787,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oanalz(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz_OInj_0) ).
fof(f10658,plain,
spl0_1511,
inference(avatar_split_clause,[],[f2767,f10656]) ).
fof(f2767,axiom,
! [X88,X86] :
( ~ c_in(X86,X88,tc_Message_Omsg)
| c_in(X86,c_Message_Oparts(X88),tc_Message_Omsg) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts_OInj_0) ).
fof(f10654,plain,
spl0_1510,
inference(avatar_split_clause,[],[f2750,f10652]) ).
fof(f10652,plain,
( spl0_1510
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1510])]) ).
fof(f2750,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONumber(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__Number_0) ).
fof(f10650,plain,
spl0_1509,
inference(avatar_split_clause,[],[f2749,f10648]) ).
fof(f10648,plain,
( spl0_1509
<=> ! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1509])]) ).
fof(f2749,axiom,
! [X88,X7] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_ONonce(X7),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__Nonce_0) ).
fof(f10646,plain,
spl0_1508,
inference(avatar_split_clause,[],[f2747,f10644]) ).
fof(f10644,plain,
( spl0_1508
<=> ! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1508])]) ).
fof(f2747,axiom,
! [X91,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OKey(X91),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__Key_0) ).
fof(f10642,plain,
( ~ spl0_59
| spl0_1507
| ~ spl0_1291
| ~ spl0_1412 ),
inference(avatar_split_clause,[],[f10282,f10120,f9555,f10639,f3303]) ).
fof(f10639,plain,
( spl0_1507
<=> c_IntDef_Oiszero(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1507])]) ).
fof(f9555,plain,
( spl0_1291
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1291])]) ).
fof(f10120,plain,
( spl0_1412
<=> c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1412])]) ).
fof(f10282,plain,
( c_IntDef_Oiszero(c_0,tc_IntDef_Oint)
| ~ class_Numeral_Onumber__ring(tc_IntDef_Oint)
| ~ spl0_1291
| ~ spl0_1412 ),
inference(superposition,[],[f9556,f10122]) ).
fof(f10122,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_1412 ),
inference(avatar_component_clause,[],[f10120]) ).
fof(f9556,plain,
( ! [X1] :
( c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1)
| ~ class_Numeral_Onumber__ring(X1) )
| ~ spl0_1291 ),
inference(avatar_component_clause,[],[f9555]) ).
fof(f10637,plain,
spl0_1506,
inference(avatar_split_clause,[],[f2746,f10635]) ).
fof(f10635,plain,
( spl0_1506
<=> ! [X86,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1506])]) ).
fof(f2746,axiom,
! [X88,X86] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OHash(X86),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__Hash_0) ).
fof(f10633,plain,
spl0_1505,
inference(avatar_split_clause,[],[f2744,f10631]) ).
fof(f10631,plain,
( spl0_1505
<=> ! [X12,X88] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1505])]) ).
fof(f2744,axiom,
! [X88,X12] : c_Message_OkeysFor(X88) = c_Message_OkeysFor(c_insert(c_Message_Omsg_OAgent(X12),X88,tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__insert__Agent_0) ).
fof(f10629,plain,
spl0_1504,
inference(avatar_split_clause,[],[f2718,f10627]) ).
fof(f10627,plain,
( spl0_1504
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1504])]) ).
fof(f2718,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Oacyclic(X5,X1)
| c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Oacyclic__converse_1) ).
fof(f10625,plain,
spl0_1503,
inference(avatar_split_clause,[],[f2717,f10623]) ).
fof(f10623,plain,
( spl0_1503
<=> ! [X5,X1] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1503])]) ).
fof(f2717,axiom,
! [X1,X5] :
( c_Wellfounded__Recursion_Oacyclic(X5,X1)
| ~ c_Wellfounded__Recursion_Oacyclic(c_Relation_Oconverse(X5,X1,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Oacyclic__converse_0) ).
fof(f10621,plain,
spl0_1502,
inference(avatar_split_clause,[],[f2710,f10619]) ).
fof(f2710,axiom,
! [X1,X5] : c_Transitive__Closure_Ortrancl(X5,X1) = c_Transitive__Closure_Ortrancl(c_Transitive__Closure_Ortrancl(X5,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Ortrancl__idemp_0) ).
fof(f10617,plain,
spl0_1501,
inference(avatar_split_clause,[],[f2704,f10615]) ).
fof(f10615,plain,
( spl0_1501
<=> ! [X2,X27,X1,X18] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1501])]) ).
fof(f2704,axiom,
! [X2,X18,X1,X27] : c_Sum__Type_OInl(X18,X1,X2) != c_Sum__Type_OInr(X27,X2,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OInr__not__Inl_0) ).
fof(f10613,plain,
spl0_1500,
inference(avatar_split_clause,[],[f2667,f10611]) ).
fof(f10611,plain,
( spl0_1500
<=> ! [X1,X3] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1500])]) ).
fof(f2667,axiom,
! [X3,X1] : c_uminus(c_uminus(X3,tc_set(X1)),tc_set(X1)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Odouble__complement_0) ).
fof(f10609,plain,
spl0_1499,
inference(avatar_split_clause,[],[f2659,f10607]) ).
fof(f2659,axiom,
! [X1,X12] :
( c_emptyset = X12
| c_in(c_Main_Oall__not__in__conv__1(X12,X1),X12,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oall__not__in__conv_0) ).
fof(f10605,plain,
spl0_1498,
inference(avatar_split_clause,[],[f2636,f10603]) ).
fof(f10603,plain,
( spl0_1498
<=> ! [X13,X12,X1] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1498])]) ).
fof(f2636,axiom,
! [X1,X12,X13] :
( c_emptyset = X13
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__empty_1) ).
fof(f10601,plain,
spl0_1497,
inference(avatar_split_clause,[],[f2635,f10599]) ).
fof(f2635,axiom,
! [X1,X12,X13] :
( c_emptyset = X12
| c_emptyset != c_union(X12,X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__empty_0) ).
fof(f10597,plain,
spl0_1496,
inference(avatar_split_clause,[],[f2626,f10595]) ).
fof(f2626,axiom,
! [X1] : c_Pow(c_emptyset,X1) = c_insert(c_emptyset,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OPow__empty_0) ).
fof(f10593,plain,
spl0_1495,
inference(avatar_split_clause,[],[f2599,f10591]) ).
fof(f10591,plain,
( spl0_1495
<=> ! [X13,X12,X1] :
( c_UNIV = X13
| c_UNIV != c_inter(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1495])]) ).
fof(f2599,axiom,
! [X1,X12,X13] :
( c_UNIV = X13
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__UNIV_1) ).
fof(f10589,plain,
spl0_1494,
inference(avatar_split_clause,[],[f2598,f10587]) ).
fof(f10587,plain,
( spl0_1494
<=> ! [X13,X12,X1] :
( c_UNIV = X12
| c_UNIV != c_inter(X12,X13,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1494])]) ).
fof(f2598,axiom,
! [X1,X12,X13] :
( c_UNIV = X12
| c_UNIV != c_inter(X12,X13,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__UNIV_0) ).
fof(f10585,plain,
spl0_1493,
inference(avatar_split_clause,[],[f2579,f10583]) ).
fof(f10583,plain,
( spl0_1493
<=> ! [X12,X1] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1493])]) ).
fof(f2579,axiom,
! [X1,X12] : c_emptyset = c_inter(X12,c_uminus(X12,tc_set(X1)),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__disjoint_0) ).
fof(f10581,plain,
spl0_1492,
inference(avatar_split_clause,[],[f2578,f10579]) ).
fof(f10579,plain,
( spl0_1492
<=> ! [X12,X1] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1492])]) ).
fof(f2578,axiom,
! [X1,X12] : c_emptyset = c_inter(c_uminus(X12,tc_set(X1)),X12,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__disjoint2_0) ).
fof(f10577,plain,
spl0_1491,
inference(avatar_split_clause,[],[f2455,f10575]) ).
fof(f10575,plain,
( spl0_1491
<=> ! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_HOL_Oinverse(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1491])]) ).
fof(f2455,axiom,
! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_0 = c_HOL_Oinverse(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__nonzero__iff__nonzero_1) ).
fof(f10573,plain,
spl0_1490,
inference(avatar_split_clause,[],[f2435,f10571]) ).
fof(f10571,plain,
( spl0_1490
<=> ! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_1 = c_HOL_Oinverse(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1490])]) ).
fof(f2435,axiom,
! [X1] :
( ~ class_Ring__and__Field_Odivision__by__zero(X1)
| ~ class_Ring__and__Field_Ofield(X1)
| c_1 = c_HOL_Oinverse(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oinverse__eq__1__iff_1) ).
fof(f10569,plain,
spl0_1489,
inference(avatar_split_clause,[],[f2390,f10567]) ).
fof(f10567,plain,
( spl0_1489
<=> ! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1489])]) ).
fof(f2390,axiom,
! [X41,X85] : c_Relation_OId = c_Nat_Opower(X85,c_0,tc_set(tc_prod(X41,X41))),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation__Power_Orelpow_Osimps__1_0) ).
fof(f10565,plain,
spl0_1488,
inference(avatar_split_clause,[],[f2389,f10563]) ).
fof(f10563,plain,
( spl0_1488
<=> ! [X1,X3] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1488])]) ).
fof(f2389,axiom,
! [X3,X1] : c_Nat_Opower(X3,c_1,tc_set(tc_prod(X1,X1))) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation__Power_Orel__pow__1_0) ).
fof(f10561,plain,
spl0_1487,
inference(avatar_split_clause,[],[f2382,f10559]) ).
fof(f10559,plain,
( spl0_1487
<=> ! [X2,X1,X3] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1487])]) ).
fof(f2382,axiom,
! [X2,X3,X1] : c_Relation_Oconverse(c_Relation_Oconverse(X3,X1,X2),X2,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Oconverse__converse_0) ).
fof(f10557,plain,
spl0_1486,
inference(avatar_split_clause,[],[f2346,f10555]) ).
fof(f2346,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_0 = c_Nat_Opower(c_0,c_Suc(X21),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__0__Suc_0) ).
fof(f10553,plain,
spl0_1485,
inference(avatar_split_clause,[],[f2298,f10551]) ).
fof(f10551,plain,
( spl0_1485
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1485])]) ).
fof(f2298,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__product_2) ).
fof(f10549,plain,
spl0_1484,
inference(avatar_split_clause,[],[f2297,f10547]) ).
fof(f10547,plain,
( spl0_1484
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1484])]) ).
fof(f2297,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_times(X0,X3,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__product_1) ).
fof(f10545,plain,
spl0_1483,
inference(avatar_split_clause,[],[f2293,f10543]) ).
fof(f10543,plain,
( spl0_1483
<=> ! [X0,X21] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1483])]) ).
fof(f2293,axiom,
! [X21,X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__power_0) ).
fof(f10541,plain,
spl0_1482,
inference(avatar_split_clause,[],[f2285,f10539]) ).
fof(f10539,plain,
( spl0_1482
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1482])]) ).
fof(f2285,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X3,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__product_2) ).
fof(f10537,plain,
spl0_1481,
inference(avatar_split_clause,[],[f2284,f10535]) ).
fof(f10535,plain,
( spl0_1481
<=> ! [X0,X3] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1481])]) ).
fof(f2284,axiom,
! [X3,X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_times(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__product_1) ).
fof(f10533,plain,
spl0_1480,
inference(avatar_split_clause,[],[f2280,f10531]) ).
fof(f10531,plain,
( spl0_1480
<=> ! [X0,X3] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1480])]) ).
fof(f2280,axiom,
! [X3,X0] :
( c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Nat_Opower(X0,X3,tc_nat),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__power_0) ).
fof(f10529,plain,
spl0_1479,
inference(avatar_split_clause,[],[f2216,f10527]) ).
fof(f2216,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_uminus(c_uminus(X3,X1),X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ominus__minus_0) ).
fof(f10525,plain,
spl0_1478,
inference(avatar_split_clause,[],[f2154,f10523]) ).
fof(f10523,plain,
( spl0_1478
<=> ! [X11] : c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) = c_Numeral_OBit(c_Numeral_Obin__succ(X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1478])]) ).
fof(f10521,plain,
spl0_1477,
inference(avatar_split_clause,[],[f2150,f10519]) ).
fof(f10519,plain,
( spl0_1477
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1477])]) ).
fof(f2150,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__7_0) ).
fof(f10517,plain,
spl0_1476,
inference(avatar_split_clause,[],[f2136,f10515]) ).
fof(f10515,plain,
( spl0_1476
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1476])]) ).
fof(f2136,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ class_Ring__and__Field_Oordered__idom(X1)
| c_IntDef_Oneg(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__11_0) ).
fof(f10513,plain,
spl0_1475,
inference(avatar_split_clause,[],[f2131,f10511]) ).
fof(f2131,axiom,
! [X11] : c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__pred(X11),c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__pred__0_0) ).
fof(f10509,plain,
spl0_1474,
inference(avatar_split_clause,[],[f2123,f10507]) ).
fof(f10507,plain,
( spl0_1474
<=> ! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1474])]) ).
fof(f2123,axiom,
! [X11] : c_Numeral_Obin__minus(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) = c_Numeral_OBit(c_Numeral_Obin__minus(X11),c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__minus__0_0) ).
fof(f10505,plain,
spl0_1473,
inference(avatar_split_clause,[],[f2118,f10503]) ).
fof(f2118,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_Numeral_Onumber__of(c_Numeral_OMin,X1) = c_uminus(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__arith__extra__simps__3_0) ).
fof(f10501,plain,
spl0_1472,
inference(avatar_split_clause,[],[f2032,f10499]) ).
fof(f10499,plain,
( spl0_1472
<=> ! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1472])]) ).
fof(f2032,axiom,
! [X21,X15] :
( c_0 = X21
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__is__0_1) ).
fof(f10497,plain,
spl0_1471,
inference(avatar_split_clause,[],[f2031,f10495]) ).
fof(f10495,plain,
( spl0_1471
<=> ! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1471])]) ).
fof(f2031,axiom,
! [X21,X15] :
( c_0 = X15
| c_0 != c_plus(X15,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__is__0_0) ).
fof(f10493,plain,
spl0_1470,
inference(avatar_split_clause,[],[f1786,f10491]) ).
fof(f1786,axiom,
! [X59,X43] :
( ~ c_lessequals(X59,X43,tc_nat)
| c_List_Olist_ONil = c_List_Oupt(X43,X59) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oupt__eq__Nil__conv_2) ).
fof(f10489,plain,
spl0_1469,
inference(avatar_split_clause,[],[f1758,f10487]) ).
fof(f10487,plain,
( spl0_1469
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1469])]) ).
fof(f1758,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orotate1(X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__rotate1_0) ).
fof(f10485,plain,
spl0_1468,
inference(avatar_split_clause,[],[f1757,f10483]) ).
fof(f10483,plain,
( spl0_1468
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1468])]) ).
fof(f1757,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Orev(X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__rev_0) ).
fof(f10481,plain,
spl0_1467,
inference(avatar_split_clause,[],[f1754,f10479]) ).
fof(f10479,plain,
( spl0_1467
<=> ! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1467])]) ).
fof(f1754,axiom,
! [X1,X23] : c_List_Oset(X23,X1) = c_List_Oset(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__remdups_0) ).
fof(f10477,plain,
( ~ spl0_1466
| ~ spl0_1236
| ~ spl0_1402 ),
inference(avatar_split_clause,[],[f10269,f10079,f9319,f10474]) ).
fof(f10474,plain,
( spl0_1466
<=> c_emptyset = c_SetInterval_OatMost(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1466])]) ).
fof(f10269,plain,
( c_emptyset != c_SetInterval_OatMost(c_0,tc_nat)
| ~ spl0_1236
| ~ spl0_1402 ),
inference(superposition,[],[f9320,f10081]) ).
fof(f10472,plain,
spl0_1465,
inference(avatar_split_clause,[],[f1740,f10470]) ).
fof(f10470,plain,
( spl0_1465
<=> ! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1465])]) ).
fof(f1740,axiom,
! [X21,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate(X21,X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate__is__Nil__conv_0) ).
fof(f10468,plain,
spl0_1464,
inference(avatar_split_clause,[],[f1720,f10466]) ).
fof(f10466,plain,
( spl0_1464
<=> ! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1464])]) ).
fof(f1720,axiom,
! [X0,X1,X23] : c_List_Oremove1(X0,c_List_Olist_OCons(X0,X23,X1),X1) = X23,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremove1_Osimps__2_0) ).
fof(f10464,plain,
spl0_1463,
inference(avatar_split_clause,[],[f1692,f10462]) ).
fof(f10462,plain,
( spl0_1463
<=> ! [X1,X23,X3] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1463])]) ).
fof(f1692,axiom,
! [X3,X1,X23] : c_List_Onth(c_List_Olist_OCons(X3,X23,X1),c_0,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onth__Cons__0_0) ).
fof(f10460,plain,
spl0_1462,
inference(avatar_split_clause,[],[f1639,f10458]) ).
fof(f10456,plain,
spl0_1461,
inference(avatar_split_clause,[],[f1607,f10454]) ).
fof(f10454,plain,
( spl0_1461
<=> ! [X0,X1,X3] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1461])]) ).
fof(f1607,axiom,
! [X3,X0,X1] : c_Nat_Osize(c_List_Oreplicate(X3,X0,X1),tc_List_Olist(X1)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__replicate_0) ).
fof(f10452,plain,
spl0_1460,
inference(avatar_split_clause,[],[f1597,f10450]) ).
fof(f10450,plain,
( spl0_1460
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1460])]) ).
fof(f1597,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_0 != c_Nat_Osize(X23,tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__0__conv_0) ).
fof(f10448,plain,
spl0_1459,
inference(avatar_split_clause,[],[f1566,f10446]) ).
fof(f10446,plain,
( spl0_1459
<=> ! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Otake(X43,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1459])]) ).
fof(f1566,axiom,
! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Otake(X43,X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__take_0) ).
fof(f10444,plain,
spl0_1458,
inference(avatar_split_clause,[],[f1565,f10442]) ).
fof(f10442,plain,
( spl0_1458
<=> ! [X1,X23,X58] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1458])]) ).
fof(f1565,axiom,
! [X58,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Osublist(X23,X58,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__sublistI_0) ).
fof(f10440,plain,
spl0_1457,
inference(avatar_split_clause,[],[f1564,f10438]) ).
fof(f10438,plain,
( spl0_1457
<=> ! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1457])]) ).
fof(f1564,axiom,
! [X21,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__rotate_1) ).
fof(f10436,plain,
spl0_1456,
inference(avatar_split_clause,[],[f1563,f10434]) ).
fof(f10434,plain,
( spl0_1456
<=> ! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1456])]) ).
fof(f1563,axiom,
! [X21,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate(X21,X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__rotate_0) ).
fof(f10432,plain,
( spl0_1455
| ~ spl0_1125
| ~ spl0_1211
| ~ spl0_1369 ),
inference(avatar_split_clause,[],[f10213,f9946,f9217,f8849,f10429]) ).
fof(f10429,plain,
( spl0_1455
<=> c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__pred(c_Numeral_OMin)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1455])]) ).
fof(f8849,plain,
( spl0_1125
<=> c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1125])]) ).
fof(f9217,plain,
( spl0_1211
<=> c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1211])]) ).
fof(f9946,plain,
( spl0_1369
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1369])]) ).
fof(f10213,plain,
( c_Numeral_OMin = c_Numeral_Obin__succ(c_Numeral_Obin__pred(c_Numeral_OMin))
| ~ spl0_1125
| ~ spl0_1211
| ~ spl0_1369 ),
inference(forward_demodulation,[],[f10211,f8851]) ).
fof(f8851,plain,
( c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1)
| ~ spl0_1125 ),
inference(avatar_component_clause,[],[f8849]) ).
fof(f10211,plain,
( c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_Obin__pred(c_Numeral_OMin))
| ~ spl0_1211
| ~ spl0_1369 ),
inference(superposition,[],[f9947,f9219]) ).
fof(f9219,plain,
( c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0)
| ~ spl0_1211 ),
inference(avatar_component_clause,[],[f9217]) ).
fof(f9947,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0))
| ~ spl0_1369 ),
inference(avatar_component_clause,[],[f9946]) ).
fof(f10427,plain,
spl0_1454,
inference(avatar_split_clause,[],[f1560,f10425]) ).
fof(f10425,plain,
( spl0_1454
<=> ! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1454])]) ).
fof(f1560,axiom,
! [X0,X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Oremove1(X0,X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__remove1_0) ).
fof(f10423,plain,
spl0_1453,
inference(avatar_split_clause,[],[f1559,f10421]) ).
fof(f10421,plain,
( spl0_1453
<=> ! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1453])]) ).
fof(f1559,axiom,
! [X1,X23,X43] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Odrop(X43,X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__drop_0) ).
fof(f10419,plain,
spl0_1452,
inference(avatar_split_clause,[],[f1556,f10417]) ).
fof(f10417,plain,
( spl0_1452
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1452])]) ).
fof(f1556,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X25,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__append_1) ).
fof(f10415,plain,
spl0_1451,
inference(avatar_split_clause,[],[f1555,f10413]) ).
fof(f10413,plain,
( spl0_1451
<=> ! [X25,X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1451])]) ).
fof(f1555,axiom,
! [X1,X25,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_append(X23,X25,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__append_0) ).
fof(f10411,plain,
spl0_1450,
inference(avatar_split_clause,[],[f1553,f10409]) ).
fof(f10409,plain,
( spl0_1450
<=> ! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1450])]) ).
fof(f1553,axiom,
! [X41,X0,X23] :
( c_List_Odistinct(X23,X41)
| ~ c_List_Odistinct(c_List_Olist_OCons(X0,X23,X41),X41) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct_Osimps__2_1) ).
fof(f10407,plain,
spl0_1449,
inference(avatar_split_clause,[],[f1533,f10405]) ).
fof(f10405,plain,
( spl0_1449
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1449])]) ).
fof(f1533,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_append(X23,X25,X1) != X23 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__self__conv_0) ).
fof(f10403,plain,
spl0_1448,
inference(avatar_split_clause,[],[f1531,f10401]) ).
fof(f10401,plain,
( spl0_1448
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1448])]) ).
fof(f1531,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_append(X23,X25,X1) != X25 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oappend__self__conv2_0) ).
fof(f10399,plain,
spl0_1447,
inference(avatar_split_clause,[],[f1511,f10397]) ).
fof(f10397,plain,
( spl0_1447
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1447])]) ).
fof(f1511,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X25
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__is__append__conv_1) ).
fof(f10395,plain,
spl0_1446,
inference(avatar_split_clause,[],[f1510,f10393]) ).
fof(f10393,plain,
( spl0_1446
<=> ! [X25,X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1446])]) ).
fof(f1510,axiom,
! [X1,X25,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_append(X23,X25,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__is__append__conv_0) ).
fof(f10391,plain,
spl0_1445,
inference(avatar_split_clause,[],[f1497,f10389]) ).
fof(f10389,plain,
( spl0_1445
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1445])]) ).
fof(f1497,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X27,X18,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__zmult__self2_0) ).
fof(f10387,plain,
( spl0_1444
| ~ spl0_1126
| ~ spl0_1212
| ~ spl0_1368 ),
inference(avatar_split_clause,[],[f10210,f9942,f9222,f8854,f10384]) ).
fof(f10384,plain,
( spl0_1444
<=> c_Numeral_OPls = c_Numeral_Obin__pred(c_Numeral_Obin__succ(c_Numeral_OPls)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1444])]) ).
fof(f9942,plain,
( spl0_1368
<=> ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1368])]) ).
fof(f10210,plain,
( c_Numeral_OPls = c_Numeral_Obin__pred(c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1126
| ~ spl0_1212
| ~ spl0_1368 ),
inference(forward_demodulation,[],[f10209,f8856]) ).
fof(f10209,plain,
( c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_Obin__succ(c_Numeral_OPls))
| ~ spl0_1212
| ~ spl0_1368 ),
inference(superposition,[],[f9943,f9224]) ).
fof(f9943,plain,
( ! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1))
| ~ spl0_1368 ),
inference(avatar_component_clause,[],[f9942]) ).
fof(f10382,plain,
spl0_1443,
inference(avatar_split_clause,[],[f1496,f10380]) ).
fof(f10380,plain,
( spl0_1443
<=> ! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1443])]) ).
fof(f1496,axiom,
! [X18,X27] : c_0 = c_Divides_Oop_Amod(c_times(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__zmult__self1_0) ).
fof(f10378,plain,
spl0_1442,
inference(avatar_split_clause,[],[f1483,f10376]) ).
fof(f10376,plain,
( spl0_1442
<=> ! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1442])]) ).
fof(f1483,axiom,
! [X21,X0] : c_lessequals(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),X21,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozero__le__zpower__abs_0) ).
fof(f10374,plain,
spl0_1441,
inference(avatar_split_clause,[],[f1471,f10372]) ).
fof(f10372,plain,
( spl0_1441
<=> ! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1441])]) ).
fof(f1471,axiom,
! [X18] :
( c_0 = X18
| c_1 = c_div(X18,X18,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__self_0) ).
fof(f10370,plain,
spl0_1440,
inference(avatar_split_clause,[],[f1441,f10368]) ).
fof(f1441,axiom,
! [X18,X27] : c_0 = c_div(c_Divides_Oop_Amod(X18,X27,tc_IntDef_Oint),X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Omod__div__trivial_0) ).
fof(f10366,plain,
spl0_1439,
inference(avatar_split_clause,[],[f1423,f10364]) ).
fof(f10364,plain,
( spl0_1439
<=> ! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1439])]) ).
fof(f1423,axiom,
! [X48] :
( ~ c_less(c_0,X48,tc_IntDef_Oint)
| c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozero__less__nat__eq_1) ).
fof(f10362,plain,
spl0_1438,
inference(avatar_split_clause,[],[f1422,f10360]) ).
fof(f10360,plain,
( spl0_1438
<=> ! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1438])]) ).
fof(f1422,axiom,
! [X48] :
( c_less(c_0,X48,tc_IntDef_Oint)
| ~ c_less(c_0,c_IntDef_Onat(X48),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozero__less__nat__eq_0) ).
fof(f10358,plain,
spl0_1437,
inference(avatar_split_clause,[],[f1421,f10356]) ).
fof(f10356,plain,
( spl0_1437
<=> ! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1437])]) ).
fof(f1421,axiom,
! [X21] :
( ~ c_less(c_0,X21,tc_nat)
| c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozero__less__int__conv_1) ).
fof(f10354,plain,
spl0_1436,
inference(avatar_split_clause,[],[f1420,f10352]) ).
fof(f10352,plain,
( spl0_1436
<=> ! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1436])]) ).
fof(f1420,axiom,
! [X21] :
( c_less(c_0,X21,tc_nat)
| ~ c_less(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozero__less__int__conv_0) ).
fof(f10350,plain,
spl0_1435,
inference(avatar_split_clause,[],[f1380,f10348]) ).
fof(f10348,plain,
( spl0_1435
<=> ! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1435])]) ).
fof(f1380,axiom,
! [X48] :
( c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_0 = c_IntDef_Oint(c_IntDef_Onat(X48)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__nat__eq_1) ).
fof(f10346,plain,
spl0_1434,
inference(avatar_split_clause,[],[f1379,f10344]) ).
fof(f10344,plain,
( spl0_1434
<=> ! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1434])]) ).
fof(f1379,axiom,
! [X48] :
( ~ c_lessequals(c_0,X48,tc_IntDef_Oint)
| c_IntDef_Oint(c_IntDef_Onat(X48)) = X48 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__nat__eq_0) ).
fof(f10341,plain,
spl0_1433,
inference(avatar_split_clause,[],[f1372,f10339]) ).
fof(f1372,axiom,
! [X15] : c_IntDef_Oint(c_Suc(X15)) = c_plus(c_1,c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__Suc_0) ).
fof(f10337,plain,
spl0_1432,
inference(avatar_split_clause,[],[f1349,f10335]) ).
fof(f10335,plain,
( spl0_1432
<=> ! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1432])]) ).
fof(f1349,axiom,
! [X48] :
( c_0 = X48
| ~ c_less(c_HOL_Oabs(X48,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Ozabs__less__one__iff_0) ).
fof(f10333,plain,
spl0_1431,
inference(avatar_split_clause,[],[f1244,f10331]) ).
fof(f10331,plain,
( spl0_1431
<=> ! [X5,X12,X1] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1431])]) ).
fof(f1244,axiom,
! [X1,X5,X12] :
( c_emptyset = X12
| c_emptyset != c_Equiv__Relations_Oquotient(X12,X5,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Equiv__Relations_Oquotient__is__empty2_0) ).
fof(f10329,plain,
spl0_1430,
inference(avatar_split_clause,[],[f1242,f10327]) ).
fof(f10327,plain,
( spl0_1430
<=> ! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1430])]) ).
fof(f1242,axiom,
! [X21,X15] : c_0 = c_div(c_Divides_Oop_Amod(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Onat__mod__div__trivial_0) ).
fof(f10325,plain,
spl0_1429,
inference(avatar_split_clause,[],[f1240,f10323]) ).
fof(f10323,plain,
( spl0_1429
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1429])]) ).
fof(f1240,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X15,X21,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__mult__self__is__0_0) ).
fof(f10321,plain,
spl0_1428,
inference(avatar_split_clause,[],[f1238,f10319]) ).
fof(f10319,plain,
( spl0_1428
<=> ! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1428])]) ).
fof(f1238,axiom,
! [X21,X15] : c_0 = c_Divides_Oop_Amod(c_times(X21,X15,tc_nat),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__mult__self1__is__0_0) ).
fof(f10317,plain,
spl0_1427,
inference(avatar_split_clause,[],[f1195,f10315]) ).
fof(f10315,plain,
( spl0_1427
<=> ! [X2,X16,X1,X18] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1427])]) ).
fof(f1195,axiom,
! [X2,X18,X1,X16] : c_Datatype__Universe_OLeaf(X18,X1,X2) != c_Datatype__Universe_ONumb(X16,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_ONumb__not__Leaf_0) ).
fof(f10313,plain,
spl0_1426,
inference(avatar_split_clause,[],[f1190,f10311]) ).
fof(f10311,plain,
( spl0_1426
<=> ! [X2,X1,X7,X9] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1426])]) ).
fof(f1190,axiom,
! [X2,X1,X9,X7] : c_Datatype__Universe_OIn0(X9,X1,X2) != c_Datatype__Universe_OIn1(X7,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_OIn0__not__In1_0) ).
fof(f10309,plain,
spl0_1425,
inference(avatar_split_clause,[],[f63,f10307]) ).
fof(f10307,plain,
( spl0_1425
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1425])]) ).
fof(f63,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Owf__lex_0) ).
fof(f10305,plain,
spl0_1424,
inference(avatar_split_clause,[],[f62,f10303]) ).
fof(f10303,plain,
( spl0_1424
<=> ! [X5,X1] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1424])]) ).
fof(f62,axiom,
! [X1,X5] :
( ~ c_Wellfounded__Recursion_Owf(X5,X1)
| c_Wellfounded__Recursion_Owf(c_List_Olenlex(X5,X1),tc_List_Olist(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Owf__lenlex_0) ).
fof(f10300,plain,
spl0_1423,
inference(avatar_split_clause,[],[f38,f10298]) ).
fof(f38,axiom,
! [X21,X15] : c_less(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onegative__zless_0) ).
fof(f10296,plain,
spl0_1422,
inference(avatar_split_clause,[],[f35,f10294]) ).
fof(f10294,plain,
( spl0_1422
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1422])]) ).
fof(f35,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__dvd2_0) ).
fof(f10292,plain,
spl0_1421,
inference(avatar_split_clause,[],[f34,f10290]) ).
fof(f10290,plain,
( spl0_1421
<=> ! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1421])]) ).
fof(f34,axiom,
! [X21,X15] : c_Divides_Oop_Advd(c_GCD_Ogcd(c_Pair(X15,X21,tc_nat,tc_nat)),X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__dvd1_0) ).
fof(f10163,plain,
( spl0_1420
| ~ spl0_45
| ~ spl0_1301 ),
inference(avatar_split_clause,[],[f9725,f9595,f3233,f10160]) ).
fof(f10160,plain,
( spl0_1420
<=> c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1420])]) ).
fof(f3233,plain,
( spl0_45
<=> class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
fof(f9595,plain,
( spl0_1301
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1301])]) ).
fof(f9725,plain,
( c_0 = c_OrderedGroup_Opprt(c_0,tc_IntDef_Oint)
| ~ spl0_45
| ~ spl0_1301 ),
inference(resolution,[],[f9596,f3235]) ).
fof(f3235,plain,
( class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint)
| ~ spl0_45 ),
inference(avatar_component_clause,[],[f3233]) ).
fof(f9596,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) )
| ~ spl0_1301 ),
inference(avatar_component_clause,[],[f9595]) ).
fof(f10157,plain,
( spl0_1419
| ~ spl0_45
| ~ spl0_1300 ),
inference(avatar_split_clause,[],[f9724,f9591,f3233,f10154]) ).
fof(f10154,plain,
( spl0_1419
<=> c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1419])]) ).
fof(f9591,plain,
( spl0_1300
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1300])]) ).
fof(f9724,plain,
( c_0 = c_OrderedGroup_Onprt(c_0,tc_IntDef_Oint)
| ~ spl0_45
| ~ spl0_1300 ),
inference(resolution,[],[f9592,f3235]) ).
fof(f9592,plain,
( ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) )
| ~ spl0_1300 ),
inference(avatar_component_clause,[],[f9591]) ).
fof(f10147,plain,
spl0_1418,
inference(avatar_split_clause,[],[f2883,f10145]) ).
fof(f2883,plain,
! [X1] :
( c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),X1)
| ~ class_Numeral_Onumber__ring(X1) ),
inference(forward_demodulation,[],[f2170,f2156]) ).
fof(f2170,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Onumeral__1__eq__1_0) ).
fof(f10143,plain,
spl0_1417,
inference(avatar_split_clause,[],[f2846,f10141]) ).
fof(f10141,plain,
( spl0_1417
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1417])]) ).
fof(f2846,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_1,X15,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f1300,f2016]) ).
fof(f1300,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(c_Suc(c_0),X15,tc_nat,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__1__left_0) ).
fof(f10139,plain,
spl0_1416,
inference(avatar_split_clause,[],[f2845,f10137]) ).
fof(f10137,plain,
( spl0_1416
<=> ! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1416])]) ).
fof(f2845,plain,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_1,tc_nat,tc_nat)),
inference(forward_demodulation,[],[f1299,f2016]) ).
fof(f1299,axiom,
! [X15] : c_1 = c_GCD_Ogcd(c_Pair(X15,c_Suc(c_0),tc_nat,tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__1_0) ).
fof(f10135,plain,
spl0_1415,
inference(avatar_split_clause,[],[f2755,f10133]) ).
fof(f10133,plain,
( spl0_1415
<=> ! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1415])]) ).
fof(f2755,axiom,
! [X96,X97] :
( X96 = X97
| c_Message_Omsg_OHash(X96) != c_Message_Omsg_OHash(X97) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__5_0) ).
fof(f10131,plain,
spl0_1414,
inference(avatar_split_clause,[],[f2754,f10129]) ).
fof(f10129,plain,
( spl0_1414
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1414])]) ).
fof(f2754,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_OKey(X90) != c_Message_Omsg_OKey(X89) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__4_0) ).
fof(f10127,plain,
spl0_1413,
inference(avatar_split_clause,[],[f2753,f10125]) ).
fof(f10125,plain,
( spl0_1413
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1413])]) ).
fof(f2753,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONonce(X90) != c_Message_Omsg_ONonce(X89) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__3_0) ).
fof(f10123,plain,
( spl0_1412
| ~ spl0_59
| ~ spl0_1297 ),
inference(avatar_split_clause,[],[f9721,f9579,f3303,f10120]) ).
fof(f9579,plain,
( spl0_1297
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1297])]) ).
fof(f9721,plain,
( c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_IntDef_Oint)
| ~ spl0_59
| ~ spl0_1297 ),
inference(resolution,[],[f9580,f3305]) ).
fof(f9580,plain,
( ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) )
| ~ spl0_1297 ),
inference(avatar_component_clause,[],[f9579]) ).
fof(f10118,plain,
spl0_1411,
inference(avatar_split_clause,[],[f2752,f10116]) ).
fof(f10116,plain,
( spl0_1411
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1411])]) ).
fof(f2752,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Omsg_ONumber(X90) != c_Message_Omsg_ONumber(X89) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__2_0) ).
fof(f10114,plain,
spl0_1410,
inference(avatar_split_clause,[],[f2751,f10112]) ).
fof(f10112,plain,
( spl0_1410
<=> ! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1410])]) ).
fof(f2751,axiom,
! [X94,X95] :
( X94 = X95
| c_Message_Omsg_OAgent(X94) != c_Message_Omsg_OAgent(X95) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Oinject__1_0) ).
fof(f10110,plain,
spl0_1409,
inference(avatar_split_clause,[],[f2741,f10108]) ).
fof(f10108,plain,
( spl0_1409
<=> ! [X92,X91] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1409])]) ).
fof(f2741,axiom,
! [X91,X92] :
( X91 = X92
| c_Message_OinvKey(X91) != c_Message_OinvKey(X92) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OinvKey__eq_0) ).
fof(f10106,plain,
spl0_1408,
inference(avatar_split_clause,[],[f2736,f10104]) ).
fof(f10104,plain,
( spl0_1408
<=> ! [X89,X90] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1408])]) ).
fof(f2736,axiom,
! [X90,X89] :
( X89 = X90
| c_Message_Oagent_OFriend(X89) != c_Message_Oagent_OFriend(X90) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Oinject_0) ).
fof(f10102,plain,
spl0_1407,
inference(avatar_split_clause,[],[f2707,f10100]) ).
fof(f10100,plain,
( spl0_1407
<=> ! [X85,X1] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1407])]) ).
fof(f2707,axiom,
! [X1,X85] : c_UNIV = c_Relation_ORange(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_ORange__rtrancl_0) ).
fof(f10098,plain,
spl0_1406,
inference(avatar_split_clause,[],[f2706,f10096]) ).
fof(f10096,plain,
( spl0_1406
<=> ! [X85,X1] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1406])]) ).
fof(f2706,axiom,
! [X1,X85] : c_UNIV = c_Relation_ODomain(c_Transitive__Closure_Ortrancl(X85,X1),X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_ODomain__rtrancl_0) ).
fof(f10094,plain,
spl0_1405,
inference(avatar_split_clause,[],[f2699,f10092]) ).
fof(f10092,plain,
( spl0_1405
<=> ! [X12,X1] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1405])]) ).
fof(f2699,axiom,
! [X1,X12] :
( c_emptyset = X12
| ~ c_lessequals(X12,c_emptyset,tc_set(X1)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osubset__empty_0) ).
fof(f10090,plain,
spl0_1404,
inference(avatar_split_clause,[],[f2660,f10088]) ).
fof(f2660,axiom,
! [X3,X1] : c_Set_Ocontents(c_insert(X3,c_emptyset,X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Ocontents__eq_0) ).
fof(f10086,plain,
spl0_1403,
inference(avatar_split_clause,[],[f2544,f10084]) ).
fof(f10084,plain,
( spl0_1403
<=> ! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1403])]) ).
fof(f2544,axiom,
! [X14] : c_Suc(X14) = c_Finite__Set_Ocard(c_SetInterval_OatMost(X14,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__atMost_0) ).
fof(f10082,plain,
spl0_1402,
inference(avatar_split_clause,[],[f2534,f10079]) ).
fof(f2534,axiom,
c_SetInterval_OatMost(c_0,tc_nat) = c_insert(c_0,c_emptyset,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatMost__0_0) ).
fof(f10077,plain,
spl0_1401,
inference(avatar_split_clause,[],[f2492,f10075]) ).
fof(f10075,plain,
( spl0_1401
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1401])]) ).
fof(f2492,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(X18,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__zero__right_0) ).
fof(f10073,plain,
spl0_1400,
inference(avatar_split_clause,[],[f2491,f10071]) ).
fof(f10071,plain,
( spl0_1400
<=> ! [X18,X1] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1400])]) ).
fof(f2491,axiom,
! [X1,X18] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X1)
| c_0 = c_times(c_0,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__zero__left_0) ).
fof(f10069,plain,
spl0_1399,
inference(avatar_split_clause,[],[f2474,f10067]) ).
fof(f10067,plain,
( spl0_1399
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1399])]) ).
fof(f2474,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(c_1,X4,X1) = X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__cancel__right1_2) ).
fof(f10065,plain,
spl0_1398,
inference(avatar_split_clause,[],[f2473,f10063]) ).
fof(f10063,plain,
( spl0_1398
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1398])]) ).
fof(f2473,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(X27,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__cancel__right1_1) ).
fof(f10061,plain,
spl0_1397,
inference(avatar_split_clause,[],[f2470,f10059]) ).
fof(f10059,plain,
( spl0_1397
<=> ! [X4,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1397])]) ).
fof(f2470,axiom,
! [X1,X4] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_times(X4,c_1,X1) = X4 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__cancel__left1_2) ).
fof(f10057,plain,
spl0_1396,
inference(avatar_split_clause,[],[f2469,f10055]) ).
fof(f10055,plain,
( spl0_1396
<=> ! [X27,X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1396])]) ).
fof(f2469,axiom,
! [X1,X27] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_times(c_0,X27,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Omult__cancel__left1_1) ).
fof(f10053,plain,
spl0_1395,
inference(avatar_split_clause,[],[f2396,f10051]) ).
fof(f10051,plain,
( spl0_1395
<=> ! [X1,X3] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X3,c_1,X1) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1395])]) ).
fof(f2396,axiom,
! [X3,X1] :
( ~ class_Ring__and__Field_Ofield(X1)
| c_divide(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Odivide__1_0) ).
fof(f10049,plain,
spl0_1394,
inference(avatar_split_clause,[],[f2379,f10047]) ).
fof(f10047,plain,
( spl0_1394
<=> ! [X1,X3] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1394])]) ).
fof(f2379,axiom,
! [X3,X1] : c_Relation_ORange(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ORange__diag_0) ).
fof(f10045,plain,
spl0_1393,
inference(avatar_split_clause,[],[f2377,f10043]) ).
fof(f10043,plain,
( spl0_1393
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1393])]) ).
fof(f2377,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(X3,c_Relation_OId,X1,X2,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OR__O__Id_0) ).
fof(f10041,plain,
spl0_1392,
inference(avatar_split_clause,[],[f2371,f10039]) ).
fof(f10039,plain,
( spl0_1392
<=> ! [X2,X1,X3] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1392])]) ).
fof(f2371,axiom,
! [X2,X3,X1] : c_Relation_Orel__comp(c_Relation_OId,X3,X2,X2,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OId__O__R_0) ).
fof(f10037,plain,
spl0_1391,
inference(avatar_split_clause,[],[f2369,f10035]) ).
fof(f10035,plain,
( spl0_1391
<=> ! [X1,X3] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1391])]) ).
fof(f2369,axiom,
! [X3,X1] : c_Relation_ODomain(c_Relation_Odiag(X3,X1),X1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ODomain__diag_0) ).
fof(f10033,plain,
spl0_1390,
inference(avatar_split_clause,[],[f2357,f10031]) ).
fof(f10031,plain,
( spl0_1390
<=> ! [X18,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1390])]) ).
fof(f2357,axiom,
! [X1,X18] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(X18,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Orecpower__class_Oaxioms__1_0) ).
fof(f10029,plain,
spl0_1389,
inference(avatar_split_clause,[],[f2354,f10027]) ).
fof(f2354,axiom,
! [X3,X1] :
( ~ class_Power_Orecpower(X1)
| c_Nat_Opower(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__one__right_0) ).
fof(f10025,plain,
spl0_1388,
inference(avatar_split_clause,[],[f2353,f10023]) ).
fof(f2353,axiom,
! [X21,X1] :
( ~ class_Power_Orecpower(X1)
| c_1 = c_Nat_Opower(c_1,X21,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower__one_0) ).
fof(f10021,plain,
spl0_1387,
inference(avatar_split_clause,[],[f2292,f10019]) ).
fof(f10019,plain,
( spl0_1387
<=> ! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1387])]) ).
fof(f2292,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_IntDef_Oint)
| c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__neg_1) ).
fof(f10017,plain,
spl0_1386,
inference(avatar_split_clause,[],[f2291,f10015]) ).
fof(f10015,plain,
( spl0_1386
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1386])]) ).
fof(f2291,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_IntDef_Oint)
| ~ c_Parity_Oeven(c_uminus(X0,tc_IntDef_Oint),tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__neg_0) ).
fof(f10013,plain,
spl0_1385,
inference(avatar_split_clause,[],[f2267,f10011]) ).
fof(f2267,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omax(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__sup_Osup__idem_0) ).
fof(f10009,plain,
spl0_1384,
inference(avatar_split_clause,[],[f2262,f10007]) ).
fof(f2262,axiom,
! [X2,X3] :
( ~ class_Orderings_Olinorder(X2)
| c_Orderings_Omin(X3,X3,X2) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Omin__max_Obelow__inf_Oinf__idem_0) ).
fof(f10005,plain,
spl0_1383,
inference(avatar_split_clause,[],[f2251,f10003]) ).
fof(f10003,plain,
( spl0_1383
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1383])]) ).
fof(f2251,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_0,c_HOL_Oabs(c_0,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ozero__less__abs__iff_0) ).
fof(f10001,plain,
spl0_1382,
inference(avatar_split_clause,[],[f2250,f9999]) ).
fof(f9999,plain,
( spl0_1382
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1382])]) ).
fof(f2250,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_0,c_OrderedGroup_Opprt(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ozero__le__pprt_0) ).
fof(f9997,plain,
spl0_1381,
inference(avatar_split_clause,[],[f2241,f9995]) ).
fof(f2241,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_lessequals(c_OrderedGroup_Onprt(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Onprt__le__zero_0) ).
fof(f9993,plain,
spl0_1380,
inference(avatar_split_clause,[],[f2218,f9991]) ).
fof(f2218,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(X3,c_1,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__2_0) ).
fof(f9989,plain,
spl0_1379,
inference(avatar_split_clause,[],[f2217,f9987]) ).
fof(f2217,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Omonoid__mult(X1)
| c_times(c_1,X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Omonoid__mult__class_Oaxioms__1_0) ).
fof(f9985,plain,
spl0_1378,
inference(avatar_split_clause,[],[f2205,f9983]) ).
fof(f2205,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_minus(X18,X18,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__self_0) ).
fof(f9981,plain,
spl0_1377,
inference(avatar_split_clause,[],[f2198,f9979]) ).
fof(f2198,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_minus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Odiff__0__right_0) ).
fof(f9977,plain,
spl0_1376,
inference(avatar_split_clause,[],[f2196,f9975]) ).
fof(f2196,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(c_0,X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Ocomm__monoid__add__class_Oaxioms_0) ).
fof(f9973,plain,
spl0_1375,
inference(avatar_split_clause,[],[f2185,f9971]) ).
fof(f2185,axiom,
! [X3,X1] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X1)
| c_plus(X3,c_0,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oadd__0__right_0) ).
fof(f9969,plain,
spl0_1374,
inference(avatar_split_clause,[],[f2182,f9967]) ).
fof(f9967,plain,
( spl0_1374
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1374])]) ).
fof(f2182,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| ~ c_less(c_HOL_Oabs(X18,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__not__less__zero_0) ).
fof(f9965,plain,
spl0_1373,
inference(avatar_split_clause,[],[f2180,f9963]) ).
fof(f9963,plain,
( spl0_1373
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1373])]) ).
fof(f2180,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_HOL_Oabs(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__le__zero__iff_1) ).
fof(f9961,plain,
spl0_1372,
inference(avatar_split_clause,[],[f2177,f9959]) ).
fof(f9959,plain,
( spl0_1372
<=> ! [X18,X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1372])]) ).
fof(f2177,axiom,
! [X1,X18] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_lessequals(c_0,c_HOL_Oabs(X18,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__ge__zero_0) ).
fof(f9957,plain,
( ~ spl0_1370
| spl0_1371
| ~ spl0_1124
| ~ spl0_1291 ),
inference(avatar_split_clause,[],[f9715,f9555,f8844,f9954,f9950]) ).
fof(f9950,plain,
( spl0_1370
<=> class_Numeral_Onumber__ring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1370])]) ).
fof(f9954,plain,
( spl0_1371
<=> c_IntDef_Oiszero(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1371])]) ).
fof(f9715,plain,
( c_IntDef_Oiszero(c_0,tc_nat)
| ~ class_Numeral_Onumber__ring(tc_nat)
| ~ spl0_1124
| ~ spl0_1291 ),
inference(superposition,[],[f9556,f8846]) ).
fof(f9948,plain,
spl0_1369,
inference(avatar_split_clause,[],[f2153,f9946]) ).
fof(f2153,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB1) = c_Numeral_Obin__succ(c_Numeral_OBit(X11,c_Numeral_Obit_OB0)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__succ__0_0) ).
fof(f9944,plain,
spl0_1368,
inference(avatar_split_clause,[],[f2132,f9942]) ).
fof(f2132,axiom,
! [X11] : c_Numeral_OBit(X11,c_Numeral_Obit_OB0) = c_Numeral_Obin__pred(c_Numeral_OBit(X11,c_Numeral_Obit_OB1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__pred__1_0) ).
fof(f9940,plain,
spl0_1367,
inference(avatar_split_clause,[],[f2017,f9938]) ).
fof(f2017,axiom,
! [X21,X15] :
( X15 = X21
| c_Suc(X21) != c_Suc(X15) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__Suc__eq_0) ).
fof(f9936,plain,
spl0_1366,
inference(avatar_split_clause,[],[f1865,f9934]) ).
fof(f9934,plain,
( spl0_1366
<=> ! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1366])]) ).
fof(f1865,axiom,
! [X11] : c_IntDef_Onat(c_Numeral_Onumber__of(X11,tc_IntDef_Oint)) = c_Numeral_Onumber__of(X11,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Onat__number__of_0) ).
fof(f9932,plain,
spl0_1365,
inference(avatar_split_clause,[],[f1818,f9930]) ).
fof(f9930,plain,
( spl0_1365
<=> ! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1365])]) ).
fof(f1818,axiom,
! [X1,X15] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_NatArith_Oof__nat(X15,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__less__0__iff_0) ).
fof(f9928,plain,
spl0_1364,
inference(avatar_split_clause,[],[f1815,f9926]) ).
fof(f9926,plain,
( spl0_1364
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1364])]) ).
fof(f1815,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_NatArith_Oof__nat(c_0,X1),c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__le__0__iff_1) ).
fof(f9924,plain,
spl0_1363,
inference(avatar_split_clause,[],[f1805,f9922]) ).
fof(f9922,plain,
( spl0_1363
<=> ! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1363])]) ).
fof(f1805,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_NatArith_Oof__nat(X21,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__0__le__iff_0) ).
fof(f9920,plain,
spl0_1362,
inference(avatar_split_clause,[],[f1779,f9918]) ).
fof(f9918,plain,
( spl0_1362
<=> ! [X41,X0,X3] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1362])]) ).
fof(f1779,axiom,
! [X3,X41,X0] : c_List_Otl(c_List_Olist_OCons(X0,X3,X41),X41) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otl_Osimps__2_0) ).
fof(f9916,plain,
spl0_1361,
inference(avatar_split_clause,[],[f1752,f9914]) ).
fof(f9914,plain,
( spl0_1361
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1361])]) ).
fof(f1752,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_emptyset != c_List_Oset(X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__empty_0) ).
fof(f9912,plain,
spl0_1360,
inference(avatar_split_clause,[],[f1735,f9910]) ).
fof(f9910,plain,
( spl0_1360
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1360])]) ).
fof(f1735,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orotate1(X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate1__is__Nil__conv_0) ).
fof(f9908,plain,
( spl0_1359
| ~ spl0_24
| ~ spl0_1284 ),
inference(avatar_split_clause,[],[f9695,f9527,f3128,f9905]) ).
fof(f9905,plain,
( spl0_1359
<=> c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1359])]) ).
fof(f3128,plain,
( spl0_24
<=> class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f9527,plain,
( spl0_1284
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1284])]) ).
fof(f9695,plain,
( c_1 = c_NatArith_Oof__nat(c_1,tc_IntDef_Oint)
| ~ spl0_24
| ~ spl0_1284 ),
inference(resolution,[],[f9528,f3130]) ).
fof(f3130,plain,
( class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint)
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f3128]) ).
fof(f9528,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) )
| ~ spl0_1284 ),
inference(avatar_component_clause,[],[f9527]) ).
fof(f9903,plain,
spl0_1358,
inference(avatar_split_clause,[],[f1728,f9901]) ).
fof(f9901,plain,
( spl0_1358
<=> ! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1358])]) ).
fof(f1728,axiom,
! [X1,X23] :
( c_List_Olist_ONil = X23
| c_List_Olist_ONil != c_List_Orev(X23,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__is__Nil__conv_0) ).
fof(f9899,plain,
spl0_1357,
inference(avatar_split_clause,[],[f1715,f9897]) ).
fof(f9897,plain,
( spl0_1357
<=> ! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1357])]) ).
fof(f1715,axiom,
! [X0,X1] :
( c_List_Olist_ONil = X0
| c_List_Olist_ONil != c_List_Oremdups(X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremdups__eq__nil__iff_0) ).
fof(f9895,plain,
spl0_1356,
inference(avatar_split_clause,[],[f1588,f9893]) ).
fof(f9893,plain,
( spl0_1356
<=> ! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1356])]) ).
fof(f1588,axiom,
! [X0,X1] : c_List_Olast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X1),X1) = X0,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olast_Osimps_0) ).
fof(f9891,plain,
spl0_1355,
inference(avatar_split_clause,[],[f1579,f9889]) ).
fof(f9889,plain,
( spl0_1355
<=> ! [X1,X23,X3] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1355])]) ).
fof(f1579,axiom,
! [X3,X1,X23] : c_List_Ohd(c_List_Olist_OCons(X3,X23,X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ohd_Osimps_0) ).
fof(f9887,plain,
spl0_1354,
inference(avatar_split_clause,[],[f1562,f9885]) ).
fof(f9885,plain,
( spl0_1354
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1354])]) ).
fof(f1562,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__rev_1) ).
fof(f9883,plain,
spl0_1353,
inference(avatar_split_clause,[],[f1561,f9881]) ).
fof(f9881,plain,
( spl0_1353
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1353])]) ).
fof(f1561,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orev(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__rev_0) ).
fof(f9879,plain,
spl0_1352,
inference(avatar_split_clause,[],[f1550,f9877]) ).
fof(f9877,plain,
( spl0_1352
<=> ! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1352])]) ).
fof(f1550,axiom,
! [X1,X23] :
( ~ c_List_Odistinct(X23,X1)
| c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct1__rotate_1) ).
fof(f9875,plain,
spl0_1351,
inference(avatar_split_clause,[],[f1549,f9873]) ).
fof(f9873,plain,
( spl0_1351
<=> ! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1351])]) ).
fof(f1549,axiom,
! [X1,X23] :
( c_List_Odistinct(X23,X1)
| ~ c_List_Odistinct(c_List_Orotate1(X23,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct1__rotate_0) ).
fof(f9871,plain,
spl0_1350,
inference(avatar_split_clause,[],[f1537,f9869]) ).
fof(f9869,plain,
( spl0_1350
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1350])]) ).
fof(f1537,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_OCons(X0,c_List_Olist_ONil,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Obutlast_Osimps__2_0) ).
fof(f9867,plain,
spl0_1349,
inference(avatar_split_clause,[],[f1499,f9865]) ).
fof(f1499,axiom,
! [X3,X1] :
( ~ class_LOrder_Omeet__semilorder(X1)
| c_LOrder_Omeet(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_LOrder_Omeet__idempotent_0) ).
fof(f9863,plain,
( spl0_1348
| ~ spl0_54
| ~ spl0_1283 ),
inference(avatar_split_clause,[],[f9693,f9523,f3278,f9860]) ).
fof(f9860,plain,
( spl0_1348
<=> c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1348])]) ).
fof(f3278,plain,
( spl0_54
<=> class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_54])]) ).
fof(f9523,plain,
( spl0_1283
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1283])]) ).
fof(f9693,plain,
( c_0 = c_NatArith_Oof__nat(c_0,tc_IntDef_Oint)
| ~ spl0_54
| ~ spl0_1283 ),
inference(resolution,[],[f9524,f3280]) ).
fof(f3280,plain,
( class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint)
| ~ spl0_54 ),
inference(avatar_component_clause,[],[f3278]) ).
fof(f9524,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) )
| ~ spl0_1283 ),
inference(avatar_component_clause,[],[f9523]) ).
fof(f9858,plain,
spl0_1347,
inference(avatar_split_clause,[],[f1498,f9856]) ).
fof(f1498,axiom,
! [X3,X1] :
( ~ class_LOrder_Ojoin__semilorder(X1)
| c_LOrder_Ojoin(X3,X3,X1) = X3 ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_LOrder_Ojoin__idempotent_0) ).
fof(f9854,plain,
spl0_1346,
inference(avatar_split_clause,[],[f1490,f9852]) ).
fof(f9852,plain,
( spl0_1346
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1346])]) ).
fof(f1490,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_Numeral_Onumber__of(c_Numeral_OMin,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__minus1__right_0) ).
fof(f9850,plain,
spl0_1345,
inference(avatar_split_clause,[],[f1419,f9848]) ).
fof(f1419,axiom,
! [X21,X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_NatArith_Oof__nat(X21,X1),c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__nat__in__Nats_0) ).
fof(f9846,plain,
spl0_1344,
inference(avatar_split_clause,[],[f1394,f9844]) ).
fof(f1394,axiom,
! [X21] : ~ c_lessequals(c_0,c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onot__zle__0__negative_0) ).
fof(f9842,plain,
spl0_1343,
inference(avatar_split_clause,[],[f1392,f9840]) ).
fof(f1392,axiom,
! [X21,X15] : ~ c_less(c_IntDef_Oint(X21),c_uminus(c_IntDef_Oint(X15),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onot__int__zless__negative_0) ).
fof(f9838,plain,
spl0_1342,
inference(avatar_split_clause,[],[f1385,f9836]) ).
fof(f9836,plain,
( spl0_1342
<=> ! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1342])]) ).
fof(f1385,axiom,
! [X48] :
( ~ c_lessequals(X48,c_0,tc_IntDef_Oint)
| c_0 = c_IntDef_Onat(X48) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onat__le__0_0) ).
fof(f9834,plain,
spl0_1341,
inference(avatar_split_clause,[],[f1376,f9832]) ).
fof(f1376,axiom,
! [X21] :
( c_0 = X21
| ~ c_lessequals(c_IntDef_Oint(X21),c_0,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__le__0__conv_0) ).
fof(f9830,plain,
spl0_1340,
inference(avatar_split_clause,[],[f1375,f9828]) ).
fof(f1375,axiom,
! [X21,X15] :
( X15 = X21
| c_IntDef_Oint(X21) != c_IntDef_Oint(X15) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__int__eq_0) ).
fof(f9826,plain,
spl0_1339,
inference(avatar_split_clause,[],[f1308,f9824]) ).
fof(f9824,plain,
( spl0_1339
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1339])]) ).
fof(f1308,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__self_0) ).
fof(f9822,plain,
spl0_1338,
inference(avatar_split_clause,[],[f1298,f9820]) ).
fof(f9820,plain,
( spl0_1338
<=> ! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1338])]) ).
fof(f1298,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(c_0,X3,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__0__left_0) ).
fof(f9818,plain,
( spl0_1337
| ~ spl0_26
| ~ spl0_1275 ),
inference(avatar_split_clause,[],[f9687,f9491,f3138,f9815]) ).
fof(f9815,plain,
( spl0_1337
<=> c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1337])]) ).
fof(f3138,plain,
( spl0_26
<=> class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f9491,plain,
( spl0_1275
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1275])]) ).
fof(f9687,plain,
( c_1 = c_IntDef_Oof__int(c_1,tc_IntDef_Oint)
| ~ spl0_26
| ~ spl0_1275 ),
inference(resolution,[],[f9492,f3140]) ).
fof(f3140,plain,
( class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint)
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f3138]) ).
fof(f9492,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) )
| ~ spl0_1275 ),
inference(avatar_component_clause,[],[f9491]) ).
fof(f9813,plain,
spl0_1336,
inference(avatar_split_clause,[],[f1297,f9811]) ).
fof(f9811,plain,
( spl0_1336
<=> ! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1336])]) ).
fof(f1297,axiom,
! [X3] : c_GCD_Ogcd(c_Pair(X3,c_0,tc_nat,tc_nat)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_GCD_Ogcd__0_0) ).
fof(f9809,plain,
spl0_1335,
inference(avatar_split_clause,[],[f1177,f9807]) ).
fof(f9807,plain,
( spl0_1335
<=> ! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1335])]) ).
fof(f1177,axiom,
! [X18,X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_OSome(X18,X1),tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ooption_Osize__2_0) ).
fof(f9805,plain,
spl0_1334,
inference(avatar_split_clause,[],[f1171,f9803]) ).
fof(f9803,plain,
( spl0_1334
<=> ! [X1,X40] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1334])]) ).
fof(f1171,axiom,
! [X40,X1] :
( c_Datatype_Ooption_ONone = X40
| c_emptyset != c_Datatype_Oo2s(X40,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Oo2s__empty__eq_0) ).
fof(f9800,plain,
spl0_1333,
inference(avatar_split_clause,[],[f1167,f9798]) ).
fof(f9798,plain,
( spl0_1333
<=> ! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1333])]) ).
fof(f1167,axiom,
! [X0,X1] : c_in(X0,c_Datatype_Oo2s(c_Datatype_Ooption_OSome(X0,X1),X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Oelem__o2s_1) ).
fof(f9796,plain,
spl0_1332,
inference(avatar_split_clause,[],[f252,f9794]) ).
fof(f9794,plain,
( spl0_1332
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1332])]) ).
fof(f252,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_sum(X38,X37)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_sum_0) ).
fof(f9792,plain,
spl0_1331,
inference(avatar_split_clause,[],[f246,f9790]) ).
fof(f9790,plain,
( spl0_1331
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1331])]) ).
fof(f246,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_prod(X38,X37)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_prod_0) ).
fof(f9788,plain,
spl0_1330,
inference(avatar_split_clause,[],[f196,f9786]) ).
fof(f9786,plain,
( spl0_1330
<=> ! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1330])]) ).
fof(f196,axiom,
! [X38,X37] :
( ~ class_Finite__Set_Ofinite(X38)
| ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_fun(X38,X37)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_fun_0) ).
fof(f9784,plain,
spl0_1329,
inference(avatar_split_clause,[],[f94,f9782]) ).
fof(f9782,plain,
( spl0_1329
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1329])]) ).
fof(f94,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__greaterThanLessThan__int_0) ).
fof(f9780,plain,
spl0_1328,
inference(avatar_split_clause,[],[f93,f9778]) ).
fof(f9778,plain,
( spl0_1328
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1328])]) ).
fof(f93,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__greaterThanLessThan_0) ).
fof(f9776,plain,
spl0_1327,
inference(avatar_split_clause,[],[f92,f9774]) ).
fof(f9774,plain,
( spl0_1327
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1327])]) ).
fof(f92,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__greaterThanAtMost__int_0) ).
fof(f9772,plain,
( spl0_1326
| ~ spl0_56
| ~ spl0_1274 ),
inference(avatar_split_clause,[],[f9686,f9487,f3288,f9769]) ).
fof(f9769,plain,
( spl0_1326
<=> c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1326])]) ).
fof(f3288,plain,
( spl0_56
<=> class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_56])]) ).
fof(f9487,plain,
( spl0_1274
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1274])]) ).
fof(f9686,plain,
( c_0 = c_IntDef_Oof__int(c_0,tc_IntDef_Oint)
| ~ spl0_56
| ~ spl0_1274 ),
inference(resolution,[],[f9488,f3290]) ).
fof(f3290,plain,
( class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint)
| ~ spl0_56 ),
inference(avatar_component_clause,[],[f3288]) ).
fof(f9488,plain,
( ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) )
| ~ spl0_1274 ),
inference(avatar_component_clause,[],[f9487]) ).
fof(f9767,plain,
spl0_1325,
inference(avatar_split_clause,[],[f91,f9765]) ).
fof(f9765,plain,
( spl0_1325
<=> ! [X14,X26] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1325])]) ).
fof(f91,axiom,
! [X26,X14] : c_in(c_SetInterval_OgreaterThanAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__greaterThanAtMost_0) ).
fof(f9763,plain,
spl0_1324,
inference(avatar_split_clause,[],[f89,f9761]) ).
fof(f9761,plain,
( spl0_1324
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1324])]) ).
fof(f89,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__atLeastLessThan__int_0) ).
fof(f9759,plain,
spl0_1323,
inference(avatar_split_clause,[],[f88,f9757]) ).
fof(f9757,plain,
( spl0_1323
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1323])]) ).
fof(f88,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastLessThan(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__atLeastLessThan_0) ).
fof(f9755,plain,
spl0_1322,
inference(avatar_split_clause,[],[f87,f9753]) ).
fof(f9753,plain,
( spl0_1322
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1322])]) ).
fof(f87,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_IntDef_Oint),c_Finite__Set_OFinites,tc_set(tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__atLeastAtMost__int_0) ).
fof(f9751,plain,
spl0_1321,
inference(avatar_split_clause,[],[f86,f9749]) ).
fof(f9749,plain,
( spl0_1321
<=> ! [X14,X26] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1321])]) ).
fof(f86,axiom,
! [X26,X14] : c_in(c_SetInterval_OatLeastAtMost(X26,X14,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__atLeastAtMost_0) ).
fof(f9747,plain,
spl0_1320,
inference(avatar_split_clause,[],[f37,f9745]) ).
fof(f37,axiom,
! [X21,X15] : c_lessequals(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint),c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onegative__zle_0) ).
fof(f9741,plain,
( spl0_1319
| ~ spl0_1051
| ~ spl0_1057
| ~ spl0_1273 ),
inference(avatar_split_clause,[],[f9685,f9483,f7368,f7341,f9738]) ).
fof(f9738,plain,
( spl0_1319
<=> c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1319])]) ).
fof(f9483,plain,
( spl0_1273
<=> ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1273])]) ).
fof(f9685,plain,
( c_IntDef_Oneg(c_uminus(c_1,tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1057
| ~ spl0_1273 ),
inference(forward_demodulation,[],[f9684,f7343]) ).
fof(f9684,plain,
( c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_1),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1057
| ~ spl0_1273 ),
inference(superposition,[],[f9484,f7370]) ).
fof(f9484,plain,
( ! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint)
| ~ spl0_1273 ),
inference(avatar_component_clause,[],[f9483]) ).
fof(f9730,plain,
( spl0_1318
| ~ spl0_1052
| ~ spl0_1270 ),
inference(avatar_split_clause,[],[f9674,f9471,f7346,f9727]) ).
fof(f9471,plain,
( spl0_1270
<=> ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1270])]) ).
fof(f9674,plain,
( c_0 = c_HOL_Oabs(c_0,tc_IntDef_Oint)
| ~ spl0_1052
| ~ spl0_1270 ),
inference(superposition,[],[f9472,f7348]) ).
fof(f9472,plain,
( ! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint)
| ~ spl0_1270 ),
inference(avatar_component_clause,[],[f9471]) ).
fof(f9720,plain,
( spl0_1317
| ~ spl0_1051
| ~ spl0_1270 ),
inference(avatar_split_clause,[],[f9673,f9471,f7341,f9717]) ).
fof(f9717,plain,
( spl0_1317
<=> c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1317])]) ).
fof(f9673,plain,
( c_1 = c_HOL_Oabs(c_1,tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1270 ),
inference(superposition,[],[f9472,f7343]) ).
fof(f9680,plain,
( spl0_1316
| ~ spl0_1252
| ~ spl0_1264 ),
inference(avatar_split_clause,[],[f9667,f9447,f9385,f9678]) ).
fof(f9385,plain,
( spl0_1252
<=> ! [X3] : c_div(X3,c_1,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1252])]) ).
fof(f9667,plain,
( ! [X1] : c_lessequals(X1,X1,tc_nat)
| ~ spl0_1252
| ~ spl0_1264 ),
inference(superposition,[],[f9448,f9386]) ).
fof(f9386,plain,
( ! [X3] : c_div(X3,c_1,tc_nat) = X3
| ~ spl0_1252 ),
inference(avatar_component_clause,[],[f9385]) ).
fof(f9653,plain,
spl0_1315,
inference(avatar_split_clause,[],[f2903,f9651]) ).
fof(f9651,plain,
( spl0_1315
<=> ! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1315])]) ).
fof(f2903,plain,
! [X15] :
( ~ c_Divides_Oop_Advd(X15,c_1,tc_nat)
| c_1 = X15 ),
inference(forward_demodulation,[],[f2902,f2016]) ).
fof(f2902,plain,
! [X15] :
( c_1 = X15
| ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
inference(forward_demodulation,[],[f1227,f2016]) ).
fof(f1227,axiom,
! [X15] :
( c_Suc(c_0) = X15
| ~ c_Divides_Oop_Advd(X15,c_Suc(c_0),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__1__iff__1_0) ).
fof(f9649,plain,
spl0_1314,
inference(avatar_split_clause,[],[f2705,f9647]) ).
fof(f9647,plain,
( spl0_1314
<=> ! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1314])]) ).
fof(f2705,axiom,
! [X2,X1] : c_UNIV = c_Sum__Type_OPlus(c_UNIV,c_UNIV,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Sum__Type_OUNIV__Plus__UNIV_0) ).
fof(f9645,plain,
spl0_1313,
inference(avatar_split_clause,[],[f2684,f9643]) ).
fof(f2684,axiom,
! [X0,X1,X12] : c_in(X0,c_insert(X0,X12,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__iff_1) ).
fof(f9641,plain,
spl0_1312,
inference(avatar_split_clause,[],[f2668,f9639]) ).
fof(f9639,plain,
( spl0_1312
<=> ! [X12,X1] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1312])]) ).
fof(f2668,axiom,
! [X1,X12] : c_emptyset = c_minus(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oempty__Diff_0) ).
fof(f9637,plain,
spl0_1311,
inference(avatar_split_clause,[],[f2648,f9635]) ).
fof(f9635,plain,
( spl0_1311
<=> ! [X1,X3] : c_Union(c_Pow(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1311])]) ).
fof(f2648,axiom,
! [X3,X1] : c_Union(c_Pow(X3,X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__Pow__eq_0) ).
fof(f9633,plain,
spl0_1310,
inference(avatar_split_clause,[],[f2590,f9631]) ).
fof(f9631,plain,
( spl0_1310
<=> ! [X1,X3] : c_minus(X3,c_emptyset,tc_set(X1)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1310])]) ).
fof(f2590,axiom,
! [X3,X1] : c_minus(X3,c_emptyset,tc_set(X1)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__empty_0) ).
fof(f9629,plain,
spl0_1309,
inference(avatar_split_clause,[],[f2588,f9627]) ).
fof(f9627,plain,
( spl0_1309
<=> ! [X12,X1] : c_emptyset = c_minus(X12,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1309])]) ).
fof(f2588,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__cancel_0) ).
fof(f9625,plain,
spl0_1308,
inference(avatar_split_clause,[],[f2587,f9623]) ).
fof(f9623,plain,
( spl0_1308
<=> ! [X12,X1] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1308])]) ).
fof(f2587,axiom,
! [X1,X12] : c_emptyset = c_minus(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_ODiff__UNIV_0) ).
fof(f9621,plain,
spl0_1307,
inference(avatar_split_clause,[],[f2549,f9619]) ).
fof(f9619,plain,
( spl0_1307
<=> ! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1307])]) ).
fof(f2549,axiom,
! [X3] : c_Finite__Set_Ocard(c_SetInterval_OlessThan(X3,tc_nat),tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ocard__lessThan_0) ).
fof(f9617,plain,
spl0_1306,
inference(avatar_split_clause,[],[f2394,f9615]) ).
fof(f9615,plain,
( spl0_1306
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1306])]) ).
fof(f2394,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_1 = c_HOL_Oabs(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oabs__one_0) ).
fof(f9613,plain,
spl0_1305,
inference(avatar_split_clause,[],[f2374,f9611]) ).
fof(f9611,plain,
( spl0_1305
<=> ! [X2,X85,X1] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1305])]) ).
fof(f2374,axiom,
! [X2,X1,X85] : c_emptyset = c_Relation_OImage(X85,c_emptyset,X2,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImage__empty_0) ).
fof(f9609,plain,
spl0_1304,
inference(avatar_split_clause,[],[f2372,f9607]) ).
fof(f9607,plain,
( spl0_1304
<=> ! [X1,X3] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1304])]) ).
fof(f2372,axiom,
! [X3,X1] : c_Relation_OImage(c_Relation_OId,X3,X1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_OImage__Id_0) ).
fof(f9605,plain,
spl0_1303,
inference(avatar_split_clause,[],[f2279,f9603]) ).
fof(f9603,plain,
( spl0_1303
<=> ! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Suc(X0),tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1303])]) ).
fof(f2279,axiom,
! [X0] :
( c_Parity_Oeven(X0,tc_nat)
| c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__Suc_1) ).
fof(f9601,plain,
spl0_1302,
inference(avatar_split_clause,[],[f2278,f9599]) ).
fof(f2278,axiom,
! [X0] :
( ~ c_Parity_Oeven(X0,tc_nat)
| ~ c_Parity_Oeven(c_Suc(X0),tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__Suc_0) ).
fof(f9597,plain,
spl0_1301,
inference(avatar_split_clause,[],[f2243,f9595]) ).
fof(f2243,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Opprt(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Opprt__0_0) ).
fof(f9593,plain,
spl0_1300,
inference(avatar_split_clause,[],[f2238,f9591]) ).
fof(f2238,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group(X1)
| c_0 = c_OrderedGroup_Onprt(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Onprt__0_0) ).
fof(f9589,plain,
spl0_1299,
inference(avatar_split_clause,[],[f2220,f9587]) ).
fof(f9587,plain,
( spl0_1299
<=> ! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1299])]) ).
fof(f2220,axiom,
! [X1] :
( ~ class_OrderedGroup_Oab__group__add(X1)
| c_0 = c_uminus(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oneg__0__equal__iff__equal_1) ).
fof(f9585,plain,
spl0_1298,
inference(avatar_split_clause,[],[f2173,f9583]) ).
fof(f9583,plain,
( spl0_1298
<=> ! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1298])]) ).
fof(f2173,axiom,
! [X1] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X1)
| c_0 = c_HOL_Oabs(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_OrderedGroup_Oabs__0__eq_1) ).
fof(f9581,plain,
spl0_1297,
inference(avatar_split_clause,[],[f2169,f9579]) ).
fof(f2169,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Onumeral__0__eq__0_0) ).
fof(f9577,plain,
spl0_1296,
inference(avatar_split_clause,[],[f2162,f9575]) ).
fof(f9575,plain,
( spl0_1296
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1296])]) ).
fof(f2162,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__rec(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Orecs__2_0) ).
fof(f9573,plain,
spl0_1295,
inference(avatar_split_clause,[],[f2161,f9571]) ).
fof(f9571,plain,
( spl0_1295
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1295])]) ).
fof(f2161,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__rec(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Orecs__1_0) ).
fof(f9569,plain,
spl0_1294,
inference(avatar_split_clause,[],[f2158,f9567]) ).
fof(f9567,plain,
( spl0_1294
<=> ! [X45,X1,X3] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1294])]) ).
fof(f2158,axiom,
! [X3,X1,X45] : c_Numeral_Obit_Obit__case(X45,X3,c_Numeral_Obit_OB1,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Ocases__2_0) ).
fof(f9565,plain,
spl0_1293,
inference(avatar_split_clause,[],[f2157,f9563]) ).
fof(f9563,plain,
( spl0_1293
<=> ! [X44,X1,X3] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1293])]) ).
fof(f2157,axiom,
! [X3,X1,X44] : c_Numeral_Obit_Obit__case(X3,X44,c_Numeral_Obit_OB0,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Ocases__1_0) ).
fof(f9561,plain,
spl0_1292,
inference(avatar_split_clause,[],[f2144,f9559]) ).
fof(f9559,plain,
( spl0_1292
<=> ! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1292])]) ).
fof(f2144,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| ~ c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OMin,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__3_0) ).
fof(f9557,plain,
spl0_1291,
inference(avatar_split_clause,[],[f2143,f9555]) ).
fof(f2143,axiom,
! [X1] :
( ~ class_Numeral_Onumber__ring(X1)
| c_IntDef_Oiszero(c_Numeral_Onumber__of(c_Numeral_OPls,X1),X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__2_0) ).
fof(f9553,plain,
spl0_1290,
inference(avatar_split_clause,[],[f2089,f9551]) ).
fof(f9551,plain,
( spl0_1290
<=> ! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1290])]) ).
fof(f2089,axiom,
! [X21] :
( c_0 = X21
| c_less(c_0,X21,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onot__gr0_0) ).
fof(f9549,plain,
spl0_1289,
inference(avatar_split_clause,[],[f2088,f9547]) ).
fof(f2088,axiom,
! [X59,X43] : ~ c_less(c_plus(X59,X43,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onot__add__less2_0) ).
fof(f9545,plain,
spl0_1288,
inference(avatar_split_clause,[],[f2087,f9543]) ).
fof(f2087,axiom,
! [X59,X43] : ~ c_less(c_plus(X43,X59,tc_nat),X43,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onot__add__less1_0) ).
fof(f9541,plain,
spl0_1287,
inference(avatar_split_clause,[],[f2048,f9539]) ).
fof(f9539,plain,
( spl0_1287
<=> ! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1287])]) ).
fof(f2048,axiom,
! [X21] :
( c_0 = X21
| ~ c_less(X21,c_1,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oless__one_0) ).
fof(f9537,plain,
spl0_1286,
inference(avatar_split_clause,[],[f2042,f9535]) ).
fof(f2042,axiom,
! [X43] :
( c_0 = X43
| ~ c_lessequals(X43,c_0,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ole__0__eq_0) ).
fof(f9533,plain,
spl0_1285,
inference(avatar_split_clause,[],[f2040,f9531]) ).
fof(f9531,plain,
( spl0_1285
<=> ! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1285])]) ).
fof(f2040,axiom,
! [X21,X15] : c_lessequals(c_minus(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__le__self_0) ).
fof(f9529,plain,
spl0_1284,
inference(avatar_split_clause,[],[f1808,f9527]) ).
fof(f1808,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_1 = c_NatArith_Oof__nat(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__1_0) ).
fof(f9525,plain,
spl0_1283,
inference(avatar_split_clause,[],[f1804,f9523]) ).
fof(f1804,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_0 = c_NatArith_Oof__nat(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatArith_Oof__nat__0__eq__iff_1) ).
fof(f9521,plain,
spl0_1282,
inference(avatar_split_clause,[],[f1790,f9519]) ).
fof(f9519,plain,
( spl0_1282
<=> ! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1282])]) ).
fof(f1790,axiom,
! [X2,X1,X25] : c_List_Olist_ONil = c_List_Ozip(c_List_Olist_ONil,X25,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ozip__Nil_0) ).
fof(f9517,plain,
spl0_1281,
inference(avatar_split_clause,[],[f1788,f9515]) ).
fof(f9515,plain,
( spl0_1281
<=> ! [X41,X82,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1281])]) ).
fof(f1788,axiom,
! [X82,X41,X23] : c_List_Olist_ONil = c_List_Ozip(X23,c_List_Olist_ONil,X41,X82),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ozip_Osimps__1_0) ).
fof(f9513,plain,
spl0_1280,
inference(avatar_split_clause,[],[f1732,f9511]) ).
fof(f9511,plain,
( spl0_1280
<=> ! [X1,X3] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1280])]) ).
fof(f1732,axiom,
! [X3,X1] : c_List_Orev(c_List_Orev(X3,X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orev__rev__ident_0) ).
fof(f9509,plain,
spl0_1279,
inference(avatar_split_clause,[],[f1711,f9507]) ).
fof(f9507,plain,
( spl0_1279
<=> ! [X25,X0,X1] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1279])]) ).
fof(f1711,axiom,
! [X0,X1,X25] : c_List_Oop_Amem(X0,c_List_Olist_OCons(X0,X25,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oop_Amem_Osimps__2_1) ).
fof(f9505,plain,
spl0_1278,
inference(avatar_split_clause,[],[f1631,f9503]) ).
fof(f9503,plain,
( spl0_1278
<=> ! [X41,X43,X47] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1278])]) ).
fof(f1631,axiom,
! [X41,X47,X43] : c_List_Olist_ONil = c_List_Olist__update(c_List_Olist_ONil,X43,X47,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__update_Osimps__1_0) ).
fof(f9501,plain,
spl0_1277,
inference(avatar_split_clause,[],[f1542,f9499]) ).
fof(f9499,plain,
( spl0_1277
<=> ! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1277])]) ).
fof(f1542,axiom,
! [X54,X55] : c_0 = c_Nat_Osize(c_List_Ochar_OChar(X54,X55),tc_List_Ochar),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ochar_Osize_0) ).
fof(f9497,plain,
spl0_1276,
inference(avatar_split_clause,[],[f1478,f9495]) ).
fof(f1478,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_IntDef_Oint) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__0__left_0) ).
fof(f9493,plain,
spl0_1275,
inference(avatar_split_clause,[],[f1401,f9491]) ).
fof(f1401,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_1 = c_IntDef_Oof__int(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__1_0) ).
fof(f9489,plain,
spl0_1274,
inference(avatar_split_clause,[],[f1396,f9487]) ).
fof(f1396,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| c_0 = c_IntDef_Oof__int(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oof__int__0__eq__iff_1) ).
fof(f9485,plain,
spl0_1273,
inference(avatar_split_clause,[],[f1388,f9483]) ).
fof(f1388,axiom,
! [X21] : c_IntDef_Oneg(c_uminus(c_IntDef_Oint(c_Suc(X21)),tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oneg__zminus__int_0) ).
fof(f9481,plain,
spl0_1272,
inference(avatar_split_clause,[],[f1387,f9479]) ).
fof(f1387,axiom,
! [X21] : c_0 = c_IntDef_Onat(c_uminus(c_IntDef_Oint(X21),tc_IntDef_Oint)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onat__zminus__int_0) ).
fof(f9477,plain,
spl0_1271,
inference(avatar_split_clause,[],[f1373,f9475]) ).
fof(f9475,plain,
( spl0_1271
<=> ! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1271])]) ).
fof(f1373,axiom,
! [X21] :
( c_0 = X21
| c_0 != c_IntDef_Oint(X21) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__eq__0__conv_0) ).
fof(f9473,plain,
spl0_1270,
inference(avatar_split_clause,[],[f1367,f9471]) ).
fof(f1367,axiom,
! [X15] : c_IntDef_Oint(X15) = c_HOL_Oabs(c_IntDef_Oint(X15),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oabs__int__eq_0) ).
fof(f9469,plain,
spl0_1269,
inference(avatar_split_clause,[],[f1253,f9467]) ).
fof(f9467,plain,
( spl0_1269
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1269])]) ).
fof(f1253,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__rec(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Orecs__2_0) ).
fof(f9465,plain,
spl0_1268,
inference(avatar_split_clause,[],[f1252,f9463]) ).
fof(f9463,plain,
( spl0_1268
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1268])]) ).
fof(f1252,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__rec(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Orecs__1_0) ).
fof(f9461,plain,
spl0_1267,
inference(avatar_split_clause,[],[f1249,f9459]) ).
fof(f9459,plain,
( spl0_1267
<=> ! [X45,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1267])]) ).
fof(f1249,axiom,
! [X3,X1,X45] : c_Extraction_Osumbool_Osumbool__case(X45,X3,c_Extraction_Osumbool_ORight,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Ocases__2_0) ).
fof(f9457,plain,
spl0_1266,
inference(avatar_split_clause,[],[f1248,f9455]) ).
fof(f9455,plain,
( spl0_1266
<=> ! [X44,X1,X3] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1266])]) ).
fof(f1248,axiom,
! [X3,X1,X44] : c_Extraction_Osumbool_Osumbool__case(X3,X44,c_Extraction_Osumbool_OLeft,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Ocases__1_0) ).
fof(f9453,plain,
spl0_1265,
inference(avatar_split_clause,[],[f1225,f9451]) ).
fof(f9451,plain,
( spl0_1265
<=> ! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1265])]) ).
fof(f1225,axiom,
! [X15] :
( c_0 = X15
| ~ c_Divides_Oop_Advd(c_0,X15,tc_nat) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__0__left__iff_0) ).
fof(f9449,plain,
spl0_1264,
inference(avatar_split_clause,[],[f1215,f9447]) ).
fof(f1215,axiom,
! [X21,X15] : c_lessequals(c_div(X15,X21,tc_nat),X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__le__dividend_0) ).
fof(f9445,plain,
spl0_1263,
inference(avatar_split_clause,[],[f1202,f9443]) ).
fof(f9443,plain,
( spl0_1263
<=> ! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1263])]) ).
fof(f1202,axiom,
! [X2,X1,X9] : c_emptyset = c_Datatype__Universe_Ontrunc(c_0,X9,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype__Universe_Ontrunc__0_0) ).
fof(f9441,plain,
spl0_1262,
inference(avatar_split_clause,[],[f1181,f9439]) ).
fof(f9439,plain,
( spl0_1262
<=> ! [X1,X3] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1262])]) ).
fof(f1181,axiom,
! [X3,X1] : c_Datatype_Othe(c_Datatype_Ooption_OSome(X3,X1),X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Othe_Osimps_0) ).
fof(f9437,plain,
spl0_1261,
inference(avatar_split_clause,[],[f1163,f9435]) ).
fof(f9435,plain,
( spl0_1261
<=> ! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1261])]) ).
fof(f1163,axiom,
! [X21] : c_Suc(X21) = c_Binomial_Obinomial(c_Suc(X21),X21),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Binomial_Obinomial__Suc__n_0) ).
fof(f9433,plain,
spl0_1260,
inference(avatar_split_clause,[],[f95,f9431]) ).
fof(f9431,plain,
( spl0_1260
<=> ! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1260])]) ).
fof(f95,axiom,
! [X16] : c_in(c_SetInterval_OlessThan(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__lessThan_0) ).
fof(f9429,plain,
spl0_1259,
inference(avatar_split_clause,[],[f90,f9427]) ).
fof(f9427,plain,
( spl0_1259
<=> ! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1259])]) ).
fof(f90,axiom,
! [X16] : c_in(c_SetInterval_OatMost(X16,tc_nat),c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_Ofinite__atMost_0) ).
fof(f9425,plain,
spl0_1258,
inference(avatar_split_clause,[],[f61,f9423]) ).
fof(f9423,plain,
( spl0_1258
<=> ! [X12,X1] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1258])]) ).
fof(f61,axiom,
! [X1,X12] : c_in(c_List_Olist_ONil,c_List_Olists(X12,X1),tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olists_ONil_0) ).
fof(f9421,plain,
spl0_1257,
inference(avatar_split_clause,[],[f45,f9419]) ).
fof(f9419,plain,
( spl0_1257
<=> ! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1257])]) ).
fof(f45,axiom,
! [X1,X23] : c_in(c_List_Oset(X23,X1),c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Ofinite__set_0) ).
fof(f9417,plain,
spl0_1256,
inference(avatar_split_clause,[],[f42,f9415]) ).
fof(f42,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__triv__right_0) ).
fof(f9413,plain,
spl0_1255,
inference(avatar_split_clause,[],[f41,f9411]) ).
fof(f41,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__triv__left_0) ).
fof(f9409,plain,
spl0_1254,
inference(avatar_split_clause,[],[f26,f9407]) ).
fof(f9407,plain,
( spl0_1254
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1254])]) ).
fof(f26,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X15,X16,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__triv__right_0) ).
fof(f9405,plain,
spl0_1253,
inference(avatar_split_clause,[],[f25,f9403]) ).
fof(f9403,plain,
( spl0_1253
<=> ! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1253])]) ).
fof(f25,axiom,
! [X16,X15] : c_Divides_Oop_Advd(X16,c_times(X16,X15,tc_nat),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__triv__left_0) ).
fof(f9387,plain,
spl0_1252,
inference(avatar_split_clause,[],[f2843,f9385]) ).
fof(f2843,plain,
! [X3] : c_div(X3,c_1,tc_nat) = X3,
inference(forward_demodulation,[],[f1214,f2016]) ).
fof(f1214,axiom,
! [X3] : c_div(X3,c_Suc(c_0),tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__1_0) ).
fof(f9383,plain,
spl0_1251,
inference(avatar_split_clause,[],[f2841,f9380]) ).
fof(f9380,plain,
( spl0_1251
<=> c_1 = c_times(c_1,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1251])]) ).
fof(f2841,plain,
c_1 = c_times(c_1,c_1,tc_nat),
inference(forward_demodulation,[],[f2094,f2016]) ).
fof(f2094,axiom,
c_Suc(c_0) = c_times(c_1,c_1,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oone__eq__mult__iff_2) ).
fof(f9378,plain,
spl0_1250,
inference(avatar_split_clause,[],[f2839,f9376]) ).
fof(f9376,plain,
( spl0_1250
<=> ! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1250])]) ).
fof(f2839,plain,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_1,tc_nat),
inference(forward_demodulation,[],[f1231,f2016]) ).
fof(f1231,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(X15,c_Suc(c_0),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__1_0) ).
fof(f9374,plain,
spl0_1249,
inference(avatar_split_clause,[],[f2838,f9371]) ).
fof(f9371,plain,
( spl0_1249
<=> c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1249])]) ).
fof(f2838,plain,
c_1 = c_Numeral_Onumber__of(c_Numeral_Obin__succ(c_Numeral_OPls),tc_nat),
inference(forward_demodulation,[],[f1867,f2156]) ).
fof(f1867,axiom,
c_1 = c_Numeral_Onumber__of(c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Onat__numeral__1__eq__1_0) ).
fof(f9369,plain,
spl0_1248,
inference(avatar_split_clause,[],[f2825,f9367]) ).
fof(f2825,axiom,
! [X88] : c_lessequals(X88,c_Message_Osynth(X88),tc_set(tc_Message_Omsg)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Osynth__increasing_0) ).
fof(f9365,plain,
spl0_1247,
inference(avatar_split_clause,[],[f2805,f9363]) ).
fof(f9363,plain,
( spl0_1247
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1247])]) ).
fof(f2805,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__idem_0) ).
fof(f9361,plain,
spl0_1246,
inference(avatar_split_clause,[],[f2803,f9359]) ).
fof(f9359,plain,
( spl0_1246
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1246])]) ).
fof(f2803,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oparts(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__analz_0) ).
fof(f9357,plain,
spl0_1245,
inference(avatar_split_clause,[],[f2799,f9355]) ).
fof(f9355,plain,
( spl0_1245
<=> ! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1245])]) ).
fof(f2799,axiom,
! [X88] : c_Message_Oparts(X88) = c_Message_Oanalz(c_Message_Oparts(X88)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__parts_0) ).
fof(f9353,plain,
spl0_1244,
inference(avatar_split_clause,[],[f2792,f9351]) ).
fof(f9351,plain,
( spl0_1244
<=> ! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1244])]) ).
fof(f2792,axiom,
! [X88] : c_Message_Oanalz(X88) = c_Message_Oanalz(c_Message_Oanalz(X88)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__idem_0) ).
fof(f9349,plain,
spl0_1243,
inference(avatar_split_clause,[],[f2785,f9347]) ).
fof(f2785,axiom,
! [X21,X88] : c_in(c_Message_Omsg_ONumber(X21),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_ONumber__synth_0) ).
fof(f9345,plain,
spl0_1242,
inference(avatar_split_clause,[],[f2772,f9343]) ).
fof(f2772,axiom,
! [X88,X12] : c_in(c_Message_Omsg_OAgent(X12),c_Message_Osynth(X88),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OAgent__synth_0) ).
fof(f9341,plain,
spl0_1241,
inference(avatar_split_clause,[],[f2763,f9339]) ).
fof(f2763,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_OKey(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__4_0) ).
fof(f9337,plain,
spl0_1240,
inference(avatar_split_clause,[],[f2762,f9335]) ).
fof(f2762,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONonce(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__3_0) ).
fof(f9333,plain,
spl0_1239,
inference(avatar_split_clause,[],[f2761,f9331]) ).
fof(f2761,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Omsg_ONumber(X90),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__2_0) ).
fof(f9329,plain,
spl0_1238,
inference(avatar_split_clause,[],[f2760,f9327]) ).
fof(f2760,axiom,
! [X94] : c_0 = c_Nat_Osize(c_Message_Omsg_OAgent(X94),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Omsg_Osize__1_0) ).
fof(f9325,plain,
spl0_1237,
inference(avatar_split_clause,[],[f2738,f9323]) ).
fof(f9323,plain,
( spl0_1237
<=> ! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1237])]) ).
fof(f2738,axiom,
! [X90] : c_0 = c_Nat_Osize(c_Message_Oagent_OFriend(X90),tc_Message_Oagent),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Osize__2_0) ).
fof(f9321,plain,
spl0_1236,
inference(avatar_split_clause,[],[f2687,f9319]) ).
fof(f2687,axiom,
! [X18,X1,X12] : c_emptyset != c_insert(X18,X12,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oinsert__not__empty_0) ).
fof(f9317,plain,
spl0_1235,
inference(avatar_split_clause,[],[f2639,f9315]) ).
fof(f2639,axiom,
! [X3,X1] : c_union(X3,c_emptyset,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__empty__right_0) ).
fof(f9313,plain,
spl0_1234,
inference(avatar_split_clause,[],[f2638,f9311]) ).
fof(f2638,axiom,
! [X3,X1] : c_union(c_emptyset,X3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__empty__left_0) ).
fof(f9309,plain,
spl0_1233,
inference(avatar_split_clause,[],[f2634,f9307]) ).
fof(f2634,axiom,
! [X3,X1] : c_union(X3,X3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__absorb_0) ).
fof(f9305,plain,
spl0_1232,
inference(avatar_split_clause,[],[f2633,f9303]) ).
fof(f9303,plain,
( spl0_1232
<=> ! [X12,X1] : c_UNIV = c_union(X12,c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1232])]) ).
fof(f2633,axiom,
! [X1,X12] : c_UNIV = c_union(X12,c_UNIV,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__UNIV__right_0) ).
fof(f9301,plain,
spl0_1231,
inference(avatar_split_clause,[],[f2632,f9299]) ).
fof(f2632,axiom,
! [X1,X13] : c_UNIV = c_union(c_UNIV,X13,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUn__UNIV__left_0) ).
fof(f9297,plain,
spl0_1230,
inference(avatar_split_clause,[],[f2605,f9295]) ).
fof(f9295,plain,
( spl0_1230
<=> ! [X12,X1] : c_emptyset = c_inter(X12,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1230])]) ).
fof(f2605,axiom,
! [X1,X12] : c_emptyset = c_inter(X12,c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__empty__right_0) ).
fof(f9293,plain,
spl0_1229,
inference(avatar_split_clause,[],[f2604,f9291]) ).
fof(f2604,axiom,
! [X1,X13] : c_emptyset = c_inter(c_emptyset,X13,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__empty__left_0) ).
fof(f9289,plain,
spl0_1228,
inference(avatar_split_clause,[],[f2603,f9287]) ).
fof(f9287,plain,
( spl0_1228
<=> ! [X1,X3] : c_inter(X3,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1228])]) ).
fof(f2603,axiom,
! [X3,X1] : c_inter(X3,X3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__absorb_0) ).
fof(f9285,plain,
spl0_1227,
inference(avatar_split_clause,[],[f2602,f9283]) ).
fof(f9283,plain,
( spl0_1227
<=> ! [X1,X3] : c_inter(X3,c_UNIV,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1227])]) ).
fof(f2602,axiom,
! [X3,X1] : c_inter(X3,c_UNIV,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__UNIV__right_0) ).
fof(f9281,plain,
spl0_1226,
inference(avatar_split_clause,[],[f2601,f9279]) ).
fof(f9279,plain,
( spl0_1226
<=> ! [X1,X3] : c_inter(c_UNIV,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1226])]) ).
fof(f2601,axiom,
! [X3,X1] : c_inter(c_UNIV,X3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInt__UNIV__left_0) ).
fof(f9277,plain,
spl0_1225,
inference(avatar_split_clause,[],[f2580,f9275]) ).
fof(f2580,axiom,
! [X1] : c_UNIV = c_uminus(c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__empty__eq_0) ).
fof(f9273,plain,
spl0_1224,
inference(avatar_split_clause,[],[f2576,f9271]) ).
fof(f9271,plain,
( spl0_1224
<=> ! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1224])]) ).
fof(f2576,axiom,
! [X1] : c_emptyset = c_uminus(c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OCompl__UNIV__eq_0) ).
fof(f9269,plain,
spl0_1223,
inference(avatar_split_clause,[],[f2511,f9267]) ).
fof(f9267,plain,
( spl0_1223
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1223])]) ).
fof(f2511,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_lessequals(c_0,c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Ozero__le__one_0) ).
fof(f9265,plain,
spl0_1222,
inference(avatar_split_clause,[],[f2499,f9263]) ).
fof(f9263,plain,
( spl0_1222
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1222])]) ).
fof(f2499,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| c_less(c_0,c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Oordered__semidom__class_Oaxioms_0) ).
fof(f9261,plain,
spl0_1221,
inference(avatar_split_clause,[],[f2494,f9259]) ).
fof(f9259,plain,
( spl0_1221
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1221])]) ).
fof(f2494,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_less(c_1,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Onot__one__less__zero_0) ).
fof(f9257,plain,
spl0_1220,
inference(avatar_split_clause,[],[f2493,f9255]) ).
fof(f9255,plain,
( spl0_1220
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1220])]) ).
fof(f2493,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__semidom(X1)
| ~ c_lessequals(c_1,c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Ring__and__Field_Onot__one__le__zero_0) ).
fof(f9253,plain,
spl0_1219,
inference(avatar_split_clause,[],[f2381,f9251]) ).
fof(f9251,plain,
( spl0_1219
<=> ! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1219])]) ).
fof(f2381,axiom,
! [X1] : c_Relation_OId = c_Relation_Oconverse(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Oconverse__Id_0) ).
fof(f9249,plain,
spl0_1218,
inference(avatar_split_clause,[],[f2380,f9247]) ).
fof(f9247,plain,
( spl0_1218
<=> ! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1218])]) ).
fof(f2380,axiom,
! [X2,X1] : c_emptyset = c_Relation_ORange(c_emptyset,X2,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ORange__empty_0) ).
fof(f9245,plain,
spl0_1217,
inference(avatar_split_clause,[],[f2378,f9243]) ).
fof(f9243,plain,
( spl0_1217
<=> ! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1217])]) ).
fof(f2378,axiom,
! [X1] : c_UNIV = c_Relation_ORange(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ORange__Id_0) ).
fof(f9241,plain,
spl0_1216,
inference(avatar_split_clause,[],[f2370,f9239]) ).
fof(f9239,plain,
( spl0_1216
<=> ! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1216])]) ).
fof(f2370,axiom,
! [X2,X1] : c_emptyset = c_Relation_ODomain(c_emptyset,X1,X2),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ODomain__empty_0) ).
fof(f9237,plain,
spl0_1215,
inference(avatar_split_clause,[],[f2368,f9235]) ).
fof(f9235,plain,
( spl0_1215
<=> ! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1215])]) ).
fof(f2368,axiom,
! [X1] : c_UNIV = c_Relation_ODomain(c_Relation_OId,X1,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_ODomain__Id_0) ).
fof(f9233,plain,
spl0_1214,
inference(avatar_split_clause,[],[f2344,f9231]) ).
fof(f9231,plain,
( spl0_1214
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1214])]) ).
fof(f2344,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Power_Opower_Osimps__1_0) ).
fof(f9229,plain,
spl0_1213,
inference(avatar_split_clause,[],[f2269,f9227]) ).
fof(f9227,plain,
( spl0_1213
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1213])]) ).
fof(f2269,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| ~ c_less(X0,X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Oorder__less__irrefl_0) ).
fof(f9225,plain,
spl0_1212,
inference(avatar_split_clause,[],[f2156,f9222]) ).
fof(f9220,plain,
spl0_1211,
inference(avatar_split_clause,[],[f2133,f9217]) ).
fof(f2133,axiom,
c_Numeral_Obin__pred(c_Numeral_OMin) = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__pred__Min_0) ).
fof(f9215,plain,
spl0_1210,
inference(avatar_split_clause,[],[f2129,f9213]) ).
fof(f9213,plain,
( spl0_1210
<=> ! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1210])]) ).
fof(f2129,axiom,
! [X11] : c_Numeral_Obin__minus(X11) = c_Numeral_Obin__mult(c_Numeral_OMin,X11),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__mult__Min_0) ).
fof(f9211,plain,
spl0_1209,
inference(avatar_split_clause,[],[f2113,f9209]) ).
fof(f2113,axiom,
! [X11] : c_Numeral_Obin__pred(X11) = c_Numeral_Obin__add(X11,c_Numeral_OMin),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__Min__right_0) ).
fof(f9207,plain,
spl0_1208,
inference(avatar_split_clause,[],[f2112,f9205]) ).
fof(f9205,plain,
( spl0_1208
<=> ! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1208])]) ).
fof(f2112,axiom,
! [X11] : c_Numeral_Obin__add(c_Numeral_OMin,X11) = c_Numeral_Obin__pred(X11),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__add__Min_0) ).
fof(f9203,plain,
spl0_1207,
inference(avatar_split_clause,[],[f2102,f9201]) ).
fof(f2102,axiom,
! [X3] : c_minus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oop_A_N_Odiff__0_0) ).
fof(f9199,plain,
spl0_1206,
inference(avatar_split_clause,[],[f2100,f9197]) ).
fof(f2100,axiom,
! [X3] : c_plus(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oop_A_L_Oadd__0_0) ).
fof(f9195,plain,
spl0_1205,
inference(avatar_split_clause,[],[f2098,f9193]) ).
fof(f9193,plain,
( spl0_1205
<=> ! [X21] : c_0 = c_times(c_0,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1205])]) ).
fof(f2098,axiom,
! [X21] : c_0 = c_times(c_0,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oop_A_K_Omult__0_0) ).
fof(f9191,plain,
spl0_1204,
inference(avatar_split_clause,[],[f2056,f9189]) ).
fof(f9189,plain,
( spl0_1204
<=> ! [X15] : c_0 = c_times(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1204])]) ).
fof(f2056,axiom,
! [X15] : c_0 = c_times(X15,c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omult__0__right_0) ).
fof(f9187,plain,
spl0_1203,
inference(avatar_split_clause,[],[f2054,f9185]) ).
fof(f2054,axiom,
! [X21] : c_0 = c_Orderings_Omin(X21,c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omin__0R_0) ).
fof(f9183,plain,
spl0_1202,
inference(avatar_split_clause,[],[f2053,f9181]) ).
fof(f2053,axiom,
! [X21] : c_0 = c_Orderings_Omin(c_0,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omin__0L_0) ).
fof(f9179,plain,
spl0_1201,
inference(avatar_split_clause,[],[f2051,f9177]) ).
fof(f9177,plain,
( spl0_1201
<=> ! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1201])]) ).
fof(f2051,axiom,
! [X3] : c_Orderings_Omax(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omax__0R_0) ).
fof(f9175,plain,
spl0_1200,
inference(avatar_split_clause,[],[f2050,f9173]) ).
fof(f9173,plain,
( spl0_1200
<=> ! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1200])]) ).
fof(f2050,axiom,
! [X3] : c_Orderings_Omax(c_0,X3,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Omax__0L_0) ).
fof(f9171,plain,
spl0_1199,
inference(avatar_split_clause,[],[f2041,f9169]) ).
fof(f2041,axiom,
! [X15] : c_0 = c_minus(X15,X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__self__eq__0_0) ).
fof(f9167,plain,
spl0_1198,
inference(avatar_split_clause,[],[f2034,f9165]) ).
fof(f2034,axiom,
! [X21] : c_0 = c_minus(c_0,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Odiff__0__eq__0_0) ).
fof(f9163,plain,
spl0_1197,
inference(avatar_split_clause,[],[f2026,f9161]) ).
fof(f2026,axiom,
! [X3] : c_plus(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oadd__0__right_0) ).
fof(f9159,plain,
spl0_1196,
inference(avatar_split_clause,[],[f1774,f9157]) ).
fof(f9157,plain,
( spl0_1196
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Otake(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1196])]) ).
fof(f1774,axiom,
! [X21,X1] : c_List_Olist_ONil = c_List_Otake(X21,c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__eq__Nil_2) ).
fof(f9155,plain,
spl0_1195,
inference(avatar_split_clause,[],[f1773,f9153]) ).
fof(f9153,plain,
( spl0_1195
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Otake(c_0,X23,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1195])]) ).
fof(f1773,axiom,
! [X1,X23] : c_List_Olist_ONil = c_List_Otake(c_0,X23,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otake__eq__Nil_1) ).
fof(f9151,plain,
spl0_1194,
inference(avatar_split_clause,[],[f1763,f9149]) ).
fof(f9149,plain,
( spl0_1194
<=> ! [X12,X1] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1194])]) ).
fof(f1763,axiom,
! [X1,X12] : c_List_Olist_ONil = c_List_Osublist(c_List_Olist_ONil,X12,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osublist__nil_0) ).
fof(f9147,plain,
spl0_1193,
inference(avatar_split_clause,[],[f1762,f9145]) ).
fof(f9145,plain,
( spl0_1193
<=> ! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1193])]) ).
fof(f1762,axiom,
! [X1,X23] : c_List_Olist_ONil = c_List_Osublist(X23,c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Osublist__empty_0) ).
fof(f9143,plain,
spl0_1192,
inference(avatar_split_clause,[],[f1747,f9141]) ).
fof(f9141,plain,
( spl0_1192
<=> ! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1192])]) ).
fof(f1747,axiom,
! [X1,X23] : c_append(X23,c_List_Olist_ONil,X1) = X23,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oself__append__conv_1) ).
fof(f9139,plain,
spl0_1191,
inference(avatar_split_clause,[],[f1745,f9137]) ).
fof(f9137,plain,
( spl0_1191
<=> ! [X25,X1] : c_append(c_List_Olist_ONil,X25,X1) = X25 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1191])]) ).
fof(f1745,axiom,
! [X1,X25] : c_append(c_List_Olist_ONil,X25,X1) = X25,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oself__append__conv2_1) ).
fof(f9135,plain,
spl0_1190,
inference(avatar_split_clause,[],[f1741,f9133]) ).
fof(f9133,plain,
( spl0_1190
<=> ! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1190])]) ).
fof(f1741,axiom,
! [X21,X1] : c_List_Olist_ONil = c_List_Orotate(X21,c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate__is__Nil__conv_1) ).
fof(f9131,plain,
spl0_1189,
inference(avatar_split_clause,[],[f1722,f9129]) ).
fof(f1722,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oreplicate(c_0,X0,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oreplicate_Oreplicate__0_0) ).
fof(f9127,plain,
spl0_1188,
inference(avatar_split_clause,[],[f1719,f9125]) ).
fof(f9125,plain,
( spl0_1188
<=> ! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1188])]) ).
fof(f1719,axiom,
! [X41,X0] : c_List_Olist_ONil = c_List_Oremove1(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremove1_Osimps__1_0) ).
fof(f9123,plain,
spl0_1187,
inference(avatar_split_clause,[],[f1707,f9121]) ).
fof(f1707,axiom,
! [X41,X0,X23] : ~ c_List_Onull(c_List_Olist_OCons(X0,X23,X41),X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onull_Osimps__2_0) ).
fof(f9119,plain,
spl0_1186,
inference(avatar_split_clause,[],[f1689,f9117]) ).
fof(f9117,plain,
( spl0_1186
<=> ! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1186])]) ).
fof(f1689,axiom,
! [X0,X1,X23] : c_List_Olist_OCons(X0,X23,X1) != X23,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onot__Cons__self_0) ).
fof(f9115,plain,
spl0_1185,
inference(avatar_split_clause,[],[f1628,f9113]) ).
fof(f9113,plain,
( spl0_1185
<=> ! [X41,X65] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1185])]) ).
fof(f1628,axiom,
! [X65,X41] : c_List_Olist_ONil = c_List_Olist__inter(c_List_Olist_ONil,X65,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist__inter_Osimps__1_0) ).
fof(f9111,plain,
spl0_1184,
inference(avatar_split_clause,[],[f1623,f9109]) ).
fof(f1623,axiom,
! [X1,X63,X42] : c_List_Olist_ONil != c_List_Olist_OCons(X42,X63,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olist_Odistinct__1_0) ).
fof(f9107,plain,
spl0_1183,
inference(avatar_split_clause,[],[f1615,f9105]) ).
fof(f9105,plain,
( spl0_1183
<=> ! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1183])]) ).
fof(f1615,axiom,
! [X41,X5] : c_emptyset = c_List_Olexn(X5,c_0,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olexn_Osimps__1_0) ).
fof(f9103,plain,
spl0_1182,
inference(avatar_split_clause,[],[f1598,f9101]) ).
fof(f9101,plain,
( spl0_1182
<=> ! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1182])]) ).
fof(f1598,axiom,
! [X1] : c_0 = c_Nat_Osize(c_List_Olist_ONil,tc_List_Olist(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olength__0__conv_1) ).
fof(f9099,plain,
spl0_1181,
inference(avatar_split_clause,[],[f1586,f9097]) ).
fof(f9097,plain,
( spl0_1181
<=> ! [X41,X3] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1181])]) ).
fof(f1586,axiom,
! [X3,X41] : c_List_Oitrev(c_List_Olist_ONil,X3,X41) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oitrev_Osimps__1_0) ).
fof(f9095,plain,
spl0_1180,
inference(avatar_split_clause,[],[f1569,f9093]) ).
fof(f9093,plain,
( spl0_1180
<=> ! [X1,X3] : c_List_Odrop(c_0,X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1180])]) ).
fof(f1569,axiom,
! [X3,X1] : c_List_Odrop(c_0,X3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop__0_0) ).
fof(f9091,plain,
spl0_1179,
inference(avatar_split_clause,[],[f1568,f9089]) ).
fof(f9089,plain,
( spl0_1179
<=> ! [X41,X21] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1179])]) ).
fof(f1568,axiom,
! [X21,X41] : c_List_Olist_ONil = c_List_Odrop(X21,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odrop_Odrop__Nil_0) ).
fof(f9087,plain,
spl0_1178,
inference(avatar_split_clause,[],[f1494,f9085]) ).
fof(f9085,plain,
( spl0_1178
<=> ! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1178])]) ).
fof(f1494,axiom,
! [X27] : c_0 = c_Divides_Oop_Amod(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__zero_0) ).
fof(f9083,plain,
spl0_1177,
inference(avatar_split_clause,[],[f1491,f9081]) ).
fof(f9081,plain,
( spl0_1177
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1177])]) ).
fof(f1491,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,X18,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__self_0) ).
fof(f9079,plain,
spl0_1176,
inference(avatar_split_clause,[],[f1489,f9077]) ).
fof(f9077,plain,
( spl0_1176
<=> ! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1176])]) ).
fof(f1489,axiom,
! [X18] : c_0 = c_Divides_Oop_Amod(X18,c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozmod__1_0) ).
fof(f9075,plain,
spl0_1175,
inference(avatar_split_clause,[],[f1474,f9073]) ).
fof(f9073,plain,
( spl0_1175
<=> ! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1175])]) ).
fof(f1474,axiom,
! [X27] : c_0 = c_div(c_0,X27,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__zero_0) ).
fof(f9071,plain,
spl0_1174,
inference(avatar_split_clause,[],[f1466,f9069]) ).
fof(f9069,plain,
( spl0_1174
<=> ! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1174])]) ).
fof(f1466,axiom,
! [X3] : c_div(X3,c_1,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdiv__1_0) ).
fof(f9067,plain,
spl0_1173,
inference(avatar_split_clause,[],[f1464,f9065]) ).
fof(f9065,plain,
( spl0_1173
<=> ! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1173])]) ).
fof(f1464,axiom,
! [X28] : c_1 = c_Nat_Opower(X28,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Opower_Osimps__1_0) ).
fof(f9063,plain,
spl0_1172,
inference(avatar_split_clause,[],[f1432,f9061]) ).
fof(f1432,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_IntDef_Oint) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_ODIVISION__BY__ZERO_0) ).
fof(f9059,plain,
spl0_1171,
inference(avatar_split_clause,[],[f1364,f9057]) ).
fof(f9057,plain,
( spl0_1171
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1171])]) ).
fof(f1364,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_1,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_ONats__1_0) ).
fof(f9055,plain,
spl0_1170,
inference(avatar_split_clause,[],[f1363,f9053]) ).
fof(f9053,plain,
( spl0_1170
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1170])]) ).
fof(f1363,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| c_in(c_0,c_IntDef_ONats,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_ONats__0_0) ).
fof(f9051,plain,
spl0_1169,
inference(avatar_split_clause,[],[f1358,f9049]) ).
fof(f9049,plain,
( spl0_1169
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1169])]) ).
fof(f1358,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_1,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInts__1_0) ).
fof(f9047,plain,
spl0_1168,
inference(avatar_split_clause,[],[f1357,f9045]) ).
fof(f9045,plain,
( spl0_1168
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1168])]) ).
fof(f1357,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X1)
| c_in(c_0,c_IntDef_OInts,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_OInts__0_0) ).
fof(f9043,plain,
spl0_1167,
inference(avatar_split_clause,[],[f1350,f9040]) ).
fof(f9040,plain,
( spl0_1167
<=> c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1167])]) ).
fof(f1350,axiom,
c_less(c_HOL_Oabs(c_0,tc_IntDef_Oint),c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Ozabs__less__one__iff_1) ).
fof(f9038,plain,
spl0_1166,
inference(avatar_split_clause,[],[f1245,f9036]) ).
fof(f9036,plain,
( spl0_1166
<=> ! [X5,X1] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1166])]) ).
fof(f1245,axiom,
! [X1,X5] : c_emptyset = c_Equiv__Relations_Oquotient(c_emptyset,X5,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Equiv__Relations_Oquotient__is__empty2_1) ).
fof(f9034,plain,
spl0_1165,
inference(avatar_split_clause,[],[f1241,f9032]) ).
fof(f9032,plain,
( spl0_1165
<=> ! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1165])]) ).
fof(f1241,axiom,
! [X21] : c_0 = c_Divides_Oop_Amod(X21,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__self_0) ).
fof(f9030,plain,
spl0_1164,
inference(avatar_split_clause,[],[f1230,f9028]) ).
fof(f1230,axiom,
! [X15] : c_0 = c_Divides_Oop_Amod(c_0,X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Omod__0_0) ).
fof(f9026,plain,
spl0_1163,
inference(avatar_split_clause,[],[f1213,f9024]) ).
fof(f9024,plain,
( spl0_1163
<=> ! [X15] : c_0 = c_div(c_0,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1163])]) ).
fof(f1213,axiom,
! [X15] : c_0 = c_div(c_0,X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odiv__0_0) ).
fof(f9022,plain,
spl0_1162,
inference(avatar_split_clause,[],[f1212,f9020]) ).
fof(f9020,plain,
( spl0_1162
<=> ! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1162])]) ).
fof(f1212,axiom,
! [X3] : c_Divides_Oop_Amod(X3,c_0,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_ODIVISION__BY__ZERO__MOD_0) ).
fof(f9018,plain,
spl0_1161,
inference(avatar_split_clause,[],[f1211,f9016]) ).
fof(f9016,plain,
( spl0_1161
<=> ! [X18] : c_0 = c_div(X18,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1161])]) ).
fof(f1211,axiom,
! [X18] : c_0 = c_div(X18,c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_ODIVISION__BY__ZERO__DIV_0) ).
fof(f9014,plain,
spl0_1160,
inference(avatar_split_clause,[],[f1183,f9012]) ).
fof(f9012,plain,
( spl0_1160
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1160])]) ).
fof(f1183,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__rec(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ounit_Orecs_0) ).
fof(f9010,plain,
spl0_1159,
inference(avatar_split_clause,[],[f1182,f9008]) ).
fof(f9008,plain,
( spl0_1159
<=> ! [X1,X3] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1159])]) ).
fof(f1182,axiom,
! [X3,X1] : c_Datatype_Ounit_Ounit__case(X3,c_Product__Type_OUnity,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ounit_Ocases_0) ).
fof(f9006,plain,
spl0_1158,
inference(avatar_split_clause,[],[f1176,f9004]) ).
fof(f9004,plain,
( spl0_1158
<=> ! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1158])]) ).
fof(f1176,axiom,
! [X1] : c_0 = c_Nat_Osize(c_Datatype_Ooption_ONone,tc_Datatype_Ooption(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ooption_Osize__1_0) ).
fof(f9002,plain,
spl0_1157,
inference(avatar_split_clause,[],[f1160,f9000]) ).
fof(f1160,axiom,
! [X16] : c_0 = c_Binomial_Obinomial(c_0,c_Suc(X16)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Binomial_Obinomial__0__Suc_0) ).
fof(f8998,plain,
spl0_1156,
inference(avatar_split_clause,[],[f68,f8996]) ).
fof(f8996,plain,
( spl0_1156
<=> ! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1156])]) ).
fof(f68,axiom,
! [X0,X1] :
( ~ class_Orderings_Oorder(X1)
| c_lessequals(X0,X0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Orderings_Oorder__class_Oaxioms__1_0) ).
fof(f8994,plain,
( spl0_1155
| ~ spl0_1051
| ~ spl0_1097 ),
inference(avatar_split_clause,[],[f8976,f8720,f7341,f8991]) ).
fof(f8991,plain,
( spl0_1155
<=> c_lessequals(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1155])]) ).
fof(f8720,plain,
( spl0_1097
<=> ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1097])]) ).
fof(f8976,plain,
( c_lessequals(c_0,c_1,tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1097 ),
inference(superposition,[],[f8721,f7343]) ).
fof(f8721,plain,
( ! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_1097 ),
inference(avatar_component_clause,[],[f8720]) ).
fof(f8987,plain,
( ~ spl0_1154
| ~ spl0_1052
| ~ spl0_1095 ),
inference(avatar_split_clause,[],[f8973,f8712,f7346,f8984]) ).
fof(f8984,plain,
( spl0_1154
<=> c_less(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1154])]) ).
fof(f8712,plain,
( spl0_1095
<=> ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1095])]) ).
fof(f8973,plain,
( ~ c_less(c_0,c_0,tc_IntDef_Oint)
| ~ spl0_1052
| ~ spl0_1095 ),
inference(superposition,[],[f8713,f7348]) ).
fof(f8713,plain,
( ! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint)
| ~ spl0_1095 ),
inference(avatar_component_clause,[],[f8712]) ).
fof(f8982,plain,
( ~ spl0_1153
| ~ spl0_1051
| ~ spl0_1095 ),
inference(avatar_split_clause,[],[f8972,f8712,f7341,f8979]) ).
fof(f8979,plain,
( spl0_1153
<=> c_less(c_1,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1153])]) ).
fof(f8972,plain,
( ~ c_less(c_1,c_0,tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1095 ),
inference(superposition,[],[f8713,f7343]) ).
fof(f8969,plain,
spl0_1152,
inference(avatar_split_clause,[],[f2840,f8966]) ).
fof(f8966,plain,
( spl0_1152
<=> c_0 = c_uminus(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1152])]) ).
fof(f2840,plain,
c_0 = c_uminus(c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1391,f1374]) ).
fof(f1374,axiom,
c_0 = c_IntDef_Oint(c_0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__eq__0__conv_1) ).
fof(f1391,axiom,
c_IntDef_Oint(c_0) = c_uminus(c_IntDef_Oint(c_0),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onegative__eq__positive_2) ).
fof(f8964,plain,
spl0_1151,
inference(avatar_split_clause,[],[f2836,f8962]) ).
fof(f8962,plain,
( spl0_1151
<=> ! [X3] : c_Binomial_Obinomial(X3,c_1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1151])]) ).
fof(f2836,plain,
! [X3] : c_Binomial_Obinomial(X3,c_1) = X3,
inference(forward_demodulation,[],[f1161,f2016]) ).
fof(f1161,axiom,
! [X3] : c_Binomial_Obinomial(X3,c_Suc(c_0)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Binomial_Obinomial__1_0) ).
fof(f8960,plain,
spl0_1150,
inference(avatar_split_clause,[],[f2835,f8957]) ).
fof(f8957,plain,
( spl0_1150
<=> c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_Obin__succ(c_Numeral_OPls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1150])]) ).
fof(f2835,plain,
c_Numeral_Obin__minus(c_Numeral_OMin) = c_Numeral_Obin__succ(c_Numeral_OPls),
inference(forward_demodulation,[],[f2125,f2156]) ).
fof(f2125,axiom,
c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB1) = c_Numeral_Obin__minus(c_Numeral_OMin),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__minus__Min_0) ).
fof(f8955,plain,
spl0_1149,
inference(avatar_split_clause,[],[f2740,f8953]) ).
fof(f8953,plain,
( spl0_1149
<=> ! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1149])]) ).
fof(f2740,axiom,
! [X3] : c_Message_OinvKey(c_Message_OinvKey(X3)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
fof(f8951,plain,
spl0_1148,
inference(avatar_split_clause,[],[f2739,f8948]) ).
fof(f8948,plain,
( spl0_1148
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1148])]) ).
fof(f2739,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OSpy,tc_Message_Oagent),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Osize__3_0) ).
fof(f8946,plain,
spl0_1147,
inference(avatar_split_clause,[],[f2737,f8943]) ).
fof(f8943,plain,
( spl0_1147
<=> c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1147])]) ).
fof(f2737,axiom,
c_0 = c_Nat_Osize(c_Message_Oagent_OServer,tc_Message_Oagent),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Osize__1_0) ).
fof(f8941,plain,
spl0_1146,
inference(avatar_split_clause,[],[f2714,f8939]) ).
fof(f8939,plain,
( spl0_1146
<=> ! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1146])]) ).
fof(f2714,axiom,
! [X1] : c_emptyset = c_Transitive__Closure_Otrancl(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Otrancl__empty_0) ).
fof(f8937,plain,
spl0_1145,
inference(avatar_split_clause,[],[f2709,f8935]) ).
fof(f2709,axiom,
! [X1] : c_Relation_OId = c_Transitive__Closure_Ortrancl(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Transitive__Closure_Ortrancl__empty_0) ).
fof(f8933,plain,
spl0_1144,
inference(avatar_split_clause,[],[f2698,f8931]) ).
fof(f2698,axiom,
! [X1,X12] : c_lessequals(X12,c_UNIV,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osubset__UNIV_0) ).
fof(f8929,plain,
spl0_1143,
inference(avatar_split_clause,[],[f2691,f8927]) ).
fof(f8927,plain,
( spl0_1143
<=> ! [X12,X1] : ~ c_less(X12,c_emptyset,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1143])]) ).
fof(f2691,axiom,
! [X1,X12] : ~ c_less(X12,c_emptyset,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Onot__psubset__empty_0) ).
fof(f8925,plain,
spl0_1142,
inference(avatar_split_clause,[],[f2651,f8923]) ).
fof(f8923,plain,
( spl0_1142
<=> ! [X1] : c_emptyset = c_Union(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1142])]) ).
fof(f2651,axiom,
! [X1] : c_emptyset = c_Union(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__empty_0) ).
fof(f8921,plain,
spl0_1141,
inference(avatar_split_clause,[],[f2649,f8919]) ).
fof(f8919,plain,
( spl0_1141
<=> ! [X1] : c_UNIV = c_Union(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1141])]) ).
fof(f2649,axiom,
! [X1] : c_UNIV = c_Union(c_UNIV,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUnion__UNIV_0) ).
fof(f8917,plain,
spl0_1140,
inference(avatar_split_clause,[],[f2625,f8915]) ).
fof(f8915,plain,
( spl0_1140
<=> ! [X1] : c_UNIV = c_Pow(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1140])]) ).
fof(f2625,axiom,
! [X1] : c_UNIV = c_Pow(c_UNIV,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OPow__UNIV_0) ).
fof(f8913,plain,
spl0_1139,
inference(avatar_split_clause,[],[f2619,f8911]) ).
fof(f8911,plain,
( spl0_1139
<=> ! [X1] : c_UNIV = c_Inter(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1139])]) ).
fof(f2619,axiom,
! [X1] : c_UNIV = c_Inter(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__empty_0) ).
fof(f8909,plain,
spl0_1138,
inference(avatar_split_clause,[],[f2612,f8907]) ).
fof(f8907,plain,
( spl0_1138
<=> ! [X1] : c_emptyset = c_Inter(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1138])]) ).
fof(f2612,axiom,
! [X1] : c_emptyset = c_Inter(c_UNIV,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OInter__UNIV_0) ).
fof(f8905,plain,
spl0_1137,
inference(avatar_split_clause,[],[f2567,f8902]) ).
fof(f8902,plain,
( spl0_1137
<=> c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1137])]) ).
fof(f2567,axiom,
c_emptyset = c_SetInterval_OlessThan(c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OlessThan__0_0) ).
fof(f8900,plain,
spl0_1136,
inference(avatar_split_clause,[],[f2528,f8897]) ).
fof(f8897,plain,
( spl0_1136
<=> c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1136])]) ).
fof(f2528,axiom,
c_UNIV = c_SetInterval_OatLeast(c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_SetInterval_OatLeast__0_0) ).
fof(f8895,plain,
spl0_1135,
inference(avatar_split_clause,[],[f2386,f8893]) ).
fof(f2386,axiom,
! [X1] : c_emptyset = c_Relation_Odiag(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Relation_Odiag__empty_0) ).
fof(f8891,plain,
spl0_1134,
inference(avatar_split_clause,[],[f2164,f8888]) ).
fof(f8888,plain,
( spl0_1134
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1134])]) ).
fof(f2164,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB1,tc_Numeral_Obit),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Osize__2_0) ).
fof(f8886,plain,
spl0_1133,
inference(avatar_split_clause,[],[f2163,f8883]) ).
fof(f8883,plain,
( spl0_1133
<=> c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1133])]) ).
fof(f2163,axiom,
c_0 = c_Nat_Osize(c_Numeral_Obit_OB0,tc_Numeral_Obit),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Osize__1_0) ).
fof(f8881,plain,
spl0_1132,
inference(avatar_split_clause,[],[f2152,f8879]) ).
fof(f8879,plain,
( spl0_1132
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1132])]) ).
fof(f2152,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__9_0) ).
fof(f8877,plain,
spl0_1131,
inference(avatar_split_clause,[],[f2151,f8875]) ).
fof(f8875,plain,
( spl0_1131
<=> ! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1131])]) ).
fof(f2151,axiom,
! [X1] :
( ~ class_Ring__and__Field_Oordered__idom(X1)
| ~ c_IntDef_Oneg(c_0,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__8_0) ).
fof(f8873,plain,
spl0_1130,
inference(avatar_split_clause,[],[f2135,f8871]) ).
fof(f8871,plain,
( spl0_1130
<=> ! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1130])]) ).
fof(f2135,axiom,
! [X1] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X1)
| ~ c_IntDef_Oiszero(c_1,X1) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__rel__simps__10_0) ).
fof(f8869,plain,
spl0_1129,
inference(avatar_split_clause,[],[f2130,f8867]) ).
fof(f2130,axiom,
! [X11] : c_Numeral_OPls = c_Numeral_Obin__mult(c_Numeral_OPls,X11),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__mult__Pls_0) ).
fof(f8865,plain,
spl0_1128,
inference(avatar_split_clause,[],[f2115,f8863]) ).
fof(f8863,plain,
( spl0_1128
<=> ! [X3] : c_Numeral_Obin__add(X3,c_Numeral_OPls) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1128])]) ).
fof(f8861,plain,
spl0_1127,
inference(avatar_split_clause,[],[f2114,f8859]) ).
fof(f8857,plain,
spl0_1126,
inference(avatar_split_clause,[],[f2106,f8854]) ).
fof(f2106,axiom,
c_Numeral_OPls = c_Numeral_OBit(c_Numeral_OPls,c_Numeral_Obit_OB0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_OPls__0__eq_0) ).
fof(f8852,plain,
spl0_1125,
inference(avatar_split_clause,[],[f2105,f8849]) ).
fof(f2105,axiom,
c_Numeral_OMin = c_Numeral_OBit(c_Numeral_OMin,c_Numeral_Obit_OB1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_OMin__1__eq_0) ).
fof(f8847,plain,
spl0_1124,
inference(avatar_split_clause,[],[f1866,f8844]) ).
fof(f1866,axiom,
c_0 = c_Numeral_Onumber__of(c_Numeral_OPls,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_NatBin_Onat__numeral__0__eq__0_0) ).
fof(f8842,plain,
spl0_1123,
inference(avatar_split_clause,[],[f1785,f8840]) ).
fof(f8840,plain,
( spl0_1123
<=> ! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1123])]) ).
fof(f1785,axiom,
! [X43] : c_List_Olist_ONil = c_List_Oupt(X43,c_0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oupt__eq__Nil__conv_1) ).
fof(f8838,plain,
spl0_1122,
inference(avatar_split_clause,[],[f1778,f8836]) ).
fof(f8836,plain,
( spl0_1122
<=> ! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1122])]) ).
fof(f1778,axiom,
! [X41] : c_List_Olist_ONil = c_List_Otl(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Otl_Osimps__1_0) ).
fof(f8834,plain,
spl0_1121,
inference(avatar_split_clause,[],[f1753,f8832]) ).
fof(f8832,plain,
( spl0_1121
<=> ! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1121])]) ).
fof(f1753,axiom,
! [X1] : c_emptyset = c_List_Oset(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oset__empty_1) ).
fof(f8830,plain,
spl0_1120,
inference(avatar_split_clause,[],[f1736,f8828]) ).
fof(f8828,plain,
( spl0_1120
<=> ! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1120])]) ).
fof(f1736,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orotate1(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Orotate1__is__Nil__conv_1) ).
fof(f8826,plain,
spl0_1119,
inference(avatar_split_clause,[],[f1718,f8824]) ).
fof(f8824,plain,
( spl0_1119
<=> ! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1119])]) ).
fof(f1718,axiom,
! [X1] : c_List_Olist_ONil = c_List_Oremdups(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oremdups__eq__nil__right__iff_1) ).
fof(f8822,plain,
spl0_1118,
inference(avatar_split_clause,[],[f1688,f8819]) ).
fof(f8819,plain,
( spl0_1118
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1118])]) ).
fof(f1688,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble8,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__9_0) ).
fof(f8817,plain,
spl0_1117,
inference(avatar_split_clause,[],[f1687,f8814]) ).
fof(f8814,plain,
( spl0_1117
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1117])]) ).
fof(f1687,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble7,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__8_0) ).
fof(f8812,plain,
spl0_1116,
inference(avatar_split_clause,[],[f1686,f8809]) ).
fof(f8809,plain,
( spl0_1116
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1116])]) ).
fof(f1686,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble6,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__7_0) ).
fof(f8807,plain,
spl0_1115,
inference(avatar_split_clause,[],[f1685,f8804]) ).
fof(f8804,plain,
( spl0_1115
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1115])]) ).
fof(f1685,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble5,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__6_0) ).
fof(f8802,plain,
spl0_1114,
inference(avatar_split_clause,[],[f1684,f8799]) ).
fof(f8799,plain,
( spl0_1114
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1114])]) ).
fof(f1684,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble4,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__5_0) ).
fof(f8797,plain,
spl0_1113,
inference(avatar_split_clause,[],[f1683,f8794]) ).
fof(f8794,plain,
( spl0_1113
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1113])]) ).
fof(f1683,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble3,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__4_0) ).
fof(f8792,plain,
spl0_1112,
inference(avatar_split_clause,[],[f1682,f8789]) ).
fof(f8789,plain,
( spl0_1112
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1112])]) ).
fof(f1682,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble2,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__3_0) ).
fof(f8787,plain,
spl0_1111,
inference(avatar_split_clause,[],[f1681,f8784]) ).
fof(f8784,plain,
( spl0_1111
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1111])]) ).
fof(f1681,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble1,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__2_0) ).
fof(f8782,plain,
spl0_1110,
inference(avatar_split_clause,[],[f1680,f8779]) ).
fof(f8779,plain,
( spl0_1110
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1110])]) ).
fof(f1680,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble0,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__1_0) ).
fof(f8777,plain,
spl0_1109,
inference(avatar_split_clause,[],[f1679,f8774]) ).
fof(f8774,plain,
( spl0_1109
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1109])]) ).
fof(f1679,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleF,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__16_0) ).
fof(f8772,plain,
spl0_1108,
inference(avatar_split_clause,[],[f1678,f8769]) ).
fof(f8769,plain,
( spl0_1108
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1108])]) ).
fof(f1678,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleE,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__15_0) ).
fof(f8767,plain,
spl0_1107,
inference(avatar_split_clause,[],[f1677,f8764]) ).
fof(f8764,plain,
( spl0_1107
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1107])]) ).
fof(f1677,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleD,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__14_0) ).
fof(f8762,plain,
spl0_1106,
inference(avatar_split_clause,[],[f1676,f8759]) ).
fof(f8759,plain,
( spl0_1106
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1106])]) ).
fof(f1676,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleC,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__13_0) ).
fof(f8757,plain,
spl0_1105,
inference(avatar_split_clause,[],[f1675,f8754]) ).
fof(f8754,plain,
( spl0_1105
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1105])]) ).
fof(f1675,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleB,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__12_0) ).
fof(f8752,plain,
spl0_1104,
inference(avatar_split_clause,[],[f1674,f8749]) ).
fof(f8749,plain,
( spl0_1104
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1104])]) ).
fof(f1674,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibbleA,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__11_0) ).
fof(f8747,plain,
spl0_1103,
inference(avatar_split_clause,[],[f1673,f8744]) ).
fof(f8744,plain,
( spl0_1103
<=> c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1103])]) ).
fof(f1673,axiom,
c_0 = c_Nat_Osize(c_List_Onibble_ONibble9,tc_List_Onibble),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onibble_Osize__10_0) ).
fof(f8742,plain,
spl0_1102,
inference(avatar_split_clause,[],[f1638,f8740]) ).
fof(f8740,plain,
( spl0_1102
<=> ! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1102])]) ).
fof(f1638,axiom,
! [X1] : c_UNIV = c_List_Olists(c_UNIV,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Olists__UNIV_0) ).
fof(f8738,plain,
spl0_1101,
inference(avatar_split_clause,[],[f1567,f8736]) ).
fof(f8736,plain,
( spl0_1101
<=> ! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1101])]) ).
fof(f1567,axiom,
! [X59,X43] : c_List_Odistinct(c_List_Oupt(X43,X59),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__upt_0) ).
fof(f8734,plain,
spl0_1100,
inference(avatar_split_clause,[],[f1543,f8732]) ).
fof(f8732,plain,
( spl0_1100
<=> ! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1100])]) ).
fof(f1543,axiom,
! [X41] : c_List_Olist_ONil = c_List_Oconcat(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oconcat_Osimps__1_0) ).
fof(f8730,plain,
spl0_1099,
inference(avatar_split_clause,[],[f1536,f8728]) ).
fof(f8728,plain,
( spl0_1099
<=> ! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1099])]) ).
fof(f1536,axiom,
! [X41] : c_List_Olist_ONil = c_List_Obutlast(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Obutlast_Osimps__1_0) ).
fof(f8726,plain,
spl0_1098,
inference(avatar_split_clause,[],[f1514,f8724]) ).
fof(f8724,plain,
( spl0_1098
<=> ! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1098])]) ).
fof(f1514,axiom,
! [X1] : c_List_Olist_ONil = c_List_Orev(c_List_Olist_ONil,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_ONil__is__rev__conv_1) ).
fof(f8722,plain,
spl0_1097,
inference(avatar_split_clause,[],[f1424,f8720]) ).
fof(f1424,axiom,
! [X21] : c_lessequals(c_0,c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Ozero__zle__int_0) ).
fof(f8718,plain,
spl0_1096,
inference(avatar_split_clause,[],[f1384,f8716]) ).
fof(f8716,plain,
( spl0_1096
<=> ! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1096])]) ).
fof(f1384,axiom,
! [X3] : c_IntDef_Onat(c_IntDef_Oint(X3)) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onat__int_0) ).
fof(f8714,plain,
spl0_1095,
inference(avatar_split_clause,[],[f1378,f8712]) ).
fof(f1378,axiom,
! [X16] : ~ c_less(c_IntDef_Oint(X16),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__less__0__conv_0) ).
fof(f8710,plain,
~ spl0_1094,
inference(avatar_split_clause,[],[f1309,f8707]) ).
fof(f1309,axiom,
~ c_in(c_UNIV,c_Finite__Set_OFinites,tc_set(tc_nat)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Infinite__Set_Onat__infinite_0) ).
fof(f8705,plain,
spl0_1093,
inference(avatar_split_clause,[],[f1296,f8703]) ).
fof(f8703,plain,
( spl0_1093
<=> ! [X1,X3] : c_Fun_Oid(X3,X1) = X3 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1093])]) ).
fof(f1296,axiom,
! [X3,X1] : c_Fun_Oid(X3,X1) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Fun_Oid__apply_0) ).
fof(f8701,plain,
spl0_1092,
inference(avatar_split_clause,[],[f1295,f8699]) ).
fof(f1295,axiom,
! [X3] : c_NatArith_Oof__nat(X3,tc_nat) = X3,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Oof__nat__id_0) ).
fof(f8697,plain,
spl0_1091,
inference(avatar_split_clause,[],[f1278,f8695]) ).
fof(f8695,plain,
( spl0_1091
<=> ! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1091])]) ).
fof(f1278,axiom,
! [X1] : c_0 = c_Finite__Set_Ocard(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_Ocard__empty_0) ).
fof(f8693,plain,
spl0_1090,
inference(avatar_split_clause,[],[f1255,f8690]) ).
fof(f8690,plain,
( spl0_1090
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1090])]) ).
fof(f1255,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_ORight,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Osize__2_0) ).
fof(f8688,plain,
spl0_1089,
inference(avatar_split_clause,[],[f1254,f8685]) ).
fof(f8685,plain,
( spl0_1089
<=> c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1089])]) ).
fof(f1254,axiom,
c_0 = c_Nat_Osize(c_Extraction_Osumbool_OLeft,tc_Extraction_Osumbool),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Osize__1_0) ).
fof(f8683,plain,
spl0_1088,
inference(avatar_split_clause,[],[f1184,f8680]) ).
fof(f8680,plain,
( spl0_1088
<=> c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1088])]) ).
fof(f1184,axiom,
c_0 = c_Nat_Osize(c_Product__Type_OUnity,tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ounit_Osize_0) ).
fof(f8678,plain,
spl0_1087,
inference(avatar_split_clause,[],[f1174,f8676]) ).
fof(f8676,plain,
( spl0_1087
<=> ! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1087])]) ).
fof(f1174,axiom,
! [X1,X42] : c_Datatype_Ooption_ONone != c_Datatype_Ooption_OSome(X42,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Ooption_Odistinct__2_0) ).
fof(f8674,plain,
spl0_1086,
inference(avatar_split_clause,[],[f1172,f8672]) ).
fof(f8672,plain,
( spl0_1086
<=> ! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1086])]) ).
fof(f1172,axiom,
! [X1] : c_emptyset = c_Datatype_Oo2s(c_Datatype_Ooption_ONone,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Datatype_Oo2s__empty__eq_1) ).
fof(f8670,plain,
spl0_1085,
inference(avatar_split_clause,[],[f1165,f8668]) ).
fof(f8668,plain,
( spl0_1085
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,X21) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1085])]) ).
fof(f1165,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,X21),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Binomial_Obinomial__n__n_0) ).
fof(f8666,plain,
spl0_1084,
inference(avatar_split_clause,[],[f1164,f8664]) ).
fof(f8664,plain,
( spl0_1084
<=> ! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1084])]) ).
fof(f1164,axiom,
! [X21] : c_1 = c_Binomial_Obinomial(X21,c_0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Binomial_Obinomial__n__0_0) ).
fof(f8662,plain,
spl0_1083,
inference(avatar_split_clause,[],[f250,f8660]) ).
fof(f8660,plain,
( spl0_1083
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1083])]) ).
fof(f250,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_set(X37)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_set_3) ).
fof(f8658,plain,
spl0_1082,
inference(avatar_split_clause,[],[f128,f8656]) ).
fof(f8656,plain,
( spl0_1082
<=> ! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1082])]) ).
fof(f128,axiom,
! [X37] :
( ~ class_Finite__Set_Ofinite(X37)
| class_Finite__Set_Ofinite(tc_Datatype_Ooption(X37)) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_Datatype__Ooption_0) ).
fof(f8654,plain,
spl0_1081,
inference(avatar_split_clause,[],[f112,f8652]) ).
fof(f112,axiom,
! [X1,X12] : c_lessequals(X12,X12,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Osubset__refl_0) ).
fof(f8650,plain,
spl0_1080,
inference(avatar_split_clause,[],[f101,f8648]) ).
fof(f8648,plain,
( spl0_1080
<=> ! [X12,X1] : c_lessequals(c_emptyset,X12,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1080])]) ).
fof(f101,axiom,
! [X1,X12] : c_lessequals(c_emptyset,X12,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oempty__subsetI_0) ).
fof(f8646,plain,
spl0_1079,
inference(avatar_split_clause,[],[f67,f8644]) ).
fof(f8644,plain,
( spl0_1079
<=> ! [X21] : c_less(c_0,c_Suc(X21),tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1079])]) ).
fof(f67,axiom,
! [X21] : c_less(c_0,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ozero__less__Suc_0) ).
fof(f8642,plain,
spl0_1078,
inference(avatar_split_clause,[],[f65,f8640]) ).
fof(f65,axiom,
! [X21] : c_less(X21,c_Suc(X21),tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OlessI_0) ).
fof(f8638,plain,
spl0_1077,
inference(avatar_split_clause,[],[f44,f8636]) ).
fof(f8636,plain,
( spl0_1077
<=> ! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1077])]) ).
fof(f44,axiom,
! [X1,X23] : c_List_Odistinct(c_List_Oremdups(X23,X1),X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct__remdups_0) ).
fof(f8634,plain,
spl0_1076,
inference(avatar_split_clause,[],[f28,f8632]) ).
fof(f8632,plain,
( spl0_1076
<=> ! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1076])]) ).
fof(f28,axiom,
! [X1] : c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(X1)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Finite__Set_OFinites_OemptyI_0) ).
fof(f8630,plain,
( ~ spl0_1075
| ~ spl0_1052
| ~ spl0_1054 ),
inference(avatar_split_clause,[],[f8619,f7356,f7346,f8627]) ).
fof(f8627,plain,
( spl0_1075
<=> c_IntDef_Oneg(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1075])]) ).
fof(f7356,plain,
( spl0_1054
<=> ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1054])]) ).
fof(f8619,plain,
( ~ c_IntDef_Oneg(c_0,tc_IntDef_Oint)
| ~ spl0_1052
| ~ spl0_1054 ),
inference(superposition,[],[f7357,f7348]) ).
fof(f7357,plain,
( ! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint)
| ~ spl0_1054 ),
inference(avatar_component_clause,[],[f7356]) ).
fof(f8625,plain,
( ~ spl0_1074
| ~ spl0_1051
| ~ spl0_1054 ),
inference(avatar_split_clause,[],[f8618,f7356,f7341,f8622]) ).
fof(f8622,plain,
( spl0_1074
<=> c_IntDef_Oneg(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1074])]) ).
fof(f8618,plain,
( ~ c_IntDef_Oneg(c_1,tc_IntDef_Oint)
| ~ spl0_1051
| ~ spl0_1054 ),
inference(superposition,[],[f7357,f7343]) ).
fof(f7445,plain,
spl0_1073,
inference(avatar_split_clause,[],[f2849,f7442]) ).
fof(f7442,plain,
( spl0_1073
<=> c_less(c_0,c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1073])]) ).
fof(f2849,plain,
c_less(c_0,c_1,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1486,f1464]) ).
fof(f1486,axiom,
! [X0] : c_less(c_0,c_Nat_Opower(c_HOL_Oabs(X0,tc_IntDef_Oint),c_0,tc_IntDef_Oint),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozero__less__zpower__abs__iff_2) ).
fof(f7440,plain,
spl0_1072,
inference(avatar_split_clause,[],[f2834,f7438]) ).
fof(f7438,plain,
( spl0_1072
<=> ! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1072])]) ).
fof(f2834,plain,
! [X16] : c_Divides_Oop_Advd(c_1,X16,tc_nat),
inference(forward_demodulation,[],[f24,f2016]) ).
fof(f24,axiom,
! [X16] : c_Divides_Oop_Advd(c_Suc(c_0),X16,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__1__left_0) ).
fof(f7436,plain,
spl0_1071,
inference(avatar_split_clause,[],[f2832,f7433]) ).
fof(f7433,plain,
( spl0_1071
<=> c_lessequals(c_0,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1071])]) ).
fof(f2832,plain,
c_lessequals(c_0,c_0,tc_IntDef_Oint),
inference(forward_demodulation,[],[f1377,f1374]) ).
fof(f1377,axiom,
c_lessequals(c_IntDef_Oint(c_0),c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__le__0__conv_1) ).
fof(f7431,plain,
spl0_1070,
inference(avatar_split_clause,[],[f2831,f7428]) ).
fof(f7428,plain,
( spl0_1070
<=> c_1 = c_IntDef_Onat(c_1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1070])]) ).
fof(f2831,plain,
c_1 = c_IntDef_Onat(c_1),
inference(forward_demodulation,[],[f1344,f2016]) ).
fof(f1344,axiom,
c_Suc(c_0) = c_IntDef_Onat(c_1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntArith_Onat__1_0) ).
fof(f7426,plain,
spl0_1069,
inference(avatar_split_clause,[],[f2791,f7423]) ).
fof(f7423,plain,
( spl0_1069
<=> c_emptyset = c_Message_Oanalz(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1069])]) ).
fof(f2791,axiom,
c_emptyset = c_Message_Oanalz(c_emptyset),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oanalz__empty_0) ).
fof(f7421,plain,
spl0_1068,
inference(avatar_split_clause,[],[f2770,f7418]) ).
fof(f2770,axiom,
c_emptyset = c_Message_Oparts(c_emptyset),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oparts__empty_0) ).
fof(f7416,plain,
spl0_1067,
inference(avatar_split_clause,[],[f2743,f7413]) ).
fof(f7413,plain,
( spl0_1067
<=> c_emptyset = c_Message_OkeysFor(c_emptyset) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1067])]) ).
fof(f2743,axiom,
c_emptyset = c_Message_OkeysFor(c_emptyset),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_OkeysFor__empty_0) ).
fof(f7411,plain,
spl0_1066,
inference(avatar_split_clause,[],[f2735,f7409]) ).
fof(f7409,plain,
( spl0_1066
<=> ! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1066])]) ).
fof(f2735,axiom,
! [X90] : c_Message_Oagent_OSpy != c_Message_Oagent_OFriend(X90),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Odistinct__6_0) ).
fof(f7407,plain,
spl0_1065,
inference(avatar_split_clause,[],[f2730,f7405]) ).
fof(f7405,plain,
( spl0_1065
<=> ! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1065])]) ).
fof(f2730,axiom,
! [X89] : c_Message_Oagent_OServer != c_Message_Oagent_OFriend(X89),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Odistinct__1_0) ).
fof(f7403,plain,
spl0_1064,
inference(avatar_split_clause,[],[f2672,f7401]) ).
fof(f7401,plain,
( spl0_1064
<=> ! [X4,X1] : ~ c_in(X4,c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1064])]) ).
fof(f2672,axiom,
! [X1,X4] : ~ c_in(X4,c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_Oempty__iff_0) ).
fof(f7399,plain,
spl0_1063,
inference(avatar_split_clause,[],[f2155,f7396]) ).
fof(f7396,plain,
( spl0_1063
<=> c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1063])]) ).
fof(f2155,axiom,
c_Numeral_OPls = c_Numeral_Obin__succ(c_Numeral_OMin),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__succ__Min_0) ).
fof(f7394,plain,
spl0_1062,
inference(avatar_split_clause,[],[f2134,f7391]) ).
fof(f2134,axiom,
c_Numeral_OMin = c_Numeral_Obin__pred(c_Numeral_OPls),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obin__pred__Pls_0) ).
fof(f7389,plain,
spl0_1061,
inference(avatar_split_clause,[],[f2126,f7386]) ).
fof(f7384,plain,
spl0_1060,
inference(avatar_split_clause,[],[f2091,f7382]) ).
fof(f7382,plain,
( spl0_1060
<=> ! [X21] : ~ c_less(X21,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1060])]) ).
fof(f2091,axiom,
! [X21] : ~ c_less(X21,c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Onot__less0_0) ).
fof(f7380,plain,
spl0_1059,
inference(avatar_split_clause,[],[f2049,f7377]) ).
fof(f2049,axiom,
c_less(c_0,c_1,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oless__one_1) ).
fof(f7375,plain,
spl0_1058,
inference(avatar_split_clause,[],[f2023,f7373]) ).
fof(f7373,plain,
( spl0_1058
<=> ! [X15] : c_0 != c_Suc(X15) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1058])]) ).
fof(f2023,axiom,
! [X15] : c_0 != c_Suc(X15),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_OSuc__not__Zero_0) ).
fof(f7371,plain,
spl0_1057,
inference(avatar_split_clause,[],[f2016,f7368]) ).
fof(f7366,plain,
spl0_1056,
inference(avatar_split_clause,[],[f1709,f7364]) ).
fof(f7364,plain,
( spl0_1056
<=> ! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1056])]) ).
fof(f1709,axiom,
! [X41,X0] : ~ c_List_Oop_Amem(X0,c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Oop_Amem_Osimps__1_0) ).
fof(f7362,plain,
spl0_1055,
inference(avatar_split_clause,[],[f1482,f7360]) ).
fof(f1482,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__refl_0) ).
fof(f7358,plain,
spl0_1054,
inference(avatar_split_clause,[],[f1393,f7356]) ).
fof(f1393,axiom,
! [X21] : ~ c_IntDef_Oneg(c_IntDef_Oint(X21),tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onot__neg__int_0) ).
fof(f7354,plain,
spl0_1053,
inference(avatar_split_clause,[],[f1386,f7351]) ).
fof(f7351,plain,
( spl0_1053
<=> c_0 = c_IntDef_Onat(c_0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1053])]) ).
fof(f1386,axiom,
c_0 = c_IntDef_Onat(c_0),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Onat__zero_0) ).
fof(f7349,plain,
spl0_1052,
inference(avatar_split_clause,[],[f1374,f7346]) ).
fof(f7344,plain,
spl0_1051,
inference(avatar_split_clause,[],[f1371,f7341]) ).
fof(f1371,axiom,
c_1 = c_IntDef_Oint(c_1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__1_0) ).
fof(f7339,plain,
spl0_1050,
inference(avatar_split_clause,[],[f1229,f7337]) ).
fof(f7337,plain,
( spl0_1050
<=> ! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1050])]) ).
fof(f1229,axiom,
! [X15] : c_Divides_Oop_Advd(X15,X15,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__refl_0) ).
fof(f7335,plain,
spl0_1049,
inference(avatar_split_clause,[],[f1159,f7333]) ).
fof(f7333,plain,
( spl0_1049
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1049])]) ).
fof(f1159,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Wellfounded__Recursion_Owellorder_5) ).
fof(f7331,plain,
spl0_1048,
inference(avatar_split_clause,[],[f1158,f7329]) ).
fof(f7329,plain,
( spl0_1048
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1048])]) ).
fof(f1158,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Wellfounded__Recursion_Owellorder_4) ).
fof(f7327,plain,
spl0_1047,
inference(avatar_split_clause,[],[f1157,f7325]) ).
fof(f7325,plain,
( spl0_1047
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1047])]) ).
fof(f1157,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Wellfounded__Recursion_Owellorder_3) ).
fof(f7323,plain,
spl0_1046,
inference(avatar_split_clause,[],[f1156,f7321]) ).
fof(f7321,plain,
( spl0_1046
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1046])]) ).
fof(f1156,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Wellfounded__Recursion_Owellorder_2) ).
fof(f7319,plain,
spl0_1045,
inference(avatar_split_clause,[],[f1155,f7317]) ).
fof(f7317,plain,
( spl0_1045
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1045])]) ).
fof(f1155,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Wellfounded__Recursion_Owellorder_1) ).
fof(f7315,plain,
spl0_1044,
inference(avatar_split_clause,[],[f1154,f7313]) ).
fof(f7313,plain,
( spl0_1044
<=> ! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1044])]) ).
fof(f1154,axiom,
! [X39] :
( ~ class_Wellfounded__Recursion_Owellorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Wellfounded__Recursion_Owellorder_0) ).
fof(f7311,plain,
spl0_1043,
inference(avatar_split_clause,[],[f1153,f7309]) ).
fof(f7309,plain,
( spl0_1043
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1043])]) ).
fof(f1153,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_9) ).
fof(f7307,plain,
spl0_1042,
inference(avatar_split_clause,[],[f1152,f7305]) ).
fof(f7305,plain,
( spl0_1042
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1042])]) ).
fof(f1152,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_8) ).
fof(f7303,plain,
spl0_1041,
inference(avatar_split_clause,[],[f1151,f7301]) ).
fof(f7301,plain,
( spl0_1041
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1041])]) ).
fof(f1151,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_7) ).
fof(f7299,plain,
spl0_1040,
inference(avatar_split_clause,[],[f1150,f7297]) ).
fof(f7297,plain,
( spl0_1040
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1040])]) ).
fof(f1150,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_6) ).
fof(f7295,plain,
spl0_1039,
inference(avatar_split_clause,[],[f1149,f7293]) ).
fof(f7293,plain,
( spl0_1039
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1039])]) ).
fof(f1149,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_5) ).
fof(f7291,plain,
spl0_1038,
inference(avatar_split_clause,[],[f1148,f7289]) ).
fof(f7289,plain,
( spl0_1038
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1038])]) ).
fof(f1148,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_4) ).
fof(f7287,plain,
spl0_1037,
inference(avatar_split_clause,[],[f1147,f7285]) ).
fof(f7285,plain,
( spl0_1037
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1037])]) ).
fof(f1147,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_3) ).
fof(f7283,plain,
spl0_1036,
inference(avatar_split_clause,[],[f1146,f7281]) ).
fof(f7281,plain,
( spl0_1036
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1036])]) ).
fof(f1146,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_2) ).
fof(f7279,plain,
spl0_1035,
inference(avatar_split_clause,[],[f1145,f7277]) ).
fof(f7277,plain,
( spl0_1035
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1035])]) ).
fof(f1145,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_15) ).
fof(f7275,plain,
spl0_1034,
inference(avatar_split_clause,[],[f1144,f7273]) ).
fof(f7273,plain,
( spl0_1034
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1034])]) ).
fof(f1144,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_14) ).
fof(f7271,plain,
spl0_1033,
inference(avatar_split_clause,[],[f1143,f7269]) ).
fof(f7269,plain,
( spl0_1033
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1033])]) ).
fof(f1143,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_13) ).
fof(f7267,plain,
spl0_1032,
inference(avatar_split_clause,[],[f1142,f7265]) ).
fof(f7265,plain,
( spl0_1032
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1032])]) ).
fof(f1142,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_12) ).
fof(f7263,plain,
spl0_1031,
inference(avatar_split_clause,[],[f1141,f7261]) ).
fof(f7261,plain,
( spl0_1031
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1031])]) ).
fof(f1141,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_11) ).
fof(f7259,plain,
spl0_1030,
inference(avatar_split_clause,[],[f1140,f7257]) ).
fof(f7257,plain,
( spl0_1030
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1030])]) ).
fof(f1140,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_10) ).
fof(f7255,plain,
spl0_1029,
inference(avatar_split_clause,[],[f1139,f7253]) ).
fof(f7253,plain,
( spl0_1029
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1029])]) ).
fof(f1139,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_1) ).
fof(f7251,plain,
spl0_1028,
inference(avatar_split_clause,[],[f1138,f7249]) ).
fof(f7249,plain,
( spl0_1028
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1028])]) ).
fof(f1138,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1__cancel_0) ).
fof(f7247,plain,
spl0_1027,
inference(avatar_split_clause,[],[f1137,f7245]) ).
fof(f7245,plain,
( spl0_1027
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1027])]) ).
fof(f1137,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_9) ).
fof(f7243,plain,
spl0_1026,
inference(avatar_split_clause,[],[f1136,f7241]) ).
fof(f7241,plain,
( spl0_1026
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1026])]) ).
fof(f1136,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_8) ).
fof(f7239,plain,
spl0_1025,
inference(avatar_split_clause,[],[f1135,f7237]) ).
fof(f7237,plain,
( spl0_1025
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1025])]) ).
fof(f1135,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_7) ).
fof(f7235,plain,
spl0_1024,
inference(avatar_split_clause,[],[f1134,f7233]) ).
fof(f7233,plain,
( spl0_1024
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1024])]) ).
fof(f1134,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_6) ).
fof(f7231,plain,
spl0_1023,
inference(avatar_split_clause,[],[f1133,f7229]) ).
fof(f7229,plain,
( spl0_1023
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1023])]) ).
fof(f1133,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_5) ).
fof(f7227,plain,
spl0_1022,
inference(avatar_split_clause,[],[f1132,f7225]) ).
fof(f7225,plain,
( spl0_1022
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1022])]) ).
fof(f1132,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_4) ).
fof(f7223,plain,
spl0_1021,
inference(avatar_split_clause,[],[f1131,f7221]) ).
fof(f7221,plain,
( spl0_1021
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1021])]) ).
fof(f1131,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_3) ).
fof(f7219,plain,
spl0_1020,
inference(avatar_split_clause,[],[f1130,f7217]) ).
fof(f7217,plain,
( spl0_1020
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1020])]) ).
fof(f1130,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_2) ).
fof(f7215,plain,
spl0_1019,
inference(avatar_split_clause,[],[f1129,f7213]) ).
fof(f7213,plain,
( spl0_1019
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1019])]) ).
fof(f1129,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_11) ).
fof(f7211,plain,
spl0_1018,
inference(avatar_split_clause,[],[f1128,f7209]) ).
fof(f7209,plain,
( spl0_1018
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1018])]) ).
fof(f1128,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_10) ).
fof(f7207,plain,
spl0_1017,
inference(avatar_split_clause,[],[f1127,f7205]) ).
fof(f7205,plain,
( spl0_1017
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1017])]) ).
fof(f1127,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_1) ).
fof(f7203,plain,
spl0_1016,
inference(avatar_split_clause,[],[f1126,f7201]) ).
fof(f7201,plain,
( spl0_1016
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1016])]) ).
fof(f1126,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__1_0) ).
fof(f7199,plain,
spl0_1015,
inference(avatar_split_clause,[],[f1125,f7197]) ).
fof(f7197,plain,
( spl0_1015
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1015])]) ).
fof(f1125,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_9) ).
fof(f7195,plain,
spl0_1014,
inference(avatar_split_clause,[],[f1124,f7193]) ).
fof(f7193,plain,
( spl0_1014
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1014])]) ).
fof(f1124,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_8) ).
fof(f7191,plain,
spl0_1013,
inference(avatar_split_clause,[],[f1123,f7189]) ).
fof(f7189,plain,
( spl0_1013
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1013])]) ).
fof(f1123,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_7) ).
fof(f7187,plain,
spl0_1012,
inference(avatar_split_clause,[],[f1122,f7185]) ).
fof(f7185,plain,
( spl0_1012
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1012])]) ).
fof(f1122,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_6) ).
fof(f7183,plain,
spl0_1011,
inference(avatar_split_clause,[],[f1121,f7181]) ).
fof(f7181,plain,
( spl0_1011
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1011])]) ).
fof(f1121,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_5) ).
fof(f7179,plain,
spl0_1010,
inference(avatar_split_clause,[],[f1120,f7177]) ).
fof(f7177,plain,
( spl0_1010
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1010])]) ).
fof(f1120,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_4) ).
fof(f7175,plain,
spl0_1009,
inference(avatar_split_clause,[],[f1119,f7173]) ).
fof(f7173,plain,
( spl0_1009
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1009])]) ).
fof(f1119,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_3) ).
fof(f7171,plain,
spl0_1008,
inference(avatar_split_clause,[],[f1118,f7169]) ).
fof(f7169,plain,
( spl0_1008
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1008])]) ).
fof(f1118,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_2) ).
fof(f7167,plain,
spl0_1007,
inference(avatar_split_clause,[],[f1117,f7165]) ).
fof(f7165,plain,
( spl0_1007
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1007])]) ).
fof(f1117,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_10) ).
fof(f7163,plain,
spl0_1006,
inference(avatar_split_clause,[],[f1116,f7161]) ).
fof(f7161,plain,
( spl0_1006
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1006])]) ).
fof(f1116,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_1) ).
fof(f7159,plain,
spl0_1005,
inference(avatar_split_clause,[],[f1115,f7157]) ).
fof(f7157,plain,
( spl0_1005
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1005])]) ).
fof(f1115,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0__cancel_0) ).
fof(f7155,plain,
spl0_1004,
inference(avatar_split_clause,[],[f1114,f7153]) ).
fof(f7153,plain,
( spl0_1004
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1004])]) ).
fof(f1114,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_7) ).
fof(f7151,plain,
spl0_1003,
inference(avatar_split_clause,[],[f1113,f7149]) ).
fof(f7149,plain,
( spl0_1003
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1003])]) ).
fof(f1113,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_6) ).
fof(f7147,plain,
spl0_1002,
inference(avatar_split_clause,[],[f1112,f7145]) ).
fof(f7145,plain,
( spl0_1002
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1002])]) ).
fof(f1112,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_5) ).
fof(f7143,plain,
spl0_1001,
inference(avatar_split_clause,[],[f1111,f7141]) ).
fof(f7141,plain,
( spl0_1001
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1001])]) ).
fof(f1111,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_4) ).
fof(f7139,plain,
spl0_1000,
inference(avatar_split_clause,[],[f1110,f7137]) ).
fof(f7137,plain,
( spl0_1000
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1000])]) ).
fof(f1110,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_3) ).
fof(f7135,plain,
spl0_999,
inference(avatar_split_clause,[],[f1109,f7133]) ).
fof(f7133,plain,
( spl0_999
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_999])]) ).
fof(f1109,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_2) ).
fof(f7131,plain,
spl0_998,
inference(avatar_split_clause,[],[f1108,f7129]) ).
fof(f7129,plain,
( spl0_998
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_998])]) ).
fof(f1108,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_1) ).
fof(f7127,plain,
spl0_997,
inference(avatar_split_clause,[],[f1107,f7125]) ).
fof(f7125,plain,
( spl0_997
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_997])]) ).
fof(f1107,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring__0_0) ).
fof(f7123,plain,
spl0_996,
inference(avatar_split_clause,[],[f1106,f7121]) ).
fof(f7121,plain,
( spl0_996
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_996])]) ).
fof(f1106,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring_4) ).
fof(f7119,plain,
spl0_995,
inference(avatar_split_clause,[],[f1105,f7117]) ).
fof(f7117,plain,
( spl0_995
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_995])]) ).
fof(f1105,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring_3) ).
fof(f7115,plain,
spl0_994,
inference(avatar_split_clause,[],[f1104,f7113]) ).
fof(f7113,plain,
( spl0_994
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_994])]) ).
fof(f1104,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring_2) ).
fof(f7111,plain,
spl0_993,
inference(avatar_split_clause,[],[f1103,f7109]) ).
fof(f7109,plain,
( spl0_993
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_993])]) ).
fof(f1103,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring_1) ).
fof(f7107,plain,
spl0_992,
inference(avatar_split_clause,[],[f1102,f7105]) ).
fof(f7105,plain,
( spl0_992
<=> ! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_992])]) ).
fof(f1102,axiom,
! [X39] :
( ~ class_Ring__and__Field_Osemiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Osemiring_0) ).
fof(f7103,plain,
spl0_991,
inference(avatar_split_clause,[],[f1101,f7101]) ).
fof(f7101,plain,
( spl0_991
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_991])]) ).
fof(f1101,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_9) ).
fof(f7099,plain,
spl0_990,
inference(avatar_split_clause,[],[f1100,f7097]) ).
fof(f7097,plain,
( spl0_990
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_990])]) ).
fof(f1100,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_8) ).
fof(f7095,plain,
spl0_989,
inference(avatar_split_clause,[],[f1099,f7093]) ).
fof(f7093,plain,
( spl0_989
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_989])]) ).
fof(f1099,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_7) ).
fof(f7091,plain,
spl0_988,
inference(avatar_split_clause,[],[f1098,f7089]) ).
fof(f7089,plain,
( spl0_988
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_988])]) ).
fof(f1098,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_6) ).
fof(f7087,plain,
spl0_987,
inference(avatar_split_clause,[],[f1097,f7085]) ).
fof(f7085,plain,
( spl0_987
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_987])]) ).
fof(f1097,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_5) ).
fof(f7083,plain,
spl0_986,
inference(avatar_split_clause,[],[f1096,f7081]) ).
fof(f7081,plain,
( spl0_986
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_986])]) ).
fof(f1096,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_4) ).
fof(f7079,plain,
spl0_985,
inference(avatar_split_clause,[],[f1095,f7077]) ).
fof(f7077,plain,
( spl0_985
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_985])]) ).
fof(f1095,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_3) ).
fof(f7075,plain,
spl0_984,
inference(avatar_split_clause,[],[f1094,f7073]) ).
fof(f7073,plain,
( spl0_984
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_984])]) ).
fof(f1094,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_2) ).
fof(f7071,plain,
spl0_983,
inference(avatar_split_clause,[],[f1093,f7069]) ).
fof(f7069,plain,
( spl0_983
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_983])]) ).
fof(f1093,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_19) ).
fof(f7067,plain,
spl0_982,
inference(avatar_split_clause,[],[f1092,f7065]) ).
fof(f7065,plain,
( spl0_982
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_982])]) ).
fof(f1092,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_18) ).
fof(f7063,plain,
spl0_981,
inference(avatar_split_clause,[],[f1091,f7061]) ).
fof(f7061,plain,
( spl0_981
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_981])]) ).
fof(f1091,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_17) ).
fof(f7059,plain,
spl0_980,
inference(avatar_split_clause,[],[f1090,f7057]) ).
fof(f7057,plain,
( spl0_980
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_980])]) ).
fof(f1090,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_16) ).
fof(f7055,plain,
spl0_979,
inference(avatar_split_clause,[],[f1089,f7053]) ).
fof(f7053,plain,
( spl0_979
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_979])]) ).
fof(f1089,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_15) ).
fof(f7051,plain,
spl0_978,
inference(avatar_split_clause,[],[f1088,f7049]) ).
fof(f7049,plain,
( spl0_978
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_978])]) ).
fof(f1088,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_14) ).
fof(f7047,plain,
spl0_977,
inference(avatar_split_clause,[],[f1087,f7045]) ).
fof(f7045,plain,
( spl0_977
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_977])]) ).
fof(f1087,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_13) ).
fof(f7043,plain,
spl0_976,
inference(avatar_split_clause,[],[f1086,f7041]) ).
fof(f7041,plain,
( spl0_976
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_976])]) ).
fof(f1086,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_12) ).
fof(f7039,plain,
spl0_975,
inference(avatar_split_clause,[],[f1085,f7037]) ).
fof(f7037,plain,
( spl0_975
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_975])]) ).
fof(f1085,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_11) ).
fof(f7035,plain,
spl0_974,
inference(avatar_split_clause,[],[f1084,f7033]) ).
fof(f7033,plain,
( spl0_974
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_974])]) ).
fof(f1084,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_10) ).
fof(f7031,plain,
spl0_973,
inference(avatar_split_clause,[],[f1083,f7029]) ).
fof(f7029,plain,
( spl0_973
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_973])]) ).
fof(f1083,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_1) ).
fof(f7027,plain,
spl0_972,
inference(avatar_split_clause,[],[f1082,f7025]) ).
fof(f7025,plain,
( spl0_972
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_972])]) ).
fof(f1082,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring__1_0) ).
fof(f7023,plain,
spl0_971,
inference(avatar_split_clause,[],[f1081,f7021]) ).
fof(f7021,plain,
( spl0_971
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_971])]) ).
fof(f1081,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_9) ).
fof(f7019,plain,
spl0_970,
inference(avatar_split_clause,[],[f1080,f7017]) ).
fof(f7017,plain,
( spl0_970
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_970])]) ).
fof(f1080,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_8) ).
fof(f7015,plain,
spl0_969,
inference(avatar_split_clause,[],[f1079,f7013]) ).
fof(f7013,plain,
( spl0_969
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_969])]) ).
fof(f1079,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_7) ).
fof(f7011,plain,
spl0_968,
inference(avatar_split_clause,[],[f1078,f7009]) ).
fof(f7009,plain,
( spl0_968
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_968])]) ).
fof(f1078,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_6) ).
fof(f7007,plain,
spl0_967,
inference(avatar_split_clause,[],[f1077,f7005]) ).
fof(f7005,plain,
( spl0_967
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_967])]) ).
fof(f1077,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_5) ).
fof(f7003,plain,
spl0_966,
inference(avatar_split_clause,[],[f1076,f7001]) ).
fof(f7001,plain,
( spl0_966
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_966])]) ).
fof(f1076,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_4) ).
fof(f6999,plain,
spl0_965,
inference(avatar_split_clause,[],[f1075,f6997]) ).
fof(f6997,plain,
( spl0_965
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_965])]) ).
fof(f1075,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_3) ).
fof(f6995,plain,
spl0_964,
inference(avatar_split_clause,[],[f1074,f6993]) ).
fof(f6993,plain,
( spl0_964
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_964])]) ).
fof(f1074,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_2) ).
fof(f6991,plain,
spl0_963,
inference(avatar_split_clause,[],[f1073,f6989]) ).
fof(f6989,plain,
( spl0_963
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_963])]) ).
fof(f1073,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_13) ).
fof(f6987,plain,
spl0_962,
inference(avatar_split_clause,[],[f1072,f6985]) ).
fof(f6985,plain,
( spl0_962
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_962])]) ).
fof(f1072,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_12) ).
fof(f6983,plain,
spl0_961,
inference(avatar_split_clause,[],[f1071,f6981]) ).
fof(f6981,plain,
( spl0_961
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_961])]) ).
fof(f1071,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_11) ).
fof(f6979,plain,
spl0_960,
inference(avatar_split_clause,[],[f1070,f6977]) ).
fof(f6977,plain,
( spl0_960
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_960])]) ).
fof(f1070,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_10) ).
fof(f6975,plain,
spl0_959,
inference(avatar_split_clause,[],[f1069,f6973]) ).
fof(f6973,plain,
( spl0_959
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_959])]) ).
fof(f1069,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_1) ).
fof(f6971,plain,
spl0_958,
inference(avatar_split_clause,[],[f1068,f6969]) ).
fof(f6969,plain,
( spl0_958
<=> ! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_958])]) ).
fof(f1068,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oring_0) ).
fof(f6967,plain,
spl0_957,
inference(avatar_split_clause,[],[f1067,f6965]) ).
fof(f6965,plain,
( spl0_957
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_957])]) ).
fof(f1067,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_9) ).
fof(f6963,plain,
spl0_956,
inference(avatar_split_clause,[],[f1066,f6961]) ).
fof(f6961,plain,
( spl0_956
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_956])]) ).
fof(f1066,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_8) ).
fof(f6959,plain,
spl0_955,
inference(avatar_split_clause,[],[f1065,f6957]) ).
fof(f6957,plain,
( spl0_955
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_955])]) ).
fof(f1065,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_7) ).
fof(f6955,plain,
spl0_954,
inference(avatar_split_clause,[],[f1064,f6953]) ).
fof(f6953,plain,
( spl0_954
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_954])]) ).
fof(f1064,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_6) ).
fof(f6951,plain,
spl0_953,
inference(avatar_split_clause,[],[f1063,f6949]) ).
fof(f6949,plain,
( spl0_953
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_953])]) ).
fof(f1063,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_5) ).
fof(f6947,plain,
spl0_952,
inference(avatar_split_clause,[],[f1062,f6945]) ).
fof(f6945,plain,
( spl0_952
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_952])]) ).
fof(f1062,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_4) ).
fof(f6943,plain,
spl0_951,
inference(avatar_split_clause,[],[f1061,f6941]) ).
fof(f6941,plain,
( spl0_951
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_951])]) ).
fof(f1061,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_3) ).
fof(f6939,plain,
spl0_950,
inference(avatar_split_clause,[],[f1060,f6937]) ).
fof(f6937,plain,
( spl0_950
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_950])]) ).
fof(f1060,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_2) ).
fof(f6935,plain,
spl0_949,
inference(avatar_split_clause,[],[f1059,f6933]) ).
fof(f6933,plain,
( spl0_949
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_949])]) ).
fof(f1059,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_11) ).
fof(f6931,plain,
spl0_948,
inference(avatar_split_clause,[],[f1058,f6929]) ).
fof(f6929,plain,
( spl0_948
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_948])]) ).
fof(f1058,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_10) ).
fof(f6927,plain,
spl0_947,
inference(avatar_split_clause,[],[f1057,f6925]) ).
fof(f6925,plain,
( spl0_947
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_947])]) ).
fof(f1057,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_1) ).
fof(f6923,plain,
spl0_946,
inference(avatar_split_clause,[],[f1056,f6921]) ).
fof(f6921,plain,
( spl0_946
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_946])]) ).
fof(f1056,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__semiring_0) ).
fof(f6919,plain,
spl0_945,
inference(avatar_split_clause,[],[f1055,f6917]) ).
fof(f6917,plain,
( spl0_945
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_945])]) ).
fof(f1055,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_9) ).
fof(f6915,plain,
spl0_944,
inference(avatar_split_clause,[],[f1054,f6913]) ).
fof(f6913,plain,
( spl0_944
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_944])]) ).
fof(f1054,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_8) ).
fof(f6911,plain,
spl0_943,
inference(avatar_split_clause,[],[f1053,f6909]) ).
fof(f6909,plain,
( spl0_943
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_943])]) ).
fof(f1053,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_7) ).
fof(f6907,plain,
spl0_942,
inference(avatar_split_clause,[],[f1052,f6905]) ).
fof(f6905,plain,
( spl0_942
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_942])]) ).
fof(f1052,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_6) ).
fof(f6903,plain,
spl0_941,
inference(avatar_split_clause,[],[f1051,f6901]) ).
fof(f6901,plain,
( spl0_941
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_941])]) ).
fof(f1051,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_5) ).
fof(f6899,plain,
spl0_940,
inference(avatar_split_clause,[],[f1050,f6897]) ).
fof(f6897,plain,
( spl0_940
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_940])]) ).
fof(f1050,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_4) ).
fof(f6895,plain,
spl0_939,
inference(avatar_split_clause,[],[f1049,f6893]) ).
fof(f6893,plain,
( spl0_939
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_939])]) ).
fof(f1049,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_3) ).
fof(f6891,plain,
spl0_938,
inference(avatar_split_clause,[],[f1048,f6889]) ).
fof(f6889,plain,
( spl0_938
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_938])]) ).
fof(f1048,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_22) ).
fof(f6887,plain,
spl0_937,
inference(avatar_split_clause,[],[f1047,f6885]) ).
fof(f6885,plain,
( spl0_937
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_937])]) ).
fof(f1047,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_21) ).
fof(f6883,plain,
spl0_936,
inference(avatar_split_clause,[],[f1046,f6881]) ).
fof(f6881,plain,
( spl0_936
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_936])]) ).
fof(f1046,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_20) ).
fof(f6879,plain,
spl0_935,
inference(avatar_split_clause,[],[f1045,f6877]) ).
fof(f6877,plain,
( spl0_935
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_935])]) ).
fof(f1045,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_2) ).
fof(f6875,plain,
spl0_934,
inference(avatar_split_clause,[],[f1044,f6873]) ).
fof(f6873,plain,
( spl0_934
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_934])]) ).
fof(f1044,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_19) ).
fof(f6871,plain,
spl0_933,
inference(avatar_split_clause,[],[f1043,f6869]) ).
fof(f6869,plain,
( spl0_933
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_933])]) ).
fof(f1043,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_18) ).
fof(f6867,plain,
spl0_932,
inference(avatar_split_clause,[],[f1042,f6865]) ).
fof(f6865,plain,
( spl0_932
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_932])]) ).
fof(f1042,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_17) ).
fof(f6863,plain,
spl0_931,
inference(avatar_split_clause,[],[f1041,f6861]) ).
fof(f6861,plain,
( spl0_931
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_931])]) ).
fof(f1041,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_16) ).
fof(f6859,plain,
spl0_930,
inference(avatar_split_clause,[],[f1040,f6857]) ).
fof(f6857,plain,
( spl0_930
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_930])]) ).
fof(f1040,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_15) ).
fof(f6855,plain,
spl0_929,
inference(avatar_split_clause,[],[f1039,f6853]) ).
fof(f6853,plain,
( spl0_929
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_929])]) ).
fof(f1039,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_14) ).
fof(f6851,plain,
spl0_928,
inference(avatar_split_clause,[],[f1038,f6849]) ).
fof(f6849,plain,
( spl0_928
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_928])]) ).
fof(f1038,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_13) ).
fof(f6847,plain,
spl0_927,
inference(avatar_split_clause,[],[f1037,f6845]) ).
fof(f6845,plain,
( spl0_927
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_927])]) ).
fof(f1037,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_12) ).
fof(f6843,plain,
spl0_926,
inference(avatar_split_clause,[],[f1036,f6841]) ).
fof(f6841,plain,
( spl0_926
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_926])]) ).
fof(f1036,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_11) ).
fof(f6839,plain,
spl0_925,
inference(avatar_split_clause,[],[f1035,f6837]) ).
fof(f6837,plain,
( spl0_925
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_925])]) ).
fof(f1035,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_10) ).
fof(f6835,plain,
spl0_924,
inference(avatar_split_clause,[],[f1034,f6833]) ).
fof(f6833,plain,
( spl0_924
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_924])]) ).
fof(f1034,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_1) ).
fof(f6831,plain,
spl0_923,
inference(avatar_split_clause,[],[f1033,f6829]) ).
fof(f6829,plain,
( spl0_923
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_923])]) ).
fof(f1033,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__ring_0) ).
fof(f6827,plain,
spl0_922,
inference(avatar_split_clause,[],[f1032,f6825]) ).
fof(f6825,plain,
( spl0_922
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_922])]) ).
fof(f1032,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_9) ).
fof(f6823,plain,
spl0_921,
inference(avatar_split_clause,[],[f1031,f6821]) ).
fof(f6821,plain,
( spl0_921
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_921])]) ).
fof(f1031,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_8) ).
fof(f6819,plain,
spl0_920,
inference(avatar_split_clause,[],[f1030,f6817]) ).
fof(f6817,plain,
( spl0_920
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_920])]) ).
fof(f1030,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_7) ).
fof(f6815,plain,
spl0_919,
inference(avatar_split_clause,[],[f1029,f6813]) ).
fof(f6813,plain,
( spl0_919
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_919])]) ).
fof(f1029,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_6) ).
fof(f6811,plain,
spl0_918,
inference(avatar_split_clause,[],[f1028,f6809]) ).
fof(f6809,plain,
( spl0_918
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_918])]) ).
fof(f1028,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_5) ).
fof(f6807,plain,
spl0_917,
inference(avatar_split_clause,[],[f1027,f6805]) ).
fof(f6805,plain,
( spl0_917
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_917])]) ).
fof(f1027,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_4) ).
fof(f6803,plain,
spl0_916,
inference(avatar_split_clause,[],[f1026,f6801]) ).
fof(f6801,plain,
( spl0_916
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_916])]) ).
fof(f1026,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_3) ).
fof(f6799,plain,
spl0_915,
inference(avatar_split_clause,[],[f1025,f6797]) ).
fof(f6797,plain,
( spl0_915
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_915])]) ).
fof(f1025,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_2) ).
fof(f6795,plain,
spl0_914,
inference(avatar_split_clause,[],[f1024,f6793]) ).
fof(f6793,plain,
( spl0_914
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_914])]) ).
fof(f1024,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_15) ).
fof(f6791,plain,
spl0_913,
inference(avatar_split_clause,[],[f1023,f6789]) ).
fof(f6789,plain,
( spl0_913
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_913])]) ).
fof(f1023,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_14) ).
fof(f6787,plain,
spl0_912,
inference(avatar_split_clause,[],[f1022,f6785]) ).
fof(f6785,plain,
( spl0_912
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_912])]) ).
fof(f1022,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_13) ).
fof(f6783,plain,
spl0_911,
inference(avatar_split_clause,[],[f1021,f6781]) ).
fof(f6781,plain,
( spl0_911
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_911])]) ).
fof(f1021,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_12) ).
fof(f6779,plain,
spl0_910,
inference(avatar_split_clause,[],[f1020,f6777]) ).
fof(f6777,plain,
( spl0_910
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_910])]) ).
fof(f1020,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_11) ).
fof(f6775,plain,
spl0_909,
inference(avatar_split_clause,[],[f1019,f6773]) ).
fof(f6773,plain,
( spl0_909
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_909])]) ).
fof(f1019,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_10) ).
fof(f6771,plain,
spl0_908,
inference(avatar_split_clause,[],[f1018,f6769]) ).
fof(f6769,plain,
( spl0_908
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_908])]) ).
fof(f1018,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_1) ).
fof(f6767,plain,
spl0_907,
inference(avatar_split_clause,[],[f1017,f6765]) ).
fof(f6765,plain,
( spl0_907
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_907])]) ).
fof(f1017,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__semiring_0) ).
fof(f6763,plain,
spl0_906,
inference(avatar_split_clause,[],[f1016,f6761]) ).
fof(f6761,plain,
( spl0_906
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_906])]) ).
fof(f1016,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_9) ).
fof(f6759,plain,
spl0_905,
inference(avatar_split_clause,[],[f1015,f6757]) ).
fof(f6757,plain,
( spl0_905
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_905])]) ).
fof(f1015,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_8) ).
fof(f6755,plain,
spl0_904,
inference(avatar_split_clause,[],[f1014,f6753]) ).
fof(f6753,plain,
( spl0_904
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_904])]) ).
fof(f1014,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_7) ).
fof(f6751,plain,
spl0_903,
inference(avatar_split_clause,[],[f1013,f6749]) ).
fof(f6749,plain,
( spl0_903
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_903])]) ).
fof(f1013,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_6) ).
fof(f6747,plain,
spl0_902,
inference(avatar_split_clause,[],[f1012,f6745]) ).
fof(f6745,plain,
( spl0_902
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_902])]) ).
fof(f1012,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_5) ).
fof(f6743,plain,
spl0_901,
inference(avatar_split_clause,[],[f1011,f6741]) ).
fof(f6741,plain,
( spl0_901
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_901])]) ).
fof(f1011,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_4) ).
fof(f6739,plain,
spl0_900,
inference(avatar_split_clause,[],[f1010,f6737]) ).
fof(f6737,plain,
( spl0_900
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_900])]) ).
fof(f1010,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_3) ).
fof(f6735,plain,
spl0_899,
inference(avatar_split_clause,[],[f1009,f6733]) ).
fof(f6733,plain,
( spl0_899
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_899])]) ).
fof(f1009,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_24) ).
fof(f6731,plain,
spl0_898,
inference(avatar_split_clause,[],[f1008,f6729]) ).
fof(f6729,plain,
( spl0_898
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_898])]) ).
fof(f1008,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_23) ).
fof(f6727,plain,
spl0_897,
inference(avatar_split_clause,[],[f1007,f6725]) ).
fof(f6725,plain,
( spl0_897
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_897])]) ).
fof(f1007,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_22) ).
fof(f6723,plain,
spl0_896,
inference(avatar_split_clause,[],[f1006,f6721]) ).
fof(f6721,plain,
( spl0_896
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_896])]) ).
fof(f1006,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_21) ).
fof(f6719,plain,
spl0_895,
inference(avatar_split_clause,[],[f1005,f6717]) ).
fof(f6717,plain,
( spl0_895
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_895])]) ).
fof(f1005,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_20) ).
fof(f6715,plain,
spl0_894,
inference(avatar_split_clause,[],[f1004,f6713]) ).
fof(f6713,plain,
( spl0_894
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_894])]) ).
fof(f1004,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_2) ).
fof(f6711,plain,
spl0_893,
inference(avatar_split_clause,[],[f1003,f6709]) ).
fof(f6709,plain,
( spl0_893
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_893])]) ).
fof(f1003,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_19) ).
fof(f6707,plain,
spl0_892,
inference(avatar_split_clause,[],[f1002,f6705]) ).
fof(f6705,plain,
( spl0_892
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_892])]) ).
fof(f1002,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_18) ).
fof(f6703,plain,
spl0_891,
inference(avatar_split_clause,[],[f1001,f6701]) ).
fof(f6701,plain,
( spl0_891
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_891])]) ).
fof(f1001,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_17) ).
fof(f6699,plain,
spl0_890,
inference(avatar_split_clause,[],[f1000,f6697]) ).
fof(f6697,plain,
( spl0_890
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_890])]) ).
fof(f1000,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_16) ).
fof(f6695,plain,
spl0_889,
inference(avatar_split_clause,[],[f999,f6693]) ).
fof(f6693,plain,
( spl0_889
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_889])]) ).
fof(f999,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_15) ).
fof(f6691,plain,
spl0_888,
inference(avatar_split_clause,[],[f998,f6689]) ).
fof(f6689,plain,
( spl0_888
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_888])]) ).
fof(f998,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_14) ).
fof(f6687,plain,
spl0_887,
inference(avatar_split_clause,[],[f997,f6685]) ).
fof(f6685,plain,
( spl0_887
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_887])]) ).
fof(f997,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_13) ).
fof(f6683,plain,
spl0_886,
inference(avatar_split_clause,[],[f996,f6681]) ).
fof(f6681,plain,
( spl0_886
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_886])]) ).
fof(f996,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_12) ).
fof(f6679,plain,
spl0_885,
inference(avatar_split_clause,[],[f995,f6677]) ).
fof(f6677,plain,
( spl0_885
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_885])]) ).
fof(f995,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_11) ).
fof(f6675,plain,
spl0_884,
inference(avatar_split_clause,[],[f994,f6673]) ).
fof(f6673,plain,
( spl0_884
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_884])]) ).
fof(f994,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_10) ).
fof(f6671,plain,
spl0_883,
inference(avatar_split_clause,[],[f993,f6669]) ).
fof(f6669,plain,
( spl0_883
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_883])]) ).
fof(f993,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_1) ).
fof(f6667,plain,
spl0_882,
inference(avatar_split_clause,[],[f992,f6665]) ).
fof(f6665,plain,
( spl0_882
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_882])]) ).
fof(f992,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__comm__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__comm__ring_0) ).
fof(f6663,plain,
spl0_881,
inference(avatar_split_clause,[],[f991,f6661]) ).
fof(f6661,plain,
( spl0_881
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_881])]) ).
fof(f991,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_9) ).
fof(f6659,plain,
spl0_880,
inference(avatar_split_clause,[],[f990,f6657]) ).
fof(f6657,plain,
( spl0_880
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_880])]) ).
fof(f990,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_8) ).
fof(f6655,plain,
spl0_879,
inference(avatar_split_clause,[],[f989,f6653]) ).
fof(f6653,plain,
( spl0_879
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_879])]) ).
fof(f989,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_7) ).
fof(f6651,plain,
spl0_878,
inference(avatar_split_clause,[],[f988,f6649]) ).
fof(f6649,plain,
( spl0_878
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_878])]) ).
fof(f988,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_6) ).
fof(f6647,plain,
spl0_877,
inference(avatar_split_clause,[],[f987,f6645]) ).
fof(f6645,plain,
( spl0_877
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_877])]) ).
fof(f987,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_5) ).
fof(f6643,plain,
spl0_876,
inference(avatar_split_clause,[],[f986,f6641]) ).
fof(f6641,plain,
( spl0_876
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_876])]) ).
fof(f986,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_4) ).
fof(f6639,plain,
spl0_875,
inference(avatar_split_clause,[],[f985,f6637]) ).
fof(f6637,plain,
( spl0_875
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_875])]) ).
fof(f985,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_3) ).
fof(f6635,plain,
spl0_874,
inference(avatar_split_clause,[],[f984,f6633]) ).
fof(f6633,plain,
( spl0_874
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_874])]) ).
fof(f984,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_2) ).
fof(f6631,plain,
spl0_873,
inference(avatar_split_clause,[],[f983,f6629]) ).
fof(f6629,plain,
( spl0_873
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_873])]) ).
fof(f983,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_15) ).
fof(f6627,plain,
spl0_872,
inference(avatar_split_clause,[],[f982,f6625]) ).
fof(f6625,plain,
( spl0_872
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_872])]) ).
fof(f982,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_14) ).
fof(f6623,plain,
spl0_871,
inference(avatar_split_clause,[],[f981,f6621]) ).
fof(f6621,plain,
( spl0_871
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_871])]) ).
fof(f981,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_13) ).
fof(f6619,plain,
spl0_870,
inference(avatar_split_clause,[],[f980,f6617]) ).
fof(f6617,plain,
( spl0_870
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_870])]) ).
fof(f980,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_12) ).
fof(f6615,plain,
spl0_869,
inference(avatar_split_clause,[],[f979,f6613]) ).
fof(f6613,plain,
( spl0_869
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_869])]) ).
fof(f979,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_11) ).
fof(f6611,plain,
spl0_868,
inference(avatar_split_clause,[],[f978,f6609]) ).
fof(f6609,plain,
( spl0_868
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_868])]) ).
fof(f978,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_10) ).
fof(f6607,plain,
spl0_867,
inference(avatar_split_clause,[],[f977,f6605]) ).
fof(f6605,plain,
( spl0_867
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_867])]) ).
fof(f977,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_1) ).
fof(f6603,plain,
spl0_866,
inference(avatar_split_clause,[],[f976,f6601]) ).
fof(f6601,plain,
( spl0_866
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_866])]) ).
fof(f976,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__semiring_0) ).
fof(f6599,plain,
spl0_865,
inference(avatar_split_clause,[],[f975,f6597]) ).
fof(f6597,plain,
( spl0_865
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_865])]) ).
fof(f975,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_9) ).
fof(f6595,plain,
spl0_864,
inference(avatar_split_clause,[],[f974,f6593]) ).
fof(f6593,plain,
( spl0_864
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_864])]) ).
fof(f974,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_8) ).
fof(f6591,plain,
spl0_863,
inference(avatar_split_clause,[],[f973,f6589]) ).
fof(f6589,plain,
( spl0_863
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_863])]) ).
fof(f973,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_7) ).
fof(f6587,plain,
spl0_862,
inference(avatar_split_clause,[],[f972,f6585]) ).
fof(f6585,plain,
( spl0_862
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_862])]) ).
fof(f972,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_6) ).
fof(f6583,plain,
spl0_861,
inference(avatar_split_clause,[],[f971,f6581]) ).
fof(f6581,plain,
( spl0_861
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_861])]) ).
fof(f971,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_5) ).
fof(f6579,plain,
spl0_860,
inference(avatar_split_clause,[],[f970,f6577]) ).
fof(f6577,plain,
( spl0_860
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_860])]) ).
fof(f970,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_4) ).
fof(f6575,plain,
spl0_859,
inference(avatar_split_clause,[],[f969,f6573]) ).
fof(f6573,plain,
( spl0_859
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_859])]) ).
fof(f969,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_3) ).
fof(f6571,plain,
spl0_858,
inference(avatar_split_clause,[],[f968,f6569]) ).
fof(f6569,plain,
( spl0_858
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_858])]) ).
fof(f968,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_20) ).
fof(f6567,plain,
spl0_857,
inference(avatar_split_clause,[],[f967,f6565]) ).
fof(f6565,plain,
( spl0_857
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_857])]) ).
fof(f967,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_2) ).
fof(f6563,plain,
spl0_856,
inference(avatar_split_clause,[],[f966,f6561]) ).
fof(f6561,plain,
( spl0_856
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_856])]) ).
fof(f966,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_19) ).
fof(f6559,plain,
spl0_855,
inference(avatar_split_clause,[],[f965,f6557]) ).
fof(f6557,plain,
( spl0_855
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_855])]) ).
fof(f965,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_18) ).
fof(f6555,plain,
spl0_854,
inference(avatar_split_clause,[],[f964,f6553]) ).
fof(f6553,plain,
( spl0_854
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_854])]) ).
fof(f964,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_17) ).
fof(f6551,plain,
spl0_853,
inference(avatar_split_clause,[],[f963,f6549]) ).
fof(f6549,plain,
( spl0_853
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_853])]) ).
fof(f963,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_16) ).
fof(f6547,plain,
spl0_852,
inference(avatar_split_clause,[],[f962,f6545]) ).
fof(f6545,plain,
( spl0_852
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_852])]) ).
fof(f962,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_15) ).
fof(f6543,plain,
spl0_851,
inference(avatar_split_clause,[],[f961,f6541]) ).
fof(f6541,plain,
( spl0_851
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_851])]) ).
fof(f961,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_14) ).
fof(f6539,plain,
spl0_850,
inference(avatar_split_clause,[],[f960,f6537]) ).
fof(f6537,plain,
( spl0_850
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_850])]) ).
fof(f960,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_13) ).
fof(f6535,plain,
spl0_849,
inference(avatar_split_clause,[],[f959,f6533]) ).
fof(f6533,plain,
( spl0_849
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_849])]) ).
fof(f959,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_12) ).
fof(f6531,plain,
spl0_848,
inference(avatar_split_clause,[],[f958,f6529]) ).
fof(f6529,plain,
( spl0_848
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_848])]) ).
fof(f958,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_11) ).
fof(f6527,plain,
spl0_847,
inference(avatar_split_clause,[],[f957,f6525]) ).
fof(f6525,plain,
( spl0_847
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_847])]) ).
fof(f957,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_10) ).
fof(f6523,plain,
spl0_846,
inference(avatar_split_clause,[],[f956,f6521]) ).
fof(f6521,plain,
( spl0_846
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_846])]) ).
fof(f956,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_1) ).
fof(f6519,plain,
spl0_845,
inference(avatar_split_clause,[],[f955,f6517]) ).
fof(f6517,plain,
( spl0_845
<=> ! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_845])]) ).
fof(f955,axiom,
! [X39] :
( ~ class_Ring__and__Field_Opordered__cancel__comm__semiring(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Opordered__cancel__comm__semiring_0) ).
fof(f6515,plain,
spl0_844,
inference(avatar_split_clause,[],[f954,f6513]) ).
fof(f6513,plain,
( spl0_844
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_844])]) ).
fof(f954,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_9) ).
fof(f6511,plain,
spl0_843,
inference(avatar_split_clause,[],[f953,f6509]) ).
fof(f6509,plain,
( spl0_843
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_843])]) ).
fof(f953,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_8) ).
fof(f6507,plain,
spl0_842,
inference(avatar_split_clause,[],[f952,f6505]) ).
fof(f6505,plain,
( spl0_842
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_842])]) ).
fof(f952,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_7) ).
fof(f6503,plain,
spl0_841,
inference(avatar_split_clause,[],[f951,f6501]) ).
fof(f6501,plain,
( spl0_841
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_841])]) ).
fof(f951,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_6) ).
fof(f6499,plain,
spl0_840,
inference(avatar_split_clause,[],[f950,f6497]) ).
fof(f6497,plain,
( spl0_840
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_840])]) ).
fof(f950,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_5) ).
fof(f6495,plain,
spl0_839,
inference(avatar_split_clause,[],[f949,f6493]) ).
fof(f6493,plain,
( spl0_839
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_839])]) ).
fof(f949,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_4) ).
fof(f6491,plain,
spl0_838,
inference(avatar_split_clause,[],[f948,f6489]) ).
fof(f6489,plain,
( spl0_838
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_838])]) ).
fof(f948,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_3) ).
fof(f6487,plain,
spl0_837,
inference(avatar_split_clause,[],[f947,f6485]) ).
fof(f6485,plain,
( spl0_837
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_837])]) ).
fof(f947,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_23) ).
fof(f6483,plain,
spl0_836,
inference(avatar_split_clause,[],[f946,f6481]) ).
fof(f6481,plain,
( spl0_836
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_836])]) ).
fof(f946,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_22) ).
fof(f6479,plain,
spl0_835,
inference(avatar_split_clause,[],[f945,f6477]) ).
fof(f6477,plain,
( spl0_835
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_835])]) ).
fof(f945,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_21) ).
fof(f6475,plain,
spl0_834,
inference(avatar_split_clause,[],[f944,f6473]) ).
fof(f6473,plain,
( spl0_834
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_834])]) ).
fof(f944,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_20) ).
fof(f6471,plain,
spl0_833,
inference(avatar_split_clause,[],[f943,f6469]) ).
fof(f6469,plain,
( spl0_833
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_833])]) ).
fof(f943,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_2) ).
fof(f6467,plain,
spl0_832,
inference(avatar_split_clause,[],[f942,f6465]) ).
fof(f6465,plain,
( spl0_832
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_832])]) ).
fof(f942,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_19) ).
fof(f6463,plain,
spl0_831,
inference(avatar_split_clause,[],[f941,f6461]) ).
fof(f6461,plain,
( spl0_831
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_831])]) ).
fof(f941,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_18) ).
fof(f6459,plain,
spl0_830,
inference(avatar_split_clause,[],[f940,f6457]) ).
fof(f6457,plain,
( spl0_830
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_830])]) ).
fof(f940,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_17) ).
fof(f6455,plain,
spl0_829,
inference(avatar_split_clause,[],[f939,f6453]) ).
fof(f6453,plain,
( spl0_829
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_829])]) ).
fof(f939,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_16) ).
fof(f6451,plain,
spl0_828,
inference(avatar_split_clause,[],[f938,f6449]) ).
fof(f6449,plain,
( spl0_828
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_828])]) ).
fof(f938,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_15) ).
fof(f6447,plain,
spl0_827,
inference(avatar_split_clause,[],[f937,f6445]) ).
fof(f6445,plain,
( spl0_827
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_827])]) ).
fof(f937,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_14) ).
fof(f6443,plain,
spl0_826,
inference(avatar_split_clause,[],[f936,f6441]) ).
fof(f6441,plain,
( spl0_826
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_826])]) ).
fof(f936,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_13) ).
fof(f6439,plain,
spl0_825,
inference(avatar_split_clause,[],[f935,f6437]) ).
fof(f6437,plain,
( spl0_825
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_825])]) ).
fof(f935,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_12) ).
fof(f6435,plain,
spl0_824,
inference(avatar_split_clause,[],[f934,f6433]) ).
fof(f6433,plain,
( spl0_824
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_824])]) ).
fof(f934,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_11) ).
fof(f6431,plain,
spl0_823,
inference(avatar_split_clause,[],[f933,f6429]) ).
fof(f6429,plain,
( spl0_823
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_823])]) ).
fof(f933,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_10) ).
fof(f6427,plain,
spl0_822,
inference(avatar_split_clause,[],[f932,f6425]) ).
fof(f6425,plain,
( spl0_822
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_822])]) ).
fof(f932,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_1) ).
fof(f6423,plain,
spl0_821,
inference(avatar_split_clause,[],[f931,f6421]) ).
fof(f6421,plain,
( spl0_821
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_821])]) ).
fof(f931,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semiring__strict_0) ).
fof(f6419,plain,
spl0_820,
inference(avatar_split_clause,[],[f930,f6417]) ).
fof(f6417,plain,
( spl0_820
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_820])]) ).
fof(f930,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_9) ).
fof(f6415,plain,
spl0_819,
inference(avatar_split_clause,[],[f929,f6413]) ).
fof(f6413,plain,
( spl0_819
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_819])]) ).
fof(f929,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_8) ).
fof(f6411,plain,
spl0_818,
inference(avatar_split_clause,[],[f928,f6409]) ).
fof(f6409,plain,
( spl0_818
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_818])]) ).
fof(f928,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_7) ).
fof(f6407,plain,
spl0_817,
inference(avatar_split_clause,[],[f927,f6405]) ).
fof(f6405,plain,
( spl0_817
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_817])]) ).
fof(f927,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_6) ).
fof(f6403,plain,
spl0_816,
inference(avatar_split_clause,[],[f926,f6401]) ).
fof(f6401,plain,
( spl0_816
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_816])]) ).
fof(f926,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_5) ).
fof(f6399,plain,
spl0_815,
inference(avatar_split_clause,[],[f925,f6397]) ).
fof(f6397,plain,
( spl0_815
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_815])]) ).
fof(f925,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_4) ).
fof(f6395,plain,
spl0_814,
inference(avatar_split_clause,[],[f924,f6393]) ).
fof(f6393,plain,
( spl0_814
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_814])]) ).
fof(f924,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_39) ).
fof(f6391,plain,
spl0_813,
inference(avatar_split_clause,[],[f923,f6389]) ).
fof(f6389,plain,
( spl0_813
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_813])]) ).
fof(f923,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_38) ).
fof(f6387,plain,
spl0_812,
inference(avatar_split_clause,[],[f922,f6385]) ).
fof(f6385,plain,
( spl0_812
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_812])]) ).
fof(f922,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_37) ).
fof(f6383,plain,
spl0_811,
inference(avatar_split_clause,[],[f921,f6381]) ).
fof(f6381,plain,
( spl0_811
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_811])]) ).
fof(f921,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_36) ).
fof(f6379,plain,
spl0_810,
inference(avatar_split_clause,[],[f920,f6377]) ).
fof(f6377,plain,
( spl0_810
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_810])]) ).
fof(f920,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_35) ).
fof(f6375,plain,
spl0_809,
inference(avatar_split_clause,[],[f919,f6373]) ).
fof(f6373,plain,
( spl0_809
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_809])]) ).
fof(f919,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_34) ).
fof(f6371,plain,
spl0_808,
inference(avatar_split_clause,[],[f918,f6369]) ).
fof(f6369,plain,
( spl0_808
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_808])]) ).
fof(f918,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_33) ).
fof(f6367,plain,
spl0_807,
inference(avatar_split_clause,[],[f917,f6365]) ).
fof(f6365,plain,
( spl0_807
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_807])]) ).
fof(f917,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_32) ).
fof(f6363,plain,
spl0_806,
inference(avatar_split_clause,[],[f916,f6361]) ).
fof(f6361,plain,
( spl0_806
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_806])]) ).
fof(f916,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_31) ).
fof(f6359,plain,
spl0_805,
inference(avatar_split_clause,[],[f915,f6357]) ).
fof(f6357,plain,
( spl0_805
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_805])]) ).
fof(f915,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_30) ).
fof(f6355,plain,
spl0_804,
inference(avatar_split_clause,[],[f914,f6353]) ).
fof(f6353,plain,
( spl0_804
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_804])]) ).
fof(f914,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_3) ).
fof(f6351,plain,
spl0_803,
inference(avatar_split_clause,[],[f913,f6349]) ).
fof(f6349,plain,
( spl0_803
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_803])]) ).
fof(f913,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_29) ).
fof(f6347,plain,
spl0_802,
inference(avatar_split_clause,[],[f912,f6345]) ).
fof(f6345,plain,
( spl0_802
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_802])]) ).
fof(f912,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_28) ).
fof(f6343,plain,
spl0_801,
inference(avatar_split_clause,[],[f911,f6341]) ).
fof(f6341,plain,
( spl0_801
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_801])]) ).
fof(f911,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_27) ).
fof(f6339,plain,
spl0_800,
inference(avatar_split_clause,[],[f910,f6337]) ).
fof(f6337,plain,
( spl0_800
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_800])]) ).
fof(f910,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_26) ).
fof(f6335,plain,
spl0_799,
inference(avatar_split_clause,[],[f909,f6333]) ).
fof(f6333,plain,
( spl0_799
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_799])]) ).
fof(f909,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_25) ).
fof(f6331,plain,
spl0_798,
inference(avatar_split_clause,[],[f908,f6329]) ).
fof(f6329,plain,
( spl0_798
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_798])]) ).
fof(f908,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_24) ).
fof(f6327,plain,
spl0_797,
inference(avatar_split_clause,[],[f907,f6325]) ).
fof(f6325,plain,
( spl0_797
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_797])]) ).
fof(f907,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_23) ).
fof(f6323,plain,
spl0_796,
inference(avatar_split_clause,[],[f906,f6321]) ).
fof(f6321,plain,
( spl0_796
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_796])]) ).
fof(f906,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_22) ).
fof(f6319,plain,
spl0_795,
inference(avatar_split_clause,[],[f905,f6317]) ).
fof(f6317,plain,
( spl0_795
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_795])]) ).
fof(f905,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_21) ).
fof(f6315,plain,
spl0_794,
inference(avatar_split_clause,[],[f904,f6313]) ).
fof(f6313,plain,
( spl0_794
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_794])]) ).
fof(f904,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_20) ).
fof(f6311,plain,
spl0_793,
inference(avatar_split_clause,[],[f903,f6309]) ).
fof(f6309,plain,
( spl0_793
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_793])]) ).
fof(f903,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_2) ).
fof(f6307,plain,
spl0_792,
inference(avatar_split_clause,[],[f902,f6305]) ).
fof(f6305,plain,
( spl0_792
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_792])]) ).
fof(f902,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_19) ).
fof(f6303,plain,
spl0_791,
inference(avatar_split_clause,[],[f901,f6301]) ).
fof(f6301,plain,
( spl0_791
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_791])]) ).
fof(f901,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_18) ).
fof(f6299,plain,
spl0_790,
inference(avatar_split_clause,[],[f900,f6297]) ).
fof(f6297,plain,
( spl0_790
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_790])]) ).
fof(f900,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_17) ).
fof(f6295,plain,
spl0_789,
inference(avatar_split_clause,[],[f899,f6293]) ).
fof(f6293,plain,
( spl0_789
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_789])]) ).
fof(f899,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_16) ).
fof(f6291,plain,
spl0_788,
inference(avatar_split_clause,[],[f898,f6289]) ).
fof(f6289,plain,
( spl0_788
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_788])]) ).
fof(f898,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_15) ).
fof(f6287,plain,
spl0_787,
inference(avatar_split_clause,[],[f897,f6285]) ).
fof(f6285,plain,
( spl0_787
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_787])]) ).
fof(f897,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_14) ).
fof(f6283,plain,
spl0_786,
inference(avatar_split_clause,[],[f896,f6281]) ).
fof(f6281,plain,
( spl0_786
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_786])]) ).
fof(f896,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_13) ).
fof(f6279,plain,
spl0_785,
inference(avatar_split_clause,[],[f895,f6277]) ).
fof(f6277,plain,
( spl0_785
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_785])]) ).
fof(f895,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_12) ).
fof(f6275,plain,
spl0_784,
inference(avatar_split_clause,[],[f894,f6273]) ).
fof(f6273,plain,
( spl0_784
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_784])]) ).
fof(f894,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_11) ).
fof(f6271,plain,
spl0_783,
inference(avatar_split_clause,[],[f893,f6269]) ).
fof(f6269,plain,
( spl0_783
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_783])]) ).
fof(f893,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_10) ).
fof(f6267,plain,
spl0_782,
inference(avatar_split_clause,[],[f892,f6265]) ).
fof(f6265,plain,
( spl0_782
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_782])]) ).
fof(f892,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_1) ).
fof(f6263,plain,
spl0_781,
inference(avatar_split_clause,[],[f891,f6261]) ).
fof(f6261,plain,
( spl0_781
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_781])]) ).
fof(f891,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__semidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__semidom_0) ).
fof(f6259,plain,
spl0_780,
inference(avatar_split_clause,[],[f890,f6257]) ).
fof(f6257,plain,
( spl0_780
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_780])]) ).
fof(f890,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_9) ).
fof(f6255,plain,
spl0_779,
inference(avatar_split_clause,[],[f889,f6253]) ).
fof(f6253,plain,
( spl0_779
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_779])]) ).
fof(f889,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_8) ).
fof(f6251,plain,
spl0_778,
inference(avatar_split_clause,[],[f888,f6249]) ).
fof(f6249,plain,
( spl0_778
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_778])]) ).
fof(f888,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_7) ).
fof(f6247,plain,
spl0_777,
inference(avatar_split_clause,[],[f887,f6245]) ).
fof(f6245,plain,
( spl0_777
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_777])]) ).
fof(f887,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_6) ).
fof(f6243,plain,
spl0_776,
inference(avatar_split_clause,[],[f886,f6241]) ).
fof(f6241,plain,
( spl0_776
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_776])]) ).
fof(f886,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_5) ).
fof(f6239,plain,
spl0_775,
inference(avatar_split_clause,[],[f885,f6237]) ).
fof(f6237,plain,
( spl0_775
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_775])]) ).
fof(f885,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_4) ).
fof(f6235,plain,
spl0_774,
inference(avatar_split_clause,[],[f884,f6233]) ).
fof(f6233,plain,
( spl0_774
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_774])]) ).
fof(f884,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_36) ).
fof(f6231,plain,
spl0_773,
inference(avatar_split_clause,[],[f883,f6229]) ).
fof(f6229,plain,
( spl0_773
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_773])]) ).
fof(f883,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_35) ).
fof(f6227,plain,
spl0_772,
inference(avatar_split_clause,[],[f882,f6225]) ).
fof(f6225,plain,
( spl0_772
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_772])]) ).
fof(f882,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_34) ).
fof(f6223,plain,
spl0_771,
inference(avatar_split_clause,[],[f881,f6221]) ).
fof(f6221,plain,
( spl0_771
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_771])]) ).
fof(f881,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_33) ).
fof(f6219,plain,
spl0_770,
inference(avatar_split_clause,[],[f880,f6217]) ).
fof(f6217,plain,
( spl0_770
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_770])]) ).
fof(f880,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_32) ).
fof(f6215,plain,
spl0_769,
inference(avatar_split_clause,[],[f879,f6213]) ).
fof(f6213,plain,
( spl0_769
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_769])]) ).
fof(f879,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_31) ).
fof(f6211,plain,
spl0_768,
inference(avatar_split_clause,[],[f878,f6209]) ).
fof(f6209,plain,
( spl0_768
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_768])]) ).
fof(f878,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_30) ).
fof(f6207,plain,
spl0_767,
inference(avatar_split_clause,[],[f877,f6205]) ).
fof(f6205,plain,
( spl0_767
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_767])]) ).
fof(f877,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_3) ).
fof(f6203,plain,
spl0_766,
inference(avatar_split_clause,[],[f876,f6201]) ).
fof(f6201,plain,
( spl0_766
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_766])]) ).
fof(f876,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_29) ).
fof(f6199,plain,
spl0_765,
inference(avatar_split_clause,[],[f875,f6197]) ).
fof(f6197,plain,
( spl0_765
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_765])]) ).
fof(f875,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_28) ).
fof(f6195,plain,
spl0_764,
inference(avatar_split_clause,[],[f874,f6193]) ).
fof(f6193,plain,
( spl0_764
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_764])]) ).
fof(f874,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_27) ).
fof(f6191,plain,
spl0_763,
inference(avatar_split_clause,[],[f873,f6189]) ).
fof(f6189,plain,
( spl0_763
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_763])]) ).
fof(f873,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_26) ).
fof(f6187,plain,
spl0_762,
inference(avatar_split_clause,[],[f872,f6185]) ).
fof(f6185,plain,
( spl0_762
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_762])]) ).
fof(f872,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_25) ).
fof(f6183,plain,
spl0_761,
inference(avatar_split_clause,[],[f871,f6181]) ).
fof(f6181,plain,
( spl0_761
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_761])]) ).
fof(f871,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_24) ).
fof(f6179,plain,
spl0_760,
inference(avatar_split_clause,[],[f870,f6177]) ).
fof(f6177,plain,
( spl0_760
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_760])]) ).
fof(f870,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_23) ).
fof(f6175,plain,
spl0_759,
inference(avatar_split_clause,[],[f869,f6173]) ).
fof(f6173,plain,
( spl0_759
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_759])]) ).
fof(f869,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_22) ).
fof(f6171,plain,
spl0_758,
inference(avatar_split_clause,[],[f868,f6169]) ).
fof(f6169,plain,
( spl0_758
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_758])]) ).
fof(f868,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_21) ).
fof(f6167,plain,
spl0_757,
inference(avatar_split_clause,[],[f867,f6165]) ).
fof(f6165,plain,
( spl0_757
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_757])]) ).
fof(f867,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_20) ).
fof(f6163,plain,
spl0_756,
inference(avatar_split_clause,[],[f866,f6161]) ).
fof(f6161,plain,
( spl0_756
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_756])]) ).
fof(f866,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_2) ).
fof(f6159,plain,
spl0_755,
inference(avatar_split_clause,[],[f865,f6157]) ).
fof(f6157,plain,
( spl0_755
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_755])]) ).
fof(f865,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_19) ).
fof(f6155,plain,
spl0_754,
inference(avatar_split_clause,[],[f864,f6153]) ).
fof(f6153,plain,
( spl0_754
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_754])]) ).
fof(f864,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_18) ).
fof(f6151,plain,
spl0_753,
inference(avatar_split_clause,[],[f863,f6149]) ).
fof(f6149,plain,
( spl0_753
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_753])]) ).
fof(f863,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_17) ).
fof(f6147,plain,
spl0_752,
inference(avatar_split_clause,[],[f862,f6145]) ).
fof(f6145,plain,
( spl0_752
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_752])]) ).
fof(f862,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_16) ).
fof(f6143,plain,
spl0_751,
inference(avatar_split_clause,[],[f861,f6141]) ).
fof(f6141,plain,
( spl0_751
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_751])]) ).
fof(f861,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_15) ).
fof(f6139,plain,
spl0_750,
inference(avatar_split_clause,[],[f860,f6137]) ).
fof(f6137,plain,
( spl0_750
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_750])]) ).
fof(f860,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_14) ).
fof(f6135,plain,
spl0_749,
inference(avatar_split_clause,[],[f859,f6133]) ).
fof(f6133,plain,
( spl0_749
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_749])]) ).
fof(f859,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_13) ).
fof(f6131,plain,
spl0_748,
inference(avatar_split_clause,[],[f858,f6129]) ).
fof(f6129,plain,
( spl0_748
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_748])]) ).
fof(f858,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_12) ).
fof(f6127,plain,
spl0_747,
inference(avatar_split_clause,[],[f857,f6125]) ).
fof(f6125,plain,
( spl0_747
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_747])]) ).
fof(f857,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_11) ).
fof(f6123,plain,
spl0_746,
inference(avatar_split_clause,[],[f856,f6121]) ).
fof(f6121,plain,
( spl0_746
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_746])]) ).
fof(f856,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_10) ).
fof(f6119,plain,
spl0_745,
inference(avatar_split_clause,[],[f855,f6117]) ).
fof(f6117,plain,
( spl0_745
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_745])]) ).
fof(f855,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_1) ).
fof(f6115,plain,
spl0_744,
inference(avatar_split_clause,[],[f854,f6113]) ).
fof(f6113,plain,
( spl0_744
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_744])]) ).
fof(f854,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__ring__strict(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__ring__strict_0) ).
fof(f6111,plain,
spl0_743,
inference(avatar_split_clause,[],[f853,f6109]) ).
fof(f6109,plain,
( spl0_743
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_743])]) ).
fof(f853,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_9) ).
fof(f6107,plain,
spl0_742,
inference(avatar_split_clause,[],[f852,f6105]) ).
fof(f6105,plain,
( spl0_742
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_742])]) ).
fof(f852,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_8) ).
fof(f6103,plain,
spl0_741,
inference(avatar_split_clause,[],[f851,f6101]) ).
fof(f6101,plain,
( spl0_741
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_741])]) ).
fof(f851,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_7) ).
fof(f6099,plain,
spl0_740,
inference(avatar_split_clause,[],[f850,f6097]) ).
fof(f6097,plain,
( spl0_740
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_740])]) ).
fof(f850,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_6) ).
fof(f6095,plain,
spl0_739,
inference(avatar_split_clause,[],[f849,f6093]) ).
fof(f6093,plain,
( spl0_739
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_739])]) ).
fof(f849,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_57) ).
fof(f6091,plain,
spl0_738,
inference(avatar_split_clause,[],[f848,f6089]) ).
fof(f6089,plain,
( spl0_738
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_738])]) ).
fof(f848,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_56) ).
fof(f6087,plain,
spl0_737,
inference(avatar_split_clause,[],[f847,f6085]) ).
fof(f6085,plain,
( spl0_737
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_737])]) ).
fof(f847,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_55) ).
fof(f6083,plain,
spl0_736,
inference(avatar_split_clause,[],[f846,f6081]) ).
fof(f6081,plain,
( spl0_736
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_736])]) ).
fof(f846,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_54) ).
fof(f6079,plain,
spl0_735,
inference(avatar_split_clause,[],[f845,f6077]) ).
fof(f6077,plain,
( spl0_735
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_735])]) ).
fof(f845,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_53) ).
fof(f6075,plain,
spl0_734,
inference(avatar_split_clause,[],[f844,f6073]) ).
fof(f6073,plain,
( spl0_734
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_734])]) ).
fof(f844,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_52) ).
fof(f6071,plain,
spl0_733,
inference(avatar_split_clause,[],[f843,f6069]) ).
fof(f6069,plain,
( spl0_733
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_733])]) ).
fof(f843,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_51) ).
fof(f6067,plain,
spl0_732,
inference(avatar_split_clause,[],[f842,f6065]) ).
fof(f6065,plain,
( spl0_732
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_732])]) ).
fof(f842,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_50) ).
fof(f6063,plain,
spl0_731,
inference(avatar_split_clause,[],[f841,f6061]) ).
fof(f6061,plain,
( spl0_731
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_731])]) ).
fof(f841,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_5) ).
fof(f6059,plain,
spl0_730,
inference(avatar_split_clause,[],[f840,f6057]) ).
fof(f6057,plain,
( spl0_730
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_730])]) ).
fof(f840,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_49) ).
fof(f6055,plain,
spl0_729,
inference(avatar_split_clause,[],[f839,f6053]) ).
fof(f6053,plain,
( spl0_729
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_729])]) ).
fof(f839,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_48) ).
fof(f6051,plain,
spl0_728,
inference(avatar_split_clause,[],[f838,f6049]) ).
fof(f6049,plain,
( spl0_728
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_728])]) ).
fof(f838,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_47) ).
fof(f6047,plain,
spl0_727,
inference(avatar_split_clause,[],[f837,f6045]) ).
fof(f6045,plain,
( spl0_727
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_727])]) ).
fof(f837,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_46) ).
fof(f6043,plain,
spl0_726,
inference(avatar_split_clause,[],[f836,f6041]) ).
fof(f6041,plain,
( spl0_726
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_726])]) ).
fof(f836,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_45) ).
fof(f6039,plain,
spl0_725,
inference(avatar_split_clause,[],[f835,f6037]) ).
fof(f6037,plain,
( spl0_725
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_725])]) ).
fof(f835,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_44) ).
fof(f6035,plain,
spl0_724,
inference(avatar_split_clause,[],[f834,f6033]) ).
fof(f6033,plain,
( spl0_724
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_724])]) ).
fof(f834,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_43) ).
fof(f6031,plain,
spl0_723,
inference(avatar_split_clause,[],[f833,f6029]) ).
fof(f6029,plain,
( spl0_723
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_723])]) ).
fof(f833,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_42) ).
fof(f6027,plain,
spl0_722,
inference(avatar_split_clause,[],[f832,f6025]) ).
fof(f6025,plain,
( spl0_722
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_722])]) ).
fof(f832,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_41) ).
fof(f6023,plain,
spl0_721,
inference(avatar_split_clause,[],[f831,f6021]) ).
fof(f6021,plain,
( spl0_721
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_721])]) ).
fof(f831,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_40) ).
fof(f6019,plain,
spl0_720,
inference(avatar_split_clause,[],[f830,f6017]) ).
fof(f6017,plain,
( spl0_720
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_720])]) ).
fof(f830,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_4) ).
fof(f6015,plain,
spl0_719,
inference(avatar_split_clause,[],[f829,f6013]) ).
fof(f6013,plain,
( spl0_719
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_719])]) ).
fof(f829,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_39) ).
fof(f6011,plain,
spl0_718,
inference(avatar_split_clause,[],[f828,f6009]) ).
fof(f6009,plain,
( spl0_718
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_718])]) ).
fof(f828,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_38) ).
fof(f6007,plain,
spl0_717,
inference(avatar_split_clause,[],[f827,f6005]) ).
fof(f6005,plain,
( spl0_717
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_717])]) ).
fof(f827,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_37) ).
fof(f6003,plain,
spl0_716,
inference(avatar_split_clause,[],[f826,f6001]) ).
fof(f6001,plain,
( spl0_716
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_716])]) ).
fof(f826,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_36) ).
fof(f5999,plain,
spl0_715,
inference(avatar_split_clause,[],[f825,f5997]) ).
fof(f5997,plain,
( spl0_715
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_715])]) ).
fof(f825,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_35) ).
fof(f5995,plain,
spl0_714,
inference(avatar_split_clause,[],[f824,f5993]) ).
fof(f5993,plain,
( spl0_714
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_714])]) ).
fof(f824,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_34) ).
fof(f5991,plain,
spl0_713,
inference(avatar_split_clause,[],[f823,f5989]) ).
fof(f5989,plain,
( spl0_713
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_713])]) ).
fof(f823,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_33) ).
fof(f5987,plain,
spl0_712,
inference(avatar_split_clause,[],[f822,f5985]) ).
fof(f5985,plain,
( spl0_712
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_712])]) ).
fof(f822,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_32) ).
fof(f5983,plain,
spl0_711,
inference(avatar_split_clause,[],[f821,f5981]) ).
fof(f5981,plain,
( spl0_711
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_711])]) ).
fof(f821,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_31) ).
fof(f5979,plain,
spl0_710,
inference(avatar_split_clause,[],[f820,f5977]) ).
fof(f5977,plain,
( spl0_710
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_710])]) ).
fof(f820,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_30) ).
fof(f5975,plain,
spl0_709,
inference(avatar_split_clause,[],[f819,f5973]) ).
fof(f5973,plain,
( spl0_709
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_709])]) ).
fof(f819,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_3) ).
fof(f5971,plain,
spl0_708,
inference(avatar_split_clause,[],[f818,f5969]) ).
fof(f5969,plain,
( spl0_708
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_708])]) ).
fof(f818,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_29) ).
fof(f5967,plain,
spl0_707,
inference(avatar_split_clause,[],[f817,f5965]) ).
fof(f5965,plain,
( spl0_707
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_707])]) ).
fof(f817,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_28) ).
fof(f5963,plain,
spl0_706,
inference(avatar_split_clause,[],[f816,f5961]) ).
fof(f5961,plain,
( spl0_706
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_706])]) ).
fof(f816,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_27) ).
fof(f5959,plain,
spl0_705,
inference(avatar_split_clause,[],[f815,f5957]) ).
fof(f5957,plain,
( spl0_705
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_705])]) ).
fof(f815,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_26) ).
fof(f5955,plain,
spl0_704,
inference(avatar_split_clause,[],[f814,f5953]) ).
fof(f5953,plain,
( spl0_704
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_704])]) ).
fof(f814,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_25) ).
fof(f5951,plain,
spl0_703,
inference(avatar_split_clause,[],[f813,f5949]) ).
fof(f5949,plain,
( spl0_703
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_703])]) ).
fof(f813,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_24) ).
fof(f5947,plain,
spl0_702,
inference(avatar_split_clause,[],[f812,f5945]) ).
fof(f5945,plain,
( spl0_702
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_702])]) ).
fof(f812,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_23) ).
fof(f5943,plain,
spl0_701,
inference(avatar_split_clause,[],[f811,f5941]) ).
fof(f5941,plain,
( spl0_701
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_701])]) ).
fof(f811,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_22) ).
fof(f5939,plain,
spl0_700,
inference(avatar_split_clause,[],[f810,f5937]) ).
fof(f5937,plain,
( spl0_700
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_700])]) ).
fof(f810,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_21) ).
fof(f5935,plain,
spl0_699,
inference(avatar_split_clause,[],[f809,f5933]) ).
fof(f5933,plain,
( spl0_699
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_699])]) ).
fof(f809,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_20) ).
fof(f5931,plain,
spl0_698,
inference(avatar_split_clause,[],[f808,f5929]) ).
fof(f5929,plain,
( spl0_698
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_698])]) ).
fof(f808,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_2) ).
fof(f5927,plain,
spl0_697,
inference(avatar_split_clause,[],[f807,f5925]) ).
fof(f5925,plain,
( spl0_697
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_697])]) ).
fof(f807,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_19) ).
fof(f5923,plain,
spl0_696,
inference(avatar_split_clause,[],[f806,f5921]) ).
fof(f5921,plain,
( spl0_696
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_696])]) ).
fof(f806,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_18) ).
fof(f5919,plain,
spl0_695,
inference(avatar_split_clause,[],[f805,f5917]) ).
fof(f5917,plain,
( spl0_695
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_695])]) ).
fof(f805,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_17) ).
fof(f5915,plain,
spl0_694,
inference(avatar_split_clause,[],[f804,f5913]) ).
fof(f5913,plain,
( spl0_694
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_694])]) ).
fof(f804,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_16) ).
fof(f5911,plain,
spl0_693,
inference(avatar_split_clause,[],[f803,f5909]) ).
fof(f5909,plain,
( spl0_693
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_693])]) ).
fof(f803,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_15) ).
fof(f5907,plain,
spl0_692,
inference(avatar_split_clause,[],[f802,f5905]) ).
fof(f5905,plain,
( spl0_692
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_692])]) ).
fof(f802,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_14) ).
fof(f5903,plain,
spl0_691,
inference(avatar_split_clause,[],[f801,f5901]) ).
fof(f5901,plain,
( spl0_691
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_691])]) ).
fof(f801,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_13) ).
fof(f5899,plain,
spl0_690,
inference(avatar_split_clause,[],[f800,f5897]) ).
fof(f5897,plain,
( spl0_690
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_690])]) ).
fof(f800,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_12) ).
fof(f5895,plain,
spl0_689,
inference(avatar_split_clause,[],[f799,f5893]) ).
fof(f5893,plain,
( spl0_689
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_689])]) ).
fof(f799,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_11) ).
fof(f5891,plain,
spl0_688,
inference(avatar_split_clause,[],[f798,f5889]) ).
fof(f5889,plain,
( spl0_688
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_688])]) ).
fof(f798,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_10) ).
fof(f5887,plain,
spl0_687,
inference(avatar_split_clause,[],[f797,f5885]) ).
fof(f5885,plain,
( spl0_687
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_687])]) ).
fof(f797,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_1) ).
fof(f5883,plain,
spl0_686,
inference(avatar_split_clause,[],[f796,f5881]) ).
fof(f5881,plain,
( spl0_686
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_686])]) ).
fof(f796,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__idom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__idom_0) ).
fof(f5879,plain,
spl0_685,
inference(avatar_split_clause,[],[f795,f5877]) ).
fof(f5877,plain,
( spl0_685
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_685])]) ).
fof(f795,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_9) ).
fof(f5875,plain,
spl0_684,
inference(avatar_split_clause,[],[f794,f5873]) ).
fof(f5873,plain,
( spl0_684
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_684])]) ).
fof(f794,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_8) ).
fof(f5871,plain,
spl0_683,
inference(avatar_split_clause,[],[f793,f5869]) ).
fof(f5869,plain,
( spl0_683
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_683])]) ).
fof(f793,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_7) ).
fof(f5867,plain,
spl0_682,
inference(avatar_split_clause,[],[f792,f5865]) ).
fof(f5865,plain,
( spl0_682
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_682])]) ).
fof(f792,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__semidom(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_60) ).
fof(f5863,plain,
spl0_681,
inference(avatar_split_clause,[],[f791,f5861]) ).
fof(f5861,plain,
( spl0_681
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_681])]) ).
fof(f791,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_6) ).
fof(f5859,plain,
spl0_680,
inference(avatar_split_clause,[],[f790,f5857]) ).
fof(f5857,plain,
( spl0_680
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_680])]) ).
fof(f790,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_59) ).
fof(f5855,plain,
spl0_679,
inference(avatar_split_clause,[],[f789,f5853]) ).
fof(f5853,plain,
( spl0_679
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_679])]) ).
fof(f789,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_58) ).
fof(f5851,plain,
spl0_678,
inference(avatar_split_clause,[],[f788,f5849]) ).
fof(f5849,plain,
( spl0_678
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_678])]) ).
fof(f788,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_57) ).
fof(f5847,plain,
spl0_677,
inference(avatar_split_clause,[],[f787,f5845]) ).
fof(f5845,plain,
( spl0_677
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_677])]) ).
fof(f787,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_56) ).
fof(f5843,plain,
spl0_676,
inference(avatar_split_clause,[],[f786,f5841]) ).
fof(f5841,plain,
( spl0_676
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_676])]) ).
fof(f786,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_55) ).
fof(f5839,plain,
spl0_675,
inference(avatar_split_clause,[],[f785,f5837]) ).
fof(f5837,plain,
( spl0_675
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_675])]) ).
fof(f785,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_54) ).
fof(f5835,plain,
spl0_674,
inference(avatar_split_clause,[],[f784,f5833]) ).
fof(f5833,plain,
( spl0_674
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_674])]) ).
fof(f784,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_53) ).
fof(f5831,plain,
spl0_673,
inference(avatar_split_clause,[],[f783,f5829]) ).
fof(f5829,plain,
( spl0_673
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_673])]) ).
fof(f783,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_52) ).
fof(f5827,plain,
spl0_672,
inference(avatar_split_clause,[],[f782,f5825]) ).
fof(f5825,plain,
( spl0_672
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_672])]) ).
fof(f782,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_51) ).
fof(f5823,plain,
spl0_671,
inference(avatar_split_clause,[],[f781,f5821]) ).
fof(f5821,plain,
( spl0_671
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_671])]) ).
fof(f781,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_50) ).
fof(f5819,plain,
spl0_670,
inference(avatar_split_clause,[],[f780,f5817]) ).
fof(f5817,plain,
( spl0_670
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_670])]) ).
fof(f780,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_5) ).
fof(f5815,plain,
spl0_669,
inference(avatar_split_clause,[],[f779,f5813]) ).
fof(f5813,plain,
( spl0_669
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_669])]) ).
fof(f779,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_49) ).
fof(f5811,plain,
spl0_668,
inference(avatar_split_clause,[],[f778,f5809]) ).
fof(f5809,plain,
( spl0_668
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_668])]) ).
fof(f778,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_48) ).
fof(f5807,plain,
spl0_667,
inference(avatar_split_clause,[],[f777,f5805]) ).
fof(f5805,plain,
( spl0_667
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_667])]) ).
fof(f777,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_47) ).
fof(f5803,plain,
spl0_666,
inference(avatar_split_clause,[],[f776,f5801]) ).
fof(f5801,plain,
( spl0_666
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_666])]) ).
fof(f776,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_46) ).
fof(f5799,plain,
spl0_665,
inference(avatar_split_clause,[],[f775,f5797]) ).
fof(f5797,plain,
( spl0_665
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_665])]) ).
fof(f775,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_45) ).
fof(f5795,plain,
spl0_664,
inference(avatar_split_clause,[],[f774,f5793]) ).
fof(f5793,plain,
( spl0_664
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_664])]) ).
fof(f774,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_44) ).
fof(f5791,plain,
spl0_663,
inference(avatar_split_clause,[],[f773,f5789]) ).
fof(f5789,plain,
( spl0_663
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Olordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_663])]) ).
fof(f773,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Olordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_43) ).
fof(f5787,plain,
spl0_662,
inference(avatar_split_clause,[],[f772,f5785]) ).
fof(f5785,plain,
( spl0_662
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_662])]) ).
fof(f772,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oaxclass__abs__if(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_42) ).
fof(f5783,plain,
spl0_661,
inference(avatar_split_clause,[],[f771,f5781]) ).
fof(f5781,plain,
( spl0_661
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_661])]) ).
fof(f771,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_41) ).
fof(f5779,plain,
spl0_660,
inference(avatar_split_clause,[],[f770,f5777]) ).
fof(f5777,plain,
( spl0_660
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_660])]) ).
fof(f770,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_40) ).
fof(f5775,plain,
spl0_659,
inference(avatar_split_clause,[],[f769,f5773]) ).
fof(f5773,plain,
( spl0_659
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_659])]) ).
fof(f769,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_4) ).
fof(f5771,plain,
spl0_658,
inference(avatar_split_clause,[],[f768,f5769]) ).
fof(f5769,plain,
( spl0_658
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_658])]) ).
fof(f768,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_39) ).
fof(f5767,plain,
spl0_657,
inference(avatar_split_clause,[],[f767,f5765]) ).
fof(f5765,plain,
( spl0_657
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_657])]) ).
fof(f767,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__ring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_38) ).
fof(f5763,plain,
spl0_656,
inference(avatar_split_clause,[],[f766,f5761]) ).
fof(f5761,plain,
( spl0_656
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_656])]) ).
fof(f766,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_37) ).
fof(f5759,plain,
spl0_655,
inference(avatar_split_clause,[],[f765,f5757]) ).
fof(f5757,plain,
( spl0_655
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_655])]) ).
fof(f765,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_36) ).
fof(f5755,plain,
spl0_654,
inference(avatar_split_clause,[],[f764,f5753]) ).
fof(f5753,plain,
( spl0_654
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_654])]) ).
fof(f764,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__comm__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_35) ).
fof(f5751,plain,
spl0_653,
inference(avatar_split_clause,[],[f763,f5749]) ).
fof(f5749,plain,
( spl0_653
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__idom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_653])]) ).
fof(f763,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oordered__idom(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_34) ).
fof(f5747,plain,
spl0_652,
inference(avatar_split_clause,[],[f762,f5745]) ).
fof(f5745,plain,
( spl0_652
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_652])]) ).
fof(f762,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_33) ).
fof(f5743,plain,
spl0_651,
inference(avatar_split_clause,[],[f761,f5741]) ).
fof(f5741,plain,
( spl0_651
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_651])]) ).
fof(f761,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_32) ).
fof(f5739,plain,
spl0_650,
inference(avatar_split_clause,[],[f760,f5737]) ).
fof(f5737,plain,
( spl0_650
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_650])]) ).
fof(f760,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_31) ).
fof(f5735,plain,
spl0_649,
inference(avatar_split_clause,[],[f759,f5733]) ).
fof(f5733,plain,
( spl0_649
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_649])]) ).
fof(f759,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_30) ).
fof(f5731,plain,
spl0_648,
inference(avatar_split_clause,[],[f758,f5729]) ).
fof(f5729,plain,
( spl0_648
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_648])]) ).
fof(f758,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_3) ).
fof(f5727,plain,
spl0_647,
inference(avatar_split_clause,[],[f757,f5725]) ).
fof(f5725,plain,
( spl0_647
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_647])]) ).
fof(f757,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_29) ).
fof(f5723,plain,
spl0_646,
inference(avatar_split_clause,[],[f756,f5721]) ).
fof(f5721,plain,
( spl0_646
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_646])]) ).
fof(f756,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_28) ).
fof(f5719,plain,
spl0_645,
inference(avatar_split_clause,[],[f755,f5717]) ).
fof(f5717,plain,
( spl0_645
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_645])]) ).
fof(f755,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_27) ).
fof(f5715,plain,
spl0_644,
inference(avatar_split_clause,[],[f754,f5713]) ).
fof(f5713,plain,
( spl0_644
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_644])]) ).
fof(f754,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_26) ).
fof(f5711,plain,
spl0_643,
inference(avatar_split_clause,[],[f753,f5709]) ).
fof(f5709,plain,
( spl0_643
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_643])]) ).
fof(f753,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_25) ).
fof(f5707,plain,
spl0_642,
inference(avatar_split_clause,[],[f752,f5705]) ).
fof(f5705,plain,
( spl0_642
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_642])]) ).
fof(f752,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_24) ).
fof(f5703,plain,
spl0_641,
inference(avatar_split_clause,[],[f751,f5701]) ).
fof(f5701,plain,
( spl0_641
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_641])]) ).
fof(f751,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_23) ).
fof(f5699,plain,
spl0_640,
inference(avatar_split_clause,[],[f750,f5697]) ).
fof(f5697,plain,
( spl0_640
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_640])]) ).
fof(f750,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_22) ).
fof(f5695,plain,
spl0_639,
inference(avatar_split_clause,[],[f749,f5693]) ).
fof(f5693,plain,
( spl0_639
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_639])]) ).
fof(f749,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_21) ).
fof(f5691,plain,
spl0_638,
inference(avatar_split_clause,[],[f748,f5689]) ).
fof(f5689,plain,
( spl0_638
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_638])]) ).
fof(f748,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_20) ).
fof(f5687,plain,
spl0_637,
inference(avatar_split_clause,[],[f747,f5685]) ).
fof(f5685,plain,
( spl0_637
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_637])]) ).
fof(f747,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_2) ).
fof(f5683,plain,
spl0_636,
inference(avatar_split_clause,[],[f746,f5681]) ).
fof(f5681,plain,
( spl0_636
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_636])]) ).
fof(f746,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_19) ).
fof(f5679,plain,
spl0_635,
inference(avatar_split_clause,[],[f745,f5677]) ).
fof(f5677,plain,
( spl0_635
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_635])]) ).
fof(f745,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_18) ).
fof(f5675,plain,
spl0_634,
inference(avatar_split_clause,[],[f744,f5673]) ).
fof(f5673,plain,
( spl0_634
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_634])]) ).
fof(f744,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_17) ).
fof(f5671,plain,
spl0_633,
inference(avatar_split_clause,[],[f743,f5669]) ).
fof(f5669,plain,
( spl0_633
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_633])]) ).
fof(f743,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_16) ).
fof(f5667,plain,
spl0_632,
inference(avatar_split_clause,[],[f742,f5665]) ).
fof(f5665,plain,
( spl0_632
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_632])]) ).
fof(f742,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_15) ).
fof(f5663,plain,
spl0_631,
inference(avatar_split_clause,[],[f741,f5661]) ).
fof(f5661,plain,
( spl0_631
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_631])]) ).
fof(f741,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_14) ).
fof(f5659,plain,
spl0_630,
inference(avatar_split_clause,[],[f740,f5657]) ).
fof(f5657,plain,
( spl0_630
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_630])]) ).
fof(f740,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_13) ).
fof(f5655,plain,
spl0_629,
inference(avatar_split_clause,[],[f739,f5653]) ).
fof(f5653,plain,
( spl0_629
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_629])]) ).
fof(f739,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_12) ).
fof(f5651,plain,
spl0_628,
inference(avatar_split_clause,[],[f738,f5649]) ).
fof(f5649,plain,
( spl0_628
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_628])]) ).
fof(f738,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_11) ).
fof(f5647,plain,
spl0_627,
inference(avatar_split_clause,[],[f737,f5645]) ).
fof(f5645,plain,
( spl0_627
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_627])]) ).
fof(f737,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_10) ).
fof(f5643,plain,
spl0_626,
inference(avatar_split_clause,[],[f736,f5641]) ).
fof(f5641,plain,
( spl0_626
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Oinverse(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_626])]) ).
fof(f736,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_HOL_Oinverse(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_1) ).
fof(f5639,plain,
spl0_625,
inference(avatar_split_clause,[],[f735,f5637]) ).
fof(f5637,plain,
( spl0_625
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ofield(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_625])]) ).
fof(f735,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__field(X39)
| class_Ring__and__Field_Ofield(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__field_0) ).
fof(f5635,plain,
spl0_624,
inference(avatar_split_clause,[],[f734,f5633]) ).
fof(f5633,plain,
( spl0_624
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_624])]) ).
fof(f734,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_9) ).
fof(f5631,plain,
spl0_623,
inference(avatar_split_clause,[],[f733,f5629]) ).
fof(f5629,plain,
( spl0_623
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_623])]) ).
fof(f733,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_8) ).
fof(f5627,plain,
spl0_622,
inference(avatar_split_clause,[],[f732,f5625]) ).
fof(f5625,plain,
( spl0_622
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_622])]) ).
fof(f732,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_7) ).
fof(f5623,plain,
spl0_621,
inference(avatar_split_clause,[],[f731,f5621]) ).
fof(f5621,plain,
( spl0_621
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_621])]) ).
fof(f731,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_6) ).
fof(f5619,plain,
spl0_620,
inference(avatar_split_clause,[],[f730,f5617]) ).
fof(f5617,plain,
( spl0_620
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_620])]) ).
fof(f730,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_5) ).
fof(f5615,plain,
spl0_619,
inference(avatar_split_clause,[],[f729,f5613]) ).
fof(f5613,plain,
( spl0_619
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_619])]) ).
fof(f729,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_4) ).
fof(f5611,plain,
spl0_618,
inference(avatar_split_clause,[],[f728,f5609]) ).
fof(f5609,plain,
( spl0_618
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_618])]) ).
fof(f728,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_3) ).
fof(f5607,plain,
spl0_617,
inference(avatar_split_clause,[],[f727,f5605]) ).
fof(f5605,plain,
( spl0_617
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_617])]) ).
fof(f727,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_29) ).
fof(f5603,plain,
spl0_616,
inference(avatar_split_clause,[],[f726,f5601]) ).
fof(f5601,plain,
( spl0_616
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_616])]) ).
fof(f726,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__comm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_28) ).
fof(f5599,plain,
spl0_615,
inference(avatar_split_clause,[],[f725,f5597]) ).
fof(f5597,plain,
( spl0_615
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_615])]) ).
fof(f725,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_27) ).
fof(f5595,plain,
spl0_614,
inference(avatar_split_clause,[],[f724,f5593]) ).
fof(f5593,plain,
( spl0_614
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_614])]) ).
fof(f724,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_26) ).
fof(f5591,plain,
spl0_613,
inference(avatar_split_clause,[],[f723,f5589]) ).
fof(f5589,plain,
( spl0_613
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_613])]) ).
fof(f723,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_25) ).
fof(f5587,plain,
spl0_612,
inference(avatar_split_clause,[],[f722,f5585]) ).
fof(f5585,plain,
( spl0_612
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_612])]) ).
fof(f722,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Oordered__semiring__strict(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_24) ).
fof(f5583,plain,
spl0_611,
inference(avatar_split_clause,[],[f721,f5581]) ).
fof(f5581,plain,
( spl0_611
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_611])]) ).
fof(f721,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_23) ).
fof(f5579,plain,
spl0_610,
inference(avatar_split_clause,[],[f720,f5577]) ).
fof(f5577,plain,
( spl0_610
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_610])]) ).
fof(f720,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_22) ).
fof(f5575,plain,
spl0_609,
inference(avatar_split_clause,[],[f719,f5573]) ).
fof(f5573,plain,
( spl0_609
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_609])]) ).
fof(f719,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_21) ).
fof(f5571,plain,
spl0_608,
inference(avatar_split_clause,[],[f718,f5569]) ).
fof(f5569,plain,
( spl0_608
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_608])]) ).
fof(f718,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_20) ).
fof(f5567,plain,
spl0_607,
inference(avatar_split_clause,[],[f717,f5565]) ).
fof(f5565,plain,
( spl0_607
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_607])]) ).
fof(f717,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_2) ).
fof(f5563,plain,
spl0_606,
inference(avatar_split_clause,[],[f716,f5561]) ).
fof(f5561,plain,
( spl0_606
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_606])]) ).
fof(f716,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_19) ).
fof(f5559,plain,
spl0_605,
inference(avatar_split_clause,[],[f715,f5557]) ).
fof(f5557,plain,
( spl0_605
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_605])]) ).
fof(f715,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_18) ).
fof(f5555,plain,
spl0_604,
inference(avatar_split_clause,[],[f714,f5553]) ).
fof(f5553,plain,
( spl0_604
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_604])]) ).
fof(f714,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_17) ).
fof(f5551,plain,
spl0_603,
inference(avatar_split_clause,[],[f713,f5549]) ).
fof(f5549,plain,
( spl0_603
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_603])]) ).
fof(f713,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_16) ).
fof(f5547,plain,
spl0_602,
inference(avatar_split_clause,[],[f712,f5545]) ).
fof(f5545,plain,
( spl0_602
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_602])]) ).
fof(f712,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_15) ).
fof(f5543,plain,
spl0_601,
inference(avatar_split_clause,[],[f711,f5541]) ).
fof(f5541,plain,
( spl0_601
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_601])]) ).
fof(f711,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_14) ).
fof(f5539,plain,
spl0_600,
inference(avatar_split_clause,[],[f710,f5537]) ).
fof(f5537,plain,
( spl0_600
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_600])]) ).
fof(f710,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_13) ).
fof(f5535,plain,
spl0_599,
inference(avatar_split_clause,[],[f709,f5533]) ).
fof(f5533,plain,
( spl0_599
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_599])]) ).
fof(f709,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_12) ).
fof(f5531,plain,
spl0_598,
inference(avatar_split_clause,[],[f708,f5529]) ).
fof(f5529,plain,
( spl0_598
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_598])]) ).
fof(f708,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_11) ).
fof(f5527,plain,
spl0_597,
inference(avatar_split_clause,[],[f707,f5525]) ).
fof(f5525,plain,
( spl0_597
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_597])]) ).
fof(f707,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_10) ).
fof(f5523,plain,
spl0_596,
inference(avatar_split_clause,[],[f706,f5521]) ).
fof(f5521,plain,
( spl0_596
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_596])]) ).
fof(f706,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_1) ).
fof(f5519,plain,
spl0_595,
inference(avatar_split_clause,[],[f705,f5517]) ).
fof(f5517,plain,
( spl0_595
<=> ! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_595])]) ).
fof(f705,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oordered__comm__semiring__strict(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oordered__comm__semiring__strict_0) ).
fof(f5515,plain,
spl0_594,
inference(avatar_split_clause,[],[f704,f5513]) ).
fof(f5513,plain,
( spl0_594
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_594])]) ).
fof(f704,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_9) ).
fof(f5511,plain,
spl0_593,
inference(avatar_split_clause,[],[f703,f5509]) ).
fof(f5509,plain,
( spl0_593
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_593])]) ).
fof(f703,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_8) ).
fof(f5507,plain,
spl0_592,
inference(avatar_split_clause,[],[f702,f5505]) ).
fof(f5505,plain,
( spl0_592
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_592])]) ).
fof(f702,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__cancel__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_7) ).
fof(f5503,plain,
spl0_591,
inference(avatar_split_clause,[],[f701,f5501]) ).
fof(f5501,plain,
( spl0_591
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_591])]) ).
fof(f701,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_6) ).
fof(f5499,plain,
spl0_590,
inference(avatar_split_clause,[],[f700,f5497]) ).
fof(f5497,plain,
( spl0_590
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_590])]) ).
fof(f700,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_5) ).
fof(f5495,plain,
spl0_589,
inference(avatar_split_clause,[],[f699,f5493]) ).
fof(f5493,plain,
( spl0_589
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_589])]) ).
fof(f699,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_4) ).
fof(f5491,plain,
spl0_588,
inference(avatar_split_clause,[],[f698,f5489]) ).
fof(f5489,plain,
( spl0_588
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_588])]) ).
fof(f698,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__join(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_30) ).
fof(f5487,plain,
spl0_587,
inference(avatar_split_clause,[],[f697,f5485]) ).
fof(f5485,plain,
( spl0_587
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_587])]) ).
fof(f697,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_3) ).
fof(f5483,plain,
spl0_586,
inference(avatar_split_clause,[],[f696,f5481]) ).
fof(f5481,plain,
( spl0_586
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_586])]) ).
fof(f696,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__meet(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_29) ).
fof(f5479,plain,
spl0_585,
inference(avatar_split_clause,[],[f695,f5477]) ).
fof(f5477,plain,
( spl0_585
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_585])]) ).
fof(f695,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_28) ).
fof(f5475,plain,
spl0_584,
inference(avatar_split_clause,[],[f694,f5473]) ).
fof(f5473,plain,
( spl0_584
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_584])]) ).
fof(f694,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_27) ).
fof(f5471,plain,
spl0_583,
inference(avatar_split_clause,[],[f693,f5469]) ).
fof(f5469,plain,
( spl0_583
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_583])]) ).
fof(f693,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_26) ).
fof(f5467,plain,
spl0_582,
inference(avatar_split_clause,[],[f692,f5465]) ).
fof(f5465,plain,
( spl0_582
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_582])]) ).
fof(f692,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_25) ).
fof(f5463,plain,
spl0_581,
inference(avatar_split_clause,[],[f691,f5461]) ).
fof(f5461,plain,
( spl0_581
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_581])]) ).
fof(f691,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Olordered__ab__group__abs(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_24) ).
fof(f5459,plain,
spl0_580,
inference(avatar_split_clause,[],[f690,f5457]) ).
fof(f5457,plain,
( spl0_580
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_580])]) ).
fof(f690,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_23) ).
fof(f5455,plain,
spl0_579,
inference(avatar_split_clause,[],[f689,f5453]) ).
fof(f5453,plain,
( spl0_579
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_579])]) ).
fof(f689,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_22) ).
fof(f5451,plain,
spl0_578,
inference(avatar_split_clause,[],[f688,f5449]) ).
fof(f5449,plain,
( spl0_578
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_578])]) ).
fof(f688,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_21) ).
fof(f5447,plain,
spl0_577,
inference(avatar_split_clause,[],[f687,f5445]) ).
fof(f5445,plain,
( spl0_577
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_577])]) ).
fof(f687,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_20) ).
fof(f5443,plain,
spl0_576,
inference(avatar_split_clause,[],[f686,f5441]) ).
fof(f5441,plain,
( spl0_576
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_576])]) ).
fof(f686,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_2) ).
fof(f5439,plain,
spl0_575,
inference(avatar_split_clause,[],[f685,f5437]) ).
fof(f5437,plain,
( spl0_575
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_575])]) ).
fof(f685,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_19) ).
fof(f5435,plain,
spl0_574,
inference(avatar_split_clause,[],[f684,f5433]) ).
fof(f5433,plain,
( spl0_574
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_574])]) ).
fof(f684,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_18) ).
fof(f5431,plain,
spl0_573,
inference(avatar_split_clause,[],[f683,f5429]) ).
fof(f5429,plain,
( spl0_573
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_573])]) ).
fof(f683,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_17) ).
fof(f5427,plain,
spl0_572,
inference(avatar_split_clause,[],[f682,f5425]) ).
fof(f5425,plain,
( spl0_572
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_572])]) ).
fof(f682,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_16) ).
fof(f5423,plain,
spl0_571,
inference(avatar_split_clause,[],[f681,f5421]) ).
fof(f5421,plain,
( spl0_571
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_571])]) ).
fof(f681,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_15) ).
fof(f5419,plain,
spl0_570,
inference(avatar_split_clause,[],[f680,f5417]) ).
fof(f5417,plain,
( spl0_570
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_570])]) ).
fof(f680,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_14) ).
fof(f5415,plain,
spl0_569,
inference(avatar_split_clause,[],[f679,f5413]) ).
fof(f5413,plain,
( spl0_569
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_569])]) ).
fof(f679,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_13) ).
fof(f5411,plain,
spl0_568,
inference(avatar_split_clause,[],[f678,f5409]) ).
fof(f5409,plain,
( spl0_568
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_568])]) ).
fof(f678,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_12) ).
fof(f5407,plain,
spl0_567,
inference(avatar_split_clause,[],[f677,f5405]) ).
fof(f5405,plain,
( spl0_567
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_567])]) ).
fof(f677,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_11) ).
fof(f5403,plain,
spl0_566,
inference(avatar_split_clause,[],[f676,f5401]) ).
fof(f5401,plain,
( spl0_566
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_566])]) ).
fof(f676,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_10) ).
fof(f5399,plain,
spl0_565,
inference(avatar_split_clause,[],[f675,f5397]) ).
fof(f5397,plain,
( spl0_565
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_565])]) ).
fof(f675,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_1) ).
fof(f5395,plain,
spl0_564,
inference(avatar_split_clause,[],[f674,f5393]) ).
fof(f5393,plain,
( spl0_564
<=> ! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_564])]) ).
fof(f674,axiom,
! [X39] :
( ~ class_Ring__and__Field_Olordered__ring(X39)
| class_Ring__and__Field_Opordered__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Olordered__ring_0) ).
fof(f5391,plain,
spl0_563,
inference(avatar_split_clause,[],[f673,f5389]) ).
fof(f5389,plain,
( spl0_563
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_563])]) ).
fof(f673,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_9) ).
fof(f5387,plain,
spl0_562,
inference(avatar_split_clause,[],[f672,f5385]) ).
fof(f5385,plain,
( spl0_562
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_562])]) ).
fof(f672,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_8) ).
fof(f5383,plain,
spl0_561,
inference(avatar_split_clause,[],[f671,f5381]) ).
fof(f5381,plain,
( spl0_561
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_561])]) ).
fof(f671,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_7) ).
fof(f5379,plain,
spl0_560,
inference(avatar_split_clause,[],[f670,f5377]) ).
fof(f5377,plain,
( spl0_560
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_560])]) ).
fof(f670,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_6) ).
fof(f5375,plain,
spl0_559,
inference(avatar_split_clause,[],[f669,f5373]) ).
fof(f5373,plain,
( spl0_559
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_559])]) ).
fof(f669,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_5) ).
fof(f5371,plain,
spl0_558,
inference(avatar_split_clause,[],[f668,f5369]) ).
fof(f5369,plain,
( spl0_558
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_558])]) ).
fof(f668,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_4) ).
fof(f5367,plain,
spl0_557,
inference(avatar_split_clause,[],[f667,f5365]) ).
fof(f5365,plain,
( spl0_557
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_557])]) ).
fof(f667,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_30) ).
fof(f5363,plain,
spl0_556,
inference(avatar_split_clause,[],[f666,f5361]) ).
fof(f5361,plain,
( spl0_556
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_556])]) ).
fof(f666,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_3) ).
fof(f5359,plain,
spl0_555,
inference(avatar_split_clause,[],[f665,f5357]) ).
fof(f5357,plain,
( spl0_555
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_555])]) ).
fof(f665,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_29) ).
fof(f5355,plain,
spl0_554,
inference(avatar_split_clause,[],[f664,f5353]) ).
fof(f5353,plain,
( spl0_554
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_554])]) ).
fof(f664,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_28) ).
fof(f5351,plain,
spl0_553,
inference(avatar_split_clause,[],[f663,f5349]) ).
fof(f5349,plain,
( spl0_553
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_553])]) ).
fof(f663,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_27) ).
fof(f5347,plain,
spl0_552,
inference(avatar_split_clause,[],[f662,f5345]) ).
fof(f5345,plain,
( spl0_552
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_552])]) ).
fof(f662,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_26) ).
fof(f5343,plain,
spl0_551,
inference(avatar_split_clause,[],[f661,f5341]) ).
fof(f5341,plain,
( spl0_551
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_551])]) ).
fof(f661,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_25) ).
fof(f5339,plain,
spl0_550,
inference(avatar_split_clause,[],[f660,f5337]) ).
fof(f5337,plain,
( spl0_550
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_550])]) ).
fof(f660,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_24) ).
fof(f5335,plain,
spl0_549,
inference(avatar_split_clause,[],[f659,f5333]) ).
fof(f5333,plain,
( spl0_549
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_549])]) ).
fof(f659,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_23) ).
fof(f5331,plain,
spl0_548,
inference(avatar_split_clause,[],[f658,f5329]) ).
fof(f5329,plain,
( spl0_548
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_548])]) ).
fof(f658,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_22) ).
fof(f5327,plain,
spl0_547,
inference(avatar_split_clause,[],[f657,f5325]) ).
fof(f5325,plain,
( spl0_547
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_547])]) ).
fof(f657,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_21) ).
fof(f5323,plain,
spl0_546,
inference(avatar_split_clause,[],[f656,f5321]) ).
fof(f5321,plain,
( spl0_546
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_546])]) ).
fof(f656,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_20) ).
fof(f5319,plain,
spl0_545,
inference(avatar_split_clause,[],[f655,f5317]) ).
fof(f5317,plain,
( spl0_545
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_545])]) ).
fof(f655,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_2) ).
fof(f5315,plain,
spl0_544,
inference(avatar_split_clause,[],[f654,f5313]) ).
fof(f5313,plain,
( spl0_544
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_544])]) ).
fof(f654,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_19) ).
fof(f5311,plain,
spl0_543,
inference(avatar_split_clause,[],[f653,f5309]) ).
fof(f5309,plain,
( spl0_543
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_543])]) ).
fof(f653,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_18) ).
fof(f5307,plain,
spl0_542,
inference(avatar_split_clause,[],[f652,f5305]) ).
fof(f5305,plain,
( spl0_542
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_542])]) ).
fof(f652,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_17) ).
fof(f5303,plain,
spl0_541,
inference(avatar_split_clause,[],[f651,f5301]) ).
fof(f5301,plain,
( spl0_541
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_541])]) ).
fof(f651,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_16) ).
fof(f5299,plain,
spl0_540,
inference(avatar_split_clause,[],[f650,f5297]) ).
fof(f5297,plain,
( spl0_540
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_540])]) ).
fof(f650,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_15) ).
fof(f5295,plain,
spl0_539,
inference(avatar_split_clause,[],[f649,f5293]) ).
fof(f5293,plain,
( spl0_539
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_539])]) ).
fof(f649,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_14) ).
fof(f5291,plain,
spl0_538,
inference(avatar_split_clause,[],[f648,f5289]) ).
fof(f5289,plain,
( spl0_538
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_538])]) ).
fof(f648,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_13) ).
fof(f5287,plain,
spl0_537,
inference(avatar_split_clause,[],[f647,f5285]) ).
fof(f5285,plain,
( spl0_537
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_537])]) ).
fof(f647,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_12) ).
fof(f5283,plain,
spl0_536,
inference(avatar_split_clause,[],[f646,f5281]) ).
fof(f5281,plain,
( spl0_536
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_536])]) ).
fof(f646,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_11) ).
fof(f5279,plain,
spl0_535,
inference(avatar_split_clause,[],[f645,f5277]) ).
fof(f5277,plain,
( spl0_535
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_535])]) ).
fof(f645,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_10) ).
fof(f5275,plain,
spl0_534,
inference(avatar_split_clause,[],[f644,f5273]) ).
fof(f5273,plain,
( spl0_534
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_534])]) ).
fof(f644,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_1) ).
fof(f5271,plain,
spl0_533,
inference(avatar_split_clause,[],[f643,f5269]) ).
fof(f5269,plain,
( spl0_533
<=> ! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_533])]) ).
fof(f643,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oidom(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oidom_0) ).
fof(f5267,plain,
spl0_532,
inference(avatar_split_clause,[],[f642,f5265]) ).
fof(f5265,plain,
( spl0_532
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_532])]) ).
fof(f642,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_9) ).
fof(f5263,plain,
spl0_531,
inference(avatar_split_clause,[],[f641,f5261]) ).
fof(f5261,plain,
( spl0_531
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_531])]) ).
fof(f641,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_8) ).
fof(f5259,plain,
spl0_530,
inference(avatar_split_clause,[],[f640,f5257]) ).
fof(f5257,plain,
( spl0_530
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_530])]) ).
fof(f640,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_7) ).
fof(f5255,plain,
spl0_529,
inference(avatar_split_clause,[],[f639,f5253]) ).
fof(f5253,plain,
( spl0_529
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_529])]) ).
fof(f639,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_6) ).
fof(f5251,plain,
spl0_528,
inference(avatar_split_clause,[],[f638,f5249]) ).
fof(f5249,plain,
( spl0_528
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_528])]) ).
fof(f638,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_5) ).
fof(f5247,plain,
spl0_527,
inference(avatar_split_clause,[],[f637,f5245]) ).
fof(f5245,plain,
( spl0_527
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_527])]) ).
fof(f637,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_4) ).
fof(f5243,plain,
spl0_526,
inference(avatar_split_clause,[],[f636,f5241]) ).
fof(f5241,plain,
( spl0_526
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_526])]) ).
fof(f636,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oaxclass__no__zero__divisors(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_32) ).
fof(f5239,plain,
spl0_525,
inference(avatar_split_clause,[],[f635,f5237]) ).
fof(f5237,plain,
( spl0_525
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oidom(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_525])]) ).
fof(f635,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oidom(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_31) ).
fof(f5235,plain,
spl0_524,
inference(avatar_split_clause,[],[f634,f5233]) ).
fof(f5233,plain,
( spl0_524
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Oinverse(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_524])]) ).
fof(f634,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Oinverse(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_30) ).
fof(f5231,plain,
spl0_523,
inference(avatar_split_clause,[],[f633,f5229]) ).
fof(f5229,plain,
( spl0_523
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_523])]) ).
fof(f633,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_3) ).
fof(f5227,plain,
spl0_522,
inference(avatar_split_clause,[],[f632,f5225]) ).
fof(f5225,plain,
( spl0_522
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_522])]) ).
fof(f632,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_29) ).
fof(f5223,plain,
spl0_521,
inference(avatar_split_clause,[],[f631,f5221]) ).
fof(f5221,plain,
( spl0_521
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_521])]) ).
fof(f631,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_28) ).
fof(f5219,plain,
spl0_520,
inference(avatar_split_clause,[],[f630,f5217]) ).
fof(f5217,plain,
( spl0_520
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_520])]) ).
fof(f630,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_27) ).
fof(f5215,plain,
spl0_519,
inference(avatar_split_clause,[],[f629,f5213]) ).
fof(f5213,plain,
( spl0_519
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_519])]) ).
fof(f629,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_26) ).
fof(f5211,plain,
spl0_518,
inference(avatar_split_clause,[],[f628,f5209]) ).
fof(f5209,plain,
( spl0_518
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_518])]) ).
fof(f628,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_25) ).
fof(f5207,plain,
spl0_517,
inference(avatar_split_clause,[],[f627,f5205]) ).
fof(f5205,plain,
( spl0_517
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_517])]) ).
fof(f627,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_24) ).
fof(f5203,plain,
spl0_516,
inference(avatar_split_clause,[],[f626,f5201]) ).
fof(f5201,plain,
( spl0_516
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_516])]) ).
fof(f626,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_23) ).
fof(f5199,plain,
spl0_515,
inference(avatar_split_clause,[],[f625,f5197]) ).
fof(f5197,plain,
( spl0_515
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_515])]) ).
fof(f625,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_22) ).
fof(f5195,plain,
spl0_514,
inference(avatar_split_clause,[],[f624,f5193]) ).
fof(f5193,plain,
( spl0_514
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_514])]) ).
fof(f624,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_21) ).
fof(f5191,plain,
spl0_513,
inference(avatar_split_clause,[],[f623,f5189]) ).
fof(f5189,plain,
( spl0_513
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_513])]) ).
fof(f623,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_20) ).
fof(f5187,plain,
spl0_512,
inference(avatar_split_clause,[],[f622,f5185]) ).
fof(f5185,plain,
( spl0_512
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_512])]) ).
fof(f622,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_2) ).
fof(f5183,plain,
spl0_511,
inference(avatar_split_clause,[],[f621,f5181]) ).
fof(f5181,plain,
( spl0_511
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_511])]) ).
fof(f621,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_19) ).
fof(f5179,plain,
spl0_510,
inference(avatar_split_clause,[],[f620,f5177]) ).
fof(f5177,plain,
( spl0_510
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_510])]) ).
fof(f620,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_18) ).
fof(f5175,plain,
spl0_509,
inference(avatar_split_clause,[],[f619,f5173]) ).
fof(f5173,plain,
( spl0_509
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_509])]) ).
fof(f619,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_17) ).
fof(f5171,plain,
spl0_508,
inference(avatar_split_clause,[],[f618,f5169]) ).
fof(f5169,plain,
( spl0_508
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_508])]) ).
fof(f618,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_16) ).
fof(f5167,plain,
spl0_507,
inference(avatar_split_clause,[],[f617,f5165]) ).
fof(f5165,plain,
( spl0_507
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_507])]) ).
fof(f617,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_15) ).
fof(f5163,plain,
spl0_506,
inference(avatar_split_clause,[],[f616,f5161]) ).
fof(f5161,plain,
( spl0_506
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_506])]) ).
fof(f616,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_14) ).
fof(f5159,plain,
spl0_505,
inference(avatar_split_clause,[],[f615,f5157]) ).
fof(f5157,plain,
( spl0_505
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_505])]) ).
fof(f615,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_13) ).
fof(f5155,plain,
spl0_504,
inference(avatar_split_clause,[],[f614,f5153]) ).
fof(f5153,plain,
( spl0_504
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_504])]) ).
fof(f614,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_12) ).
fof(f5151,plain,
spl0_503,
inference(avatar_split_clause,[],[f613,f5149]) ).
fof(f5149,plain,
( spl0_503
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_503])]) ).
fof(f613,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_11) ).
fof(f5147,plain,
spl0_502,
inference(avatar_split_clause,[],[f612,f5145]) ).
fof(f5145,plain,
( spl0_502
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_502])]) ).
fof(f612,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_10) ).
fof(f5143,plain,
spl0_501,
inference(avatar_split_clause,[],[f611,f5141]) ).
fof(f5141,plain,
( spl0_501
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_501])]) ).
fof(f611,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_1) ).
fof(f5139,plain,
spl0_500,
inference(avatar_split_clause,[],[f610,f5137]) ).
fof(f5137,plain,
( spl0_500
<=> ! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_500])]) ).
fof(f610,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ofield(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ofield_0) ).
fof(f5135,plain,
spl0_499,
inference(avatar_split_clause,[],[f609,f5133]) ).
fof(f5133,plain,
( spl0_499
<=> ! [X39] :
( ~ class_Ring__and__Field_Odivision__by__zero(X39)
| class_HOL_Oinverse(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_499])]) ).
fof(f609,axiom,
! [X39] :
( ~ class_Ring__and__Field_Odivision__by__zero(X39)
| class_HOL_Oinverse(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Odivision__by__zero_1) ).
fof(f5131,plain,
spl0_498,
inference(avatar_split_clause,[],[f608,f5129]) ).
fof(f5129,plain,
( spl0_498
<=> ! [X39] :
( ~ class_Ring__and__Field_Odivision__by__zero(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_498])]) ).
fof(f608,axiom,
! [X39] :
( ~ class_Ring__and__Field_Odivision__by__zero(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Odivision__by__zero_0) ).
fof(f5127,plain,
spl0_497,
inference(avatar_split_clause,[],[f607,f5125]) ).
fof(f5125,plain,
( spl0_497
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_497])]) ).
fof(f607,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_9) ).
fof(f5123,plain,
spl0_496,
inference(avatar_split_clause,[],[f606,f5121]) ).
fof(f5121,plain,
( spl0_496
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_496])]) ).
fof(f606,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_8) ).
fof(f5119,plain,
spl0_495,
inference(avatar_split_clause,[],[f605,f5117]) ).
fof(f5117,plain,
( spl0_495
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_495])]) ).
fof(f605,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_7) ).
fof(f5115,plain,
spl0_494,
inference(avatar_split_clause,[],[f604,f5113]) ).
fof(f5113,plain,
( spl0_494
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_494])]) ).
fof(f604,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_6) ).
fof(f5111,plain,
spl0_493,
inference(avatar_split_clause,[],[f603,f5109]) ).
fof(f5109,plain,
( spl0_493
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_493])]) ).
fof(f603,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_5) ).
fof(f5107,plain,
spl0_492,
inference(avatar_split_clause,[],[f602,f5105]) ).
fof(f5105,plain,
( spl0_492
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_492])]) ).
fof(f602,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_4) ).
fof(f5103,plain,
spl0_491,
inference(avatar_split_clause,[],[f601,f5101]) ).
fof(f5101,plain,
( spl0_491
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_491])]) ).
fof(f601,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_3) ).
fof(f5099,plain,
spl0_490,
inference(avatar_split_clause,[],[f600,f5097]) ).
fof(f5097,plain,
( spl0_490
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_490])]) ).
fof(f600,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_22) ).
fof(f5095,plain,
spl0_489,
inference(avatar_split_clause,[],[f599,f5093]) ).
fof(f5093,plain,
( spl0_489
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_489])]) ).
fof(f599,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_21) ).
fof(f5091,plain,
spl0_488,
inference(avatar_split_clause,[],[f598,f5089]) ).
fof(f5089,plain,
( spl0_488
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_488])]) ).
fof(f598,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_20) ).
fof(f5087,plain,
spl0_487,
inference(avatar_split_clause,[],[f597,f5085]) ).
fof(f5085,plain,
( spl0_487
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_487])]) ).
fof(f597,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_2) ).
fof(f5083,plain,
spl0_486,
inference(avatar_split_clause,[],[f596,f5081]) ).
fof(f5081,plain,
( spl0_486
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_486])]) ).
fof(f596,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_19) ).
fof(f5079,plain,
spl0_485,
inference(avatar_split_clause,[],[f595,f5077]) ).
fof(f5077,plain,
( spl0_485
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_485])]) ).
fof(f595,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_18) ).
fof(f5075,plain,
spl0_484,
inference(avatar_split_clause,[],[f594,f5073]) ).
fof(f5073,plain,
( spl0_484
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_484])]) ).
fof(f594,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_17) ).
fof(f5071,plain,
spl0_483,
inference(avatar_split_clause,[],[f593,f5069]) ).
fof(f5069,plain,
( spl0_483
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_483])]) ).
fof(f593,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_16) ).
fof(f5067,plain,
spl0_482,
inference(avatar_split_clause,[],[f592,f5065]) ).
fof(f5065,plain,
( spl0_482
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_482])]) ).
fof(f592,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_15) ).
fof(f5063,plain,
spl0_481,
inference(avatar_split_clause,[],[f591,f5061]) ).
fof(f5061,plain,
( spl0_481
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_481])]) ).
fof(f591,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_14) ).
fof(f5059,plain,
spl0_480,
inference(avatar_split_clause,[],[f590,f5057]) ).
fof(f5057,plain,
( spl0_480
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_480])]) ).
fof(f590,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_13) ).
fof(f5055,plain,
spl0_479,
inference(avatar_split_clause,[],[f589,f5053]) ).
fof(f5053,plain,
( spl0_479
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_479])]) ).
fof(f589,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_12) ).
fof(f5051,plain,
spl0_478,
inference(avatar_split_clause,[],[f588,f5049]) ).
fof(f5049,plain,
( spl0_478
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_478])]) ).
fof(f588,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_11) ).
fof(f5047,plain,
spl0_477,
inference(avatar_split_clause,[],[f587,f5045]) ).
fof(f5045,plain,
( spl0_477
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_477])]) ).
fof(f587,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_10) ).
fof(f5043,plain,
spl0_476,
inference(avatar_split_clause,[],[f586,f5041]) ).
fof(f5041,plain,
( spl0_476
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_476])]) ).
fof(f586,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_1) ).
fof(f5039,plain,
spl0_475,
inference(avatar_split_clause,[],[f585,f5037]) ).
fof(f5037,plain,
( spl0_475
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_475])]) ).
fof(f585,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1__cancel_0) ).
fof(f5035,plain,
spl0_474,
inference(avatar_split_clause,[],[f584,f5033]) ).
fof(f5033,plain,
( spl0_474
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_474])]) ).
fof(f584,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_9) ).
fof(f5031,plain,
spl0_473,
inference(avatar_split_clause,[],[f583,f5029]) ).
fof(f5029,plain,
( spl0_473
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_473])]) ).
fof(f583,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_8) ).
fof(f5027,plain,
spl0_472,
inference(avatar_split_clause,[],[f582,f5025]) ).
fof(f5025,plain,
( spl0_472
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_472])]) ).
fof(f582,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_7) ).
fof(f5023,plain,
spl0_471,
inference(avatar_split_clause,[],[f581,f5021]) ).
fof(f5021,plain,
( spl0_471
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_471])]) ).
fof(f581,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_6) ).
fof(f5019,plain,
spl0_470,
inference(avatar_split_clause,[],[f580,f5017]) ).
fof(f5017,plain,
( spl0_470
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_470])]) ).
fof(f580,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_5) ).
fof(f5015,plain,
spl0_469,
inference(avatar_split_clause,[],[f579,f5013]) ).
fof(f5013,plain,
( spl0_469
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_469])]) ).
fof(f579,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_4) ).
fof(f5011,plain,
spl0_468,
inference(avatar_split_clause,[],[f578,f5009]) ).
fof(f5009,plain,
( spl0_468
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_468])]) ).
fof(f578,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_3) ).
fof(f5007,plain,
spl0_467,
inference(avatar_split_clause,[],[f577,f5005]) ).
fof(f5005,plain,
( spl0_467
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_467])]) ).
fof(f577,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_2) ).
fof(f5003,plain,
spl0_466,
inference(avatar_split_clause,[],[f576,f5001]) ).
fof(f5001,plain,
( spl0_466
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_466])]) ).
fof(f576,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_16) ).
fof(f4999,plain,
spl0_465,
inference(avatar_split_clause,[],[f575,f4997]) ).
fof(f4997,plain,
( spl0_465
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_465])]) ).
fof(f575,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_15) ).
fof(f4995,plain,
spl0_464,
inference(avatar_split_clause,[],[f574,f4993]) ).
fof(f4993,plain,
( spl0_464
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_464])]) ).
fof(f574,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_14) ).
fof(f4991,plain,
spl0_463,
inference(avatar_split_clause,[],[f573,f4989]) ).
fof(f4989,plain,
( spl0_463
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_463])]) ).
fof(f573,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_13) ).
fof(f4987,plain,
spl0_462,
inference(avatar_split_clause,[],[f572,f4985]) ).
fof(f4985,plain,
( spl0_462
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_462])]) ).
fof(f572,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_12) ).
fof(f4983,plain,
spl0_461,
inference(avatar_split_clause,[],[f571,f4981]) ).
fof(f4981,plain,
( spl0_461
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_461])]) ).
fof(f571,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_11) ).
fof(f4979,plain,
spl0_460,
inference(avatar_split_clause,[],[f570,f4977]) ).
fof(f4977,plain,
( spl0_460
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_460])]) ).
fof(f570,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_10) ).
fof(f4975,plain,
spl0_459,
inference(avatar_split_clause,[],[f569,f4973]) ).
fof(f4973,plain,
( spl0_459
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_459])]) ).
fof(f569,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_1) ).
fof(f4971,plain,
spl0_458,
inference(avatar_split_clause,[],[f568,f4969]) ).
fof(f4969,plain,
( spl0_458
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_458])]) ).
fof(f568,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__1_0) ).
fof(f4967,plain,
spl0_457,
inference(avatar_split_clause,[],[f567,f4965]) ).
fof(f4965,plain,
( spl0_457
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_457])]) ).
fof(f567,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_9) ).
fof(f4963,plain,
spl0_456,
inference(avatar_split_clause,[],[f566,f4961]) ).
fof(f4961,plain,
( spl0_456
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_456])]) ).
fof(f566,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_8) ).
fof(f4959,plain,
spl0_455,
inference(avatar_split_clause,[],[f565,f4957]) ).
fof(f4957,plain,
( spl0_455
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_455])]) ).
fof(f565,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_7) ).
fof(f4955,plain,
spl0_454,
inference(avatar_split_clause,[],[f564,f4953]) ).
fof(f4953,plain,
( spl0_454
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_454])]) ).
fof(f564,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_6) ).
fof(f4951,plain,
spl0_453,
inference(avatar_split_clause,[],[f563,f4949]) ).
fof(f4949,plain,
( spl0_453
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_453])]) ).
fof(f563,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_5) ).
fof(f4947,plain,
spl0_452,
inference(avatar_split_clause,[],[f562,f4945]) ).
fof(f4945,plain,
( spl0_452
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_452])]) ).
fof(f562,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_4) ).
fof(f4943,plain,
spl0_451,
inference(avatar_split_clause,[],[f561,f4941]) ).
fof(f4941,plain,
( spl0_451
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_451])]) ).
fof(f561,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_3) ).
fof(f4939,plain,
spl0_450,
inference(avatar_split_clause,[],[f560,f4937]) ).
fof(f4937,plain,
( spl0_450
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_450])]) ).
fof(f560,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_2) ).
fof(f4935,plain,
spl0_449,
inference(avatar_split_clause,[],[f559,f4933]) ).
fof(f4933,plain,
( spl0_449
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_449])]) ).
fof(f559,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_14) ).
fof(f4931,plain,
spl0_448,
inference(avatar_split_clause,[],[f558,f4929]) ).
fof(f4929,plain,
( spl0_448
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_448])]) ).
fof(f558,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_13) ).
fof(f4927,plain,
spl0_447,
inference(avatar_split_clause,[],[f557,f4925]) ).
fof(f4925,plain,
( spl0_447
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_447])]) ).
fof(f557,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_12) ).
fof(f4923,plain,
spl0_446,
inference(avatar_split_clause,[],[f556,f4921]) ).
fof(f4921,plain,
( spl0_446
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_446])]) ).
fof(f556,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_11) ).
fof(f4919,plain,
spl0_445,
inference(avatar_split_clause,[],[f555,f4917]) ).
fof(f4917,plain,
( spl0_445
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_445])]) ).
fof(f555,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_10) ).
fof(f4915,plain,
spl0_444,
inference(avatar_split_clause,[],[f554,f4913]) ).
fof(f4913,plain,
( spl0_444
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_444])]) ).
fof(f554,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_1) ).
fof(f4911,plain,
spl0_443,
inference(avatar_split_clause,[],[f553,f4909]) ).
fof(f4909,plain,
( spl0_443
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_443])]) ).
fof(f553,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0__cancel(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0__cancel_0) ).
fof(f4907,plain,
spl0_442,
inference(avatar_split_clause,[],[f552,f4905]) ).
fof(f4905,plain,
( spl0_442
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_442])]) ).
fof(f552,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_9) ).
fof(f4903,plain,
spl0_441,
inference(avatar_split_clause,[],[f551,f4901]) ).
fof(f4901,plain,
( spl0_441
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_441])]) ).
fof(f551,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_8) ).
fof(f4899,plain,
spl0_440,
inference(avatar_split_clause,[],[f550,f4897]) ).
fof(f4897,plain,
( spl0_440
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_440])]) ).
fof(f550,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_7) ).
fof(f4895,plain,
spl0_439,
inference(avatar_split_clause,[],[f549,f4893]) ).
fof(f4893,plain,
( spl0_439
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_439])]) ).
fof(f549,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_6) ).
fof(f4891,plain,
spl0_438,
inference(avatar_split_clause,[],[f548,f4889]) ).
fof(f4889,plain,
( spl0_438
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_438])]) ).
fof(f548,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_5) ).
fof(f4887,plain,
spl0_437,
inference(avatar_split_clause,[],[f547,f4885]) ).
fof(f4885,plain,
( spl0_437
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_437])]) ).
fof(f547,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_4) ).
fof(f4883,plain,
spl0_436,
inference(avatar_split_clause,[],[f546,f4881]) ).
fof(f4881,plain,
( spl0_436
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_436])]) ).
fof(f546,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_3) ).
fof(f4879,plain,
spl0_435,
inference(avatar_split_clause,[],[f545,f4877]) ).
fof(f4877,plain,
( spl0_435
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_435])]) ).
fof(f545,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_2) ).
fof(f4875,plain,
spl0_434,
inference(avatar_split_clause,[],[f544,f4873]) ).
fof(f4873,plain,
( spl0_434
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_434])]) ).
fof(f544,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_10) ).
fof(f4871,plain,
spl0_433,
inference(avatar_split_clause,[],[f543,f4869]) ).
fof(f4869,plain,
( spl0_433
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_433])]) ).
fof(f543,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_1) ).
fof(f4867,plain,
spl0_432,
inference(avatar_split_clause,[],[f542,f4865]) ).
fof(f4865,plain,
( spl0_432
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_432])]) ).
fof(f542,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring__0(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring__0_0) ).
fof(f4863,plain,
spl0_431,
inference(avatar_split_clause,[],[f541,f4861]) ).
fof(f4861,plain,
( spl0_431
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_431])]) ).
fof(f541,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_6) ).
fof(f4859,plain,
spl0_430,
inference(avatar_split_clause,[],[f540,f4857]) ).
fof(f4857,plain,
( spl0_430
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_430])]) ).
fof(f540,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_5) ).
fof(f4855,plain,
spl0_429,
inference(avatar_split_clause,[],[f539,f4853]) ).
fof(f4853,plain,
( spl0_429
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_429])]) ).
fof(f539,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_4) ).
fof(f4851,plain,
spl0_428,
inference(avatar_split_clause,[],[f538,f4849]) ).
fof(f4849,plain,
( spl0_428
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_428])]) ).
fof(f538,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_3) ).
fof(f4847,plain,
spl0_427,
inference(avatar_split_clause,[],[f537,f4845]) ).
fof(f4845,plain,
( spl0_427
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_427])]) ).
fof(f537,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_2) ).
fof(f4843,plain,
spl0_426,
inference(avatar_split_clause,[],[f536,f4841]) ).
fof(f4841,plain,
( spl0_426
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_426])]) ).
fof(f536,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_1) ).
fof(f4839,plain,
spl0_425,
inference(avatar_split_clause,[],[f535,f4837]) ).
fof(f4837,plain,
( spl0_425
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_425])]) ).
fof(f535,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__semiring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__semiring_0) ).
fof(f4835,plain,
spl0_424,
inference(avatar_split_clause,[],[f534,f4833]) ).
fof(f4833,plain,
( spl0_424
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_424])]) ).
fof(f534,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_9) ).
fof(f4831,plain,
spl0_423,
inference(avatar_split_clause,[],[f533,f4829]) ).
fof(f4829,plain,
( spl0_423
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_423])]) ).
fof(f533,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_8) ).
fof(f4827,plain,
spl0_422,
inference(avatar_split_clause,[],[f532,f4825]) ).
fof(f4825,plain,
( spl0_422
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_422])]) ).
fof(f532,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_7) ).
fof(f4823,plain,
spl0_421,
inference(avatar_split_clause,[],[f531,f4821]) ).
fof(f4821,plain,
( spl0_421
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_421])]) ).
fof(f531,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_6) ).
fof(f4819,plain,
spl0_420,
inference(avatar_split_clause,[],[f530,f4817]) ).
fof(f4817,plain,
( spl0_420
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_420])]) ).
fof(f530,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_5) ).
fof(f4815,plain,
spl0_419,
inference(avatar_split_clause,[],[f529,f4813]) ).
fof(f4813,plain,
( spl0_419
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_419])]) ).
fof(f529,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_4) ).
fof(f4811,plain,
spl0_418,
inference(avatar_split_clause,[],[f528,f4809]) ).
fof(f4809,plain,
( spl0_418
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_418])]) ).
fof(f528,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_3) ).
fof(f4807,plain,
spl0_417,
inference(avatar_split_clause,[],[f527,f4805]) ).
fof(f4805,plain,
( spl0_417
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_417])]) ).
fof(f527,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_28) ).
fof(f4803,plain,
spl0_416,
inference(avatar_split_clause,[],[f526,f4801]) ).
fof(f4801,plain,
( spl0_416
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_416])]) ).
fof(f526,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_27) ).
fof(f4799,plain,
spl0_415,
inference(avatar_split_clause,[],[f525,f4797]) ).
fof(f4797,plain,
( spl0_415
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_415])]) ).
fof(f525,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_26) ).
fof(f4795,plain,
spl0_414,
inference(avatar_split_clause,[],[f524,f4793]) ).
fof(f4793,plain,
( spl0_414
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_414])]) ).
fof(f524,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_25) ).
fof(f4791,plain,
spl0_413,
inference(avatar_split_clause,[],[f523,f4789]) ).
fof(f4789,plain,
( spl0_413
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_413])]) ).
fof(f523,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_24) ).
fof(f4787,plain,
spl0_412,
inference(avatar_split_clause,[],[f522,f4785]) ).
fof(f4785,plain,
( spl0_412
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_412])]) ).
fof(f522,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_23) ).
fof(f4783,plain,
spl0_411,
inference(avatar_split_clause,[],[f521,f4781]) ).
fof(f4781,plain,
( spl0_411
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_411])]) ).
fof(f521,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_22) ).
fof(f4779,plain,
spl0_410,
inference(avatar_split_clause,[],[f520,f4777]) ).
fof(f4777,plain,
( spl0_410
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_410])]) ).
fof(f520,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_21) ).
fof(f4775,plain,
spl0_409,
inference(avatar_split_clause,[],[f519,f4773]) ).
fof(f4773,plain,
( spl0_409
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_409])]) ).
fof(f519,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_20) ).
fof(f4771,plain,
spl0_408,
inference(avatar_split_clause,[],[f518,f4769]) ).
fof(f4769,plain,
( spl0_408
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_408])]) ).
fof(f518,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_2) ).
fof(f4767,plain,
spl0_407,
inference(avatar_split_clause,[],[f517,f4765]) ).
fof(f4765,plain,
( spl0_407
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_407])]) ).
fof(f517,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_19) ).
fof(f4763,plain,
spl0_406,
inference(avatar_split_clause,[],[f516,f4761]) ).
fof(f4761,plain,
( spl0_406
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_406])]) ).
fof(f516,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_18) ).
fof(f4759,plain,
spl0_405,
inference(avatar_split_clause,[],[f515,f4757]) ).
fof(f4757,plain,
( spl0_405
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_405])]) ).
fof(f515,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_17) ).
fof(f4755,plain,
spl0_404,
inference(avatar_split_clause,[],[f514,f4753]) ).
fof(f4753,plain,
( spl0_404
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_404])]) ).
fof(f514,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_16) ).
fof(f4751,plain,
spl0_403,
inference(avatar_split_clause,[],[f513,f4749]) ).
fof(f4749,plain,
( spl0_403
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_403])]) ).
fof(f513,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_15) ).
fof(f4747,plain,
spl0_402,
inference(avatar_split_clause,[],[f512,f4745]) ).
fof(f4745,plain,
( spl0_402
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_402])]) ).
fof(f512,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_14) ).
fof(f4743,plain,
spl0_401,
inference(avatar_split_clause,[],[f511,f4741]) ).
fof(f4741,plain,
( spl0_401
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_401])]) ).
fof(f511,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_13) ).
fof(f4739,plain,
spl0_400,
inference(avatar_split_clause,[],[f510,f4737]) ).
fof(f4737,plain,
( spl0_400
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_400])]) ).
fof(f510,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_12) ).
fof(f4735,plain,
spl0_399,
inference(avatar_split_clause,[],[f509,f4733]) ).
fof(f4733,plain,
( spl0_399
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_399])]) ).
fof(f509,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_11) ).
fof(f4731,plain,
spl0_398,
inference(avatar_split_clause,[],[f508,f4729]) ).
fof(f4729,plain,
( spl0_398
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_398])]) ).
fof(f508,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_10) ).
fof(f4727,plain,
spl0_397,
inference(avatar_split_clause,[],[f507,f4725]) ).
fof(f4725,plain,
( spl0_397
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_397])]) ).
fof(f507,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_1) ).
fof(f4723,plain,
spl0_396,
inference(avatar_split_clause,[],[f506,f4721]) ).
fof(f4721,plain,
( spl0_396
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_396])]) ).
fof(f506,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring__1(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring__1_0) ).
fof(f4719,plain,
spl0_395,
inference(avatar_split_clause,[],[f505,f4717]) ).
fof(f4717,plain,
( spl0_395
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_395])]) ).
fof(f505,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_9) ).
fof(f4715,plain,
spl0_394,
inference(avatar_split_clause,[],[f504,f4713]) ).
fof(f4713,plain,
( spl0_394
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_394])]) ).
fof(f504,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_8) ).
fof(f4711,plain,
spl0_393,
inference(avatar_split_clause,[],[f503,f4709]) ).
fof(f4709,plain,
( spl0_393
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_393])]) ).
fof(f503,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_7) ).
fof(f4707,plain,
spl0_392,
inference(avatar_split_clause,[],[f502,f4705]) ).
fof(f4705,plain,
( spl0_392
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_392])]) ).
fof(f502,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_6) ).
fof(f4703,plain,
spl0_391,
inference(avatar_split_clause,[],[f501,f4701]) ).
fof(f4701,plain,
( spl0_391
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_391])]) ).
fof(f501,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_5) ).
fof(f4699,plain,
spl0_390,
inference(avatar_split_clause,[],[f500,f4697]) ).
fof(f4697,plain,
( spl0_390
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_390])]) ).
fof(f500,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_4) ).
fof(f4695,plain,
spl0_389,
inference(avatar_split_clause,[],[f499,f4693]) ).
fof(f4693,plain,
( spl0_389
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_389])]) ).
fof(f499,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_3) ).
fof(f4691,plain,
spl0_388,
inference(avatar_split_clause,[],[f498,f4689]) ).
fof(f4689,plain,
( spl0_388
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_388])]) ).
fof(f498,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_2) ).
fof(f4687,plain,
spl0_387,
inference(avatar_split_clause,[],[f497,f4685]) ).
fof(f4685,plain,
( spl0_387
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_387])]) ).
fof(f497,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_18) ).
fof(f4683,plain,
spl0_386,
inference(avatar_split_clause,[],[f496,f4681]) ).
fof(f4681,plain,
( spl0_386
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_386])]) ).
fof(f496,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_17) ).
fof(f4679,plain,
spl0_385,
inference(avatar_split_clause,[],[f495,f4677]) ).
fof(f4677,plain,
( spl0_385
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_385])]) ).
fof(f495,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_16) ).
fof(f4675,plain,
spl0_384,
inference(avatar_split_clause,[],[f494,f4673]) ).
fof(f4673,plain,
( spl0_384
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_384])]) ).
fof(f494,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_15) ).
fof(f4671,plain,
spl0_383,
inference(avatar_split_clause,[],[f493,f4669]) ).
fof(f4669,plain,
( spl0_383
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_383])]) ).
fof(f493,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_14) ).
fof(f4667,plain,
spl0_382,
inference(avatar_split_clause,[],[f492,f4665]) ).
fof(f4665,plain,
( spl0_382
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_382])]) ).
fof(f492,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_13) ).
fof(f4663,plain,
spl0_381,
inference(avatar_split_clause,[],[f491,f4661]) ).
fof(f4661,plain,
( spl0_381
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_381])]) ).
fof(f491,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_12) ).
fof(f4659,plain,
spl0_380,
inference(avatar_split_clause,[],[f490,f4657]) ).
fof(f4657,plain,
( spl0_380
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_380])]) ).
fof(f490,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_11) ).
fof(f4655,plain,
spl0_379,
inference(avatar_split_clause,[],[f489,f4653]) ).
fof(f4653,plain,
( spl0_379
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_379])]) ).
fof(f489,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_10) ).
fof(f4651,plain,
spl0_378,
inference(avatar_split_clause,[],[f488,f4649]) ).
fof(f4649,plain,
( spl0_378
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_378])]) ).
fof(f488,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_1) ).
fof(f4647,plain,
spl0_377,
inference(avatar_split_clause,[],[f487,f4645]) ).
fof(f4645,plain,
( spl0_377
<=> ! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_377])]) ).
fof(f487,axiom,
! [X39] :
( ~ class_Ring__and__Field_Ocomm__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Ocomm__ring_0) ).
fof(f4643,plain,
spl0_376,
inference(avatar_split_clause,[],[f486,f4641]) ).
fof(f4641,plain,
( spl0_376
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_376])]) ).
fof(f486,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_1) ).
fof(f4639,plain,
spl0_375,
inference(avatar_split_clause,[],[f485,f4637]) ).
fof(f4637,plain,
( spl0_375
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_375])]) ).
fof(f485,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__no__zero__divisors(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__no__zero__divisors_0) ).
fof(f4635,plain,
spl0_374,
inference(avatar_split_clause,[],[f484,f4633]) ).
fof(f4633,plain,
( spl0_374
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_374])]) ).
fof(f484,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__abs__if_2) ).
fof(f4631,plain,
spl0_373,
inference(avatar_split_clause,[],[f483,f4629]) ).
fof(f4629,plain,
( spl0_373
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_373])]) ).
fof(f483,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__abs__if_1) ).
fof(f4627,plain,
spl0_372,
inference(avatar_split_clause,[],[f482,f4625]) ).
fof(f4625,plain,
( spl0_372
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_372])]) ).
fof(f482,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__abs__if(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__abs__if_0) ).
fof(f4623,plain,
spl0_371,
inference(avatar_split_clause,[],[f481,f4621]) ).
fof(f4621,plain,
( spl0_371
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_371])]) ).
fof(f481,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__0__neq__1_1) ).
fof(f4619,plain,
spl0_370,
inference(avatar_split_clause,[],[f480,f4617]) ).
fof(f4617,plain,
( spl0_370
<=> ! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_370])]) ).
fof(f480,axiom,
! [X39] :
( ~ class_Ring__and__Field_Oaxclass__0__neq__1(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Ring__and__Field_Oaxclass__0__neq__1_0) ).
fof(f4615,plain,
spl0_369,
inference(avatar_split_clause,[],[f479,f4613]) ).
fof(f4613,plain,
( spl0_369
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_369])]) ).
fof(f479,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_9) ).
fof(f4611,plain,
spl0_368,
inference(avatar_split_clause,[],[f478,f4609]) ).
fof(f4609,plain,
( spl0_368
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_368])]) ).
fof(f478,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_8) ).
fof(f4607,plain,
spl0_367,
inference(avatar_split_clause,[],[f477,f4605]) ).
fof(f4605,plain,
( spl0_367
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_367])]) ).
fof(f477,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_7) ).
fof(f4603,plain,
spl0_366,
inference(avatar_split_clause,[],[f476,f4601]) ).
fof(f4601,plain,
( spl0_366
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_366])]) ).
fof(f476,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_6) ).
fof(f4599,plain,
spl0_365,
inference(avatar_split_clause,[],[f475,f4597]) ).
fof(f4597,plain,
( spl0_365
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_365])]) ).
fof(f475,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_5) ).
fof(f4595,plain,
spl0_364,
inference(avatar_split_clause,[],[f474,f4593]) ).
fof(f4593,plain,
( spl0_364
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_364])]) ).
fof(f474,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_4) ).
fof(f4591,plain,
spl0_363,
inference(avatar_split_clause,[],[f473,f4589]) ).
fof(f4589,plain,
( spl0_363
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_363])]) ).
fof(f473,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_3) ).
fof(f4587,plain,
spl0_362,
inference(avatar_split_clause,[],[f472,f4585]) ).
fof(f4585,plain,
( spl0_362
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_362])]) ).
fof(f472,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_24) ).
fof(f4583,plain,
spl0_361,
inference(avatar_split_clause,[],[f471,f4581]) ).
fof(f4581,plain,
( spl0_361
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_361])]) ).
fof(f471,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_23) ).
fof(f4579,plain,
spl0_360,
inference(avatar_split_clause,[],[f470,f4577]) ).
fof(f4577,plain,
( spl0_360
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_360])]) ).
fof(f470,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_22) ).
fof(f4575,plain,
spl0_359,
inference(avatar_split_clause,[],[f469,f4573]) ).
fof(f4573,plain,
( spl0_359
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_359])]) ).
fof(f469,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_21) ).
fof(f4571,plain,
spl0_358,
inference(avatar_split_clause,[],[f468,f4569]) ).
fof(f4569,plain,
( spl0_358
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_358])]) ).
fof(f468,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_20) ).
fof(f4567,plain,
spl0_357,
inference(avatar_split_clause,[],[f467,f4565]) ).
fof(f4565,plain,
( spl0_357
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_357])]) ).
fof(f467,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_2) ).
fof(f4563,plain,
spl0_356,
inference(avatar_split_clause,[],[f466,f4561]) ).
fof(f4561,plain,
( spl0_356
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_356])]) ).
fof(f466,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_19) ).
fof(f4559,plain,
spl0_355,
inference(avatar_split_clause,[],[f465,f4557]) ).
fof(f4557,plain,
( spl0_355
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_355])]) ).
fof(f465,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_18) ).
fof(f4555,plain,
spl0_354,
inference(avatar_split_clause,[],[f464,f4553]) ).
fof(f4553,plain,
( spl0_354
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_354])]) ).
fof(f464,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_17) ).
fof(f4551,plain,
spl0_353,
inference(avatar_split_clause,[],[f463,f4549]) ).
fof(f4549,plain,
( spl0_353
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_353])]) ).
fof(f463,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_16) ).
fof(f4547,plain,
spl0_352,
inference(avatar_split_clause,[],[f462,f4545]) ).
fof(f4545,plain,
( spl0_352
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_352])]) ).
fof(f462,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_15) ).
fof(f4543,plain,
spl0_351,
inference(avatar_split_clause,[],[f461,f4541]) ).
fof(f4541,plain,
( spl0_351
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_351])]) ).
fof(f461,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_14) ).
fof(f4539,plain,
spl0_350,
inference(avatar_split_clause,[],[f460,f4537]) ).
fof(f4537,plain,
( spl0_350
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_350])]) ).
fof(f460,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_13) ).
fof(f4535,plain,
spl0_349,
inference(avatar_split_clause,[],[f459,f4533]) ).
fof(f4533,plain,
( spl0_349
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_349])]) ).
fof(f459,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_12) ).
fof(f4531,plain,
spl0_348,
inference(avatar_split_clause,[],[f458,f4529]) ).
fof(f4529,plain,
( spl0_348
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_348])]) ).
fof(f458,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_11) ).
fof(f4527,plain,
spl0_347,
inference(avatar_split_clause,[],[f457,f4525]) ).
fof(f4525,plain,
( spl0_347
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_347])]) ).
fof(f457,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_10) ).
fof(f4523,plain,
spl0_346,
inference(avatar_split_clause,[],[f456,f4521]) ).
fof(f4521,plain,
( spl0_346
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_346])]) ).
fof(f456,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_1) ).
fof(f4519,plain,
spl0_345,
inference(avatar_split_clause,[],[f455,f4517]) ).
fof(f4517,plain,
( spl0_345
<=> ! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Nat_Opower(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_345])]) ).
fof(f455,axiom,
! [X39] :
( ~ class_Power_Orecpower(X39)
| class_Nat_Opower(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Power_Orecpower_0) ).
fof(f4515,plain,
spl0_344,
inference(avatar_split_clause,[],[f454,f4513]) ).
fof(f4513,plain,
( spl0_344
<=> ! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_344])]) ).
fof(f454,axiom,
! [X39] :
( ~ class_Orderings_Oorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Orderings_Oorder_0) ).
fof(f4511,plain,
spl0_343,
inference(avatar_split_clause,[],[f453,f4509]) ).
fof(f4509,plain,
( spl0_343
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_343])]) ).
fof(f453,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Orderings_Olinorder_4) ).
fof(f4507,plain,
spl0_342,
inference(avatar_split_clause,[],[f452,f4505]) ).
fof(f4505,plain,
( spl0_342
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_342])]) ).
fof(f452,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Orderings_Olinorder_3) ).
fof(f4503,plain,
spl0_341,
inference(avatar_split_clause,[],[f451,f4501]) ).
fof(f4501,plain,
( spl0_341
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_341])]) ).
fof(f451,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Orderings_Olinorder_2) ).
fof(f4499,plain,
spl0_340,
inference(avatar_split_clause,[],[f450,f4497]) ).
fof(f4497,plain,
( spl0_340
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_340])]) ).
fof(f450,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Orderings_Olinorder_1) ).
fof(f4495,plain,
spl0_339,
inference(avatar_split_clause,[],[f449,f4493]) ).
fof(f4493,plain,
( spl0_339
<=> ! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_339])]) ).
fof(f449,axiom,
! [X39] :
( ~ class_Orderings_Olinorder(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Orderings_Olinorder_0) ).
fof(f4491,plain,
spl0_338,
inference(avatar_split_clause,[],[f448,f4489]) ).
fof(f4489,plain,
( spl0_338
<=> ! [X39] :
( ~ class_OrderedGroup_Osemigroup__mult(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_338])]) ).
fof(f448,axiom,
! [X39] :
( ~ class_OrderedGroup_Osemigroup__mult(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Osemigroup__mult_0) ).
fof(f4487,plain,
spl0_337,
inference(avatar_split_clause,[],[f447,f4485]) ).
fof(f4485,plain,
( spl0_337
<=> ! [X39] :
( ~ class_OrderedGroup_Osemigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_337])]) ).
fof(f447,axiom,
! [X39] :
( ~ class_OrderedGroup_Osemigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Osemigroup__add_0) ).
fof(f4483,plain,
spl0_336,
inference(avatar_split_clause,[],[f446,f4481]) ).
fof(f4481,plain,
( spl0_336
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_336])]) ).
fof(f446,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_7) ).
fof(f4479,plain,
spl0_335,
inference(avatar_split_clause,[],[f445,f4477]) ).
fof(f4477,plain,
( spl0_335
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_335])]) ).
fof(f445,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_6) ).
fof(f4475,plain,
spl0_334,
inference(avatar_split_clause,[],[f444,f4473]) ).
fof(f4473,plain,
( spl0_334
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_334])]) ).
fof(f444,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_5) ).
fof(f4471,plain,
spl0_333,
inference(avatar_split_clause,[],[f443,f4469]) ).
fof(f4469,plain,
( spl0_333
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_333])]) ).
fof(f443,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_4) ).
fof(f4467,plain,
spl0_332,
inference(avatar_split_clause,[],[f442,f4465]) ).
fof(f4465,plain,
( spl0_332
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_332])]) ).
fof(f442,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_3) ).
fof(f4463,plain,
spl0_331,
inference(avatar_split_clause,[],[f441,f4461]) ).
fof(f4461,plain,
( spl0_331
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_331])]) ).
fof(f441,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_2) ).
fof(f4459,plain,
spl0_330,
inference(avatar_split_clause,[],[f440,f4457]) ).
fof(f4457,plain,
( spl0_330
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_330])]) ).
fof(f440,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_1) ).
fof(f4455,plain,
spl0_329,
inference(avatar_split_clause,[],[f439,f4453]) ).
fof(f4453,plain,
( spl0_329
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_329])]) ).
fof(f439,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__cancel__ab__semigroup__add_0) ).
fof(f4451,plain,
spl0_328,
inference(avatar_split_clause,[],[f438,f4449]) ).
fof(f4449,plain,
( spl0_328
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_328])]) ).
fof(f438,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_8) ).
fof(f4447,plain,
spl0_327,
inference(avatar_split_clause,[],[f437,f4445]) ).
fof(f4445,plain,
( spl0_327
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_327])]) ).
fof(f437,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_7) ).
fof(f4443,plain,
spl0_326,
inference(avatar_split_clause,[],[f436,f4441]) ).
fof(f4441,plain,
( spl0_326
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_326])]) ).
fof(f436,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_6) ).
fof(f4439,plain,
spl0_325,
inference(avatar_split_clause,[],[f435,f4437]) ).
fof(f4437,plain,
( spl0_325
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_325])]) ).
fof(f435,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_5) ).
fof(f4435,plain,
spl0_324,
inference(avatar_split_clause,[],[f434,f4433]) ).
fof(f4433,plain,
( spl0_324
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_324])]) ).
fof(f434,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_4) ).
fof(f4431,plain,
spl0_323,
inference(avatar_split_clause,[],[f433,f4429]) ).
fof(f4429,plain,
( spl0_323
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_323])]) ).
fof(f433,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_3) ).
fof(f4427,plain,
spl0_322,
inference(avatar_split_clause,[],[f432,f4425]) ).
fof(f4425,plain,
( spl0_322
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_322])]) ).
fof(f432,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_2) ).
fof(f4423,plain,
spl0_321,
inference(avatar_split_clause,[],[f431,f4421]) ).
fof(f4421,plain,
( spl0_321
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_321])]) ).
fof(f431,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_1) ).
fof(f4419,plain,
spl0_320,
inference(avatar_split_clause,[],[f430,f4417]) ).
fof(f4417,plain,
( spl0_320
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_320])]) ).
fof(f430,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add__imp__le_0) ).
fof(f4415,plain,
spl0_319,
inference(avatar_split_clause,[],[f429,f4413]) ).
fof(f4413,plain,
( spl0_319
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_319])]) ).
fof(f429,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add_4) ).
fof(f4411,plain,
spl0_318,
inference(avatar_split_clause,[],[f428,f4409]) ).
fof(f4409,plain,
( spl0_318
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_318])]) ).
fof(f428,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add_3) ).
fof(f4407,plain,
spl0_317,
inference(avatar_split_clause,[],[f427,f4405]) ).
fof(f4405,plain,
( spl0_317
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_317])]) ).
fof(f427,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add_2) ).
fof(f4403,plain,
spl0_316,
inference(avatar_split_clause,[],[f426,f4401]) ).
fof(f4401,plain,
( spl0_316
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_316])]) ).
fof(f426,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add_1) ).
fof(f4399,plain,
spl0_315,
inference(avatar_split_clause,[],[f425,f4397]) ).
fof(f4397,plain,
( spl0_315
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_315])]) ).
fof(f425,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__semigroup__add_0) ).
fof(f4395,plain,
spl0_314,
inference(avatar_split_clause,[],[f424,f4393]) ).
fof(f4393,plain,
( spl0_314
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_314])]) ).
fof(f424,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_9) ).
fof(f4391,plain,
spl0_313,
inference(avatar_split_clause,[],[f423,f4389]) ).
fof(f4389,plain,
( spl0_313
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_313])]) ).
fof(f423,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_8) ).
fof(f4387,plain,
spl0_312,
inference(avatar_split_clause,[],[f422,f4385]) ).
fof(f4385,plain,
( spl0_312
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_312])]) ).
fof(f422,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_7) ).
fof(f4383,plain,
spl0_311,
inference(avatar_split_clause,[],[f421,f4381]) ).
fof(f4381,plain,
( spl0_311
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_311])]) ).
fof(f421,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_6) ).
fof(f4379,plain,
spl0_310,
inference(avatar_split_clause,[],[f420,f4377]) ).
fof(f4377,plain,
( spl0_310
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_310])]) ).
fof(f420,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_5) ).
fof(f4375,plain,
spl0_309,
inference(avatar_split_clause,[],[f419,f4373]) ).
fof(f4373,plain,
( spl0_309
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_309])]) ).
fof(f419,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_4) ).
fof(f4371,plain,
spl0_308,
inference(avatar_split_clause,[],[f418,f4369]) ).
fof(f4369,plain,
( spl0_308
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_308])]) ).
fof(f418,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_3) ).
fof(f4367,plain,
spl0_307,
inference(avatar_split_clause,[],[f417,f4365]) ).
fof(f4365,plain,
( spl0_307
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_307])]) ).
fof(f417,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_2) ).
fof(f4363,plain,
spl0_306,
inference(avatar_split_clause,[],[f416,f4361]) ).
fof(f4361,plain,
( spl0_306
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_306])]) ).
fof(f416,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_13) ).
fof(f4359,plain,
spl0_305,
inference(avatar_split_clause,[],[f415,f4357]) ).
fof(f4357,plain,
( spl0_305
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_305])]) ).
fof(f415,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_12) ).
fof(f4355,plain,
spl0_304,
inference(avatar_split_clause,[],[f414,f4353]) ).
fof(f4353,plain,
( spl0_304
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_304])]) ).
fof(f414,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_11) ).
fof(f4351,plain,
spl0_303,
inference(avatar_split_clause,[],[f413,f4349]) ).
fof(f4349,plain,
( spl0_303
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_303])]) ).
fof(f413,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_10) ).
fof(f4347,plain,
spl0_302,
inference(avatar_split_clause,[],[f412,f4345]) ).
fof(f4345,plain,
( spl0_302
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_302])]) ).
fof(f412,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_1) ).
fof(f4343,plain,
spl0_301,
inference(avatar_split_clause,[],[f411,f4341]) ).
fof(f4341,plain,
( spl0_301
<=> ! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_301])]) ).
fof(f411,axiom,
! [X39] :
( ~ class_OrderedGroup_Opordered__ab__group__add(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Opordered__ab__group__add_0) ).
fof(f4339,plain,
spl0_300,
inference(avatar_split_clause,[],[f410,f4337]) ).
fof(f4337,plain,
( spl0_300
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_300])]) ).
fof(f410,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Olinorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_9) ).
fof(f4335,plain,
spl0_299,
inference(avatar_split_clause,[],[f409,f4333]) ).
fof(f4333,plain,
( spl0_299
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_299])]) ).
fof(f409,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_8) ).
fof(f4331,plain,
spl0_298,
inference(avatar_split_clause,[],[f408,f4329]) ).
fof(f4329,plain,
( spl0_298
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_298])]) ).
fof(f408,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_7) ).
fof(f4327,plain,
spl0_297,
inference(avatar_split_clause,[],[f407,f4325]) ).
fof(f4325,plain,
( spl0_297
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_297])]) ).
fof(f407,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_6) ).
fof(f4323,plain,
spl0_296,
inference(avatar_split_clause,[],[f406,f4321]) ).
fof(f4321,plain,
( spl0_296
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_296])]) ).
fof(f406,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_5) ).
fof(f4319,plain,
spl0_295,
inference(avatar_split_clause,[],[f405,f4317]) ).
fof(f4317,plain,
( spl0_295
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_295])]) ).
fof(f405,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_4) ).
fof(f4315,plain,
spl0_294,
inference(avatar_split_clause,[],[f404,f4313]) ).
fof(f4313,plain,
( spl0_294
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_294])]) ).
fof(f404,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_3) ).
fof(f4311,plain,
spl0_293,
inference(avatar_split_clause,[],[f403,f4309]) ).
fof(f4309,plain,
( spl0_293
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_293])]) ).
fof(f403,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_2) ).
fof(f4307,plain,
spl0_292,
inference(avatar_split_clause,[],[f402,f4305]) ).
fof(f4305,plain,
( spl0_292
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_292])]) ).
fof(f402,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_13) ).
fof(f4303,plain,
spl0_291,
inference(avatar_split_clause,[],[f401,f4301]) ).
fof(f4301,plain,
( spl0_291
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_291])]) ).
fof(f401,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_12) ).
fof(f4299,plain,
spl0_290,
inference(avatar_split_clause,[],[f400,f4297]) ).
fof(f4297,plain,
( spl0_290
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_290])]) ).
fof(f400,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_11) ).
fof(f4295,plain,
spl0_289,
inference(avatar_split_clause,[],[f399,f4293]) ).
fof(f4293,plain,
( spl0_289
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_289])]) ).
fof(f399,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_10) ).
fof(f4291,plain,
spl0_288,
inference(avatar_split_clause,[],[f398,f4289]) ).
fof(f4289,plain,
( spl0_288
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_288])]) ).
fof(f398,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_1) ).
fof(f4287,plain,
spl0_287,
inference(avatar_split_clause,[],[f397,f4285]) ).
fof(f4285,plain,
( spl0_287
<=> ! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_287])]) ).
fof(f397,axiom,
! [X39] :
( ~ class_OrderedGroup_Oordered__cancel__ab__semigroup__add(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oordered__cancel__ab__semigroup__add_0) ).
fof(f4283,plain,
spl0_286,
inference(avatar_split_clause,[],[f396,f4281]) ).
fof(f4281,plain,
( spl0_286
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_286])]) ).
fof(f396,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Omonoid__mult_2) ).
fof(f4279,plain,
spl0_285,
inference(avatar_split_clause,[],[f395,f4277]) ).
fof(f4277,plain,
( spl0_285
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_285])]) ).
fof(f395,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Omonoid__mult_1) ).
fof(f4275,plain,
spl0_284,
inference(avatar_split_clause,[],[f394,f4273]) ).
fof(f4273,plain,
( spl0_284
<=> ! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_284])]) ).
fof(f394,axiom,
! [X39] :
( ~ class_OrderedGroup_Omonoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Omonoid__mult_0) ).
fof(f4271,plain,
spl0_283,
inference(avatar_split_clause,[],[f393,f4269]) ).
fof(f4269,plain,
( spl0_283
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_283])]) ).
fof(f393,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_9) ).
fof(f4267,plain,
spl0_282,
inference(avatar_split_clause,[],[f392,f4265]) ).
fof(f4265,plain,
( spl0_282
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_282])]) ).
fof(f392,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_8) ).
fof(f4263,plain,
spl0_281,
inference(avatar_split_clause,[],[f391,f4261]) ).
fof(f4261,plain,
( spl0_281
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_281])]) ).
fof(f391,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_7) ).
fof(f4259,plain,
spl0_280,
inference(avatar_split_clause,[],[f390,f4257]) ).
fof(f4257,plain,
( spl0_280
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_280])]) ).
fof(f390,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_6) ).
fof(f4255,plain,
spl0_279,
inference(avatar_split_clause,[],[f389,f4253]) ).
fof(f4253,plain,
( spl0_279
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_279])]) ).
fof(f389,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_5) ).
fof(f4251,plain,
spl0_278,
inference(avatar_split_clause,[],[f388,f4249]) ).
fof(f4249,plain,
( spl0_278
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_278])]) ).
fof(f388,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_4) ).
fof(f4247,plain,
spl0_277,
inference(avatar_split_clause,[],[f387,f4245]) ).
fof(f4245,plain,
( spl0_277
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_277])]) ).
fof(f387,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_3) ).
fof(f4243,plain,
spl0_276,
inference(avatar_split_clause,[],[f386,f4241]) ).
fof(f4241,plain,
( spl0_276
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_276])]) ).
fof(f386,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_2) ).
fof(f4239,plain,
spl0_275,
inference(avatar_split_clause,[],[f385,f4237]) ).
fof(f4237,plain,
( spl0_275
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_275])]) ).
fof(f385,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_18) ).
fof(f4235,plain,
spl0_274,
inference(avatar_split_clause,[],[f384,f4233]) ).
fof(f4233,plain,
( spl0_274
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_274])]) ).
fof(f384,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_17) ).
fof(f4231,plain,
spl0_273,
inference(avatar_split_clause,[],[f383,f4229]) ).
fof(f4229,plain,
( spl0_273
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_273])]) ).
fof(f383,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_16) ).
fof(f4227,plain,
spl0_272,
inference(avatar_split_clause,[],[f382,f4225]) ).
fof(f4225,plain,
( spl0_272
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_272])]) ).
fof(f382,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_15) ).
fof(f4223,plain,
spl0_271,
inference(avatar_split_clause,[],[f381,f4221]) ).
fof(f4221,plain,
( spl0_271
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_271])]) ).
fof(f381,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_14) ).
fof(f4219,plain,
spl0_270,
inference(avatar_split_clause,[],[f380,f4217]) ).
fof(f4217,plain,
( spl0_270
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_270])]) ).
fof(f380,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_13) ).
fof(f4215,plain,
spl0_269,
inference(avatar_split_clause,[],[f379,f4213]) ).
fof(f4213,plain,
( spl0_269
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_269])]) ).
fof(f379,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_12) ).
fof(f4211,plain,
spl0_268,
inference(avatar_split_clause,[],[f378,f4209]) ).
fof(f4209,plain,
( spl0_268
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_268])]) ).
fof(f378,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_11) ).
fof(f4207,plain,
spl0_267,
inference(avatar_split_clause,[],[f377,f4205]) ).
fof(f4205,plain,
( spl0_267
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_267])]) ).
fof(f377,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_10) ).
fof(f4203,plain,
spl0_266,
inference(avatar_split_clause,[],[f376,f4201]) ).
fof(f4201,plain,
( spl0_266
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_266])]) ).
fof(f376,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_1) ).
fof(f4199,plain,
spl0_265,
inference(avatar_split_clause,[],[f375,f4197]) ).
fof(f4197,plain,
( spl0_265
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_265])]) ).
fof(f375,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__meet(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__meet_0) ).
fof(f4195,plain,
spl0_264,
inference(avatar_split_clause,[],[f374,f4193]) ).
fof(f4193,plain,
( spl0_264
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_264])]) ).
fof(f374,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_9) ).
fof(f4191,plain,
spl0_263,
inference(avatar_split_clause,[],[f373,f4189]) ).
fof(f4189,plain,
( spl0_263
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_263])]) ).
fof(f373,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_8) ).
fof(f4187,plain,
spl0_262,
inference(avatar_split_clause,[],[f372,f4185]) ).
fof(f4185,plain,
( spl0_262
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_262])]) ).
fof(f372,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_7) ).
fof(f4183,plain,
spl0_261,
inference(avatar_split_clause,[],[f371,f4181]) ).
fof(f4181,plain,
( spl0_261
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_261])]) ).
fof(f371,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_6) ).
fof(f4179,plain,
spl0_260,
inference(avatar_split_clause,[],[f370,f4177]) ).
fof(f4177,plain,
( spl0_260
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_260])]) ).
fof(f370,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_5) ).
fof(f4175,plain,
spl0_259,
inference(avatar_split_clause,[],[f369,f4173]) ).
fof(f4173,plain,
( spl0_259
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_259])]) ).
fof(f369,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_4) ).
fof(f4171,plain,
spl0_258,
inference(avatar_split_clause,[],[f368,f4169]) ).
fof(f4169,plain,
( spl0_258
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_258])]) ).
fof(f368,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_3) ).
fof(f4167,plain,
spl0_257,
inference(avatar_split_clause,[],[f367,f4165]) ).
fof(f4165,plain,
( spl0_257
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_257])]) ).
fof(f367,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_2) ).
fof(f4163,plain,
spl0_256,
inference(avatar_split_clause,[],[f366,f4161]) ).
fof(f4161,plain,
( spl0_256
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_256])]) ).
fof(f366,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_18) ).
fof(f4159,plain,
spl0_255,
inference(avatar_split_clause,[],[f365,f4157]) ).
fof(f4157,plain,
( spl0_255
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_255])]) ).
fof(f365,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_17) ).
fof(f4155,plain,
spl0_254,
inference(avatar_split_clause,[],[f364,f4153]) ).
fof(f4153,plain,
( spl0_254
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_254])]) ).
fof(f364,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_16) ).
fof(f4151,plain,
spl0_253,
inference(avatar_split_clause,[],[f363,f4149]) ).
fof(f4149,plain,
( spl0_253
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_253])]) ).
fof(f363,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_15) ).
fof(f4147,plain,
spl0_252,
inference(avatar_split_clause,[],[f362,f4145]) ).
fof(f4145,plain,
( spl0_252
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_252])]) ).
fof(f362,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_14) ).
fof(f4143,plain,
spl0_251,
inference(avatar_split_clause,[],[f361,f4141]) ).
fof(f4141,plain,
( spl0_251
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_251])]) ).
fof(f361,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_13) ).
fof(f4139,plain,
spl0_250,
inference(avatar_split_clause,[],[f360,f4137]) ).
fof(f4137,plain,
( spl0_250
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_250])]) ).
fof(f360,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_12) ).
fof(f4135,plain,
spl0_249,
inference(avatar_split_clause,[],[f359,f4133]) ).
fof(f4133,plain,
( spl0_249
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_249])]) ).
fof(f359,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_11) ).
fof(f4131,plain,
spl0_248,
inference(avatar_split_clause,[],[f358,f4129]) ).
fof(f4129,plain,
( spl0_248
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_248])]) ).
fof(f358,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_10) ).
fof(f4127,plain,
spl0_247,
inference(avatar_split_clause,[],[f357,f4125]) ).
fof(f4125,plain,
( spl0_247
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_247])]) ).
fof(f357,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_1) ).
fof(f4123,plain,
spl0_246,
inference(avatar_split_clause,[],[f356,f4121]) ).
fof(f4121,plain,
( spl0_246
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_246])]) ).
fof(f356,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__join(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__join_0) ).
fof(f4119,plain,
spl0_245,
inference(avatar_split_clause,[],[f355,f4117]) ).
fof(f4117,plain,
( spl0_245
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_245])]) ).
fof(f355,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_9) ).
fof(f4115,plain,
spl0_244,
inference(avatar_split_clause,[],[f354,f4113]) ).
fof(f4113,plain,
( spl0_244
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_244])]) ).
fof(f354,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_8) ).
fof(f4111,plain,
spl0_243,
inference(avatar_split_clause,[],[f353,f4109]) ).
fof(f4109,plain,
( spl0_243
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_243])]) ).
fof(f353,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_7) ).
fof(f4107,plain,
spl0_242,
inference(avatar_split_clause,[],[f352,f4105]) ).
fof(f4105,plain,
( spl0_242
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_242])]) ).
fof(f352,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_6) ).
fof(f4103,plain,
spl0_241,
inference(avatar_split_clause,[],[f351,f4101]) ).
fof(f4101,plain,
( spl0_241
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_241])]) ).
fof(f351,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_5) ).
fof(f4099,plain,
spl0_240,
inference(avatar_split_clause,[],[f350,f4097]) ).
fof(f4097,plain,
( spl0_240
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_240])]) ).
fof(f350,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_4) ).
fof(f4095,plain,
spl0_239,
inference(avatar_split_clause,[],[f349,f4093]) ).
fof(f4093,plain,
( spl0_239
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_239])]) ).
fof(f349,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_3) ).
fof(f4091,plain,
spl0_238,
inference(avatar_split_clause,[],[f348,f4089]) ).
fof(f4089,plain,
( spl0_238
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_238])]) ).
fof(f348,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_2) ).
fof(f4087,plain,
spl0_237,
inference(avatar_split_clause,[],[f347,f4085]) ).
fof(f4085,plain,
( spl0_237
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_237])]) ).
fof(f347,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_18) ).
fof(f4083,plain,
spl0_236,
inference(avatar_split_clause,[],[f346,f4081]) ).
fof(f4081,plain,
( spl0_236
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_236])]) ).
fof(f346,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_17) ).
fof(f4079,plain,
spl0_235,
inference(avatar_split_clause,[],[f345,f4077]) ).
fof(f4077,plain,
( spl0_235
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_235])]) ).
fof(f345,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_16) ).
fof(f4075,plain,
spl0_234,
inference(avatar_split_clause,[],[f344,f4073]) ).
fof(f4073,plain,
( spl0_234
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_234])]) ).
fof(f344,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_15) ).
fof(f4071,plain,
spl0_233,
inference(avatar_split_clause,[],[f343,f4069]) ).
fof(f4069,plain,
( spl0_233
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_233])]) ).
fof(f343,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_14) ).
fof(f4067,plain,
spl0_232,
inference(avatar_split_clause,[],[f342,f4065]) ).
fof(f4065,plain,
( spl0_232
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_232])]) ).
fof(f342,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_13) ).
fof(f4063,plain,
spl0_231,
inference(avatar_split_clause,[],[f341,f4061]) ).
fof(f4061,plain,
( spl0_231
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_231])]) ).
fof(f341,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_12) ).
fof(f4059,plain,
spl0_230,
inference(avatar_split_clause,[],[f340,f4057]) ).
fof(f4057,plain,
( spl0_230
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_230])]) ).
fof(f340,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_11) ).
fof(f4055,plain,
spl0_229,
inference(avatar_split_clause,[],[f339,f4053]) ).
fof(f4053,plain,
( spl0_229
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_229])]) ).
fof(f339,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_10) ).
fof(f4051,plain,
spl0_228,
inference(avatar_split_clause,[],[f338,f4049]) ).
fof(f4049,plain,
( spl0_228
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_228])]) ).
fof(f338,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_1) ).
fof(f4047,plain,
spl0_227,
inference(avatar_split_clause,[],[f337,f4045]) ).
fof(f4045,plain,
( spl0_227
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_227])]) ).
fof(f337,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group__abs(X39)
| class_OrderedGroup_Olordered__ab__group(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group__abs_0) ).
fof(f4043,plain,
spl0_226,
inference(avatar_split_clause,[],[f336,f4041]) ).
fof(f4041,plain,
( spl0_226
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_226])]) ).
fof(f336,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_9) ).
fof(f4039,plain,
spl0_225,
inference(avatar_split_clause,[],[f335,f4037]) ).
fof(f4037,plain,
( spl0_225
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_225])]) ).
fof(f335,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_8) ).
fof(f4035,plain,
spl0_224,
inference(avatar_split_clause,[],[f334,f4033]) ).
fof(f4033,plain,
( spl0_224
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_224])]) ).
fof(f334,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_7) ).
fof(f4031,plain,
spl0_223,
inference(avatar_split_clause,[],[f333,f4029]) ).
fof(f4029,plain,
( spl0_223
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_223])]) ).
fof(f333,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__cancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_6) ).
fof(f4027,plain,
spl0_222,
inference(avatar_split_clause,[],[f332,f4025]) ).
fof(f4025,plain,
( spl0_222
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_222])]) ).
fof(f332,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_5) ).
fof(f4023,plain,
spl0_221,
inference(avatar_split_clause,[],[f331,f4021]) ).
fof(f4021,plain,
( spl0_221
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_221])]) ).
fof(f331,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_4) ).
fof(f4019,plain,
spl0_220,
inference(avatar_split_clause,[],[f330,f4017]) ).
fof(f4017,plain,
( spl0_220
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_220])]) ).
fof(f330,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_3) ).
fof(f4015,plain,
spl0_219,
inference(avatar_split_clause,[],[f329,f4013]) ).
fof(f4013,plain,
( spl0_219
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_219])]) ).
fof(f329,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_2) ).
fof(f4011,plain,
spl0_218,
inference(avatar_split_clause,[],[f328,f4009]) ).
fof(f4009,plain,
( spl0_218
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_218])]) ).
fof(f328,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_17) ).
fof(f4007,plain,
spl0_217,
inference(avatar_split_clause,[],[f327,f4005]) ).
fof(f4005,plain,
( spl0_217
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_217])]) ).
fof(f327,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_16) ).
fof(f4003,plain,
spl0_216,
inference(avatar_split_clause,[],[f326,f4001]) ).
fof(f4001,plain,
( spl0_216
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_216])]) ).
fof(f326,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_LOrder_Olorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_15) ).
fof(f3999,plain,
spl0_215,
inference(avatar_split_clause,[],[f325,f3997]) ).
fof(f3997,plain,
( spl0_215
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_215])]) ).
fof(f325,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_14) ).
fof(f3995,plain,
spl0_214,
inference(avatar_split_clause,[],[f324,f3993]) ).
fof(f3993,plain,
( spl0_214
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_214])]) ).
fof(f324,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_13) ).
fof(f3991,plain,
spl0_213,
inference(avatar_split_clause,[],[f323,f3989]) ).
fof(f3989,plain,
( spl0_213
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_213])]) ).
fof(f323,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_12) ).
fof(f3987,plain,
spl0_212,
inference(avatar_split_clause,[],[f322,f3985]) ).
fof(f3985,plain,
( spl0_212
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_212])]) ).
fof(f322,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_11) ).
fof(f3983,plain,
spl0_211,
inference(avatar_split_clause,[],[f321,f3981]) ).
fof(f3981,plain,
( spl0_211
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_211])]) ).
fof(f321,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_10) ).
fof(f3979,plain,
spl0_210,
inference(avatar_split_clause,[],[f320,f3977]) ).
fof(f3977,plain,
( spl0_210
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_210])]) ).
fof(f320,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_1) ).
fof(f3975,plain,
spl0_209,
inference(avatar_split_clause,[],[f319,f3973]) ).
fof(f3973,plain,
( spl0_209
<=> ! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_209])]) ).
fof(f319,axiom,
! [X39] :
( ~ class_OrderedGroup_Olordered__ab__group(X39)
| class_OrderedGroup_Opordered__ab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Olordered__ab__group_0) ).
fof(f3971,plain,
spl0_208,
inference(avatar_split_clause,[],[f318,f3969]) ).
fof(f3969,plain,
( spl0_208
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_208])]) ).
fof(f318,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__mult_4) ).
fof(f3967,plain,
spl0_207,
inference(avatar_split_clause,[],[f317,f3965]) ).
fof(f3965,plain,
( spl0_207
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_207])]) ).
fof(f317,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__mult_3) ).
fof(f3963,plain,
spl0_206,
inference(avatar_split_clause,[],[f316,f3961]) ).
fof(f3961,plain,
( spl0_206
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_206])]) ).
fof(f316,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__mult_2) ).
fof(f3959,plain,
spl0_205,
inference(avatar_split_clause,[],[f315,f3957]) ).
fof(f3957,plain,
( spl0_205
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_205])]) ).
fof(f315,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__mult_1) ).
fof(f3955,plain,
spl0_204,
inference(avatar_split_clause,[],[f314,f3953]) ).
fof(f3953,plain,
( spl0_204
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_204])]) ).
fof(f314,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__mult(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__mult_0) ).
fof(f3951,plain,
spl0_203,
inference(avatar_split_clause,[],[f313,f3949]) ).
fof(f3949,plain,
( spl0_203
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_203])]) ).
fof(f313,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__add_3) ).
fof(f3947,plain,
spl0_202,
inference(avatar_split_clause,[],[f312,f3945]) ).
fof(f3945,plain,
( spl0_202
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_202])]) ).
fof(f312,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__add_2) ).
fof(f3943,plain,
spl0_201,
inference(avatar_split_clause,[],[f311,f3941]) ).
fof(f3941,plain,
( spl0_201
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_201])]) ).
fof(f311,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__add_1) ).
fof(f3939,plain,
spl0_200,
inference(avatar_split_clause,[],[f310,f3937]) ).
fof(f3937,plain,
( spl0_200
<=> ! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_200])]) ).
fof(f310,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocomm__monoid__add(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocomm__monoid__add_0) ).
fof(f3935,plain,
spl0_199,
inference(avatar_split_clause,[],[f309,f3933]) ).
fof(f3933,plain,
( spl0_199
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_199])]) ).
fof(f309,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocancel__semigroup__add_1) ).
fof(f3931,plain,
spl0_198,
inference(avatar_split_clause,[],[f308,f3929]) ).
fof(f3929,plain,
( spl0_198
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_198])]) ).
fof(f308,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocancel__semigroup__add_0) ).
fof(f3927,plain,
spl0_197,
inference(avatar_split_clause,[],[f307,f3925]) ).
fof(f3925,plain,
( spl0_197
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_197])]) ).
fof(f307,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_3) ).
fof(f3923,plain,
spl0_196,
inference(avatar_split_clause,[],[f306,f3921]) ).
fof(f3921,plain,
( spl0_196
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_196])]) ).
fof(f306,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_2) ).
fof(f3919,plain,
spl0_195,
inference(avatar_split_clause,[],[f305,f3917]) ).
fof(f3917,plain,
( spl0_195
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_195])]) ).
fof(f305,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_1) ).
fof(f3915,plain,
spl0_194,
inference(avatar_split_clause,[],[f304,f3913]) ).
fof(f3913,plain,
( spl0_194
<=> ! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_194])]) ).
fof(f304,axiom,
! [X39] :
( ~ class_OrderedGroup_Ocancel__ab__semigroup__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Ocancel__ab__semigroup__add_0) ).
fof(f3911,plain,
spl0_193,
inference(avatar_split_clause,[],[f303,f3909]) ).
fof(f3909,plain,
( spl0_193
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_193])]) ).
fof(f303,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__semigroup__mult_1) ).
fof(f3907,plain,
spl0_192,
inference(avatar_split_clause,[],[f302,f3905]) ).
fof(f3905,plain,
( spl0_192
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_192])]) ).
fof(f302,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__mult(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__semigroup__mult_0) ).
fof(f3903,plain,
spl0_191,
inference(avatar_split_clause,[],[f301,f3901]) ).
fof(f3901,plain,
( spl0_191
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_191])]) ).
fof(f301,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__semigroup__add_1) ).
fof(f3899,plain,
spl0_190,
inference(avatar_split_clause,[],[f300,f3897]) ).
fof(f3897,plain,
( spl0_190
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_190])]) ).
fof(f300,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__semigroup__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__semigroup__add_0) ).
fof(f3895,plain,
spl0_189,
inference(avatar_split_clause,[],[f299,f3893]) ).
fof(f3893,plain,
( spl0_189
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_189])]) ).
fof(f299,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_7) ).
fof(f3891,plain,
spl0_188,
inference(avatar_split_clause,[],[f298,f3889]) ).
fof(f3889,plain,
( spl0_188
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_188])]) ).
fof(f298,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_6) ).
fof(f3887,plain,
spl0_187,
inference(avatar_split_clause,[],[f297,f3885]) ).
fof(f3885,plain,
( spl0_187
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_187])]) ).
fof(f297,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_5) ).
fof(f3883,plain,
spl0_186,
inference(avatar_split_clause,[],[f296,f3881]) ).
fof(f3881,plain,
( spl0_186
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_186])]) ).
fof(f296,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_4) ).
fof(f3879,plain,
spl0_185,
inference(avatar_split_clause,[],[f295,f3877]) ).
fof(f3877,plain,
( spl0_185
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_185])]) ).
fof(f295,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_3) ).
fof(f3875,plain,
spl0_184,
inference(avatar_split_clause,[],[f294,f3873]) ).
fof(f3873,plain,
( spl0_184
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_184])]) ).
fof(f294,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_2) ).
fof(f3871,plain,
spl0_183,
inference(avatar_split_clause,[],[f293,f3869]) ).
fof(f3869,plain,
( spl0_183
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_183])]) ).
fof(f293,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_1) ).
fof(f3867,plain,
spl0_182,
inference(avatar_split_clause,[],[f292,f3865]) ).
fof(f3865,plain,
( spl0_182
<=> ! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_182])]) ).
fof(f292,axiom,
! [X39] :
( ~ class_OrderedGroup_Oab__group__add(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_OrderedGroup_Oab__group__add_0) ).
fof(f3863,plain,
spl0_181,
inference(avatar_split_clause,[],[f291,f3861]) ).
fof(f3861,plain,
( spl0_181
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_181])]) ).
fof(f291,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_9) ).
fof(f3859,plain,
spl0_180,
inference(avatar_split_clause,[],[f290,f3857]) ).
fof(f3857,plain,
( spl0_180
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Ozero(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_180])]) ).
fof(f290,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Ozero(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_8) ).
fof(f3855,plain,
spl0_179,
inference(avatar_split_clause,[],[f289,f3853]) ).
fof(f3853,plain,
( spl0_179
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_179])]) ).
fof(f289,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_7) ).
fof(f3851,plain,
spl0_178,
inference(avatar_split_clause,[],[f288,f3849]) ).
fof(f3849,plain,
( spl0_178
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_178])]) ).
fof(f288,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_6) ).
fof(f3847,plain,
spl0_177,
inference(avatar_split_clause,[],[f287,f3845]) ).
fof(f3845,plain,
( spl0_177
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_177])]) ).
fof(f287,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__semigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_5) ).
fof(f3843,plain,
spl0_176,
inference(avatar_split_clause,[],[f286,f3841]) ).
fof(f3841,plain,
( spl0_176
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_176])]) ).
fof(f286,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Osemigroup__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_4) ).
fof(f3839,plain,
spl0_175,
inference(avatar_split_clause,[],[f285,f3837]) ).
fof(f3837,plain,
( spl0_175
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_175])]) ).
fof(f285,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Numeral_Onumber(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_30) ).
fof(f3835,plain,
spl0_174,
inference(avatar_split_clause,[],[f284,f3833]) ).
fof(f3833,plain,
( spl0_174
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Otimes(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_174])]) ).
fof(f284,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Otimes(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_3) ).
fof(f3831,plain,
spl0_173,
inference(avatar_split_clause,[],[f283,f3829]) ).
fof(f3829,plain,
( spl0_173
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_173])]) ).
fof(f283,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_29) ).
fof(f3827,plain,
spl0_172,
inference(avatar_split_clause,[],[f282,f3825]) ).
fof(f3825,plain,
( spl0_172
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_172])]) ).
fof(f282,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_28) ).
fof(f3823,plain,
spl0_171,
inference(avatar_split_clause,[],[f281,f3821]) ).
fof(f3821,plain,
( spl0_171
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_171])]) ).
fof(f281,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_27) ).
fof(f3819,plain,
spl0_170,
inference(avatar_split_clause,[],[f280,f3817]) ).
fof(f3817,plain,
( spl0_170
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_170])]) ).
fof(f280,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_26) ).
fof(f3815,plain,
spl0_169,
inference(avatar_split_clause,[],[f279,f3813]) ).
fof(f3813,plain,
( spl0_169
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_169])]) ).
fof(f279,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_25) ).
fof(f3811,plain,
spl0_168,
inference(avatar_split_clause,[],[f278,f3809]) ).
fof(f3809,plain,
( spl0_168
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_168])]) ).
fof(f278,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_24) ).
fof(f3807,plain,
spl0_167,
inference(avatar_split_clause,[],[f277,f3805]) ).
fof(f3805,plain,
( spl0_167
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_167])]) ).
fof(f277,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocomm__monoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_23) ).
fof(f3803,plain,
spl0_166,
inference(avatar_split_clause,[],[f276,f3801]) ).
fof(f3801,plain,
( spl0_166
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_166])]) ).
fof(f276,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Omonoid__mult(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_22) ).
fof(f3799,plain,
spl0_165,
inference(avatar_split_clause,[],[f275,f3797]) ).
fof(f3797,plain,
( spl0_165
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_165])]) ).
fof(f275,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oaxclass__0__neq__1(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_21) ).
fof(f3795,plain,
spl0_164,
inference(avatar_split_clause,[],[f274,f3793]) ).
fof(f3793,plain,
( spl0_164
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_164])]) ).
fof(f274,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oone(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_20) ).
fof(f3791,plain,
spl0_163,
inference(avatar_split_clause,[],[f273,f3789]) ).
fof(f3789,plain,
( spl0_163
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_163])]) ).
fof(f273,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_2) ).
fof(f3787,plain,
spl0_162,
inference(avatar_split_clause,[],[f272,f3785]) ).
fof(f3785,plain,
( spl0_162
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_162])]) ).
fof(f272,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__ring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_19) ).
fof(f3783,plain,
spl0_161,
inference(avatar_split_clause,[],[f271,f3781]) ).
fof(f3781,plain,
( spl0_161
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_161])]) ).
fof(f271,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_18) ).
fof(f3779,plain,
spl0_160,
inference(avatar_split_clause,[],[f270,f3777]) ).
fof(f3777,plain,
( spl0_160
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_160])]) ).
fof(f270,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Oring(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_17) ).
fof(f3775,plain,
spl0_159,
inference(avatar_split_clause,[],[f269,f3773]) ).
fof(f3773,plain,
( spl0_159
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_159])]) ).
fof(f269,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0__cancel(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_16) ).
fof(f3771,plain,
spl0_158,
inference(avatar_split_clause,[],[f268,f3769]) ).
fof(f3769,plain,
( spl0_158
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_158])]) ).
fof(f268,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Oab__group__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_15) ).
fof(f3767,plain,
spl0_157,
inference(avatar_split_clause,[],[f267,f3765]) ).
fof(f3765,plain,
( spl0_157
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_157])]) ).
fof(f267,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__ab__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_14) ).
fof(f3763,plain,
spl0_156,
inference(avatar_split_clause,[],[f266,f3761]) ).
fof(f3761,plain,
( spl0_156
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_156])]) ).
fof(f266,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Ocancel__semigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_13) ).
fof(f3759,plain,
spl0_155,
inference(avatar_split_clause,[],[f265,f3757]) ).
fof(f3757,plain,
( spl0_155
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Ominus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_155])]) ).
fof(f265,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Ominus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_12) ).
fof(f3755,plain,
spl0_154,
inference(avatar_split_clause,[],[f264,f3753]) ).
fof(f3753,plain,
( spl0_154
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_154])]) ).
fof(f264,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Ocomm__semiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_11) ).
fof(f3751,plain,
spl0_153,
inference(avatar_split_clause,[],[f263,f3749]) ).
fof(f3749,plain,
( spl0_153
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_153])]) ).
fof(f263,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_Ring__and__Field_Osemiring__0(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_10) ).
fof(f3747,plain,
spl0_152,
inference(avatar_split_clause,[],[f262,f3745]) ).
fof(f3745,plain,
( spl0_152
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_152])]) ).
fof(f262,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_OrderedGroup_Osemigroup__add(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_1) ).
fof(f3743,plain,
spl0_151,
inference(avatar_split_clause,[],[f261,f3741]) ).
fof(f3741,plain,
( spl0_151
<=> ! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oplus(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_151])]) ).
fof(f261,axiom,
! [X39] :
( ~ class_Numeral_Onumber__ring(X39)
| class_HOL_Oplus(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_Numeral_Onumber__ring_0) ).
fof(f3739,plain,
spl0_150,
inference(avatar_split_clause,[],[f260,f3737]) ).
fof(f3737,plain,
( spl0_150
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_150])]) ).
fof(f260,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Omeet__semilorder_1) ).
fof(f3735,plain,
spl0_149,
inference(avatar_split_clause,[],[f259,f3733]) ).
fof(f3733,plain,
( spl0_149
<=> ! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_149])]) ).
fof(f259,axiom,
! [X39] :
( ~ class_LOrder_Omeet__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Omeet__semilorder_0) ).
fof(f3731,plain,
spl0_148,
inference(avatar_split_clause,[],[f258,f3729]) ).
fof(f3729,plain,
( spl0_148
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_148])]) ).
fof(f258,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Ojoin__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Olorder_3) ).
fof(f3727,plain,
spl0_147,
inference(avatar_split_clause,[],[f257,f3725]) ).
fof(f3725,plain,
( spl0_147
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_147])]) ).
fof(f257,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Olorder_2) ).
fof(f3723,plain,
spl0_146,
inference(avatar_split_clause,[],[f256,f3721]) ).
fof(f3721,plain,
( spl0_146
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_146])]) ).
fof(f256,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Olorder_1) ).
fof(f3719,plain,
spl0_145,
inference(avatar_split_clause,[],[f255,f3717]) ).
fof(f3717,plain,
( spl0_145
<=> ! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_145])]) ).
fof(f255,axiom,
! [X39] :
( ~ class_LOrder_Olorder(X39)
| class_LOrder_Omeet__semilorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Olorder_0) ).
fof(f3715,plain,
spl0_144,
inference(avatar_split_clause,[],[f254,f3713]) ).
fof(f3713,plain,
( spl0_144
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_144])]) ).
fof(f254,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oorder(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Ojoin__semilorder_1) ).
fof(f3711,plain,
spl0_143,
inference(avatar_split_clause,[],[f253,f3709]) ).
fof(f3709,plain,
( spl0_143
<=> ! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_143])]) ).
fof(f253,axiom,
! [X39] :
( ~ class_LOrder_Ojoin__semilorder(X39)
| class_Orderings_Oord(X39) ),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsrel_LOrder_Ojoin__semilorder_0) ).
fof(f3707,plain,
spl0_142,
inference(avatar_split_clause,[],[f197,f3705]) ).
fof(f3705,plain,
( spl0_142
<=> ! [X38,X37] : class_Nat_Opower(tc_fun(X38,X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_142])]) ).
fof(f197,axiom,
! [X38,X37] : class_Nat_Opower(tc_fun(X38,X37)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_fun_1) ).
fof(f3703,plain,
spl0_141,
inference(avatar_split_clause,[],[f98,f3701]) ).
fof(f98,axiom,
! [X0,X1] : c_in(X0,c_UNIV,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUNIV__I_0) ).
fof(f3699,plain,
spl0_140,
inference(avatar_split_clause,[],[f66,f3697]) ).
fof(f3697,plain,
( spl0_140
<=> ! [X21] : ~ c_less(X21,X21,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_140])]) ).
fof(f66,axiom,
! [X21] : ~ c_less(X21,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Oless__irrefl_0) ).
fof(f3695,plain,
spl0_139,
inference(avatar_split_clause,[],[f64,f3693]) ).
fof(f64,axiom,
! [X21] : c_lessequals(c_0,X21,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Nat_Ole0_0) ).
fof(f3691,plain,
spl0_138,
inference(avatar_split_clause,[],[f40,f3689]) ).
fof(f3689,plain,
( spl0_138
<=> ! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_138])]) ).
fof(f40,axiom,
! [X15] : c_Divides_Oop_Advd(c_1,X15,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__1__left_0) ).
fof(f3687,plain,
spl0_137,
inference(avatar_split_clause,[],[f39,f3685]) ).
fof(f3685,plain,
( spl0_137
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_137])]) ).
fof(f39,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDiv_Ozdvd__0__right_0) ).
fof(f3683,plain,
spl0_136,
inference(avatar_split_clause,[],[f23,f3681]) ).
fof(f3681,plain,
( spl0_136
<=> ! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_136])]) ).
fof(f23,axiom,
! [X15] : c_Divides_Oop_Advd(X15,c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Divides_Odvd__0__right_0) ).
fof(f3679,plain,
~ spl0_135,
inference(avatar_split_clause,[],[f2732,f3676]) ).
fof(f3676,plain,
( spl0_135
<=> c_Message_Oagent_OServer = c_Message_Oagent_OSpy ),
introduced(avatar_definition,[new_symbols(naming,[spl0_135])]) ).
fof(f2732,axiom,
c_Message_Oagent_OServer != c_Message_Oagent_OSpy,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Message_Oagent_Odistinct__3_0) ).
fof(f3674,plain,
~ spl0_134,
inference(avatar_split_clause,[],[f2629,f3671]) ).
fof(f3671,plain,
( spl0_134
<=> c_emptyset = c_UNIV ),
introduced(avatar_definition,[new_symbols(naming,[spl0_134])]) ).
fof(f2629,axiom,
c_emptyset != c_UNIV,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Set_OUNIV__not__empty_0) ).
fof(f3669,plain,
~ spl0_133,
inference(avatar_split_clause,[],[f2310,f3666]) ).
fof(f3666,plain,
( spl0_133
<=> c_Parity_Oeven(c_1,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_133])]) ).
fof(f2310,axiom,
~ c_Parity_Oeven(c_1,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oodd__one_0) ).
fof(f3664,plain,
spl0_132,
inference(avatar_split_clause,[],[f2303,f3661]) ).
fof(f3661,plain,
( spl0_132
<=> c_Parity_Oeven(c_0,tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_132])]) ).
fof(f2303,axiom,
c_Parity_Oeven(c_0,tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__zero_0) ).
fof(f3659,plain,
spl0_131,
inference(avatar_split_clause,[],[f2290,f3656]) ).
fof(f2290,axiom,
c_Parity_Oeven(c_0,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Parity_Oeven__nat__zero_0) ).
fof(f3654,plain,
~ spl0_130,
inference(avatar_split_clause,[],[f2159,f3651]) ).
fof(f3651,plain,
( spl0_130
<=> c_Numeral_Obit_OB1 = c_Numeral_Obit_OB0 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_130])]) ).
fof(f2159,axiom,
c_Numeral_Obit_OB1 != c_Numeral_Obit_OB0,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Numeral_Obit_Odistinct__1_0) ).
fof(f3649,plain,
spl0_129,
inference(avatar_split_clause,[],[f1706,f3647]) ).
fof(f3647,plain,
( spl0_129
<=> ! [X41] : c_List_Onull(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_129])]) ).
fof(f1706,axiom,
! [X41] : c_List_Onull(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Onull_Osimps__1_0) ).
fof(f3645,plain,
spl0_128,
inference(avatar_split_clause,[],[f1551,f3643]) ).
fof(f3643,plain,
( spl0_128
<=> ! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_128])]) ).
fof(f1551,axiom,
! [X41] : c_List_Odistinct(c_List_Olist_ONil,X41),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_List_Odistinct_Osimps__1_0) ).
fof(f3641,plain,
~ spl0_127,
inference(avatar_split_clause,[],[f1370,f3638]) ).
fof(f1370,axiom,
c_0 != c_1,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_IntDef_Oint__0__neq__1_0) ).
fof(f3636,plain,
~ spl0_126,
inference(avatar_split_clause,[],[f1250,f3633]) ).
fof(f3633,plain,
( spl0_126
<=> c_Extraction_Osumbool_OLeft = c_Extraction_Osumbool_ORight ),
introduced(avatar_definition,[new_symbols(naming,[spl0_126])]) ).
fof(f1250,axiom,
c_Extraction_Osumbool_OLeft != c_Extraction_Osumbool_ORight,
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Extraction_Osumbool_Odistinct__1_0) ).
fof(f3631,plain,
spl0_125,
inference(avatar_split_clause,[],[f251,f3629]) ).
fof(f3629,plain,
( spl0_125
<=> ! [X37] : class_Nat_Opower(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_125])]) ).
fof(f251,axiom,
! [X37] : class_Nat_Opower(tc_set(X37)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_set_4) ).
fof(f3627,plain,
spl0_124,
inference(avatar_split_clause,[],[f249,f3625]) ).
fof(f249,axiom,
! [X37] : class_Orderings_Oorder(tc_set(X37)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_set_2) ).
fof(f3623,plain,
spl0_123,
inference(avatar_split_clause,[],[f248,f3621]) ).
fof(f3621,plain,
( spl0_123
<=> ! [X37] : class_Orderings_Oord(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_123])]) ).
fof(f248,axiom,
! [X37] : class_Orderings_Oord(tc_set(X37)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_set_1) ).
fof(f3619,plain,
spl0_122,
inference(avatar_split_clause,[],[f247,f3617]) ).
fof(f3617,plain,
( spl0_122
<=> ! [X37] : class_HOL_Ominus(tc_set(X37)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_122])]) ).
fof(f247,axiom,
! [X37] : class_HOL_Ominus(tc_set(X37)),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_set_0) ).
fof(f3615,plain,
spl0_121,
inference(avatar_split_clause,[],[f126,f3612]) ).
fof(f3612,plain,
( spl0_121
<=> c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_121])]) ).
fof(f126,axiom,
c_Wellfounded__Recursion_Owf(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Relations_Owf__less__than_0) ).
fof(f3610,plain,
spl0_120,
inference(avatar_split_clause,[],[f124,f3607]) ).
fof(f3607,plain,
( spl0_120
<=> c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_120])]) ).
fof(f124,axiom,
c_Relation_Otrans(c_Wellfounded__Relations_Oless__than,tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Relations_Otrans__less__than_0) ).
fof(f3605,plain,
spl0_119,
inference(avatar_split_clause,[],[f123,f3603]) ).
fof(f3603,plain,
( spl0_119
<=> ! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_119])]) ).
fof(f123,axiom,
! [X1] : c_Wellfounded__Recursion_Owf(c_emptyset,X1),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_Wellfounded__Recursion_Owf__empty_0) ).
fof(f3601,plain,
spl0_118,
inference(avatar_split_clause,[],[f2827,f3598]) ).
fof(f2827,axiom,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_conjecture_1) ).
fof(f3596,plain,
~ spl0_117,
inference(avatar_split_clause,[],[f2828,f3593]) ).
fof(f2828,axiom,
~ c_in(v_X,c_union(c_Message_Oparts(v_H),c_Message_Osynth(v_H),tc_Message_Omsg),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_conjecture_2) ).
fof(f3591,plain,
spl0_116,
inference(avatar_split_clause,[],[f245,f3588]) ).
fof(f3588,plain,
( spl0_116
<=> class_HOL_Ominus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_116])]) ).
fof(f245,axiom,
class_HOL_Ominus(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_9) ).
fof(f3586,plain,
spl0_115,
inference(avatar_split_clause,[],[f244,f3583]) ).
fof(f3583,plain,
( spl0_115
<=> class_Wellfounded__Recursion_Owellorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_115])]) ).
fof(f244,axiom,
class_Wellfounded__Recursion_Owellorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_8) ).
fof(f3581,plain,
spl0_114,
inference(avatar_split_clause,[],[f243,f3578]) ).
fof(f243,axiom,
class_Orderings_Olinorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_7) ).
fof(f3576,plain,
spl0_113,
inference(avatar_split_clause,[],[f242,f3573]) ).
fof(f3573,plain,
( spl0_113
<=> class_LOrder_Olorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_113])]) ).
fof(f242,axiom,
class_LOrder_Olorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_6) ).
fof(f3571,plain,
spl0_112,
inference(avatar_split_clause,[],[f241,f3568]) ).
fof(f241,axiom,
class_LOrder_Ojoin__semilorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_5) ).
fof(f3566,plain,
spl0_111,
inference(avatar_split_clause,[],[f240,f3563]) ).
fof(f3563,plain,
( spl0_111
<=> class_Parity_Oeven__odd(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_111])]) ).
fof(f240,axiom,
class_Parity_Oeven__odd(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_47) ).
fof(f3561,plain,
spl0_110,
inference(avatar_split_clause,[],[f239,f3558]) ).
fof(f3558,plain,
( spl0_110
<=> class_Numeral_Onumber(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_110])]) ).
fof(f239,axiom,
class_Numeral_Onumber(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_46) ).
fof(f3556,plain,
spl0_109,
inference(avatar_split_clause,[],[f238,f3553]) ).
fof(f238,axiom,
class_Power_Orecpower(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_45) ).
fof(f3551,plain,
spl0_108,
inference(avatar_split_clause,[],[f237,f3548]) ).
fof(f3548,plain,
( spl0_108
<=> class_Divides_Odiv(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_108])]) ).
fof(f237,axiom,
class_Divides_Odiv(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_44) ).
fof(f3546,plain,
spl0_107,
inference(avatar_split_clause,[],[f236,f3543]) ).
fof(f3543,plain,
( spl0_107
<=> class_Ring__and__Field_Oordered__semidom(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_107])]) ).
fof(f236,axiom,
class_Ring__and__Field_Oordered__semidom(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_43) ).
fof(f3541,plain,
spl0_106,
inference(avatar_split_clause,[],[f235,f3538]) ).
fof(f3538,plain,
( spl0_106
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_106])]) ).
fof(f235,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_42) ).
fof(f3536,plain,
spl0_105,
inference(avatar_split_clause,[],[f234,f3533]) ).
fof(f3533,plain,
( spl0_105
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_105])]) ).
fof(f234,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_41) ).
fof(f3531,plain,
spl0_104,
inference(avatar_split_clause,[],[f233,f3528]) ).
fof(f3528,plain,
( spl0_104
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_104])]) ).
fof(f233,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_40) ).
fof(f3526,plain,
spl0_103,
inference(avatar_split_clause,[],[f232,f3523]) ).
fof(f232,axiom,
class_LOrder_Omeet__semilorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_4) ).
fof(f3521,plain,
spl0_102,
inference(avatar_split_clause,[],[f231,f3518]) ).
fof(f3518,plain,
( spl0_102
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_102])]) ).
fof(f231,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_39) ).
fof(f3516,plain,
spl0_101,
inference(avatar_split_clause,[],[f230,f3513]) ).
fof(f3513,plain,
( spl0_101
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_101])]) ).
fof(f230,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_38) ).
fof(f3511,plain,
spl0_100,
inference(avatar_split_clause,[],[f229,f3508]) ).
fof(f3508,plain,
( spl0_100
<=> class_Ring__and__Field_Opordered__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_100])]) ).
fof(f229,axiom,
class_Ring__and__Field_Opordered__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_37) ).
fof(f3506,plain,
spl0_99,
inference(avatar_split_clause,[],[f228,f3503]) ).
fof(f3503,plain,
( spl0_99
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_99])]) ).
fof(f228,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_36) ).
fof(f3501,plain,
spl0_98,
inference(avatar_split_clause,[],[f227,f3498]) ).
fof(f3498,plain,
( spl0_98
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_98])]) ).
fof(f227,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_35) ).
fof(f3496,plain,
spl0_97,
inference(avatar_split_clause,[],[f226,f3493]) ).
fof(f3493,plain,
( spl0_97
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_97])]) ).
fof(f226,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_34) ).
fof(f3491,plain,
spl0_96,
inference(avatar_split_clause,[],[f225,f3488]) ).
fof(f3488,plain,
( spl0_96
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_96])]) ).
fof(f225,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_33) ).
fof(f3486,plain,
spl0_95,
inference(avatar_split_clause,[],[f224,f3483]) ).
fof(f224,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_32) ).
fof(f3481,plain,
spl0_94,
inference(avatar_split_clause,[],[f223,f3478]) ).
fof(f3478,plain,
( spl0_94
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_94])]) ).
fof(f223,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_31) ).
fof(f3476,plain,
spl0_93,
inference(avatar_split_clause,[],[f222,f3473]) ).
fof(f3473,plain,
( spl0_93
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_93])]) ).
fof(f222,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_30) ).
fof(f3471,plain,
spl0_92,
inference(avatar_split_clause,[],[f221,f3468]) ).
fof(f3468,plain,
( spl0_92
<=> class_Orderings_Oorder(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_92])]) ).
fof(f221,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_3) ).
fof(f3466,plain,
spl0_91,
inference(avatar_split_clause,[],[f220,f3463]) ).
fof(f3463,plain,
( spl0_91
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_91])]) ).
fof(f220,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_29) ).
fof(f3461,plain,
spl0_90,
inference(avatar_split_clause,[],[f219,f3458]) ).
fof(f3458,plain,
( spl0_90
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_90])]) ).
fof(f219,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_28) ).
fof(f3456,plain,
spl0_89,
inference(avatar_split_clause,[],[f218,f3453]) ).
fof(f3453,plain,
( spl0_89
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_89])]) ).
fof(f218,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_27) ).
fof(f3451,plain,
spl0_88,
inference(avatar_split_clause,[],[f217,f3448]) ).
fof(f3448,plain,
( spl0_88
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_88])]) ).
fof(f217,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_26) ).
fof(f3446,plain,
spl0_87,
inference(avatar_split_clause,[],[f216,f3443]) ).
fof(f3443,plain,
( spl0_87
<=> class_Ring__and__Field_Osemiring__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_87])]) ).
fof(f216,axiom,
class_Ring__and__Field_Osemiring__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_25) ).
fof(f3441,plain,
spl0_86,
inference(avatar_split_clause,[],[f215,f3438]) ).
fof(f3438,plain,
( spl0_86
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_86])]) ).
fof(f215,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_24) ).
fof(f3436,plain,
spl0_85,
inference(avatar_split_clause,[],[f214,f3433]) ).
fof(f214,axiom,
class_OrderedGroup_Omonoid__mult(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_23) ).
fof(f3431,plain,
spl0_84,
inference(avatar_split_clause,[],[f213,f3428]) ).
fof(f3428,plain,
( spl0_84
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_84])]) ).
fof(f213,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_22) ).
fof(f3426,plain,
spl0_83,
inference(avatar_split_clause,[],[f212,f3423]) ).
fof(f3423,plain,
( spl0_83
<=> class_Ring__and__Field_Osemiring__0(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_83])]) ).
fof(f212,axiom,
class_Ring__and__Field_Osemiring__0(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_21) ).
fof(f3421,plain,
spl0_82,
inference(avatar_split_clause,[],[f211,f3418]) ).
fof(f3418,plain,
( spl0_82
<=> class_OrderedGroup_Ocomm__monoid__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_82])]) ).
fof(f211,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_20) ).
fof(f3416,plain,
spl0_81,
inference(avatar_split_clause,[],[f210,f3413]) ).
fof(f3413,plain,
( spl0_81
<=> class_Orderings_Oord(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_81])]) ).
fof(f210,axiom,
class_Orderings_Oord(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_2) ).
fof(f3411,plain,
spl0_80,
inference(avatar_split_clause,[],[f209,f3408]) ).
fof(f3408,plain,
( spl0_80
<=> class_Ring__and__Field_Ocomm__semiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_80])]) ).
fof(f209,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_19) ).
fof(f3406,plain,
spl0_79,
inference(avatar_split_clause,[],[f208,f3403]) ).
fof(f3403,plain,
( spl0_79
<=> class_Ring__and__Field_Osemiring(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_79])]) ).
fof(f208,axiom,
class_Ring__and__Field_Osemiring(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_18) ).
fof(f3401,plain,
spl0_78,
inference(avatar_split_clause,[],[f207,f3398]) ).
fof(f3398,plain,
( spl0_78
<=> class_OrderedGroup_Oab__semigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
fof(f207,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_17) ).
fof(f3396,plain,
spl0_77,
inference(avatar_split_clause,[],[f206,f3393]) ).
fof(f3393,plain,
( spl0_77
<=> class_OrderedGroup_Osemigroup__mult(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_77])]) ).
fof(f206,axiom,
class_OrderedGroup_Osemigroup__mult(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_16) ).
fof(f3391,plain,
spl0_76,
inference(avatar_split_clause,[],[f205,f3388]) ).
fof(f3388,plain,
( spl0_76
<=> class_OrderedGroup_Oab__semigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_76])]) ).
fof(f205,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_15) ).
fof(f3386,plain,
spl0_75,
inference(avatar_split_clause,[],[f204,f3383]) ).
fof(f3383,plain,
( spl0_75
<=> class_OrderedGroup_Osemigroup__add(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_75])]) ).
fof(f204,axiom,
class_OrderedGroup_Osemigroup__add(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_14) ).
fof(f3381,plain,
spl0_74,
inference(avatar_split_clause,[],[f203,f3378]) ).
fof(f3378,plain,
( spl0_74
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_74])]) ).
fof(f203,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_13) ).
fof(f3376,plain,
spl0_73,
inference(avatar_split_clause,[],[f202,f3373]) ).
fof(f3373,plain,
( spl0_73
<=> class_Nat_Opower(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_73])]) ).
fof(f202,axiom,
class_Nat_Opower(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_12) ).
fof(f3371,plain,
spl0_72,
inference(avatar_split_clause,[],[f201,f3368]) ).
fof(f3368,plain,
( spl0_72
<=> class_HOL_Otimes(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_72])]) ).
fof(f201,axiom,
class_HOL_Otimes(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_11) ).
fof(f3366,plain,
spl0_71,
inference(avatar_split_clause,[],[f200,f3363]) ).
fof(f3363,plain,
( spl0_71
<=> class_HOL_Oplus(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_71])]) ).
fof(f200,axiom,
class_HOL_Oplus(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_10) ).
fof(f3361,plain,
spl0_70,
inference(avatar_split_clause,[],[f199,f3358]) ).
fof(f3358,plain,
( spl0_70
<=> class_HOL_Ozero(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_70])]) ).
fof(f199,axiom,
class_HOL_Ozero(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_1) ).
fof(f3356,plain,
spl0_69,
inference(avatar_split_clause,[],[f198,f3353]) ).
fof(f3353,plain,
( spl0_69
<=> class_HOL_Oone(tc_nat) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_69])]) ).
fof(f198,axiom,
class_HOL_Oone(tc_nat),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_nat_0) ).
fof(f3351,plain,
spl0_68,
inference(avatar_split_clause,[],[f195,f3348]) ).
fof(f3348,plain,
( spl0_68
<=> class_Finite__Set_Ofinite(tc_bool) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_68])]) ).
fof(f195,axiom,
class_Finite__Set_Ofinite(tc_bool),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_bool_0) ).
fof(f3346,plain,
spl0_67,
inference(avatar_split_clause,[],[f194,f3343]) ).
fof(f3343,plain,
( spl0_67
<=> class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_67])]) ).
fof(f194,axiom,
class_Finite__Set_Ofinite(tc_Product__Type_Ounit),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_Product____Type__Ounit_0) ).
fof(f3341,plain,
spl0_66,
inference(avatar_split_clause,[],[f193,f3338]) ).
fof(f3338,plain,
( spl0_66
<=> class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_66])]) ).
fof(f193,axiom,
class_OrderedGroup_Oab__semigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_9) ).
fof(f3336,plain,
spl0_65,
inference(avatar_split_clause,[],[f192,f3333]) ).
fof(f3333,plain,
( spl0_65
<=> class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_65])]) ).
fof(f192,axiom,
class_OrderedGroup_Osemigroup__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_8) ).
fof(f3331,plain,
spl0_64,
inference(avatar_split_clause,[],[f191,f3328]) ).
fof(f3328,plain,
( spl0_64
<=> class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_64])]) ).
fof(f191,axiom,
class_OrderedGroup_Oab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_7) ).
fof(f3326,plain,
spl0_63,
inference(avatar_split_clause,[],[f190,f3323]) ).
fof(f3323,plain,
( spl0_63
<=> class_Parity_Oeven__odd(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_63])]) ).
fof(f190,axiom,
class_Parity_Oeven__odd(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_64) ).
fof(f3321,plain,
spl0_62,
inference(avatar_split_clause,[],[f189,f3318]) ).
fof(f189,axiom,
class_Power_Orecpower(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_63) ).
fof(f3316,plain,
spl0_61,
inference(avatar_split_clause,[],[f188,f3313]) ).
fof(f3313,plain,
( spl0_61
<=> class_Nat_Opower(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_61])]) ).
fof(f188,axiom,
class_Nat_Opower(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_62) ).
fof(f3311,plain,
spl0_60,
inference(avatar_split_clause,[],[f187,f3308]) ).
fof(f3308,plain,
( spl0_60
<=> class_Divides_Odiv(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_60])]) ).
fof(f187,axiom,
class_Divides_Odiv(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_61) ).
fof(f3306,plain,
spl0_59,
inference(avatar_split_clause,[],[f186,f3303]) ).
fof(f186,axiom,
class_Numeral_Onumber__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_60) ).
fof(f3301,plain,
spl0_58,
inference(avatar_split_clause,[],[f185,f3298]) ).
fof(f3298,plain,
( spl0_58
<=> class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_58])]) ).
fof(f185,axiom,
class_OrderedGroup_Osemigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_6) ).
fof(f3296,plain,
spl0_57,
inference(avatar_split_clause,[],[f184,f3293]) ).
fof(f3293,plain,
( spl0_57
<=> class_Numeral_Onumber(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_57])]) ).
fof(f184,axiom,
class_Numeral_Onumber(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_59) ).
fof(f3291,plain,
spl0_56,
inference(avatar_split_clause,[],[f183,f3288]) ).
fof(f183,axiom,
class_Ring__and__Field_Oordered__idom(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_58) ).
fof(f3286,plain,
spl0_55,
inference(avatar_split_clause,[],[f182,f3283]) ).
fof(f3283,plain,
( spl0_55
<=> class_Ring__and__Field_Oidom(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_55])]) ).
fof(f182,axiom,
class_Ring__and__Field_Oidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_57) ).
fof(f3281,plain,
spl0_54,
inference(avatar_split_clause,[],[f181,f3278]) ).
fof(f181,axiom,
class_Ring__and__Field_Oordered__semidom(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_56) ).
fof(f3276,plain,
spl0_53,
inference(avatar_split_clause,[],[f180,f3273]) ).
fof(f3273,plain,
( spl0_53
<=> class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
fof(f180,axiom,
class_Ring__and__Field_Oordered__ring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_55) ).
fof(f3271,plain,
spl0_52,
inference(avatar_split_clause,[],[f179,f3268]) ).
fof(f3268,plain,
( spl0_52
<=> class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_52])]) ).
fof(f179,axiom,
class_Ring__and__Field_Oaxclass__no__zero__divisors(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_54) ).
fof(f3266,plain,
spl0_51,
inference(avatar_split_clause,[],[f178,f3263]) ).
fof(f3263,plain,
( spl0_51
<=> class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_51])]) ).
fof(f178,axiom,
class_Ring__and__Field_Olordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_53) ).
fof(f3261,plain,
spl0_50,
inference(avatar_split_clause,[],[f177,f3258]) ).
fof(f3258,plain,
( spl0_50
<=> class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_50])]) ).
fof(f177,axiom,
class_OrderedGroup_Olordered__ab__group__join(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_52) ).
fof(f3256,plain,
spl0_49,
inference(avatar_split_clause,[],[f176,f3253]) ).
fof(f3253,plain,
( spl0_49
<=> class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_49])]) ).
fof(f176,axiom,
class_OrderedGroup_Olordered__ab__group__meet(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_51) ).
fof(f3251,plain,
spl0_48,
inference(avatar_split_clause,[],[f175,f3248]) ).
fof(f3248,plain,
( spl0_48
<=> class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_48])]) ).
fof(f175,axiom,
class_OrderedGroup_Olordered__ab__group__abs(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_50) ).
fof(f3246,plain,
spl0_47,
inference(avatar_split_clause,[],[f174,f3243]) ).
fof(f3243,plain,
( spl0_47
<=> class_Orderings_Oord(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_47])]) ).
fof(f174,axiom,
class_Orderings_Oord(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_5) ).
fof(f3241,plain,
spl0_46,
inference(avatar_split_clause,[],[f173,f3238]) ).
fof(f3238,plain,
( spl0_46
<=> class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_46])]) ).
fof(f173,axiom,
class_Ring__and__Field_Opordered__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_49) ).
fof(f3236,plain,
spl0_45,
inference(avatar_split_clause,[],[f172,f3233]) ).
fof(f172,axiom,
class_OrderedGroup_Olordered__ab__group(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_48) ).
fof(f3231,plain,
spl0_44,
inference(avatar_split_clause,[],[f171,f3228]) ).
fof(f3228,plain,
( spl0_44
<=> class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
fof(f171,axiom,
class_OrderedGroup_Opordered__ab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_47) ).
fof(f3226,plain,
spl0_43,
inference(avatar_split_clause,[],[f170,f3223]) ).
fof(f3223,plain,
( spl0_43
<=> class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
fof(f170,axiom,
class_Ring__and__Field_Oaxclass__abs__if(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_46) ).
fof(f3221,plain,
spl0_42,
inference(avatar_split_clause,[],[f169,f3218]) ).
fof(f3218,plain,
( spl0_42
<=> class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
fof(f169,axiom,
class_Ring__and__Field_Oordered__comm__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_45) ).
fof(f3216,plain,
spl0_41,
inference(avatar_split_clause,[],[f168,f3213]) ).
fof(f3213,plain,
( spl0_41
<=> class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
fof(f168,axiom,
class_Ring__and__Field_Opordered__cancel__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_44) ).
fof(f3211,plain,
spl0_40,
inference(avatar_split_clause,[],[f167,f3208]) ).
fof(f3208,plain,
( spl0_40
<=> class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
fof(f167,axiom,
class_Ring__and__Field_Opordered__comm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_43) ).
fof(f3206,plain,
spl0_39,
inference(avatar_split_clause,[],[f166,f3203]) ).
fof(f3203,plain,
( spl0_39
<=> class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
fof(f166,axiom,
class_Ring__and__Field_Oordered__semiring__strict(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_42) ).
fof(f3201,plain,
spl0_38,
inference(avatar_split_clause,[],[f165,f3198]) ).
fof(f3198,plain,
( spl0_38
<=> class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
fof(f165,axiom,
class_Ring__and__Field_Opordered__cancel__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_41) ).
fof(f3196,plain,
spl0_37,
inference(avatar_split_clause,[],[f164,f3193]) ).
fof(f3193,plain,
( spl0_37
<=> class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
fof(f164,axiom,
class_Ring__and__Field_Opordered__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_40) ).
fof(f3191,plain,
spl0_36,
inference(avatar_split_clause,[],[f163,f3188]) ).
fof(f3188,plain,
( spl0_36
<=> class_HOL_Ozero(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f163,axiom,
class_HOL_Ozero(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_4) ).
fof(f3186,plain,
spl0_35,
inference(avatar_split_clause,[],[f162,f3183]) ).
fof(f3183,plain,
( spl0_35
<=> class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f162,axiom,
class_OrderedGroup_Oordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_39) ).
fof(f3181,plain,
spl0_34,
inference(avatar_split_clause,[],[f161,f3178]) ).
fof(f3178,plain,
( spl0_34
<=> class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f161,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add__imp__le(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_38) ).
fof(f3176,plain,
spl0_33,
inference(avatar_split_clause,[],[f160,f3173]) ).
fof(f3173,plain,
( spl0_33
<=> class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f160,axiom,
class_OrderedGroup_Opordered__cancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_37) ).
fof(f3171,plain,
spl0_32,
inference(avatar_split_clause,[],[f159,f3168]) ).
fof(f3168,plain,
( spl0_32
<=> class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f159,axiom,
class_OrderedGroup_Opordered__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_36) ).
fof(f3166,plain,
spl0_31,
inference(avatar_split_clause,[],[f158,f3163]) ).
fof(f158,axiom,
class_Orderings_Olinorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_35) ).
fof(f3161,plain,
spl0_30,
inference(avatar_split_clause,[],[f157,f3158]) ).
fof(f3158,plain,
( spl0_30
<=> class_LOrder_Olorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f157,axiom,
class_LOrder_Olorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_34) ).
fof(f3156,plain,
spl0_29,
inference(avatar_split_clause,[],[f156,f3153]) ).
fof(f156,axiom,
class_LOrder_Ojoin__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_33) ).
fof(f3151,plain,
spl0_28,
inference(avatar_split_clause,[],[f155,f3148]) ).
fof(f155,axiom,
class_LOrder_Omeet__semilorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_32) ).
fof(f3146,plain,
spl0_27,
inference(avatar_split_clause,[],[f154,f3143]) ).
fof(f3143,plain,
( spl0_27
<=> class_Orderings_Oorder(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f154,axiom,
class_Orderings_Oorder(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_31) ).
fof(f3141,plain,
spl0_26,
inference(avatar_split_clause,[],[f153,f3138]) ).
fof(f153,axiom,
class_Ring__and__Field_Ocomm__ring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_30) ).
fof(f3136,plain,
spl0_25,
inference(avatar_split_clause,[],[f152,f3133]) ).
fof(f3133,plain,
( spl0_25
<=> class_HOL_Otimes(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f152,axiom,
class_HOL_Otimes(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_3) ).
fof(f3131,plain,
spl0_24,
inference(avatar_split_clause,[],[f151,f3128]) ).
fof(f151,axiom,
class_Ring__and__Field_Ocomm__semiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_29) ).
fof(f3126,plain,
spl0_23,
inference(avatar_split_clause,[],[f150,f3123]) ).
fof(f3123,plain,
( spl0_23
<=> class_Ring__and__Field_Oring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f150,axiom,
class_Ring__and__Field_Oring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_28) ).
fof(f3121,plain,
spl0_22,
inference(avatar_split_clause,[],[f149,f3118]) ).
fof(f3118,plain,
( spl0_22
<=> class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f149,axiom,
class_Ring__and__Field_Osemiring__1__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_27) ).
fof(f3116,plain,
spl0_21,
inference(avatar_split_clause,[],[f148,f3113]) ).
fof(f3113,plain,
( spl0_21
<=> class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f148,axiom,
class_Ring__and__Field_Ocomm__semiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_26) ).
fof(f3111,plain,
spl0_20,
inference(avatar_split_clause,[],[f147,f3108]) ).
fof(f3108,plain,
( spl0_20
<=> class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f147,axiom,
class_Ring__and__Field_Osemiring__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_25) ).
fof(f3106,plain,
spl0_19,
inference(avatar_split_clause,[],[f146,f3103]) ).
fof(f3103,plain,
( spl0_19
<=> class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f146,axiom,
class_OrderedGroup_Ocomm__monoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_24) ).
fof(f3101,plain,
spl0_18,
inference(avatar_split_clause,[],[f145,f3098]) ).
fof(f145,axiom,
class_OrderedGroup_Omonoid__mult(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_23) ).
fof(f3096,plain,
spl0_17,
inference(avatar_split_clause,[],[f144,f3093]) ).
fof(f3093,plain,
( spl0_17
<=> class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f144,axiom,
class_Ring__and__Field_Oaxclass__0__neq__1(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_22) ).
fof(f3091,plain,
spl0_16,
inference(avatar_split_clause,[],[f143,f3088]) ).
fof(f3088,plain,
( spl0_16
<=> class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f143,axiom,
class_Ring__and__Field_Ocomm__ring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_21) ).
fof(f3086,plain,
spl0_15,
inference(avatar_split_clause,[],[f142,f3083]) ).
fof(f3083,plain,
( spl0_15
<=> class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f142,axiom,
class_Ring__and__Field_Ocomm__semiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_20) ).
fof(f3081,plain,
spl0_14,
inference(avatar_split_clause,[],[f141,f3078]) ).
fof(f3078,plain,
( spl0_14
<=> class_HOL_Oplus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f141,axiom,
class_HOL_Oplus(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_2) ).
fof(f3076,plain,
spl0_13,
inference(avatar_split_clause,[],[f140,f3073]) ).
fof(f3073,plain,
( spl0_13
<=> class_Ring__and__Field_Oring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f140,axiom,
class_Ring__and__Field_Oring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_19) ).
fof(f3071,plain,
spl0_12,
inference(avatar_split_clause,[],[f139,f3068]) ).
fof(f3068,plain,
( spl0_12
<=> class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f139,axiom,
class_Ring__and__Field_Osemiring__0__cancel(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_18) ).
fof(f3066,plain,
spl0_11,
inference(avatar_split_clause,[],[f138,f3063]) ).
fof(f138,axiom,
class_OrderedGroup_Oab__group__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_17) ).
fof(f3061,plain,
spl0_10,
inference(avatar_split_clause,[],[f137,f3058]) ).
fof(f3058,plain,
( spl0_10
<=> class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f137,axiom,
class_OrderedGroup_Ocancel__ab__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_16) ).
fof(f3056,plain,
spl0_9,
inference(avatar_split_clause,[],[f136,f3053]) ).
fof(f3053,plain,
( spl0_9
<=> class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f136,axiom,
class_OrderedGroup_Ocancel__semigroup__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_15) ).
fof(f3051,plain,
spl0_8,
inference(avatar_split_clause,[],[f135,f3048]) ).
fof(f3048,plain,
( spl0_8
<=> class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f135,axiom,
class_Ring__and__Field_Ocomm__semiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_14) ).
fof(f3046,plain,
spl0_7,
inference(avatar_split_clause,[],[f134,f3043]) ).
fof(f3043,plain,
( spl0_7
<=> class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f134,axiom,
class_Ring__and__Field_Osemiring__0(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_13) ).
fof(f3041,plain,
spl0_6,
inference(avatar_split_clause,[],[f133,f3038]) ).
fof(f133,axiom,
class_OrderedGroup_Ocomm__monoid__add(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_12) ).
fof(f3036,plain,
spl0_5,
inference(avatar_split_clause,[],[f132,f3033]) ).
fof(f3033,plain,
( spl0_5
<=> class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f132,axiom,
class_Ring__and__Field_Ocomm__semiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_11) ).
fof(f3031,plain,
spl0_4,
inference(avatar_split_clause,[],[f131,f3028]) ).
fof(f3028,plain,
( spl0_4
<=> class_Ring__and__Field_Osemiring(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f131,axiom,
class_Ring__and__Field_Osemiring(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_10) ).
fof(f3026,plain,
spl0_3,
inference(avatar_split_clause,[],[f130,f3023]) ).
fof(f3023,plain,
( spl0_3
<=> class_HOL_Oone(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f130,axiom,
class_HOL_Oone(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_1) ).
fof(f3021,plain,
spl0_2,
inference(avatar_split_clause,[],[f129,f3018]) ).
fof(f3018,plain,
( spl0_2
<=> class_HOL_Ominus(tc_IntDef_Oint) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f129,axiom,
class_HOL_Ominus(tc_IntDef_Oint),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',clsarity_IntDef__Oint_0) ).
fof(f3016,plain,
spl0_1,
inference(avatar_split_clause,[],[f2826,f3013]) ).
fof(f2826,axiom,
c_in(c_Message_Omsg_OCrypt(v_K,v_X),c_Message_Oparts(c_Message_Osynth(v_H)),tc_Message_Omsg),
file('/export/starexec/sandbox/tmp/tmp.2Vl5nJ4cer/Vampire---4.8_30404',cls_conjecture_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SWV272-1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.12 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 30 17:54:26 EDT 2023
% 0.13/0.33 % CPUTime :
% 0.17/0.39 % (30551)Running in auto input_syntax mode. Trying TPTP
% 0.17/0.47 % (30557)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.47 % (30553)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on Vampire---4 for (846ds/0Mi)
% 0.17/0.47 % (30556)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 Vampire---4 for (569ds/0Mi)
% 0.17/0.47 % (30560)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 Vampire---4 for (497ds/0Mi)
% 0.17/0.47 % (30554)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on Vampire---4 for (793ds/0Mi)
% 0.17/0.47 % (30559)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 Vampire---4 for (522ds/0Mi)
% 0.17/0.47 % (30558)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 Vampire---4 for (531ds/0Mi)
% 0.17/0.70 TRYING [1]
% 5.41/1.30 TRYING [2]
% 6.82/1.44 TRYING [1]
% 9.39/1.79 TRYING [1]
% 10.06/1.90 % (30558)First to succeed.
% 10.06/1.91 TRYING [2]
% 10.06/2.00 % (30558)Refutation found. Thanks to Tanya!
% 10.06/2.00 % SZS status Unsatisfiable for Vampire---4
% 10.06/2.00 % SZS output start Proof for Vampire---4
% See solution above
% 10.99/2.06 % (30558)------------------------------
% 10.99/2.06 % (30558)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 10.99/2.06 % (30558)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 10.99/2.06 % (30558)Termination reason: Refutation
% 10.99/2.06
% 10.99/2.06 % (30558)Memory used [KB]: 42984
% 10.99/2.06 % (30558)Time elapsed: 1.515 s
% 10.99/2.06 % (30558)------------------------------
% 10.99/2.06 % (30558)------------------------------
% 10.99/2.06 % (30551)Success in time 1.695 s
% 10.99/2.06 % Vampire---4.8 exiting
%------------------------------------------------------------------------------